1,1,98,123,0.029000," ","int(x^4*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{-d a \left(\frac{1}{7} c^{7} x^{7}-\frac{1}{5} c^{5} x^{5}\right)-d b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{7} x^{7}}{7}-\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(75 c^{6} x^{6}-57 c^{4} x^{4}-76 c^{2} x^{2}-152\right)}{3675}\right)}{c^{5}}"," ",0,"1/c^5*(-d*a*(1/7*c^7*x^7-1/5*c^5*x^5)-d*b*(1/7*arccosh(c*x)*c^7*x^7-1/5*arccosh(c*x)*c^5*x^5-1/3675*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(75*c^6*x^6-57*c^4*x^4-76*c^2*x^2-152)))","A"
2,1,160,111,0.018000," ","int(x^3*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","-\frac{c^{2} d a \,x^{6}}{6}+\frac{d a \,x^{4}}{4}-\frac{c^{2} d b \,\mathrm{arccosh}\left(c x \right) x^{6}}{6}+\frac{d b \,\mathrm{arccosh}\left(c x \right) x^{4}}{4}+\frac{b c d \,x^{5} \sqrt{c x -1}\, \sqrt{c x +1}}{36}-\frac{b d \,x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{36 c}-\frac{b d x \sqrt{c x -1}\, \sqrt{c x +1}}{24 c^{3}}-\frac{d b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{24 c^{4} \sqrt{c^{2} x^{2}-1}}"," ",0,"-1/6*c^2*d*a*x^6+1/4*d*a*x^4-1/6*c^2*d*b*arccosh(c*x)*x^6+1/4*d*b*arccosh(c*x)*x^4+1/36*b*c*d*x^5*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/36*b*d*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/24*b*d*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-1/24/c^4*d*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))","A"
3,1,90,99,0.011000," ","int(x^2*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{-d a \left(\frac{1}{5} c^{5} x^{5}-\frac{1}{3} c^{3} x^{3}\right)-d b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}-\frac{c^{3} x^{3} \mathrm{arccosh}\left(c x \right)}{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(9 c^{4} x^{4}-13 c^{2} x^{2}-26\right)}{225}\right)}{c^{3}}"," ",0,"1/c^3*(-d*a*(1/5*c^5*x^5-1/3*c^3*x^3)-d*b*(1/5*arccosh(c*x)*c^5*x^5-1/3*c^3*x^3*arccosh(c*x)-1/225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(9*c^4*x^4-13*c^2*x^2-26)))","A"
4,1,136,82,0.014000," ","int(x*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","-\frac{c^{2} d a \,x^{4}}{4}+\frac{d a \,x^{2}}{2}-\frac{c^{2} d b \,\mathrm{arccosh}\left(c x \right) x^{4}}{4}+\frac{d b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2}+\frac{c d b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{16}-\frac{5 b d x \sqrt{c x -1}\, \sqrt{c x +1}}{32 c}-\frac{5 d b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{32 c^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"-1/4*c^2*d*a*x^4+1/2*d*a*x^2-1/4*c^2*d*b*arccosh(c*x)*x^4+1/2*d*b*arccosh(c*x)*x^2+1/16*c*d*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-5/32*b*d*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-5/32/c^2*d*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))","A"
5,1,73,72,0.012000," ","int((-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{-d a \left(\frac{1}{3} c^{3} x^{3}-c x \right)-d b \left(\frac{c^{3} x^{3} \mathrm{arccosh}\left(c x \right)}{3}-c x \,\mathrm{arccosh}\left(c x \right)-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(c^{2} x^{2}-7\right)}{9}\right)}{c}"," ",0,"1/c*(-d*a*(1/3*c^3*x^3-c*x)-d*b*(1/3*c^3*x^3*arccosh(c*x)-c*x*arccosh(c*x)-1/9*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(c^2*x^2-7)))","A"
6,1,131,129,0.292000," ","int((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x,x)","-\frac{d a \,c^{2} x^{2}}{2}+d a \ln \left(c x \right)-\frac{d b \mathrm{arccosh}\left(c x \right)^{2}}{2}+\frac{b c d x \sqrt{c x -1}\, \sqrt{c x +1}}{4}-\frac{d b \,\mathrm{arccosh}\left(c x \right) c^{2} x^{2}}{2}+\frac{b d \,\mathrm{arccosh}\left(c x \right)}{4}+d b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)+\frac{d b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}"," ",0,"-1/2*d*a*c^2*x^2+d*a*ln(c*x)-1/2*d*b*arccosh(c*x)^2+1/4*b*c*d*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/2*d*b*arccosh(c*x)*c^2*x^2+1/4*b*d*arccosh(c*x)+d*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*d*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
7,1,100,68,0.017000," ","int((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x^2,x)","-d a \,c^{2} x -\frac{d a}{x}-d b \,\mathrm{arccosh}\left(c x \right) c^{2} x -\frac{d b \,\mathrm{arccosh}\left(c x \right)}{x}+b c d \sqrt{c x -1}\, \sqrt{c x +1}-\frac{c d b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{\sqrt{c^{2} x^{2}-1}}"," ",0,"-d*a*c^2*x-d*a/x-d*b*arccosh(c*x)*c^2*x-d*b*arccosh(c*x)/x+b*c*d*(c*x-1)^(1/2)*(c*x+1)^(1/2)-c*d*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))","A"
8,1,140,147,0.567000," ","int((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x^3,x)","-c^{2} d a \ln \left(c x \right)-\frac{d a}{2 x^{2}}+\frac{c^{2} d b \mathrm{arccosh}\left(c x \right)^{2}}{2}+\frac{b c d \sqrt{c x -1}\, \sqrt{c x +1}}{2 x}-\frac{c^{2} d b}{2}-\frac{d b \,\mathrm{arccosh}\left(c x \right)}{2 x^{2}}-c^{2} d b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)-\frac{c^{2} d b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}"," ",0,"-c^2*d*a*ln(c*x)-1/2*d*a/x^2+1/2*c^2*d*b*arccosh(c*x)^2+1/2*b*c*d*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x-1/2*c^2*d*b-1/2*d*b*arccosh(c*x)/x^2-c^2*d*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-1/2*c^2*d*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
9,1,108,76,0.022000," ","int((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x^4,x)","\frac{c^{2} d a}{x}-\frac{d a}{3 x^{3}}+\frac{c^{2} d b \,\mathrm{arccosh}\left(c x \right)}{x}-\frac{d b \,\mathrm{arccosh}\left(c x \right)}{3 x^{3}}+\frac{5 c^{3} d b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{6 \sqrt{c^{2} x^{2}-1}}+\frac{b c d \sqrt{c x -1}\, \sqrt{c x +1}}{6 x^{2}}"," ",0,"c^2*d*a/x-1/3*d*a/x^3+c^2*d*b*arccosh(c*x)/x-1/3*d*b*arccosh(c*x)/x^3+5/6*c^3*d*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))+1/6*b*c*d*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x^2","A"
10,1,128,170,0.015000," ","int(x^4*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{9} c^{9} x^{9}-\frac{2}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{2} b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{9} x^{9}}{9}-\frac{2 \,\mathrm{arccosh}\left(c x \right) c^{7} x^{7}}{7}+\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(1225 c^{8} x^{8}-2650 c^{6} x^{6}+789 c^{4} x^{4}+1052 c^{2} x^{2}+2104\right)}{99225}\right)}{c^{5}}"," ",0,"1/c^5*(d^2*a*(1/9*c^9*x^9-2/7*c^7*x^7+1/5*c^5*x^5)+d^2*b*(1/9*arccosh(c*x)*c^9*x^9-2/7*arccosh(c*x)*c^7*x^7+1/5*arccosh(c*x)*c^5*x^5-1/99225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(1225*c^8*x^8-2650*c^6*x^6+789*c^4*x^4+1052*c^2*x^2+2104)))","A"
11,1,230,168,0.017000," ","int(x^3*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{c^{4} d^{2} a \,x^{8}}{8}-\frac{c^{2} d^{2} a \,x^{6}}{3}+\frac{d^{2} a \,x^{4}}{4}+\frac{c^{4} d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{8}}{8}-\frac{c^{2} d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{6}}{3}+\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{4}}{4}-\frac{b \,c^{3} d^{2} x^{7} \sqrt{c x -1}\, \sqrt{c x +1}}{64}+\frac{43 b c \,d^{2} x^{5} \sqrt{c x -1}\, \sqrt{c x +1}}{1152}-\frac{73 b \,d^{2} x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{4608 c}-\frac{73 b \,d^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{3072 c^{3}}-\frac{73 d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3072 c^{4} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/8*c^4*d^2*a*x^8-1/3*c^2*d^2*a*x^6+1/4*d^2*a*x^4+1/8*c^4*d^2*b*arccosh(c*x)*x^8-1/3*c^2*d^2*b*arccosh(c*x)*x^6+1/4*d^2*b*arccosh(c*x)*x^4-1/64*b*c^3*d^2*x^7*(c*x-1)^(1/2)*(c*x+1)^(1/2)+43/1152*b*c*d^2*x^5*(c*x-1)^(1/2)*(c*x+1)^(1/2)-73/4608*b*d^2*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-73/3072*b*d^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-73/3072/c^4*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))","A"
12,1,120,147,0.012000," ","int(x^2*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{7} c^{7} x^{7}-\frac{2}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{2} b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{7} x^{7}}{7}-\frac{2 \,\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}+\frac{c^{3} x^{3} \mathrm{arccosh}\left(c x \right)}{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(225 c^{6} x^{6}-612 c^{4} x^{4}+409 c^{2} x^{2}+818\right)}{11025}\right)}{c^{3}}"," ",0,"1/c^3*(d^2*a*(1/7*c^7*x^7-2/5*c^5*x^5+1/3*c^3*x^3)+d^2*b*(1/7*arccosh(c*x)*c^7*x^7-2/5*arccosh(c*x)*c^5*x^5+1/3*c^3*x^3*arccosh(c*x)-1/11025*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(225*c^6*x^6-612*c^4*x^4+409*c^2*x^2+818)))","A"
13,1,204,114,0.015000," ","int(x*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{c^{4} d^{2} a \,x^{6}}{6}-\frac{c^{2} d^{2} a \,x^{4}}{2}+\frac{d^{2} a \,x^{2}}{2}+\frac{c^{4} d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{6}}{6}-\frac{c^{2} d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{4}}{2}+\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2}-\frac{c^{3} d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5}}{36}+\frac{13 c \,d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{144}-\frac{11 b \,d^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{96 c}-\frac{11 d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{96 c^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/6*c^4*d^2*a*x^6-1/2*c^2*d^2*a*x^4+1/2*d^2*a*x^2+1/6*c^4*d^2*b*arccosh(c*x)*x^6-1/2*c^2*d^2*b*arccosh(c*x)*x^4+1/2*d^2*b*arccosh(c*x)*x^2-1/36*c^3*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5+13/144*c*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-11/96*b*d^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-11/96/c^2*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))","A"
14,1,102,121,0.012000," ","int((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{5} c^{5} x^{5}-\frac{2}{3} c^{3} x^{3}+c x \right)+d^{2} b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}-\frac{2 c^{3} x^{3} \mathrm{arccosh}\left(c x \right)}{3}+c x \,\mathrm{arccosh}\left(c x \right)-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(9 c^{4} x^{4}-38 c^{2} x^{2}+149\right)}{225}\right)}{c}"," ",0,"1/c*(d^2*a*(1/5*c^5*x^5-2/3*c^3*x^3+c*x)+d^2*b*(1/5*arccosh(c*x)*c^5*x^5-2/3*c^3*x^3*arccosh(c*x)+c*x*arccosh(c*x)-1/225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(9*c^4*x^4-38*c^2*x^2+149)))","A"
15,1,201,188,0.337000," ","int((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x,x)","\frac{d^{2} a \,c^{4} x^{4}}{4}-d^{2} a \,c^{2} x^{2}+d^{2} a \ln \left(c x \right)+\frac{13 b \,d^{2} \mathrm{arccosh}\left(c x \right)}{32}+d^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)+\frac{d^{2} b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}-\frac{d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x^{3}}{16}+\frac{13 b c \,d^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{32}+\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right) c^{4} x^{4}}{4}-d^{2} b \,\mathrm{arccosh}\left(c x \right) c^{2} x^{2}-\frac{d^{2} b \mathrm{arccosh}\left(c x \right)^{2}}{2}"," ",0,"1/4*d^2*a*c^4*x^4-d^2*a*c^2*x^2+d^2*a*ln(c*x)+13/32*b*d^2*arccosh(c*x)+d^2*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*d^2*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-1/16*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x^3+13/32*b*c*d^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)+1/4*d^2*b*arccosh(c*x)*c^4*x^4-d^2*b*arccosh(c*x)*c^2*x^2-1/2*d^2*b*arccosh(c*x)^2","A"
16,1,167,117,0.017000," ","int((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x^2,x)","\frac{d^{2} a \,c^{4} x^{3}}{3}-2 d^{2} a \,c^{2} x -\frac{d^{2} a}{x}+\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right) c^{4} x^{3}}{3}-2 d^{2} b \,\mathrm{arccosh}\left(c x \right) c^{2} x -\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right)}{x}-\frac{d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x^{2}}{9}+\frac{16 b c \,d^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{9}-\frac{c \,d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{\sqrt{c^{2} x^{2}-1}}"," ",0,"1/3*d^2*a*c^4*x^3-2*d^2*a*c^2*x-d^2*a/x+1/3*d^2*b*arccosh(c*x)*c^4*x^3-2*d^2*b*arccosh(c*x)*c^2*x-d^2*b*arccosh(c*x)/x-1/9*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x^2+16/9*b*c*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)-c*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))","A"
17,1,220,210,0.565000," ","int((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x^3,x)","\frac{c^{4} d^{2} a \,x^{2}}{2}-2 c^{2} d^{2} a \ln \left(c x \right)-\frac{d^{2} a}{2 x^{2}}+c^{2} d^{2} b \mathrm{arccosh}\left(c x \right)^{2}-\frac{b \,c^{3} d^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{4}+\frac{c^{4} d^{2} b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2}-\frac{b \,c^{2} d^{2} \mathrm{arccosh}\left(c x \right)}{4}-\frac{d^{2} b \,c^{2}}{2}+\frac{b c \,d^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{2 x}-\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right)}{2 x^{2}}-2 c^{2} d^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)-c^{2} d^{2} b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)"," ",0,"1/2*c^4*d^2*a*x^2-2*c^2*d^2*a*ln(c*x)-1/2*d^2*a/x^2+c^2*d^2*b*arccosh(c*x)^2-1/4*b*c^3*d^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)+1/2*c^4*d^2*b*arccosh(c*x)*x^2-1/4*b*c^2*d^2*arccosh(c*x)-1/2*d^2*b*c^2+1/2*b*c*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x-1/2*d^2*b*arccosh(c*x)/x^2-2*c^2*d^2*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-c^2*d^2*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
18,1,167,124,0.019000," ","int((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x^4,x)","c^{4} d^{2} a x +\frac{2 c^{2} d^{2} a}{x}-\frac{d^{2} a}{3 x^{3}}+c^{4} d^{2} b \,\mathrm{arccosh}\left(c x \right) x +\frac{2 c^{2} d^{2} b \,\mathrm{arccosh}\left(c x \right)}{x}-\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right)}{3 x^{3}}-b \,c^{3} d^{2} \sqrt{c x -1}\, \sqrt{c x +1}+\frac{11 c^{3} d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{6 \sqrt{c^{2} x^{2}-1}}+\frac{b c \,d^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{6 x^{2}}"," ",0,"c^4*d^2*a*x+2*c^2*d^2*a/x-1/3*d^2*a/x^3+c^4*d^2*b*arccosh(c*x)*x+2*c^2*d^2*b*arccosh(c*x)/x-1/3*d^2*b*arccosh(c*x)/x^3-b*c^3*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)+11/6*c^3*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))+1/6*b*c*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x^2","A"
19,1,158,212,0.021000," ","int(x^4*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{11} c^{11} x^{11}-\frac{1}{3} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}-\frac{1}{5} c^{5} x^{5}\right)-d^{3} b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{11} x^{11}}{11}-\frac{\mathrm{arccosh}\left(c x \right) c^{9} x^{9}}{3}+\frac{3 \,\mathrm{arccosh}\left(c x \right) c^{7} x^{7}}{7}-\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(33075 c^{10} x^{10}-111475 c^{8} x^{8}+117625 c^{6} x^{6}-18933 c^{4} x^{4}-25244 c^{2} x^{2}-50488\right)}{4002075}\right)}{c^{5}}"," ",0,"1/c^5*(-d^3*a*(1/11*c^11*x^11-1/3*c^9*x^9+3/7*c^7*x^7-1/5*c^5*x^5)-d^3*b*(1/11*arccosh(c*x)*c^11*x^11-1/3*arccosh(c*x)*c^9*x^9+3/7*arccosh(c*x)*c^7*x^7-1/5*arccosh(c*x)*c^5*x^5-1/4002075*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(33075*c^10*x^10-111475*c^8*x^8+117625*c^6*x^6-18933*c^4*x^4-25244*c^2*x^2-50488)))","A"
20,1,284,194,0.023000," ","int(x^3*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","-\frac{c^{6} d^{3} a \,x^{10}}{10}+\frac{3 c^{4} d^{3} a \,x^{8}}{8}-\frac{c^{2} d^{3} a \,x^{6}}{2}+\frac{d^{3} a \,x^{4}}{4}-\frac{c^{6} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{10}}{10}+\frac{3 c^{4} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{8}}{8}-\frac{c^{2} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{6}}{2}+\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{4}}{4}+\frac{c^{5} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{9}}{100}-\frac{57 c^{3} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{7}}{1600}+\frac{401 c \,d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5}}{9600}-\frac{79 d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{7680 c}-\frac{79 b \,d^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{5120 c^{3}}-\frac{79 d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{5120 c^{4} \sqrt{c^{2} x^{2}-1}}"," ",0,"-1/10*c^6*d^3*a*x^10+3/8*c^4*d^3*a*x^8-1/2*c^2*d^3*a*x^6+1/4*d^3*a*x^4-1/10*c^6*d^3*b*arccosh(c*x)*x^10+3/8*c^4*d^3*b*arccosh(c*x)*x^8-1/2*c^2*d^3*b*arccosh(c*x)*x^6+1/4*d^3*b*arccosh(c*x)*x^4+1/100*c^5*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^9-57/1600*c^3*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^7+401/9600*c*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5-79/7680/c*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-79/5120*b*d^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-79/5120/c^4*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))","A"
21,1,150,189,0.010000," ","int(x^2*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{9} c^{9} x^{9}-\frac{3}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}-\frac{1}{3} c^{3} x^{3}\right)-d^{3} b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{9} x^{9}}{9}-\frac{3 \,\mathrm{arccosh}\left(c x \right) c^{7} x^{7}}{7}+\frac{3 \,\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}-\frac{c^{3} x^{3} \mathrm{arccosh}\left(c x \right)}{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(1225 c^{8} x^{8}-4675 c^{6} x^{6}+6297 c^{4} x^{4}-2629 c^{2} x^{2}-5258\right)}{99225}\right)}{c^{3}}"," ",0,"1/c^3*(-d^3*a*(1/9*c^9*x^9-3/7*c^7*x^7+3/5*c^5*x^5-1/3*c^3*x^3)-d^3*b*(1/9*arccosh(c*x)*c^9*x^9-3/7*arccosh(c*x)*c^7*x^7+3/5*arccosh(c*x)*c^5*x^5-1/3*c^3*x^3*arccosh(c*x)-1/99225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(1225*c^8*x^8-4675*c^6*x^6+6297*c^4*x^4-2629*c^2*x^2-5258)))","A"
22,1,258,138,0.015000," ","int(x*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","-\frac{c^{6} d^{3} a \,x^{8}}{8}+\frac{c^{4} d^{3} a \,x^{6}}{2}-\frac{3 c^{2} d^{3} a \,x^{4}}{4}+\frac{d^{3} a \,x^{2}}{2}-\frac{c^{6} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{8}}{8}+\frac{c^{4} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{6}}{2}-\frac{3 c^{2} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{4}}{4}+\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2}+\frac{c^{5} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{7}}{64}-\frac{25 c^{3} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5}}{384}+\frac{163 c \,d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{1536}-\frac{93 b \,d^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{1024 c}-\frac{93 d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{1024 c^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"-1/8*c^6*d^3*a*x^8+1/2*c^4*d^3*a*x^6-3/4*c^2*d^3*a*x^4+1/2*d^3*a*x^2-1/8*c^6*d^3*b*arccosh(c*x)*x^8+1/2*c^4*d^3*b*arccosh(c*x)*x^6-3/4*c^2*d^3*b*arccosh(c*x)*x^4+1/2*d^3*b*arccosh(c*x)*x^2+1/64*c^5*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^7-25/384*c^3*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5+163/1536*c*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-93/1024*b*d^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-93/1024/c^2*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))","A"
23,1,132,163,0.011000," ","int((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{7} c^{7} x^{7}-\frac{3}{5} c^{5} x^{5}+c^{3} x^{3}-c x \right)-d^{3} b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{7} x^{7}}{7}-\frac{3 \,\mathrm{arccosh}\left(c x \right) c^{5} x^{5}}{5}+c^{3} x^{3} \mathrm{arccosh}\left(c x \right)-c x \,\mathrm{arccosh}\left(c x \right)-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(75 c^{6} x^{6}-351 c^{4} x^{4}+757 c^{2} x^{2}-2161\right)}{3675}\right)}{c}"," ",0,"1/c*(-d^3*a*(1/7*c^7*x^7-3/5*c^5*x^5+c^3*x^3-c*x)-d^3*b*(1/7*arccosh(c*x)*c^7*x^7-3/5*arccosh(c*x)*c^5*x^5+c^3*x^3*arccosh(c*x)-c*x*arccosh(c*x)-1/3675*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(75*c^6*x^6-351*c^4*x^4+757*c^2*x^2-2161)))","A"
24,1,255,235,0.466000," ","int((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x,x)","-\frac{d^{3} a \,c^{6} x^{6}}{6}+\frac{3 d^{3} a \,c^{4} x^{4}}{4}-\frac{3 d^{3} a \,c^{2} x^{2}}{2}+d^{3} a \ln \left(c x \right)+d^{3} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)+\frac{25 b \,d^{3} \mathrm{arccosh}\left(c x \right)}{48}+\frac{d^{3} b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}+\frac{d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5} x^{5}}{36}-\frac{11 d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x^{3}}{72}+\frac{25 b c \,d^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{48}+\frac{3 d^{3} b \,\mathrm{arccosh}\left(c x \right) c^{4} x^{4}}{4}-\frac{3 d^{3} b \,\mathrm{arccosh}\left(c x \right) c^{2} x^{2}}{2}-\frac{d^{3} b \mathrm{arccosh}\left(c x \right)^{2}}{2}-\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right) c^{6} x^{6}}{6}"," ",0,"-1/6*d^3*a*c^6*x^6+3/4*d^3*a*c^4*x^4-3/2*d^3*a*c^2*x^2+d^3*a*ln(c*x)+d^3*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+25/48*b*d^3*arccosh(c*x)+1/2*d^3*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/36*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^5*x^5-11/72*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x^3+25/48*b*c*d^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)+3/4*d^3*b*arccosh(c*x)*c^4*x^4-3/2*d^3*b*arccosh(c*x)*c^2*x^2-1/2*d^3*b*arccosh(c*x)^2-1/6*d^3*b*arccosh(c*x)*c^6*x^6","A"
25,1,219,156,0.020000," ","int((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x^2,x)","-\frac{d^{3} a \,c^{6} x^{5}}{5}+d^{3} a \,c^{4} x^{3}-3 d^{3} a \,c^{2} x -\frac{d^{3} a}{x}-\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right) c^{6} x^{5}}{5}+d^{3} b \,\mathrm{arccosh}\left(c x \right) c^{4} x^{3}-3 d^{3} b \,\mathrm{arccosh}\left(c x \right) c^{2} x -\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right)}{x}+\frac{d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5} x^{4}}{25}-\frac{7 d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x^{2}}{25}+\frac{61 b c \,d^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{25}-\frac{c \,d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{\sqrt{c^{2} x^{2}-1}}"," ",0,"-1/5*d^3*a*c^6*x^5+d^3*a*c^4*x^3-3*d^3*a*c^2*x-d^3*a/x-1/5*d^3*b*arccosh(c*x)*c^6*x^5+d^3*b*arccosh(c*x)*c^4*x^3-3*d^3*b*arccosh(c*x)*c^2*x-d^3*b*arccosh(c*x)/x+1/25*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^5*x^4-7/25*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x^2+61/25*b*c*d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)-c*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))","A"
26,1,275,263,0.783000," ","int((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x^3,x)","-\frac{c^{6} d^{3} a \,x^{4}}{4}+\frac{3 c^{4} d^{3} a \,x^{2}}{2}-3 c^{2} d^{3} a \ln \left(c x \right)-\frac{d^{3} a}{2 x^{2}}-\frac{d^{3} b \,c^{2}}{2}-\frac{21 b \,c^{2} d^{3} \mathrm{arccosh}\left(c x \right)}{32}+\frac{c \,d^{3} b \sqrt{c x +1}\, \sqrt{c x -1}}{2 x}+\frac{c^{5} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{16}-\frac{21 b \,c^{3} d^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{32}-\frac{c^{6} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{4}}{4}+\frac{3 c^{4} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2}-\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right)}{2 x^{2}}-\frac{3 c^{2} d^{3} b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}+\frac{3 c^{2} d^{3} b \mathrm{arccosh}\left(c x \right)^{2}}{2}-3 c^{2} d^{3} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)"," ",0,"-1/4*c^6*d^3*a*x^4+3/2*c^4*d^3*a*x^2-3*c^2*d^3*a*ln(c*x)-1/2*d^3*a/x^2-1/2*d^3*b*c^2-21/32*b*c^2*d^3*arccosh(c*x)+1/2*c*d^3*b/x*(c*x+1)^(1/2)*(c*x-1)^(1/2)+1/16*c^5*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-21/32*b*c^3*d^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/4*c^6*d^3*b*arccosh(c*x)*x^4+3/2*c^4*d^3*b*arccosh(c*x)*x^2-1/2*d^3*b*arccosh(c*x)/x^2-3/2*c^2*d^3*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+3/2*c^2*d^3*b*arccosh(c*x)^2-3*c^2*d^3*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
27,1,223,167,0.022000," ","int((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x^4,x)","-\frac{c^{6} d^{3} a \,x^{3}}{3}+3 c^{4} d^{3} a x +\frac{3 c^{2} d^{3} a}{x}-\frac{d^{3} a}{3 x^{3}}-\frac{c^{6} d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{3}}{3}+3 c^{4} d^{3} b \,\mathrm{arccosh}\left(c x \right) x +\frac{3 c^{2} d^{3} b \,\mathrm{arccosh}\left(c x \right)}{x}-\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right)}{3 x^{3}}+\frac{c^{5} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{9}-\frac{25 b \,c^{3} d^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{9}+\frac{17 c^{3} d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{6 \sqrt{c^{2} x^{2}-1}}+\frac{b c \,d^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{6 x^{2}}"," ",0,"-1/3*c^6*d^3*a*x^3+3*c^4*d^3*a*x+3*c^2*d^3*a/x-1/3*d^3*a/x^3-1/3*c^6*d^3*b*arccosh(c*x)*x^3+3*c^4*d^3*b*arccosh(c*x)*x+3*c^2*d^3*b*arccosh(c*x)/x-1/3*d^3*b*arccosh(c*x)/x^3+1/9*c^5*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2-25/9*b*c^3*d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)+17/6*c^3*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))+1/6*b*c*d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x^2","A"
28,1,263,183,0.416000," ","int(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x)","-\frac{a \,x^{3}}{3 c^{2} d}-\frac{a x}{c^{4} d}-\frac{a \ln \left(c x -1\right)}{2 c^{5} d}+\frac{a \ln \left(c x +1\right)}{2 c^{5} d}+\frac{11 b \sqrt{c x -1}\, \sqrt{c x +1}}{9 c^{5} d}+\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{5} d}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{5} d}+\frac{b \,x^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{9 c^{3} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) x^{3}}{3 c^{2} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) x}{c^{4} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{5} d}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{5} d}"," ",0,"-1/3/c^2*a/d*x^3-1/c^4*a/d*x-1/2/c^5*a/d*ln(c*x-1)+1/2/c^5*a/d*ln(c*x+1)+11/9*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^5/d+b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^5/d-b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^5/d+1/9*b*x^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3/d-1/3/c^2*b/d*arccosh(c*x)*x^3-1/c^4*b/d*arccosh(c*x)*x-1/c^5*b/d*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/c^5*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
29,1,244,152,0.293000," ","int(x^3*(a+b*arccosh(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{b \mathrm{arccosh}\left(c x \right)^{2}}{2 c^{4} d}+\frac{b x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c^{3} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2 c^{2} d}+\frac{b \,\mathrm{arccosh}\left(c x \right)}{4 d \,c^{4}}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d}-\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{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/c^4*b/d*arccosh(c*x)^2+1/4*b*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3/d-1/2/c^2*b/d*arccosh(c*x)*x^2+1/4*b*arccosh(c*x)/d/c^4-1/c^4*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^4*b/d*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^4*b/d*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^4*b/d*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
30,1,208,137,0.268000," ","int(x^2*(a+b*arccosh(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 \sqrt{c x -1}\, \sqrt{c x +1}}{c^{3} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{3} d}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{3} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) x}{c^{2} d}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{3} d}+\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{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)+b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3/d-1/c^3*b/d*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/c^3*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^2*b/d*arccosh(c*x)*x-b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^3/d+b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^3/d","A"
31,1,179,96,0.092000," ","int(x*(a+b*arccosh(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{b \mathrm{arccosh}\left(c x \right)^{2}}{2 c^{2} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d}-\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +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/c^2*b/d*arccosh(c*x)^2-1/c^2*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^2*b/d*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^2*b/d*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/c^2*b/d*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
32,1,326,98,0.606000," ","int((a+b*arccosh(c*x))/(-c^2*d*x^2+d),x)","\frac{a \arctanh \left(c x \right)}{c d}+\frac{b \arctanh \left(c x \right) \mathrm{arccosh}\left(c x \right)}{c d}+\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{c x}{2}}\, \sqrt{-\frac{1}{2}+\frac{c x}{2}}\, \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{c x}{2}}\, \sqrt{-\frac{1}{2}+\frac{c x}{2}}\, \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{c x}{2}}\, \sqrt{-\frac{1}{2}+\frac{c x}{2}}\, \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{c x}{2}}\, \sqrt{-\frac{1}{2}+\frac{c x}{2}}\, \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d \left(c^{2} x^{2}-1\right)}"," ",0,"1/c*a/d*arctanh(c*x)+1/c*b/d*arctanh(c*x)*arccosh(c*x)+2*I/c*b/d*(-c^2*x^2+1)^(1/2)*(1/2+1/2*c*x)^(1/2)*(-1/2+1/2*c*x)^(1/2)/(c^2*x^2-1)*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2*I/c*b/d*(-c^2*x^2+1)^(1/2)*(1/2+1/2*c*x)^(1/2)*(-1/2+1/2*c*x)^(1/2)/(c^2*x^2-1)*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+2*I/c*b/d*(-c^2*x^2+1)^(1/2)*(1/2+1/2*c*x)^(1/2)*(-1/2+1/2*c*x)^(1/2)/(c^2*x^2-1)*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2*I/c*b/d*(-c^2*x^2+1)^(1/2)*(1/2+1/2*c*x)^(1/2)*(-1/2+1/2*c*x)^(1/2)/(c^2*x^2-1)*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))","C"
33,1,91,96,0.136000," ","int((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c x -1\right)}{2 d}-\frac{a \ln \left(c x +1\right)}{2 d}-\frac{b \dilog \left(\frac{1}{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}}\right)}{d}+\frac{b \dilog \left(\frac{1}{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{4}}\right)}{4 d}"," ",0,"a/d*ln(c*x)-1/2*a/d*ln(c*x-1)-1/2*a/d*ln(c*x+1)-b/d*dilog(1/(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/4*b/d*dilog(1/(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^4)","A"
34,1,161,132,0.273000," ","int((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d),x)","-\frac{a}{d x}-\frac{c a \ln \left(c x -1\right)}{2 d}+\frac{c a \ln \left(c x +1\right)}{2 d}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{d x}+\frac{2 c b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}+\frac{c b \dilog \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}+\frac{c b \dilog \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}+\frac{c b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}"," ",0,"-a/d/x-1/2*c*a/d*ln(c*x-1)+1/2*c*a/d*ln(c*x+1)-b/d*arccosh(c*x)/x+2*c*b/d*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+c*b/d*dilog(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+c*b/d*dilog(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+c*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
35,1,301,148,0.284000," ","int((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d),x)","-\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{c^{2} a \ln \left(c x +1\right)}{2 d}+\frac{b c \sqrt{c x -1}\, \sqrt{c x +1}}{2 d x}-\frac{c^{2} b}{2 d}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{2 d \,x^{2}}+\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{d}+\frac{b \,c^{2} \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2 d}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}-\frac{c^{2} b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}-\frac{c^{2} b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}"," ",0,"-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*c^2*a/d*ln(c*x+1)+1/2*b*c*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/x-1/2*c^2*b/d-1/2*b/d*arccosh(c*x)/x^2+c^2*b/d*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*b*c^2*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)/d-c^2*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-c^2*b/d*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-c^2*b/d*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-c^2*b/d*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
36,1,225,185,0.350000," ","int((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d),x)","-\frac{a}{3 d \,x^{3}}-\frac{c^{2} a}{d x}-\frac{c^{3} a \ln \left(c x -1\right)}{2 d}+\frac{c^{3} a \ln \left(c x +1\right)}{2 d}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right)}{d x}+\frac{b c \sqrt{c x -1}\, \sqrt{c x +1}}{6 d \,x^{2}}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{3 d \,x^{3}}+\frac{7 c^{3} b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d}+\frac{c^{3} b \dilog \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}+\frac{c^{3} b \dilog \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}+\frac{c^{3} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}"," ",0,"-1/3*a/d/x^3-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)-c^2*b/d*arccosh(c*x)/x+1/6*b*c*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/x^2-1/3*b/d*arccosh(c*x)/x^3+7/3*c^3*b/d*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+c^3*b/d*dilog(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+c^3*b/d*dilog(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+c^3*b/d*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
37,1,300,196,0.608000," ","int(x^4*(a+b*arccosh(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 \,\mathrm{arccosh}\left(c x \right) x}{c^{4} d^{2}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}}{c^{5} d^{2}}-\frac{b \,\mathrm{arccosh}\left(c x \right) x}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{c x +1}\, \sqrt{c x -1}}{2 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c^{5} d^{2}}-\frac{3 b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c^{5} d^{2}}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c^{5} d^{2}}+\frac{3 b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +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)+1/c^4*b/d^2*arccosh(c*x)*x-b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^5/d^2-1/2/c^4*b/d^2/(c^2*x^2-1)*arccosh(c*x)*x-1/2/c^5*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-3/2/c^5*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-3/2*b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^5/d^2+3/2/c^5*b/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/2*b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^5/d^2","A"
38,1,309,185,0.606000," ","int(x^3*(a+b*arccosh(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{b \mathrm{arccosh}\left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{b \sqrt{c x +1}\, \sqrt{c x -1}\, x}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,x^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2}}+\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2}}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2}}+\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +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/c^4*b/d^2*arccosh(c*x)^2-1/2/c^3*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+1/2/c^2*b/d^2/(c^2*x^2-1)*x^2-1/2/c^4*b/d^2/(c^2*x^2-1)*arccosh(c*x)-1/2/c^4*b/d^2/(c^2*x^2-1)+1/c^4*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/c^4*b/d^2*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/c^4*b/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/c^4*b/d^2*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
39,1,255,151,0.314000," ","int(x^2*(a+b*arccosh(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 \,\mathrm{arccosh}\left(c x \right) x}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{c x +1}\, \sqrt{c x -1}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c^{3} d^{2}}-\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c^{3} d^{2}}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c^{3} d^{2}}+\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +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)*arccosh(c*x)*x-1/2/c^3*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-1/2/c^3*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/2*b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^3/d^2+1/2/c^3*b/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/2*b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^3/d^2","A"
40,1,64,53,0.016000," ","int(x*(a+b*arccosh(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{\mathrm{arccosh}\left(c x \right)}{2 \left(c^{2} x^{2}-1\right)}-\frac{c x}{2 \sqrt{c x -1}\, \sqrt{c x +1}}\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)*arccosh(c*x)-1/2/(c*x-1)^(1/2)/(c*x+1)^(1/2)*c*x))","A"
41,1,252,147,0.099000," ","int((a+b*arccosh(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 \,\mathrm{arccosh}\left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{c x +1}\, \sqrt{c x -1}}{2 c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c \,d^{2}}+\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c \,d^{2}}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 c \,d^{2}}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +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)*arccosh(c*x)*x-1/2/c*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+1/2/c*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/2*b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c/d^2-1/2/c*b/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/2*b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c/d^2","A"
42,1,339,143,0.285000," ","int((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^2,x)","\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{a}{4 d^{2} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{2 d^{2}}-\frac{b \sqrt{c x +1}\, \sqrt{c x -1}\, c x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,c^{2} x^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{d^{2}}+\frac{b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2 d^{2}}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}"," ",0,"a/d^2*ln(c*x)-1/4*a/d^2/(c*x-1)-1/2*a/d^2*ln(c*x-1)+1/4*a/d^2/(c*x+1)-1/2*a/d^2*ln(c*x+1)-1/2*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c*x+1/2*b/d^2/(c^2*x^2-1)*c^2*x^2-1/2*b/d^2/(c^2*x^2-1)*arccosh(c*x)-1/2*b/d^2/(c^2*x^2-1)+b/d^2*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)/d^2-b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-b/d^2*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-b/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-b/d^2*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
43,1,259,195,0.364000," ","int((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^2,x)","-\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{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 \,\mathrm{arccosh}\left(c x \right) c^{2} x}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{c b \sqrt{c x +1}\, \sqrt{c x -1}}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right)}{d^{2} x \left(c^{2} x^{2}-1\right)}+\frac{2 c b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}+\frac{3 c b \dilog \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 d^{2}}+\frac{3 c b \dilog \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 d^{2}}+\frac{3 c b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 d^{2}}"," ",0,"-a/d^2/x-1/4*c*a/d^2/(c*x-1)-3/4*c*a/d^2*ln(c*x-1)-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)*arccosh(c*x)*c^2*x-1/2*c*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+b/d^2/x/(c^2*x^2-1)*arccosh(c*x)+2*c*b/d^2*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/2*c*b/d^2*dilog(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/2*c*b/d^2*dilog(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/2*c*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
44,1,371,186,0.338000," ","int((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^2,x)","-\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} 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 \,\mathrm{arccosh}\left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{c b \sqrt{c x +1}\, \sqrt{c x -1}}{2 d^{2} x \left(c^{2} x^{2}-1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right)}{2 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{d^{2}}+\frac{b \,c^{2} \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{d^{2}}-\frac{2 c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{2 c^{2} b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{2 c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{2 c^{2} b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}"," ",0,"-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)+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)*arccosh(c*x)-1/2*c*b/d^2/x/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+1/2*b/d^2/x^2/(c^2*x^2-1)*arccosh(c*x)+2*c^2*b/d^2*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+b*c^2*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)/d^2-2*c^2*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*c^2*b/d^2*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*c^2*b/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*c^2*b/d^2*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
45,1,352,262,0.473000," ","int((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^2,x)","-\frac{a}{3 d^{2} x^{3}}-\frac{2 c^{2} a}{d^{2} x}-\frac{c^{3} a}{4 d^{2} \left(c x -1\right)}-\frac{5 c^{3} a \ln \left(c x -1\right)}{4 d^{2}}-\frac{c^{3} a}{4 d^{2} \left(c x +1\right)}+\frac{5 c^{3} a \ln \left(c x +1\right)}{4 d^{2}}-\frac{5 c^{4} b \,\mathrm{arccosh}\left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{c^{3} b \sqrt{c x +1}\, \sqrt{c x -1}}{3 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{5 c^{2} b \,\mathrm{arccosh}\left(c x \right)}{3 d^{2} x \left(c^{2} x^{2}-1\right)}-\frac{c b \sqrt{c x +1}\, \sqrt{c x -1}}{6 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right)}{3 d^{2} x^{3} \left(c^{2} x^{2}-1\right)}+\frac{13 c^{3} b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{2}}+\frac{5 c^{3} b \dilog \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 d^{2}}+\frac{5 c^{3} b \dilog \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 d^{2}}+\frac{5 c^{3} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 d^{2}}"," ",0,"-1/3*a/d^2/x^3-2*c^2*a/d^2/x-1/4*c^3*a/d^2/(c*x-1)-5/4*c^3*a/d^2*ln(c*x-1)-1/4*c^3*a/d^2/(c*x+1)+5/4*c^3*a/d^2*ln(c*x+1)-5/2*c^4*b/d^2/(c^2*x^2-1)*arccosh(c*x)*x-1/3*c^3*b/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+5/3*c^2*b/d^2/x/(c^2*x^2-1)*arccosh(c*x)-1/6*c*b/d^2/x^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+1/3*b/d^2/x^3/(c^2*x^2-1)*arccosh(c*x)+13/3*c^3*b/d^2*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+5/2*c^3*b/d^2*dilog(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+5/2*c^3*b/d^2*dilog(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+5/2*c^3*b/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
46,1,383,254,0.845000," ","int(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{a}{16 c^{5} d^{3} \left(c x -1\right)^{2}}+\frac{5 a}{16 c^{5} d^{3} \left(c x -1\right)}-\frac{3 a \ln \left(c x -1\right)}{16 c^{5} d^{3}}-\frac{a}{16 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{5 a}{16 c^{5} d^{3} \left(c x +1\right)}+\frac{3 a \ln \left(c x +1\right)}{16 c^{5} d^{3}}+\frac{5 b \,\mathrm{arccosh}\left(c x \right) x^{3}}{8 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{8 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b \,\mathrm{arccosh}\left(c x \right) x}{8 c^{4} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{13 b \sqrt{c x +1}\, \sqrt{c x -1}}{24 c^{5} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{5} d^{3}}+\frac{3 b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{5} d^{3}}-\frac{3 b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{5} d^{3}}-\frac{3 b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{5} d^{3}}"," ",0,"1/16/c^5*a/d^3/(c*x-1)^2+5/16/c^5*a/d^3/(c*x-1)-3/16/c^5*a/d^3*ln(c*x-1)-1/16/c^5*a/d^3/(c*x+1)^2+5/16/c^5*a/d^3/(c*x+1)+3/16/c^5*a/d^3*ln(c*x+1)+5/8/c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x^3+5/8/c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-3/8/c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x-13/24/c^5*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+3/8/c^5*b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/8*b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^5/d^3-3/8/c^5*b/d^3*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-3/8*b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^5/d^3","A"
47,1,136,114,0.023000," ","int(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{-\frac{a \left(-\frac{1}{16 \left(c x -1\right)^{2}}-\frac{3}{16 \left(c x -1\right)}-\frac{1}{16 \left(c x +1\right)^{2}}+\frac{3}{16 \left(c x +1\right)}\right)}{d^{3}}-\frac{b \left(-\frac{\mathrm{arccosh}\left(c x \right)}{16 \left(c x -1\right)^{2}}-\frac{3 \,\mathrm{arccosh}\left(c x \right)}{16 \left(c x -1\right)}-\frac{\mathrm{arccosh}\left(c x \right)}{16 \left(c x +1\right)^{2}}+\frac{3 \,\mathrm{arccosh}\left(c x \right)}{16 \left(c x +1\right)}-\frac{c x \left(4 c^{2} x^{2}-3\right)}{12 \left(c x +1\right)^{\frac{3}{2}} \left(c x -1\right)^{\frac{3}{2}}}\right)}{d^{3}}}{c^{4}}"," ",0,"1/c^4*(-a/d^3*(-1/16/(c*x-1)^2-3/16/(c*x-1)-1/16/(c*x+1)^2+3/16/(c*x+1))-b/d^3*(-1/16*arccosh(c*x)/(c*x-1)^2-3/16*arccosh(c*x)/(c*x-1)-1/16*arccosh(c*x)/(c*x+1)^2+3/16*arccosh(c*x)/(c*x+1)-1/12*c*x*(4*c^2*x^2-3)/(c*x+1)^(3/2)/(c*x-1)^(3/2)))","A"
48,1,380,203,0.581000," ","int(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{a}{16 c^{3} d^{3} \left(c x -1\right)^{2}}+\frac{a}{16 c^{3} d^{3} \left(c x -1\right)}+\frac{a \ln \left(c x -1\right)}{16 c^{3} d^{3}}-\frac{a}{16 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{a}{16 c^{3} d^{3} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{16 c^{3} d^{3}}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{8 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right) x}{8 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \sqrt{c x +1}\, \sqrt{c x -1}}{24 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{3} d^{3}}-\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{3} d^{3}}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{3} d^{3}}+\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{3} d^{3}}"," ",0,"1/16/c^3*a/d^3/(c*x-1)^2+1/16/c^3*a/d^3/(c*x-1)+1/16/c^3*a/d^3*ln(c*x-1)-1/16/c^3*a/d^3/(c*x+1)^2+1/16/c^3*a/d^3/(c*x+1)-1/16/c^3*a/d^3*ln(c*x+1)+1/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x^3+1/8/c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+1/8/c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x-1/24/c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-1/8/c^3*b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/8*b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^3/d^3+1/8/c^3*b/d^3*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/8*b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c^3/d^3","A"
49,1,86,77,0.013000," ","int(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{\frac{a}{4 d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b \left(-\frac{\mathrm{arccosh}\left(c x \right)}{4 \left(c^{2} x^{2}-1\right)^{2}}+\frac{c x \left(2 c^{2} x^{2}-3\right)}{12 \sqrt{c x -1}\, \sqrt{c x +1}\, \left(c^{2} x^{2}-1\right)}\right)}{d^{3}}}{c^{2}}"," ",0,"1/c^2*(1/4*a/d^3/(c^2*x^2-1)^2-b/d^3*(-1/4/(c^2*x^2-1)^2*arccosh(c*x)+1/12/(c*x-1)^(1/2)/(c*x+1)^(1/2)*c*x*(2*c^2*x^2-3)/(c^2*x^2-1)))","A"
50,1,378,197,0.156000," ","int((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{a}{16 c \,d^{3} \left(c x -1\right)^{2}}-\frac{3 a}{16 c \,d^{3} \left(c x -1\right)}-\frac{3 a \ln \left(c x -1\right)}{16 c \,d^{3}}-\frac{a}{16 c \,d^{3} \left(c x +1\right)^{2}}-\frac{3 a}{16 c \,d^{3} \left(c x +1\right)}+\frac{3 a \ln \left(c x +1\right)}{16 c \,d^{3}}-\frac{3 c^{2} b \,\mathrm{arccosh}\left(c x \right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c b \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{5 b \,\mathrm{arccosh}\left(c x \right) x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{11 b \sqrt{c x +1}\, \sqrt{c x -1}}{24 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c \,d^{3}}+\frac{3 b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c \,d^{3}}-\frac{3 b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c \,d^{3}}-\frac{3 b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c \,d^{3}}"," ",0,"1/16/c*a/d^3/(c*x-1)^2-3/16/c*a/d^3/(c*x-1)-3/16/c*a/d^3*ln(c*x-1)-1/16/c*a/d^3/(c*x+1)^2-3/16/c*a/d^3/(c*x+1)+3/16/c*a/d^3*ln(c*x+1)-3/8*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x^3-3/8*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+5/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x+11/24/c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+3/8/c*b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/8*b*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/c/d^3-3/8/c*b/d^3*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-3/8*b*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/c/d^3","A"
51,1,508,190,0.520000," ","int((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^3,x)","\frac{a \ln \left(c x \right)}{d^{3}}+\frac{a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{5 a}{16 d^{3} \left(c x -1\right)}-\frac{a \ln \left(c x -1\right)}{2 d^{3}}+\frac{a}{16 d^{3} \left(c x +1\right)^{2}}+\frac{5 a}{16 d^{3} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{2 d^{3}}-\frac{2 b \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3} x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 b \,c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right) c^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{c x +1}\, \sqrt{c x -1}\, c x}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 b \,c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 b \,\mathrm{arccosh}\left(c x \right)}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 b}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{d^{3}}+\frac{b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2 d^{3}}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}-\frac{b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}-\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}-\frac{b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}"," ",0,"a/d^3*ln(c*x)+1/16*a/d^3/(c*x-1)^2-5/16*a/d^3/(c*x-1)-1/2*a/d^3*ln(c*x-1)+1/16*a/d^3/(c*x+1)^2+5/16*a/d^3/(c*x+1)-1/2*a/d^3*ln(c*x+1)-2/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3*x^3+2/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^4*x^4-1/2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*c^2*x^2+3/4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c*x-4/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^2*x^2+3/4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)+2/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)+b/d^3*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)/d^3-b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-b/d^3*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-b/d^3*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-b/d^3*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
52,1,392,245,0.453000," ","int((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^3,x)","-\frac{a}{d^{3} x}+\frac{c a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{7 c a}{16 d^{3} \left(c x -1\right)}-\frac{15 c a \ln \left(c x -1\right)}{16 d^{3}}-\frac{c a}{16 d^{3} \left(c x +1\right)^{2}}-\frac{7 c a}{16 d^{3} \left(c x +1\right)}+\frac{15 c a \ln \left(c x +1\right)}{16 d^{3}}-\frac{15 b \,\mathrm{arccosh}\left(c x \right) c^{4} x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{7 b \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3} x^{2}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{25 b \,\mathrm{arccosh}\left(c x \right) c^{2} x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{23 c b \sqrt{c x +1}\, \sqrt{c x -1}}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{d^{3} x \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 c b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}+\frac{15 c b \dilog \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 d^{3}}+\frac{15 c b \dilog \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 d^{3}}+\frac{15 c b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 d^{3}}"," ",0,"-a/d^3/x+1/16*c*a/d^3/(c*x-1)^2-7/16*c*a/d^3/(c*x-1)-15/16*c*a/d^3*ln(c*x-1)-1/16*c*a/d^3/(c*x+1)^2-7/16*c*a/d^3/(c*x+1)+15/16*c*a/d^3*ln(c*x+1)-15/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*c^4*x^3-7/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3*x^2+25/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*c^2*x+23/24*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-b/d^3/x/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)+2*c*b/d^3*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+15/8*c*b/d^3*dilog(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+15/8*c*b/d^3*dilog(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+15/8*c*b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
53,1,641,264,0.647000," ","int((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^3,x)","-\frac{a}{2 d^{3} x^{2}}+\frac{3 c^{2} a \ln \left(c x \right)}{d^{3}}+\frac{c^{2} a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{9 c^{2} a}{16 d^{3} \left(c x -1\right)}-\frac{3 c^{2} a \ln \left(c x -1\right)}{2 d^{3}}+\frac{c^{2} a}{16 d^{3} \left(c x +1\right)^{2}}+\frac{9 c^{2} a}{16 d^{3} \left(c x +1\right)}-\frac{3 c^{2} a \ln \left(c x +1\right)}{2 d^{3}}-\frac{2 c^{5} b \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 c^{6} b \,x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{4} b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{c^{3} b \sqrt{c x +1}\, \sqrt{c x -1}\, x}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 c^{4} b \,x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{9 c^{2} b \,\mathrm{arccosh}\left(c x \right)}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{c b \sqrt{c x +1}\, \sqrt{c x -1}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}+\frac{2 c^{2} b}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}+\frac{3 c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{d^{3}}+\frac{3 b \,c^{2} \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2 d^{3}}-\frac{3 c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}-\frac{3 c^{2} b \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}-\frac{3 c^{2} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}-\frac{3 c^{2} b \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{3}}"," ",0,"-1/2*a/d^3/x^2+3*c^2*a/d^3*ln(c*x)+1/16*c^2*a/d^3/(c*x-1)^2-9/16*c^2*a/d^3/(c*x-1)-3/2*c^2*a/d^3*ln(c*x-1)+1/16*c^2*a/d^3/(c*x+1)^2+9/16*c^2*a/d^3/(c*x+1)-3/2*c^2*a/d^3*ln(c*x+1)-2/3*c^5*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3+2/3*c^6*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^4-3/2*c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x^2+1/4*c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-4/3*c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2+9/4*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)+1/2*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(c*x+1)^(1/2)*(c*x-1)^(1/2)+2/3*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)-1/2*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arccosh(c*x)+3*c^2*b/d^3*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+3/2*b*c^2*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)/d^3-3*c^2*b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-3*c^2*b/d^3*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-3*c^2*b/d^3*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-3*c^2*b/d^3*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
54,1,504,314,0.577000," ","int((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^3,x)","-\frac{a}{3 d^{3} x^{3}}-\frac{3 c^{2} a}{d^{3} x}+\frac{c^{3} a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{11 c^{3} a}{16 d^{3} \left(c x -1\right)}-\frac{35 c^{3} a \ln \left(c x -1\right)}{16 d^{3}}-\frac{c^{3} a}{16 d^{3} \left(c x +1\right)^{2}}-\frac{11 c^{3} a}{16 d^{3} \left(c x +1\right)}+\frac{35 c^{3} a \ln \left(c x +1\right)}{16 d^{3}}-\frac{35 c^{6} b \,\mathrm{arccosh}\left(c x \right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{29 c^{5} b \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{175 c^{4} b \,\mathrm{arccosh}\left(c x \right) x}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{9 c^{3} b \sqrt{c x +1}\, \sqrt{c x -1}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{7 c^{2} b \,\mathrm{arccosh}\left(c x \right)}{3 d^{3} x \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{c b \sqrt{c x +1}\, \sqrt{c x -1}}{6 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{3}}+\frac{19 c^{3} b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3}}+\frac{35 c^{3} b \dilog \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 d^{3}}+\frac{35 c^{3} b \dilog \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 d^{3}}+\frac{35 c^{3} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 d^{3}}"," ",0,"-1/3*a/d^3/x^3-3*c^2*a/d^3/x+1/16*c^3*a/d^3/(c*x-1)^2-11/16*c^3*a/d^3/(c*x-1)-35/16*c^3*a/d^3*ln(c*x-1)-1/16*c^3*a/d^3/(c*x+1)^2-11/16*c^3*a/d^3/(c*x+1)+35/16*c^3*a/d^3*ln(c*x+1)-35/8*c^6*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x^3-29/24*c^5*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+175/24*c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*x+9/8*c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-7/3*c^2*b/d^3/x/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)+1/6*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)-1/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^3*arccosh(c*x)+19/3*c^3*b/d^3*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+35/8*c^3*b/d^3*dilog(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+35/8*c^3*b/d^3*dilog(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+35/8*c^3*b/d^3*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","A"
55,1,309,92,0.016000," ","int(arccosh(a*x)/(-a^2*c*x^2+c),x)","\frac{\arctanh \left(a x \right) \mathrm{arccosh}\left(a x \right)}{a c}+\frac{2 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{a x}{2}}\, \sqrt{-\frac{1}{2}+\frac{a x}{2}}\, \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a c \left(a^{2} x^{2}-1\right)}-\frac{2 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{a x}{2}}\, \sqrt{-\frac{1}{2}+\frac{a x}{2}}\, \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a c \left(a^{2} x^{2}-1\right)}+\frac{2 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{a x}{2}}\, \sqrt{-\frac{1}{2}+\frac{a x}{2}}\, \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a c \left(a^{2} x^{2}-1\right)}-\frac{2 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{\frac{1}{2}+\frac{a x}{2}}\, \sqrt{-\frac{1}{2}+\frac{a x}{2}}\, \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a c \left(a^{2} x^{2}-1\right)}"," ",0,"1/a/c*arctanh(a*x)*arccosh(a*x)+2*I/a/c*(-a^2*x^2+1)^(1/2)*(1/2+1/2*a*x)^(1/2)*(-1/2+1/2*a*x)^(1/2)/(a^2*x^2-1)*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-2*I/a/c*(-a^2*x^2+1)^(1/2)*(1/2+1/2*a*x)^(1/2)*(-1/2+1/2*a*x)^(1/2)/(a^2*x^2-1)*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))+2*I/a/c*(-a^2*x^2+1)^(1/2)*(1/2+1/2*a*x)^(1/2)*(-1/2+1/2*a*x)^(1/2)/(a^2*x^2-1)*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-2*I/a/c*(-a^2*x^2+1)^(1/2)*(1/2+1/2*a*x)^(1/2)*(-1/2+1/2*a*x)^(1/2)/(a^2*x^2-1)*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","C"
56,1,184,136,0.104000," ","int(arccosh(a*x)/(-a^2*c*x^2+c)^2,x)","-\frac{x \,\mathrm{arccosh}\left(a x \right)}{2 \left(a^{2} x^{2}-1\right) c^{2}}-\frac{\sqrt{a x -1}\, \sqrt{a x +1}}{2 a \left(a^{2} x^{2}-1\right) c^{2}}+\frac{\mathrm{arccosh}\left(a x \right) \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}+\frac{\polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}-\frac{\mathrm{arccosh}\left(a x \right) \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}-\frac{\polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}"," ",0,"-1/2/(a^2*x^2-1)/c^2*x*arccosh(a*x)-1/2/a/(a^2*x^2-1)/c^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+1/2/a/c^2*arccosh(a*x)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+1/2*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2-1/2/a/c^2*arccosh(a*x)*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-1/2*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2","A"
57,1,276,181,0.298000," ","int(arccosh(a*x)/(-a^2*c*x^2+c)^3,x)","-\frac{3 a^{2} x^{3} \mathrm{arccosh}\left(a x \right)}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{3 a \sqrt{a x +1}\, \sqrt{a x -1}\, x^{2}}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{5 x \,\mathrm{arccosh}\left(a x \right)}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{11 \sqrt{a x -1}\, \sqrt{a x +1}}{24 a \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{3 \,\mathrm{arccosh}\left(a x \right) \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}+\frac{3 \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}-\frac{3 \,\mathrm{arccosh}\left(a x \right) \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}-\frac{3 \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}"," ",0,"-3/8*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*x^3*arccosh(a*x)-3/8*a/(a^4*x^4-2*a^2*x^2+1)/c^3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^2+5/8/(a^4*x^4-2*a^2*x^2+1)/c^3*x*arccosh(a*x)+11/24/a/(a^4*x^4-2*a^2*x^2+1)/c^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+3/8/a/c^3*arccosh(a*x)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+3/8*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3-3/8/a/c^3*arccosh(a*x)*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-3/8*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3","A"
58,1,449,234,0.813000," ","int(x^4*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6 c^{2} d}-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8 c^{4} d}+\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{4}}+\frac{a d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 c^{4} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{7}}{6 \left(c x +1\right) \left(c x -1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{5}}{24 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{48 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{25 b \sqrt{-d \left(c^{2} x^{2}-1\right)}}{2304 \sqrt{c x +1}\, c^{5} \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,x^{6}}{36 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4}}{96 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{32 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}"," ",0,"-1/6*a*x^3*(-c^2*d*x^2+d)^(3/2)/c^2/d-1/8*a/c^4*x*(-c^2*d*x^2+d)^(3/2)/d+1/16*a/c^4*x*(-c^2*d*x^2+d)^(1/2)+1/16*a/c^4*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/32*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^5*arccosh(c*x)^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^7-5/24*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*x^5-1/48*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x^3+1/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/c^4/(c*x-1)*arccosh(c*x)*x-25/2304*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c^5/(c*x-1)^(1/2)-1/36*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^6+1/96*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^4+1/32*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*x^2","A"
59,1,346,169,0.381000," ","int(x^2*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}}{128 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,x^{4}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{16 \sqrt{c x +1}\, c \sqrt{c x -1}}"," ",0,"-1/4*a*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*a/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*a/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^2+1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5-3/8*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/8*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x-1/128*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)-1/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+1/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2","B"
60,1,239,104,0.237000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,x^{2}}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}}{8 \sqrt{c x +1}\, \sqrt{c x -1}\, c}"," ",0,"1/2*a*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3-1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*x+1/8*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c","B"
61,1,286,102,0.493000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^2,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{d x}-a \,c^{2} x \sqrt{-c^{2} d \,x^{2}+d}-\frac{a \,c^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2}}{\left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{\left(c x +1\right) \left(c x -1\right) x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{\sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(3/2)-a*c^2*x*(-c^2*d*x^2+d)^(1/2)-a*c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*c-b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*c-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x+1)/(c*x-1)*x*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x+1)/(c*x-1)/x+b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c","B"
62,1,1017,99,0.729000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^4,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 d \,x^{3}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{18 c^{4} x^{4}-18 c^{2} x^{2}+6}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{5}}{2 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{10 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{2 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/3*a/d/x^3*(-c^2*d*x^2+d)^(3/2)+2/3*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*c^3-b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3*c^6+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8+b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5-3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x*c^4-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6-1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3+10/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4-5/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)-1/3*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3","B"
63,1,1741,167,0.905000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^6,x)","\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{12}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{5}}{4 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{5}}{15 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{5}}{15 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \mathrm{arccosh}\left(c x \right) c^{11}}{\left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right) c^{9}}{3 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \mathrm{arccosh}\left(c x \right) c^{12}}{\left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{10}}{3 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{8}}{3 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{98 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{6}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{4}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x \left(c x +1\right) \left(c x -1\right)}-\frac{27 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 d \,x^{5}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{10}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{8}}{10 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{6}}{10 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right)}-\frac{2 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,x^{3}}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{20 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{4} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} c^{9}}{2 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{5}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{7}}{12 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{21 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{20 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{14}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{12}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{10}}{6 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{8}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{6}}{10 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{5} \left(c x +1\right) \left(c x -1\right)}"," ",0,"2/15*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^7*c^12-1/4*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+4/15*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*c^5-2/15*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^5-2*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11+2/3*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9+2*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+2*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12-5/3*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10-17/3*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8+98/15*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+12/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-27/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/5*a/d/x^5*(-c^2*d*x^2+d)^(3/2)-2/15*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^5*c^10-3/10*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^3*c^8+3/10*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x*c^6-2/15*a*c^2/d/x^3*(-c^2*d*x^2+d)^(3/2)-9/20*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9-6/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5-11/12*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+21/20*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-2/15*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^9/(c*x+1)/(c*x-1)*c^14+4/15*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^7/(c*x+1)/(c*x-1)*c^12+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^5/(c*x+1)/(c*x-1)*c^10-3/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^3/(c*x+1)/(c*x-1)*c^8+3/10*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x/(c*x+1)/(c*x-1)*c^6+9/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)","B"
64,1,2534,235,0.931000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^8,x)","\frac{225 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{7} \left(c x +1\right) \left(c x -1\right)}-\frac{128 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{13} c^{20}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}+\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{11} c^{18}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}+\frac{40 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{16}}{21 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}+\frac{214 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{14}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}-\frac{152 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{12}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}-\frac{30 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{10}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}+\frac{20 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{8}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}+\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} c^{13}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{469 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{9}}{60 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{71 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{5}}{28 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{255 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{28 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{4} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{120 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{7}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{75 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{14 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{6} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{7 d \,x^{7}}-\frac{8 a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{105 d \,x^{3}}+\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{16}}{15 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right)}-\frac{10 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{10}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right)}+\frac{20 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{8}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right)}+\frac{128 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{11} c^{18}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right)}-\frac{88 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{14}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right)}-\frac{302 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{12}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right)}+\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} \mathrm{arccosh}\left(c x \right) c^{16}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}-\frac{56 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \mathrm{arccosh}\left(c x \right) c^{14}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{12}}{15 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}-\frac{351 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{10}}{5 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}+\frac{3057 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{8}}{35 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c x +1\right) \left(c x -1\right)}-\frac{594 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{6}}{35 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x \left(c x +1\right) \left(c x -1\right)}+\frac{342 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{4}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{585 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{5} \left(c x +1\right) \left(c x -1\right)}-\frac{4 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{35 d \,x^{5}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right) c^{11}}{5 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{24 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) c^{9}}{\left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{8} \mathrm{arccosh}\left(c x \right) c^{15}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \mathrm{arccosh}\left(c x \right) c^{13}}{\left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{73 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{7}}{20 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{7}}{105 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{7}}{105 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"225/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^7/(c*x+1)/(c*x-1)*arccosh(c*x)-128/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^13/(c*x+1)/(c*x-1)*c^20+16/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^11/(c*x+1)/(c*x-1)*c^18+40/21*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^9/(c*x+1)/(c*x-1)*c^16+214/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^7/(c*x+1)/(c*x-1)*c^14-152/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^5/(c*x+1)/(c*x-1)*c^12-30/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^3/(c*x+1)/(c*x-1)*c^10+20/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x/(c*x+1)/(c*x-1)*c^8+16/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^13-469/60*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9+71/28*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+255/28*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-120/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7-75/14*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-1/7*a/d/x^7*(-c^2*d*x^2+d)^(3/2)-8/105*a*c^4/d/x^3*(-c^2*d*x^2+d)^(3/2)+16/15*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^9*c^16-10/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^3*c^10+20/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x*c^8+128/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^11*c^18-88/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^7*c^14-302/105*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^5*c^12+64/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^9/(c*x+1)/(c*x-1)*arccosh(c*x)*c^16-56/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^14-4/15*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12-351/5*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10+3057/35*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-594/35*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+342/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-585/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-4/35*a*c^2/d/x^5*(-c^2*d*x^2+d)^(3/2)+8/5*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11+24*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9-64/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^15+8*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^13-73/20*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+16/105*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*c^7-8/105*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^7","B"
65,1,988,228,0.678000," ","int(x^5*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","a \left(-\frac{x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{7 c^{2} d}+\frac{-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{35 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{105 d \,c^{4}}}{c^{2}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right)}{6272 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{3200 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{1152 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{128 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{128 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{1152 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{3200 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right)}{6272 \left(c x +1\right) c^{6} \left(c x -1\right)}\right)"," ",0,"a*(-1/7*x^4*(-c^2*d*x^2+d)^(3/2)/c^2/d+4/7/c^2*(-1/5*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(-c^2*d*x^2+d)^(3/2)))+b*(1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))/(c*x+1)/c^6/(c*x-1)+3/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))/(c*x+1)/c^6/(c*x-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/(c*x+1)/c^6/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/(c*x+1)/c^6/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/(c*x+1)/c^6/(c*x-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/(c*x+1)/c^6/(c*x-1)+3/3200*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))/(c*x+1)/c^6/(c*x-1)+1/6272*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))/(c*x+1)/c^6/(c*x-1))","B"
66,1,640,163,0.537000," ","int(x^3*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","a \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)"," ",0,"a*(-1/5*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(-c^2*d*x^2+d)^(3/2))+b*(1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))/(c*x+1)/c^4/(c*x-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/(c*x+1)/c^4/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/(c*x+1)/c^4/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/(c*x+1)/c^4/(c*x-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/(c*x+1)/c^4/(c*x-1)+1/800*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))/(c*x+1)/c^4/(c*x-1))","B"
67,1,356,98,0.293000," ","int(x*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)"," ",0,"-1/3*a/c^2/d*(-c^2*d*x^2+d)^(3/2)+b*(1/72*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/(c*x+1)/c^2/(c*x-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/(c*x+1)/c^2/(c*x-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/(c*x+1)/c^2/(c*x-1)+1/72*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/(c*x+1)/c^2/(c*x-1))","B"
68,1,394,222,0.430000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x,x)","-\sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right) a +a \sqrt{-c^{2} d \,x^{2}+d}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2} c^{2}}{\left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x c}{\sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{\left(c x +1\right) \left(c x -1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{\sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)*a+a*(-c^2*d*x^2+d)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2*c^2-b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x*c-b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)+I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))","A"
69,1,438,236,0.711000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^3,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2 d \,x^{2}}+\frac{a \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right) c^{2}}{2}-\frac{a \sqrt{-c^{2} d \,x^{2}+d}\, c^{2}}{2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{2 x \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{2 x^{2} \left(c x +1\right) \left(c x -1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(3/2)+1/2*a*d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)*c^2-1/2*a*(-c^2*d*x^2+d)^(1/2)*c^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/x/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/x^2/(c*x+1)/(c*x-1)*arccosh(c*x)-1/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2+1/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2-1/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2+1/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2","A"
70,1,541,302,0.749000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^5,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 d \,x^{4}}-\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8 d \,x^{2}}+\frac{a \,c^{4} \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{8}-\frac{a \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{4}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{8 \sqrt{c x +1}\, x \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{8 \left(c x +1\right) x^{2} \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{12 \sqrt{c x +1}\, x^{3} \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{4 \left(c x +1\right) x^{4} \left(c x -1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/4*a/d/x^4*(-c^2*d*x^2+d)^(3/2)-1/8*a*c^2/d/x^2*(-c^2*d*x^2+d)^(3/2)+1/8*a*c^4*d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-1/8*a*c^4*(-c^2*d*x^2+d)^(1/2)+1/8*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4+1/8*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/x/(c*x-1)^(1/2)*c^3-3/8*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/x^2/(c*x-1)*arccosh(c*x)*c^2-1/12*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/x^3/(c*x-1)^(1/2)*c+1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/x^4/(c*x-1)*arccosh(c*x)-1/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^4+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^4-1/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^4+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^4","A"
71,1,561,304,0.619000," ","int(x^4*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","-\frac{a \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{8 c^{2} d}-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{16 c^{4} d}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{64 c^{4}}+\frac{3 a d x \sqrt{-c^{2} d \,x^{2}+d}}{128 c^{4}}+\frac{3 a \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{128 c^{4} \sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} x^{8}}{64 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,x^{6}}{32 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4}}{256 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2}}{256 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d}{256 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{9}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{7}}{16 \left(c x +1\right) \left(c x -1\right)}-\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{5}}{64 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{3}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d}{8192 \sqrt{c x +1}\, c^{5} \sqrt{c x -1}}"," ",0,"-1/8*a*x^3*(-c^2*d*x^2+d)^(5/2)/c^2/d-1/16*a/c^4*x*(-c^2*d*x^2+d)^(5/2)/d+1/64*a/c^4*x*(-c^2*d*x^2+d)^(3/2)+3/128*a/c^4*d*x*(-c^2*d*x^2+d)^(1/2)+3/128*a/c^4*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/64*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^8-1/32*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^6+1/256*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^4+3/256*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*x^2-3/256*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^5*arccosh(c*x)^2*d-1/8*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^9+5/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^7-13/64*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^5-1/128*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x^3+3/128*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/c^4/(c*x-1)*arccosh(c*x)*x-15/8192*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c^5/(c*x-1)^(1/2)","A"
72,1,456,237,0.460000," ","int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6 c^{2} d}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}+\frac{a d x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{2}}+\frac{a \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 c^{2} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} x^{6}}{36 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,x^{4}}{96 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2}}{32 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{6 \left(c x +1\right) \left(c x -1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{24 \left(c x +1\right) \left(c x -1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{3}}{48 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d}{2304 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}"," ",0,"-1/6*a*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/24*a/c^2*x*(-c^2*d*x^2+d)^(3/2)+1/16*a/c^2*d*x*(-c^2*d*x^2+d)^(1/2)+1/16*a/c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/32*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^2*d+1/36*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6-7/96*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+1/32*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^7+11/24*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5-17/48*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x+7/2304*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)","A"
73,1,344,168,0.246000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{3 a d x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{3 a \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} x^{4}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,x^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{5}}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d}{128 \sqrt{c x +1}\, \sqrt{c x -1}\, c}"," ",0,"1/4*a*x*(-c^2*d*x^2+d)^(3/2)+3/8*a*d*x*(-c^2*d*x^2+d)^(1/2)+3/8*a*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^2*d+1/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3*x^4-5/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2-1/4*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^4*arccosh(c*x)*x^5+7/8*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3-5/8*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x+17/128*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c","B"
74,1,427,169,0.516000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^2,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{d x}-a \,c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}-\frac{3 a \,c^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{2}-\frac{3 a \,c^{2} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c d}{4 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \,\mathrm{arccosh}\left(c x \right) x^{3}}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d \,x^{2}}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c d \,\mathrm{arccosh}\left(c x \right)}{\sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \,\mathrm{arccosh}\left(c x \right) x}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c d}{8 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d}{\left(c x +1\right) \left(c x -1\right) x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c d}{\sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(5/2)-a*c^2*x*(-c^2*d*x^2+d)^(3/2)-3/2*a*c^2*d*x*(-c^2*d*x^2+d)^(1/2)-3/2*a*c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*c*d-1/2*b*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/4*b*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*c*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x-1/8*b*(-d*(c^2*x^2-1))^(1/2)*c*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*d/(c*x+1)/(c*x-1)/x+b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c*d","B"
75,1,1181,173,0.745000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^4,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3 d \,x^{3}}+\frac{2 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3 d x}+\frac{2 a \,c^{4} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}+a \,c^{4} d x \sqrt{-c^{2} d \,x^{2}+d}+\frac{a \,c^{4} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d \,c^{3}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d \,c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{6}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} c^{8}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} \mathrm{arccosh}\left(c x \right) c^{5}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{52 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{4}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} c^{5}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{10 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{6}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) c^{3}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{73 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3}}{2 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{4}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) c^{2}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c}{6 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right)}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d \,c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/3*a/d/x^3*(-c^2*d*x^2+d)^(5/2)+2/3*a*c^2/d/x*(-c^2*d*x^2+d)^(5/2)+2/3*a*c^4*x*(-c^2*d*x^2+d)^(3/2)+a*c^4*d*x*(-c^2*d*x^2+d)^(1/2)+a*c^4*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d*c^3+8/3*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d*c^3-32*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+32*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-8/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3*c^6+8/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8+12*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5-52*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+2/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x*c^4-4*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-10/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6-4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3+73/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4+3/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+2/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4-14/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)-4/3*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^3","B"
76,1,2171,138,0.875000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^6,x)","\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{8}}{10 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{6}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} c^{10}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{8} \mathrm{arccosh}\left(c x \right) c^{13}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{6} \mathrm{arccosh}\left(c x \right) c^{11}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4} \mathrm{arccosh}\left(c x \right) c^{9}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{56 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,\mathrm{arccosh}\left(c x \right) c^{6}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{28 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) c^{4}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) c^{2}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{9} \mathrm{arccosh}\left(c x \right) c^{14}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d \,c^{5}}{5 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d \,c^{5}}{5 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{5}}{2 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{7} c^{12}}{25 c^{8} x^{8}-50 c^{6} x^{6}+50 c^{4} x^{4}-25 c^{2} x^{2}+5}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 d \,x^{5}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{6} c^{11}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4} c^{9}}{4 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} c^{7}}{2 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{4} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) c^{5}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{8}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{6}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right)}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{5} \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{9} c^{14}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{7} c^{12}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} c^{10}}{4 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{7} \mathrm{arccosh}\left(c x \right) c^{12}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} \mathrm{arccosh}\left(c x \right) c^{10}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} \mathrm{arccosh}\left(c x \right) c^{8}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}"," ",0,"3/10*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3*c^8-1/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x*c^6+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^7*c^12-9/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^5*c^10+b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^13-2*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11+2*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9-b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7-56/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+28/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-8/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^9/(c*x+1)/(c*x-1)*arccosh(c*x)*c^14+1/5*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^5-2/5*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d*c^5-3/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-1/5*a/d/x^5*(-c^2*d*x^2+d)^(5/2)+b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^11-9/4*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9+5/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+9/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-1/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5+7/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^8-1/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^6+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)-1/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^9/(c*x+1)/(c*x-1)*c^14+13/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^7/(c*x+1)/(c*x-1)*c^12-3/4*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^10+5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12-11*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10+14*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8","B"
77,1,3144,207,0.900000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^8,x)","\text{output too large to display}"," ",0,"-116/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^5*c^12+359/30*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7-4/35*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d*c^7+2/35*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^7-2/35*a*c^2/d/x^5*(-c^2*d*x^2+d)^(5/2)-25/42*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+2/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^13/(c*x+1)/(c*x-1)*c^20-9/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^11/(c*x+1)/(c*x-1)*c^18-1/21*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^9/(c*x+1)/(c*x-1)*c^16+142/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^7/(c*x+1)/(c*x-1)*c^14-72/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^5/(c*x+1)/(c*x-1)*c^12+25/21*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^3/(c*x+1)/(c*x-1)*c^10-5/21*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x/(c*x+1)/(c*x-1)*c^8+25/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^7/(c*x+1)/(c*x-1)*arccosh(c*x)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^15+5/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^13-11/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^11-161/30*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9+10/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7-421/42*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+55/14*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^10/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^17-2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^15-4*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^13+44/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11-6*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9-2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^11/(c*x+1)/(c*x-1)*arccosh(c*x)*c^18+3*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^9/(c*x+1)/(c*x-1)*arccosh(c*x)*c^16+12*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^14-164/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12+52/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10+1966/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-3272/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+472/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-170/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/7*a/d/x^7*(-c^2*d*x^2+d)^(5/2)+26/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^7*c^14+20/21*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^3*c^10-5/21*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x*c^8-2/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^11*c^18+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^9*c^16","B"
78,1,4259,276,1.035000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^10,x)","\text{output too large to display}"," ",0,"-35/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x*c^10-128/315*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^15*c^24-16/45*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^13*c^22+1384/945*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^11*c^20+2306/945*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^9*c^18-40/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^7*c^16-2189/189*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^5*c^14+350/27*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^3*c^12-16/315*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d*c^9+8/315*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^9-30055/504*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9-43264/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10+113594/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-174520/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+19540/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-7700/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-4/63*a*c^2/d/x^7*(-c^2*d*x^2+d)^(5/2)-829/56*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^11+25915/126*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+1225/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^9/(c*x+1)/(c*x-1)*arccosh(c*x)-1225/72*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-16/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^10/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^19+4*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^17+4189/180*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^15-1187/60*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^13-1285/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+21175/216*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+280/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9+128/315*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^17/(c*x+1)/(c*x-1)*c^26-16/315*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^15/(c*x+1)/(c*x-1)*c^24-344/189*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^13/(c*x+1)/(c*x-1)*c^22-922/945*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^11/(c*x+1)/(c*x-1)*c^20+2906/945*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^9/(c*x+1)/(c*x-1)*c^18+2069/189*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^7/(c*x+1)/(c*x-1)*c^16-4639/189*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^5/(c*x+1)/(c*x-1)*c^14+455/27*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^3/(c*x+1)/(c*x-1)*c^12-35/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x/(c*x+1)/(c*x-1)*c^10+64/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^12/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^21-24*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^10/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^19+24/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^17-208/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^15+1104/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^13-120*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11-64/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^13/(c*x+1)/(c*x-1)*arccosh(c*x)*c^22+104/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^11/(c*x+1)/(c*x-1)*arccosh(c*x)*c^20-212/15*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^9/(c*x+1)/(c*x-1)*arccosh(c*x)*c^18+3151/15*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^16-60632/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^14+59884/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12-8/315*a*c^4/d/x^5*(-c^2*d*x^2+d)^(5/2)-1/9*a/d/x^9*(-c^2*d*x^2+d)^(5/2)","B"
79,1,5518,345,1.239000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^12,x)","\text{output too large to display}"," ",0,"result too large to display","B"
80,1,1846,335,1.004000," ","int(x^7*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","a \left(-\frac{x^{6} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{11 c^{2} d}+\frac{-\frac{2 x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{33 c^{2} d}+\frac{6 \left(-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{63 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{315 d \,c^{4}}\right)}{11 c^{2}}}{c^{2}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1-3328 c^{10} x^{10}+4096 c^{8} x^{8}-2352 c^{6} x^{6}+620 c^{4} x^{4}-61 c^{2} x^{2}+1024 x^{12} c^{12}+2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-1232 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-11 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +220 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+1024 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}-2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}\right) \left(-1+11 \,\mathrm{arccosh}\left(c x \right)\right) d}{247808 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+9 \,\mathrm{arccosh}\left(c x \right)\right) d}{55296 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{100352 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{11 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{51200 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{3072 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{7 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d}{1024 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{7 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d}{1024 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{3072 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{11 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{51200 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{100352 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(1+9 \,\mathrm{arccosh}\left(c x \right)\right) d}{55296 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-1024 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}+1024 x^{12} c^{12}+2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}-3328 c^{10} x^{10}-2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+4096 c^{8} x^{8}+1232 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-2352 c^{6} x^{6}-220 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+620 c^{4} x^{4}+11 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -61 c^{2} x^{2}+1\right) \left(1+11 \,\mathrm{arccosh}\left(c x \right)\right) d}{247808 \left(c x +1\right) c^{8} \left(c x -1\right)}\right)"," ",0,"a*(-1/11*x^6*(-c^2*d*x^2+d)^(5/2)/c^2/d+6/11/c^2*(-1/9*x^4*(-c^2*d*x^2+d)^(5/2)/c^2/d+4/9/c^2*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2))))+b*(-1/247808*(-d*(c^2*x^2-1))^(1/2)*(1-3328*c^10*x^10+4096*c^8*x^8-2352*c^6*x^6+620*c^4*x^4-61*c^2*x^2+1024*x^12*c^12+2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-1232*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-11*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+220*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+1024*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11-2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9)*(-1+11*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)-1/55296*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+9*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)+1/100352*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)+11/51200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)+1/3072*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)-7/1024*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)-7/1024*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)+1/3072*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)+11/51200*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)+1/100352*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)-1/55296*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(1+9*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1)-1/247808*(-d*(c^2*x^2-1))^(1/2)*(-1024*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11+1024*x^12*c^12+2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9-3328*c^10*x^10-2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+4096*c^8*x^8+1232*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-2352*c^6*x^6-220*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+620*c^4*x^4+11*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-61*c^2*x^2+1)*(1+11*arccosh(c*x))*d/(c*x+1)/c^8/(c*x-1))","B"
81,1,1376,269,0.649000," ","int(x^5*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","a \left(-\frac{x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{9 c^{2} d}+\frac{-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{63 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{315 d \,c^{4}}}{c^{2}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+9 \,\mathrm{arccosh}\left(c x \right)\right) d}{41472 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{25088 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{3200 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{1152 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d}{256 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d}{256 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{1152 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{3200 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{25088 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(1+9 \,\mathrm{arccosh}\left(c x \right)\right) d}{41472 \left(c x +1\right) c^{6} \left(c x -1\right)}\right)"," ",0,"a*(-1/9*x^4*(-c^2*d*x^2+d)^(5/2)/c^2/d+4/9/c^2*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2)))+b*(-1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+9*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)-1/25088*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)-1/25088*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1)-1/41472*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(1+9*arccosh(c*x))*d/(c*x+1)/c^6/(c*x-1))","B"
82,1,966,203,0.582000," ","int(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","a \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{6272 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{3200 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{384 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{384 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{3200 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{6272 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)"," ",0,"a*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2))+b*(-1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)-1/6272*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1))","B"
83,1,620,137,0.307000," ","int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{800 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{96 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{96 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{800 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)"," ",0,"-1/5*a/c^2/d*(-c^2*d*x^2+d)^(5/2)+b*(-1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)+1/96*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)+1/96*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)-1/800*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1))","B"
84,1,499,287,0.475000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x,x)","\frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a}{3}-a \,d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)+a \sqrt{-c^{2} d \,x^{2}+d}\, d -\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right)}{3 \left(c x +1\right) \left(c x -1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{4} c^{4}}{3 \left(c x +1\right) \left(c x -1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{2} c^{2}}{3 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{3}}{9 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x c}{3 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d}{\sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"1/3*(-c^2*d*x^2+d)^(3/2)*a-a*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+a*(-c^2*d*x^2+d)^(1/2)*d-4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)+I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d+I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d-I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d-1/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^4*c^4+5/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2*c^2+1/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^3*c^3-4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x*c-I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d","A"
85,1,542,302,0.644000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^3,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2 d \,x^{2}}-\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2}+\frac{3 a \,c^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2}-\frac{3 a \,c^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d}{2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \,\mathrm{arccosh}\left(c x \right) x^{2}}{\left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d x}{\sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \,\mathrm{arccosh}\left(c x \right)}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c}{2 x \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right)}{2 x^{2} \left(c x +1\right) \left(c x -1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d}{2 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(5/2)-1/2*a*c^2*(-c^2*d*x^2+d)^(3/2)+3/2*a*c^2*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-3/2*a*c^2*(-c^2*d*x^2+d)^(1/2)*d-b*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2+b*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x+1/2*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c*x+1)/(c*x-1)*arccosh(c*x)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d/x/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)*d/x^2/(c*x+1)/(c*x-1)*arccosh(c*x)-3/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d+3/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d-3/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d+3/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d","A"
86,1,570,308,0.727000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^5,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{4 d \,x^{4}}+\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{8 d \,x^{2}}+\frac{a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8}-\frac{3 a \,c^{4} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{8}+\frac{3 a \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}\, d}{8}+\frac{5 b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{4}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{5 b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{8 \sqrt{c x +1}\, x \sqrt{c x -1}}-\frac{7 b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{8 \left(c x +1\right) x^{2} \left(c x -1\right)}-\frac{b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{12 \sqrt{c x +1}\, x^{3} \sqrt{c x -1}}+\frac{b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{4 \left(c x +1\right) x^{4} \left(c x -1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d \,c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d \,c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d \,c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d \,c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/4*a/d/x^4*(-c^2*d*x^2+d)^(5/2)+1/8*a*c^2/d/x^2*(-c^2*d*x^2+d)^(5/2)+1/8*a*c^4*(-c^2*d*x^2+d)^(3/2)-3/8*a*c^4*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+3/8*a*c^4*(-c^2*d*x^2+d)^(1/2)*d+5/8*b*d*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4+5/8*b*d*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/x/(c*x-1)^(1/2)*c^3-7/8*b*d*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/x^2/(c*x-1)*arccosh(c*x)*c^2-1/12*b*d*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/x^3/(c*x-1)^(1/2)*c+1/4*b*d*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/x^4/(c*x-1)*arccosh(c*x)+3/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d*c^4-3/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d*c^4+3/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d*c^4-3/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d*c^4","A"
87,1,690,386,0.809000," ","int(x^4*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","-\frac{a \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{10 c^{2} d}-\frac{3 a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{80 c^{4} d}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{160 c^{4}}+\frac{a d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{128 c^{4}}+\frac{3 a \,d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{256 c^{4}}+\frac{3 a \,d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{256 c^{4} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{10}}{100 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{21 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{8}}{640 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{31 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,x^{6}}{960 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4}}{512 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2}}{512 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{11}}{10 \left(c x +1\right) \left(c x -1\right)}-\frac{29 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{9}}{80 \left(c x +1\right) \left(c x -1\right)}+\frac{73 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{7}}{160 \left(c x +1\right) \left(c x -1\right)}-\frac{129 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{640 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{256 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{101 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2}}{1228800 \sqrt{c x +1}\, c^{5} \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{512 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5}}"," ",0,"-1/10*a*x^3*(-c^2*d*x^2+d)^(7/2)/c^2/d-3/80*a/c^4*x*(-c^2*d*x^2+d)^(7/2)/d+1/160*a/c^4*x*(-c^2*d*x^2+d)^(5/2)+1/128*a/c^4*d*x*(-c^2*d*x^2+d)^(3/2)+3/256*a/c^4*d^2*x*(-c^2*d*x^2+d)^(1/2)+3/256*a/c^4*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/100*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^10+21/640*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^8-31/960*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^6+1/512*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^4+3/512*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*x^2+1/10*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^11-29/80*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^9+73/160*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^7-129/640*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^5-1/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x^3+3/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/c^4/(c*x-1)*arccosh(c*x)*x-101/1228800*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c^5/(c*x-1)^(1/2)-3/512*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^5*arccosh(c*x)^2*d^2","A"
88,1,581,315,0.493000," ","int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 c^{2} d}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{48 c^{2}}+\frac{5 a d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{192 c^{2}}+\frac{5 a \,d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{128 c^{2}}+\frac{5 a \,d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{128 c^{2} \sqrt{c^{2} d}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{256 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{8}}{64 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{6}}{288 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{59 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,x^{4}}{768 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2}}{256 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{9}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{48 \left(c x +1\right) \left(c x -1\right)}+\frac{127 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{192 \left(c x +1\right) \left(c x -1\right)}-\frac{133 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{384 \left(c x +1\right) \left(c x -1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{359 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2}}{73728 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}"," ",0,"-1/8*a*x*(-c^2*d*x^2+d)^(7/2)/c^2/d+1/48*a/c^2*x*(-c^2*d*x^2+d)^(5/2)+5/192*a/c^2*d*x*(-c^2*d*x^2+d)^(3/2)+5/128*a/c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/128*a/c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-5/256*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^2*d^2-1/64*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^8+17/288*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6-59/768*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+5/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^9-23/48*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^7+127/192*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5-133/384*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+5/128*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x+359/73728*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)","A"
89,1,462,249,0.307000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}+\frac{5 a d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a \,d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 \sqrt{c^{2} d}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{6}}{36 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{4}}{96 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,x^{2}}{32 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{7}}{6 \left(c x +1\right) \left(c x -1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{5}}{24 \left(c x +1\right) \left(c x -1\right)}+\frac{59 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{48 \left(c x +1\right) \left(c x -1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x}{16 \left(c x +1\right) \left(c x -1\right)}+\frac{299 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2}}{2304 \sqrt{c x +1}\, \sqrt{c x -1}\, c}"," ",0,"1/6*a*x*(-c^2*d*x^2+d)^(5/2)+5/24*a*d*x*(-c^2*d*x^2+d)^(3/2)+5/16*a*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/16*a*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-5/32*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^2*d^2-1/36*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5*x^6+13/96*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3*x^4-11/32*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^6*arccosh(c*x)*x^7-17/24*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^4*arccosh(c*x)*x^5+59/48*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3-11/16*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x+299/2304*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c","A"
90,1,550,244,0.566000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^2,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{d x}-a \,c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}-\frac{5 a \,c^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}-\frac{15 a \,c^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8}-\frac{15 a \,c^{2} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2} c}{16 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d^{2}}{\left(c x +1\right) \left(c x -1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{4}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,\mathrm{arccosh}\left(c x \right)}{\sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d^{2} c}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{5}}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{33 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c}{128 \sqrt{c x +1}\, \sqrt{c x -1}}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(7/2)-a*c^2*x*(-c^2*d*x^2+d)^(5/2)-5/4*a*c^2*d*x*(-c^2*d*x^2+d)^(3/2)-15/8*a*c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)-15/8*a*c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+15/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d^2*c+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*d^2/(c*x+1)/(c*x-1)/x-1/16*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^4+9/16*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c+1/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)*x^5-11/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x-33/128*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c*x+1)^(1/2)/(c*x-1)^(1/2)","B"
91,1,1407,249,0.787000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^4,x)","\frac{4 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{3 d x}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{3 d \,x^{3}}+\frac{4 a \,c^{4} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3}-\frac{147 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{35 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} \mathrm{arccosh}\left(c x \right) c^{5}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{190 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) c^{2}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}+\frac{147 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{203 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{49 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{6}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,c^{4}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{21 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} c^{5}}{2 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) c^{3}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{3}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{49 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} c^{8}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{28 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{6}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,c^{4}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3}}{2 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{2}}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2} c^{3}}{4 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d^{2} c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d^{2} c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{5 a \,c^{4} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}+\frac{5 a \,c^{4} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{5 a \,c^{4} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}"," ",0,"4/3*a*c^2/d/x*(-c^2*d*x^2+d)^(7/2)-1/3*a/d/x^3*(-c^2*d*x^2+d)^(7/2)+4/3*a*c^4*x*(-c^2*d*x^2+d)^(5/2)-147*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+35*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5+190/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-23/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2+147*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-203*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6-49/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3*c^6+7/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x*c^4+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c*x+1)^(1/2)/(c*x-1)^(1/2)+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)-21/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-1/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-7/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)*x+49/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8-28/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+7/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4+5/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-1/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^2-5/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d^2*c^3+14/3*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d^2*c^3-7/3*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c^3+5/3*a*c^4*d*x*(-c^2*d*x^2+d)^(3/2)+5/2*a*c^4*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/2*a*c^4*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))","B"
92,1,2429,251,0.856000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^6,x)","\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d^{2} c^{5}}{15 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2} c^{5}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{46 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d^{2} c^{5}}{15 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{175 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5}}{4 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5819 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{9} c^{14}}{30 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{18791 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{7} c^{12}}{60 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{943 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} c^{10}}{6 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{207 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{8}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{69 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,c^{6}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{5} \left(c x +1\right) \left(c x -1\right)}-\frac{1329 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4} c^{9}}{4 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{1889 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} c^{7}}{12 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{141 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{4} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{69 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) c^{5}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{759 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{6} c^{11}}{2 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{15 d \,x^{3}}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{5 d \,x^{5}}-\frac{8 a \,c^{6} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{15}+\frac{759 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{8}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right)}-\frac{69 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,c^{6}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right)}+\frac{5819 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{7} c^{12}}{30 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right)}-\frac{7153 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} c^{10}}{60 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right)}-\frac{8 a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{15 d x}-\frac{2 a \,c^{6} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-a \,c^{6} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}-\frac{a \,c^{6} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}+\frac{1587 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{8} \mathrm{arccosh}\left(c x \right) c^{13}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{1173 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{6} \mathrm{arccosh}\left(c x \right) c^{11}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{1495 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4} \mathrm{arccosh}\left(c x \right) c^{9}}{3 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{115 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{1587 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{9} \mathrm{arccosh}\left(c x \right) c^{14}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{3519 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{7} \mathrm{arccosh}\left(c x \right) c^{12}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{9595 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} \mathrm{arccosh}\left(c x \right) c^{10}}{3 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{5318 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} \mathrm{arccosh}\left(c x \right) c^{8}}{3 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}-\frac{9602 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,\mathrm{arccosh}\left(c x \right) c^{6}}{15 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c x +1\right) \left(c x -1\right)}+\frac{777 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) c^{4}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x \left(c x +1\right) \left(c x -1\right)}-\frac{117 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) c^{2}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{3} \left(c x +1\right) \left(c x -1\right)}"," ",0,"23/15*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c^5+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d^2*c^5-46/15*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d^2*c^5-175/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-5819/30*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^9/(c*x+1)/(c*x-1)*c^14+18791/60*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^7/(c*x+1)/(c*x-1)*c^12-943/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^5/(c*x+1)/(c*x-1)*c^10+207/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^3/(c*x+1)/(c*x-1)*c^8-69/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x/(c*x+1)/(c*x-1)*c^6+9/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)-1329/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9+1889/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+141/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-9/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+69/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5+759/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^11+2/15*a*c^2/d/x^3*(-c^2*d*x^2+d)^(7/2)-1/5*a/d/x^5*(-c^2*d*x^2+d)^(7/2)-8/15*a*c^6*x*(-c^2*d*x^2+d)^(5/2)+759/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^3*c^8-69/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x*c^6+5819/30*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^7*c^12-7153/60*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^5*c^10-8/15*a*c^4/d/x*(-c^2*d*x^2+d)^(7/2)-2/3*a*c^6*d*x*(-c^2*d*x^2+d)^(3/2)-a*c^6*d^2*x*(-c^2*d*x^2+d)^(1/2)-a*c^6*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1587*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^13-1173*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11+1495/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9-115*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7-1587*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^9/(c*x+1)/(c*x-1)*arccosh(c*x)*c^14+3519*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12-9595/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10+5318/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-9602/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+777/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-117/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2","B"
93,1,3775,183,0.942000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^8,x)","\text{output too large to display}"," ",0,"17/28*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^5*c^12+3/14*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^13/(c*x+1)/(c*x-1)*c^20-27/28*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^11/(c*x+1)/(c*x-1)*c^18+73/42*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^9/(c*x+1)/(c*x-1)*c^16-67/42*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^7/(c*x+1)/(c*x-1)*c^14+11/14*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^12-17/84*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^10+1/42*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^8-5/28*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^3*c^10+1/42*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x*c^8-3/14*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^11*c^18+3/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^9*c^16-83/84*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^7*c^14+1/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^7/(c*x+1)/(c*x-1)*arccosh(c*x)+21/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^15-119/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^13+47/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^11-109/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^9-1/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7-41/28*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+23/84*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-1/42*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-3/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^10/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^17-165/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+55/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-11/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/7*a/d/x^7*(-c^2*d*x^2+d)^(7/2)+b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^13/(c*x+1)/(c*x-1)*arccosh(c*x)*c^20-7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^11/(c*x+1)/(c*x-1)*arccosh(c*x)*c^18-3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^11+b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^9-b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^12/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^19+3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^10/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^17+5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^6/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^13-5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^8/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^15+23*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^9/(c*x+1)/(c*x-1)*arccosh(c*x)*c^16-47*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^7/(c*x+1)/(c*x-1)*arccosh(c*x)*c^14+66*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^12-66*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^10+330/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8+55/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7-1/7*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c^7+2/7*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d^2*c^7","B"
94,1,5006,266,1.091000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^10,x)","\text{output too large to display}"," ",0,"result too large to display","B"
95,1,6379,325,1.313000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^12,x)","\text{output too large to display}"," ",0,"result too large to display","B"
96,1,2374,386,0.878000," ","int(x^7*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","a \left(-\frac{x^{6} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{13 c^{2} d}+\frac{-\frac{6 x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{143 c^{2} d}+\frac{6 \left(-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{99 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{693 d \,c^{4}}\right)}{13 c^{2}}}{c^{2}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-1+22784 c^{10} x^{10}-16896 c^{8} x^{8}+6496 c^{6} x^{6}-1204 c^{4} x^{4}+85 c^{2} x^{2}+4096 x^{14} c^{14}+4096 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{13} c^{13}-15360 x^{12} c^{12}-9984 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+2912 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -364 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-13312 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}+16640 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}\right) \left(-1+13 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{1384448 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1-3328 c^{10} x^{10}+4096 c^{8} x^{8}-2352 c^{6} x^{6}+620 c^{4} x^{4}-61 c^{2} x^{2}+1024 x^{12} c^{12}+2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-1232 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-11 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +220 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+1024 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}-2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}\right) \left(-1+11 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{991232 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{110592 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{200704 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{40960 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{24576 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{2048 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{2048 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{24576 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{40960 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{200704 \left(c x +1\right) c^{8} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{110592 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-1024 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}+1024 x^{12} c^{12}+2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}-3328 c^{10} x^{10}-2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+4096 c^{8} x^{8}+1232 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-2352 c^{6} x^{6}-220 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+620 c^{4} x^{4}+11 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -61 c^{2} x^{2}+1\right) \left(1+11 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{991232 \left(c x +1\right) c^{8} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4096 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{13} c^{13}+4096 x^{14} c^{14}+13312 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}-15360 x^{12} c^{12}-16640 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+22784 c^{10} x^{10}+9984 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-16896 c^{8} x^{8}-2912 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+6496 c^{6} x^{6}+364 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-1204 c^{4} x^{4}-13 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +85 c^{2} x^{2}-1\right) \left(1+13 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{1384448 \left(c x +1\right) c^{8} \left(c x -1\right)}\right)"," ",0,"a*(-1/13*x^6*(-c^2*d*x^2+d)^(7/2)/c^2/d+6/13/c^2*(-1/11*x^4*(-c^2*d*x^2+d)^(7/2)/c^2/d+4/11/c^2*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2))))+b*(1/1384448*(-d*(c^2*x^2-1))^(1/2)*(-1+22784*c^10*x^10-16896*c^8*x^8+6496*c^6*x^6-1204*c^4*x^4+85*c^2*x^2+4096*x^14*c^14+4096*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^13*c^13-15360*x^12*c^12-9984*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+2912*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-364*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-13312*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11+16640*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9)*(-1+13*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+1/991232*(-d*(c^2*x^2-1))^(1/2)*(1-3328*c^10*x^10+4096*c^8*x^8-2352*c^6*x^6+620*c^4*x^4-61*c^2*x^2+1024*x^12*c^12+2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-1232*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-11*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+220*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+1024*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11-2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9)*(-1+11*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)-1/110592*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+9*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)-3/200704*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+3/40960*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+5/24576*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)-5/2048*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)-5/2048*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+5/24576*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+3/40960*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)-3/200704*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)-1/110592*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(1+9*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+1/991232*(-d*(c^2*x^2-1))^(1/2)*(-1024*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11+1024*x^12*c^12+2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9-3328*c^10*x^10-2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+4096*c^8*x^8+1232*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-2352*c^6*x^6-220*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+620*c^4*x^4+11*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-61*c^2*x^2+1)*(1+11*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1)+1/1384448*(-d*(c^2*x^2-1))^(1/2)*(-4096*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^13*c^13+4096*x^14*c^14+13312*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11-15360*x^12*c^12-16640*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+22784*c^10*x^10+9984*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-16896*c^8*x^8-2912*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+6496*c^6*x^6+364*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-1204*c^4*x^4-13*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+85*c^2*x^2-1)*(1+13*arccosh(c*x))*d^2/(c*x+1)/c^8/(c*x-1))","B"
97,1,1840,318,0.736000," ","int(x^5*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","a \left(-\frac{x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{11 c^{2} d}+\frac{-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{99 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{693 d \,c^{4}}}{c^{2}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1-3328 c^{10} x^{10}+4096 c^{8} x^{8}-2352 c^{6} x^{6}+620 c^{4} x^{4}-61 c^{2} x^{2}+1024 x^{12} c^{12}+2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-1232 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-11 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +220 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+1024 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}-2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}\right) \left(-1+11 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{247808 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{165888 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{100352 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{10240 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{9216 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{1024 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{1024 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{9216 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{10240 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{100352 \left(c x +1\right) c^{6} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{165888 \left(c x +1\right) c^{6} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-1024 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{11} c^{11}+1024 x^{12} c^{12}+2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}-3328 c^{10} x^{10}-2816 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+4096 c^{8} x^{8}+1232 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-2352 c^{6} x^{6}-220 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+620 c^{4} x^{4}+11 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -61 c^{2} x^{2}+1\right) \left(1+11 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{247808 \left(c x +1\right) c^{6} \left(c x -1\right)}\right)"," ",0,"a*(-1/11*x^4*(-c^2*d*x^2+d)^(7/2)/c^2/d+4/11/c^2*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2)))+b*(1/247808*(-d*(c^2*x^2-1))^(1/2)*(1-3328*c^10*x^10+4096*c^8*x^8-2352*c^6*x^6+620*c^4*x^4-61*c^2*x^2+1024*x^12*c^12+2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-1232*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-11*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+220*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+1024*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11-2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9)*(-1+11*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)-1/165888*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+9*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)-5/100352*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)+1/10240*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)+5/9216*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)-5/1024*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)-5/1024*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)+5/9216*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)+1/10240*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)-5/100352*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)-1/165888*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(1+9*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1)+1/247808*(-d*(c^2*x^2-1))^(1/2)*(-1024*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^11*c^11+1024*x^12*c^12+2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9-3328*c^10*x^10-2816*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+4096*c^8*x^8+1232*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-2352*c^6*x^6-220*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+620*c^4*x^4+11*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-61*c^2*x^2+1)*(1+11*arccosh(c*x))*d^2/(c*x+1)/c^6/(c*x-1))","B"
98,1,1102,250,0.542000," ","int(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","a \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{41472 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{25088 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{576 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{576 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{25088 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{41472 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)"," ",0,"a*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2))+b*(1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+9*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)+1/41472*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(1+9*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1))","B"
99,1,956,182,0.351000," ","int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{6272 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{640 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{640 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{6272 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)"," ",0,"-1/7*a/c^2/d*(-c^2*d*x^2+d)^(7/2)+b*(1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-1/640*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)+1/128*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)+1/128*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-1/640*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)+1/6272*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1))","B"
100,1,620,362,0.529000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x,x)","\frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a}{5}+\frac{a d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-a \,d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)+a \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} c^{5}}{25 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{3}}{45 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x c}{15 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)}{15 \left(c x +1\right) \left(c x -1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{6} c^{6}}{5 \left(c x +1\right) \left(c x -1\right)}-\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{4} c^{4}}{15 \left(c x +1\right) \left(c x -1\right)}+\frac{34 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{2} c^{2}}{15 \left(c x +1\right) \left(c x -1\right)}"," ",0,"1/5*(-c^2*d*x^2+d)^(5/2)*a+1/3*a*d*(-c^2*d*x^2+d)^(3/2)-a*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+a*(-c^2*d*x^2+d)^(1/2)*d^2-I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2-I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2-1/25*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^5*c^5+11/45*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^3*c^3-23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x*c-23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)+I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2+I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^6*c^6-14/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^4*c^4+34/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2*c^2","A"
101,1,667,381,0.740000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^3,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{2 d \,x^{2}}-\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2}-\frac{5 a \,c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6}+\frac{5 a \,c^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2}-\frac{5 a \,c^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}}{2}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{5} d^{2} x^{3}}{9 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d^{2} x}{3 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c}{2 x \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)}{2 x^{2} \left(c x +1\right) \left(c x -1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d^{2} \mathrm{arccosh}\left(c x \right)}{6 \left(c x +1\right) \left(c x -1\right)}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2} d^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{6} d^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{3 \left(c x +1\right) \left(c x -1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d^{2} \mathrm{arccosh}\left(c x \right) x^{2}}{3 \left(c x +1\right) \left(c x -1\right)}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(7/2)-1/2*a*c^2*(-c^2*d*x^2+d)^(5/2)-5/6*a*c^2*d*(-c^2*d*x^2+d)^(3/2)+5/2*a*c^2*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-5/2*a*c^2*(-c^2*d*x^2+d)^(1/2)*d^2+5/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d^2-1/9*b*(-d*(c^2*x^2-1))^(1/2)*c^5*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^3+7/3*b*(-d*(c^2*x^2-1))^(1/2)*c^3*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/x/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+5/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d^2-5/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/x^2/(c*x+1)/(c*x-1)*arccosh(c*x)+11/6*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)-5/2*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2*d^2+1/3*b*(-d*(c^2*x^2-1))^(1/2)*c^6*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^4-8/3*b*(-d*(c^2*x^2-1))^(1/2)*c^4*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2","A"
102,1,691,384,0.835000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^5,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{4 d \,x^{4}}+\frac{3 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 d \,x^{2}}+\frac{3 a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{8}+\frac{5 a \,c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8}-\frac{15 a \,c^{4} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{8}+\frac{15 a \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}}{8}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{2}}{\left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x}{\sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right)}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{9 b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{8 \sqrt{c x +1}\, x \sqrt{c x -1}}-\frac{11 b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{8 \left(c x +1\right) x^{2} \left(c x -1\right)}-\frac{b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{12 \sqrt{c x +1}\, x^{3} \sqrt{c x -1}}+\frac{b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{4 \left(c x +1\right) x^{4} \left(c x -1\right)}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2} c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2} c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2} c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) d^{2} c^{4}}{8 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/4*a/d/x^4*(-c^2*d*x^2+d)^(7/2)+3/8*a*c^2/d/x^2*(-c^2*d*x^2+d)^(7/2)+3/8*a*c^4*(-c^2*d*x^2+d)^(5/2)+5/8*a*c^4*d*(-c^2*d*x^2+d)^(3/2)-15/8*a*c^4*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+15/8*a*c^4*(-c^2*d*x^2+d)^(1/2)*d^2+b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)+9/8*b*d^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/x/(c*x-1)^(1/2)*c^3-11/8*b*d^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/x^2/(c*x-1)*arccosh(c*x)*c^2-1/12*b*d^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/x^3/(c*x-1)^(1/2)*c+1/4*b*d^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/x^4/(c*x-1)*arccosh(c*x)-15/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2*c^4+15/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2*c^4-15/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2*c^4+15/8*I*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*d^2*c^4","A"
103,1,152,50,0.388000," ","int(arccosh(x)*(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, \mathrm{arccosh}\left(x \right)^{2}}{4 \sqrt{-1+x}\, \sqrt{1+x}}+\frac{\sqrt{-x^{2}+1}\, \left(2 x^{3}-2 x +2 \sqrt{1+x}\, \sqrt{-1+x}\, x^{2}-\sqrt{-1+x}\, \sqrt{1+x}\right) \left(-1+2 \,\mathrm{arccosh}\left(x \right)\right)}{16 \left(-1+x \right) \left(1+x \right)}+\frac{\sqrt{-x^{2}+1}\, \left(-2 \sqrt{1+x}\, \sqrt{-1+x}\, x^{2}+2 x^{3}+\sqrt{-1+x}\, \sqrt{1+x}-2 x \right) \left(1+2 \,\mathrm{arccosh}\left(x \right)\right)}{16 \left(-1+x \right) \left(1+x \right)}"," ",0,"-1/4*(-x^2+1)^(1/2)/(-1+x)^(1/2)/(1+x)^(1/2)*arccosh(x)^2+1/16*(-x^2+1)^(1/2)*(2*x^3-2*x+2*(1+x)^(1/2)*(-1+x)^(1/2)*x^2-(-1+x)^(1/2)*(1+x)^(1/2))*(-1+2*arccosh(x))/(-1+x)/(1+x)+1/16*(-x^2+1)^(1/2)*(-2*(1+x)^(1/2)*(-1+x)^(1/2)*x^2+2*x^3+(-1+x)^(1/2)*(1+x)^(1/2)-2*x)*(1+2*arccosh(x))/(-1+x)/(1+x)","B"
104,1,670,200,0.741000," ","int(x^5*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","a \left(-\frac{x^{4} \sqrt{-c^{2} d \,x^{2}+d}}{5 c^{2} d}+\frac{-\frac{4 x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{15 c^{2} d}-\frac{8 \sqrt{-c^{2} d \,x^{2}+d}}{15 d \,c^{4}}}{c^{2}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/5*x^4/c^2/d*(-c^2*d*x^2+d)^(1/2)+4/5/c^2*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2)))+b*(-1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/288*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/288*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/c^6/d/(c^2*x^2-1)-1/800*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))/c^6/d/(c^2*x^2-1))","B"
105,1,408,180,0.825000," ","int(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,x^{3} \sqrt{-c^{2} d \,x^{2}+d}}{4 c^{2} d}-\frac{3 a x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{4} d}+\frac{3 a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{4} \sqrt{c^{2} d}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{16 d \,c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4}}{16 d c \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{16 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{5}}{4 d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{8 d \,c^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{8 d \,c^{4} \left(c^{2} x^{2}-1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{128 d \,c^{5} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a*x^3/c^2/d*(-c^2*d*x^2+d)^(1/2)-3/8*a/c^4*x/d*(-c^2*d*x^2+d)^(1/2)+3/8*a/c^4/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/16*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c^5/(c^2*x^2-1)*arccosh(c*x)^2+1/16*b*(-d*(c^2*x^2-1))^(1/2)/d/c/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+3/16*b*(-d*(c^2*x^2-1))^(1/2)/d/c^3/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-1/4*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*x^5-1/8*b*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*arccosh(c*x)*x^3+3/8*b*(-d*(c^2*x^2-1))^(1/2)/d/c^4/(c^2*x^2-1)*arccosh(c*x)*x-15/128*b*(-d*(c^2*x^2-1))^(1/2)/d/c^5/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)","B"
106,1,382,132,0.559000," ","int(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","a \left(-\frac{x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2))+b*(-1/72*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/c^4/d/(c^2*x^2-1)-1/72*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/c^4/d/(c^2*x^2-1))","B"
107,1,291,112,0.534000," ","int(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{4 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{2 d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{4 d c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{2 d \,c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{8 d \,c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+1/2*a/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c^3/(c^2*x^2-1)*arccosh(c*x)^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*x^3+1/4*b*(-d*(c^2*x^2-1))^(1/2)/d/c/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*arccosh(c*x)*x-1/8*b*(-d*(c^2*x^2-1))^(1/2)/d/c^3/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)","B"
108,1,158,64,0.248000," ","int(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-a/c^2/d*(-c^2*d*x^2+d)^(1/2)+b*(-1/2*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/c^2/d/(c^2*x^2-1)-1/2*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/c^2/d/(c^2*x^2-1))","B"
109,1,89,45,0.061000," ","int((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b \sqrt{-\left(c x -1\right) \left(c x +1\right) d}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{2 c d \left(c^{2} x^{2}-1\right)}"," ",0,"a/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-(c*x-1)*(c*x+1)*d)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/d/(c^2*x^2-1)*arccosh(c*x)^2","A"
110,1,327,168,0.374000," ","int((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{\sqrt{d}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))","A"
111,1,219,63,0.381000," ","int((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{d x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c}{d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{x \left(c^{2} x^{2}-1\right) d}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*c-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*x/(c^2*x^2-1)/d*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/x/(c^2*x^2-1)/d+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c","B"
112,1,489,239,0.648000," ","int((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{2 d \,x^{2}}-\frac{a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 \sqrt{d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{2 d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{2 d \left(c^{2} x^{2}-1\right) x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{2 d \left(c^{2} x^{2}-1\right) x^{2}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(1/2)-1/2*a*c^2/d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*c^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/x*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/x^2*arccosh(c*x)+1/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2-1/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2+1/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2-1/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2","B"
113,1,854,131,0.664000," ","int((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,x^{3}}-\frac{2 a \,c^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 d x}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(c x -1\right) \left(c x +1\right) c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(c x -1\right) \left(c x +1\right) c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{2 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{6 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x^{3}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a/d/x^3*(-c^2*d*x^2+d)^(1/2)-2/3*a*c^2/d/x*(-c^2*d*x^2+d)^(1/2)-4/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*c^3-2/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*(c*x-1)*(c*x+1)*c^6+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^5*c^8+2*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^5-2*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*arccosh(c*x)*c^6-1/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*(c*x-1)*(c*x+1)*c^4-1/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*c^6+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*arccosh(c*x)*c^4-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-1/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*c^4+4/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x*arccosh(c*x)*c^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x^3*arccosh(c*x)+2/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3","B"
114,1,431,203,0.681000," ","int(x^5*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,x^{4}}{3 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a \,x^{2}}{3 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{8 a}{3 c^{6} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 c^{6} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{4}}{3 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{3 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3}}{9 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a*x^4/c^2/d/(-c^2*d*x^2+d)^(1/2)-4/3*a/c^4*x^2/d/(-c^2*d*x^2+d)^(1/2)+8/3*a/c^6/d/(-c^2*d*x^2+d)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-8/3*b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^2/(c^2*x^2-1)*arccosh(c*x)+1/3*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)*x^4+4/3*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/9*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3-5/3*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x","B"
115,1,445,196,0.757000," ","int(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,x^{3}}{2 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a x}{2 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{4} d \sqrt{c^{2} d}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{4 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{2 d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{4 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{2 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{8 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a*x^3/c^2/d/(-c^2*d*x^2+d)^(1/2)+3/2*a/c^4*x/d/(-c^2*d*x^2+d)^(1/2)-3/2*a/c^4/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/4*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^2/(c^2*x^2-1)*arccosh(c*x)*x^3-1/4*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^3/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)-3/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*arccosh(c*x)*x+1/8*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
116,1,313,134,0.535000," ","int(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*a/d/c^4/(-c^2*d*x^2+d)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)*x^2-b*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-2*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
117,1,279,125,0.472000," ","int(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{2 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)^2-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/c^2/(c^2*x^2-1)*x+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
118,1,198,68,0.241000," ","int(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a/c^2/d/(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
119,1,180,74,0.203000," ","int((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a x}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{d^{2} c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{d^{2} c \left(c^{2} x^{2}-1\right)}"," ",0,"a/d*x/(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*arccosh(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
120,1,511,238,0.423000," ","int((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^(3/2),x)","\frac{a}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{3}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a/d/(-c^2*d*x^2+d)^(1/2)-a/d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)+I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
121,1,242,142,0.357000," ","int((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a}{d x \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a \,c^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{x \left(c^{2} x^{2}-1\right) d^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{4}-1\right) c}{d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d/x/(-c^2*d*x^2+d)^(1/2)+2*a*c^2/d*x/(-c^2*d*x^2+d)^(1/2)-2*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*c-2*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*x/(c^2*x^2-1)/d^2*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/x/(c^2*x^2-1)/d^2+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^4-1)*c","A"
122,1,648,323,0.639000," ","int((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a}{2 d \,x^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a \,c^{2}}{2 d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{3}{2}}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{2 d^{2} \left(c^{2} x^{2}-1\right) x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{2 d^{2} \left(c^{2} x^{2}-1\right) x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \left(c^{2} x^{2}-1\right) d^{2}}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 \left(c^{2} x^{2}-1\right) d^{2}}"," ",0,"-1/2*a/d/x^2/(-c^2*d*x^2+d)^(1/2)+3/2*a*c^2/d/(-c^2*d*x^2+d)^(1/2)-3/2*a*c^2/d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-3/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*c^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x^2*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*c^2-b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c^2+3/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2-3/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2-3/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2+3/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2","B"
123,1,1050,217,0.657000," ","int((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a}{3 d \,x^{3} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a \,c^{2}}{3 d x \sqrt{-c^{2} d \,x^{2}+d}}+\frac{8 a \,c^{4} x}{3 d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(c x +1\right) \left(c x -1\right) c^{8}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{10}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(c x +1\right) \left(c x -1\right) c^{6}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}+\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}+\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(c x +1\right) \left(c x -1\right) c^{4}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{6 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{2} \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) x^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right) c^{3}}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a/d/x^3/(-c^2*d*x^2+d)^(1/2)-4/3*a*c^2/d/x/(-c^2*d*x^2+d)^(1/2)+8/3*a*c^4/d*x/(-c^2*d*x^2+d)^(1/2)-16/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*c^3+32/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*(c*x+1)*(c*x-1)*c^8-32/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^7*c^10-16/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*(c*x+1)*(c*x-1)*c^6+16*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*c^8+64/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5-64/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*arccosh(c*x)*c^6-4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*(c*x+1)*(c*x-1)*c^4-4*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*c^6+8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+8*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*arccosh(c*x)*c^4-4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*c^4+4*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x*arccosh(c*x)*c^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x^3*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)*c^3+5/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3","B"
124,1,466,213,0.650000," ","int(x^5*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a \,x^{4}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 a \,x^{2}}{c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{8 a}{3 c^{6} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{6 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{5}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{6 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{6 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-a*x^4/c^2/d/(-c^2*d*x^2+d)^(3/2)+4*a/c^4*x^2/d/(-c^2*d*x^2+d)^(3/2)-8/3*a/c^6/d/(-c^2*d*x^2+d)^(3/2)-b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arccosh(c*x)*x^2+b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arccosh(c*x)+2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arccosh(c*x)*x^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-5/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6*arccosh(c*x)+11/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-11/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)","B"
125,1,1519,194,0.841000," ","int(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a \,x^{3}}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a x}{c^{4} d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{4} d^{2} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{2 d^{3} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} c^{5} \left(c^{2} x^{2}-1\right)}-\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,\mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, x^{6}}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) d^{3}}+\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{7}}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) d^{3}}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c x +1\right) \left(c x -1\right) x^{5}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) d^{3}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{7}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) d^{3}}+\frac{84 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4}}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c \,d^{3}}-\frac{76 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{5}}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) d^{3}}+\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c x +1\right) \left(c x -1\right) x^{3}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{2} d^{3}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4}}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c \,d^{3}}-\frac{22 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) d^{3}}-\frac{220 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{3} d^{3}}+\frac{181 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{2} d^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c x +1\right) \left(c x -1\right) x}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{4} d^{3}}-\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{2 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{3} d^{3}}+\frac{20 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{2} d^{3}}+\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{5} d^{3}}-\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{4} d^{3}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{3 \left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{5} d^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{\left(24 c^{8} x^{8}-87 c^{6} x^{6}+118 c^{4} x^{4}-71 c^{2} x^{2}+16\right) c^{4} d^{3}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{3 d^{3} c^{5} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a*x^3/c^2/d/(-c^2*d*x^2+d)^(3/2)-a/c^4/d^2*x/(-c^2*d*x^2+d)^(1/2)+a/c^4/d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)^2+8/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)-32*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6+32*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*arccosh(c*x)*x^7-8/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*(c*x+1)*(c*x-1)*x^5+8/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*x^7+84*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-76*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*arccosh(c*x)*x^5+14/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*(c*x+1)*(c*x-1)*x^3+4*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-22/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*x^5-220/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+181/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*arccosh(c*x)*x^3-2*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*(c*x+1)*(c*x-1)*x-13/2*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+20/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*x^3+64/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-16*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*arccosh(c*x)*x+8/3*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*x-4/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
126,1,313,138,0.539000," ","int(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a \,x^{2}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a}{3 d \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{6 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{6 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{6 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}"," ",0,"a*x^2/c^2/d/(-c^2*d*x^2+d)^(3/2)-2/3*a/d/c^4/(-c^2*d*x^2+d)^(3/2)+b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arccosh(c*x)*x^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arccosh(c*x)-5/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)+5/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
127,1,1228,113,0.540000," ","int(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a x}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a x}{3 c^{2} d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{6}}{\left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{\left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(c x -1\right) \left(c x +1\right) x^{5}}{6 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} x^{7}}{6 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{4}}{\left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{\left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c x -1\right) \left(c x +1\right) x^{3}}{6 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{c x -1}\, \sqrt{c x +1}\, x^{4}}{2 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{5}}{3 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{3 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c \,d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{3 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{2 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c \,d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{6 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}}{3 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c^{3} d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{6 \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c^{3} d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{3 d^{3} c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/c^2/d*x/(-c^2*d*x^2+d)^(3/2)-1/3*a/c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)+2/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*arccosh(c*x)-b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^6+b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*arccosh(c*x)*x^7-1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*(c*x-1)*(c*x+1)*x^5+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*x^7+2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^4-b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*arccosh(c*x)*x^5+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*(c*x-1)*(c*x+1)*x^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^4-1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*x^5-4/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*arccosh(c*x)*x^3-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*x^3+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
128,1,249,107,0.292000," ","int(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{6 d^{3} \left(c^{2} x^{2}-1\right)^{2} c}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{6 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{6 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/c^2/d/(-c^2*d*x^2+d)^(3/2)+1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arccosh(c*x)+1/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-1/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
129,1,1073,138,0.296000," ","int((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{2 a x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} c \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \left(c x -1\right) \left(c x +1\right) x^{5}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{6} x^{7}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{4}}{\left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \mathrm{arccosh}\left(c x \right) x^{5}}{\left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(c x -1\right) \left(c x +1\right) x^{3}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} x^{5}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}-\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c x -1\right) \left(c x +1\right) x}{\left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{2 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{3}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c \,d^{3}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{\left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{3 \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c \,d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{\left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) d^{3}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{3 d^{3} c \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/d*x/(-c^2*d*x^2+d)^(3/2)+2/3*a/d^2*x/(-c^2*d*x^2+d)^(1/2)-4/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*arccosh(c*x)+2/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*(c*x-1)*(c*x+1)*x^5-2/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6/d^3*x^7+2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^4-2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*arccosh(c*x)*x^5-5/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*(c*x-1)*(c*x+1)*x^3+7/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*x^5-14/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2+17/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*arccosh(c*x)*x^3+b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*(c*x-1)*(c*x+1)*x+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-8/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*x^3+8/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)-4*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*arccosh(c*x)*x-2/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*x+2/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
130,1,619,312,0.476000," ","int((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^(5/2),x)","\frac{a}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{a}{d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{5}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2} c^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x c}{6 d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{6 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{6 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/d/(-c^2*d*x^2+d)^(3/2)+a/d^2/(-c^2*d*x^2+d)^(1/2)-a/d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arccosh(c*x)*x^2*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arccosh(c*x)+7/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-7/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))","A"
131,1,1350,218,0.458000," ","int((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a}{d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 a \,c^{2} x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{8 a \,c^{2} x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \left(c x +1\right) \left(c x -1\right) c^{8}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{10}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{80 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(c x +1\right) \left(c x -1\right) c^{6}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{112 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{8}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{6}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{20 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(c x +1\right) \left(c x -1\right) c^{4}}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{140 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{6}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{136 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{56 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{4}}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(c x +1\right) \left(c x -1\right) c^{2}}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{24 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{4}}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{24 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{44 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{2}}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{2 d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{2}}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{d^{3} \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) x}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right) c}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d/x/(-c^2*d*x^2+d)^(3/2)+4/3*a*c^2/d*x/(-c^2*d*x^2+d)^(3/2)+8/3*a*c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)-16/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*c+32/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*(c*x+1)*(c*x-1)*c^8-32/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^9*c^10-80/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*(c*x+1)*(c*x-1)*c^6+112/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*c^8+64/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^4*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5-64/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*arccosh(c*x)*c^6+20*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*(c*x+1)*(c*x-1)*c^4-140/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*c^6-136/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+56*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*arccosh(c*x)*c^4-4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*(c*x+1)*(c*x-1)*c^2+4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+24*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*c^4+24*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c-44*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*arccosh(c*x)*c^2-3/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c-4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*c^2+9*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/x*arccosh(c*x)+5/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)*c+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c","B"
132,1,801,451,0.737000," ","int((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a}{2 d \,x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a \,c^{2}}{6 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a \,c^{2}}{2 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{5 a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{5}{2}}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) c^{4}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{10 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}+\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) c^{2}}{6 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) c^{2}}{6 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right) c^{2}}{2 d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a/d/x^2/(-c^2*d*x^2+d)^(3/2)+5/6*a*c^2/d/(-c^2*d*x^2+d)^(3/2)+5/2*a*c^2/d^2/(-c^2*d*x^2+d)^(1/2)-5/2*a*c^2/d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-5/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*arccosh(c*x)*c^4-1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+10/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*arccosh(c*x)*c^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arccosh(c*x)+13/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*c^2-13/6*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c^2-5/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2-5/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2+5/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2+5/2*I*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))*c^2","A"
133,1,1878,295,0.671000," ","int((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^(5/2),x)","-\frac{560 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{10}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{2 a \,c^{2}}{d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a}{3 d \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(c x +1\right) \left(c x -1\right) c^{4}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{6 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) x^{2}}-\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{4}-1\right) c^{3}}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{128 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} \left(c x +1\right) \left(c x -1\right) c^{12}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{320 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \left(c x +1\right) \left(c x -1\right) c^{10}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{80 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(c x +1\right) \left(c x -1\right) c^{8}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{40 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(c x +1\right) \left(c x -1\right) c^{6}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{128 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{7}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{176 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{9}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{8 a \,c^{4} x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{16 a \,c^{4} x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{280 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) x^{3}}-\frac{128 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{11} c^{14}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{448 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{12}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \mathrm{arccosh}\left(c x \right) c^{10}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{160 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}-\frac{344 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{3 d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}+\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) x}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{d^{3} \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right)}"," ",0,"-560/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^7*c^10-2*a*c^2/d/x/(-c^2*d*x^2+d)^(3/2)-1/3*a/d/x^3/(-c^2*d*x^2+d)^(3/2)-8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x*(c*x+1)*(c*x-1)*c^4+2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c-32/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*c^3+16/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+8/3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^4-1)*c^3+128/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^9*(c*x+1)*(c*x-1)*c^12-320/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^7*(c*x+1)*(c*x-1)*c^10+80*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^5*(c*x+1)*(c*x-1)*c^8-40/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^3*(c*x+1)*(c*x-1)*c^6-128*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^4*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^7+176/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5+64*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^6*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^9+8/3*a*c^4/d*x/(-c^2*d*x^2+d)^(3/2)+16/3*a*c^4/d^2*x/(-c^2*d*x^2+d)^(1/2)+280/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^5*c^8-32/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^3*c^6-8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x*c^4+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/x^3*arccosh(c*x)-128/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^11*c^14+448/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^9*c^12-64*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^7*arccosh(c*x)*c^10+160*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^5*arccosh(c*x)*c^8-344/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x^3*arccosh(c*x)*c^6+12*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*x*arccosh(c*x)*c^4+6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/x*arccosh(c*x)*c^2-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3","B"
134,1,419,210,0.465000," ","int(arccosh(a*x)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{16 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)}{15 c^{4} a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-20 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+15 a x +16 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-8 \sqrt{a x -1}\, \sqrt{a x +1}\right) \left(-64 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{7} a^{7}-64 x^{8} a^{8}+248 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{5} a^{5}+280 x^{6} a^{6}+160 a^{4} x^{4} \mathrm{arccosh}\left(a x \right)-340 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}-456 x^{4} a^{4}-380 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)+165 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +328 a^{2} x^{2}+256 \,\mathrm{arccosh}\left(a x \right)-88\right)}{60 \left(40 a^{10} x^{10}-215 x^{8} a^{8}+469 x^{6} a^{6}-517 x^{4} a^{4}+287 a^{2} x^{2}-64\right) a \,c^{4}}+\frac{8 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}-1\right)}{15 c^{4} a \left(a^{2} x^{2}-1\right)}"," ",0,"-16/15*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)-1/60*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-20*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+15*a*x+16*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-8*(a*x-1)^(1/2)*(a*x+1)^(1/2))*(-64*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^7*a^7-64*x^8*a^8+248*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^5*a^5+280*x^6*a^6+160*a^4*x^4*arccosh(a*x)-340*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)-456*x^4*a^4-380*a^2*x^2*arccosh(a*x)+165*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+328*a^2*x^2+256*arccosh(a*x)-88)/(40*a^10*x^10-215*a^8*x^8+469*a^6*x^6-517*a^4*x^4+287*a^2*x^2-64)/a/c^4+8/15*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*ln((a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2-1)","A"
135,1,456,119,0.796000," ","int(x^4*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2}}{16 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}+8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x -8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(-1+4 \,\mathrm{arccosh}\left(a x \right)\right)}{256 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(-1+2 \,\mathrm{arccosh}\left(a x \right)\right)}{16 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(1+2 \,\mathrm{arccosh}\left(a x \right)\right)}{16 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x +8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(1+4 \,\mathrm{arccosh}\left(a x \right)\right)}{256 a^{5} \left(a^{2} x^{2}-1\right)}"," ",0,"-3/16*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*arccosh(a*x)^2-1/256*(-a^2*x^2+1)^(1/2)*(8*x^5*a^5-12*x^3*a^3+8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x-8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(-1+4*arccosh(a*x))/a^5/(a^2*x^2-1)-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(-1+2*arccosh(a*x))/a^5/(a^2*x^2-1)-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(1+2*arccosh(a*x))/a^5/(a^2*x^2-1)-1/256*(-a^2*x^2+1)^(1/2)*(8*x^5*a^5-12*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x+8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(1+4*arccosh(a*x))/a^5/(a^2*x^2-1)","B"
136,1,311,90,0.533000," ","int(x^3*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 x^{4} a^{4}-5 a^{2} x^{2}+4 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}-3 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +1\right) \left(-1+3 \,\mathrm{arccosh}\left(a x \right)\right)}{72 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{a x +1}\, \sqrt{a x -1}\, a x +a^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(a x \right)\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \left(1+\mathrm{arccosh}\left(a x \right)\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 x^{4} a^{4}-5 a^{2} x^{2}-4 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}+3 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +1\right) \left(1+3 \,\mathrm{arccosh}\left(a x \right)\right)}{72 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/72*(-a^2*x^2+1)^(1/2)*(4*x^4*a^4-5*a^2*x^2+4*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)-3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+1)*(-1+3*arccosh(a*x))/a^4/(a^2*x^2-1)-3/8*(-a^2*x^2+1)^(1/2)*((a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+a^2*x^2-1)*(-1+arccosh(a*x))/a^4/(a^2*x^2-1)-3/8*(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*(1+arccosh(a*x))/a^4/(a^2*x^2-1)-1/72*(-a^2*x^2+1)^(1/2)*(4*x^4*a^4-5*a^2*x^2-4*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+1)*(1+3*arccosh(a*x))/a^4/(a^2*x^2-1)","B"
137,1,223,72,0.482000," ","int(x^2*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2}}{4 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(-1+2 \,\mathrm{arccosh}\left(a x \right)\right)}{16 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(1+2 \,\mathrm{arccosh}\left(a x \right)\right)}{16 a^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^3/(a^2*x^2-1)*arccosh(a*x)^2-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(-1+2*arccosh(a*x))/a^3/(a^2*x^2-1)-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(1+2*arccosh(a*x))/a^3/(a^2*x^2-1)","B"
138,1,123,43,0.211000," ","int(x*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{a x +1}\, \sqrt{a x -1}\, a x +a^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(a x \right)\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \left(1+\mathrm{arccosh}\left(a x \right)\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*((a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+a^2*x^2-1)*(-1+arccosh(a*x))/a^2/(a^2*x^2-1)-1/2*(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*(1+arccosh(a*x))/a^2/(a^2*x^2-1)","B"
139,1,51,26,0.060000," ","int(arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2}}{2 a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a/(a^2*x^2-1)*arccosh(a*x)^2","A"
140,1,270,126,0.355000," ","int(arccosh(a*x)/x/(-a^2*x^2+1)^(1/2),x)","\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \ln \left(1+i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right)}{a^{2} x^{2}-1}-\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \ln \left(1-i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right)}{a^{2} x^{2}-1}+\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \dilog \left(1+i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right)}{a^{2} x^{2}-1}-\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \dilog \left(1-i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right)}{a^{2} x^{2}-1}"," ",0,"I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)*ln(1+I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))-I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)*ln(1-I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))+I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*dilog(1+I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))-I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*dilog(1-I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))","B"
141,1,168,42,0.355000," ","int(arccosh(a*x)/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) a}{a^{2} x^{2}-1}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \mathrm{arccosh}\left(a x \right)}{x \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(1+\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}\right) a}{a^{2} x^{2}-1}"," ",0,"-2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)*a-(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*arccosh(a*x)/x/(a^2*x^2-1)+(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*ln(1+(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2)*a","B"
142,1,349,176,0.612000," ","int(arccosh(a*x)/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\left(a^{2} x^{2} \mathrm{arccosh}\left(a x \right)+\sqrt{a x +1}\, \sqrt{a x -1}\, a x -\mathrm{arccosh}\left(a x \right)\right) \sqrt{-a^{2} x^{2}+1}}{2 \left(a^{2} x^{2}-1\right) x^{2}}+\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \ln \left(1+i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right) a^{2}}{2 a^{2} x^{2}-2}-\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \ln \left(1-i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right) a^{2}}{2 a^{2} x^{2}-2}+\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \dilog \left(1+i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right) a^{2}}{2 a^{2} x^{2}-2}-\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \dilog \left(1-i \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)\right) a^{2}}{2 a^{2} x^{2}-2}"," ",0,"-1/2*(a^2*x^2*arccosh(a*x)+(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-arccosh(a*x))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)/x^2+I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)*ln(1+I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))*a^2/(2*a^2*x^2-2)-I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)*ln(1-I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))*a^2/(2*a^2*x^2-2)+I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*dilog(1+I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))*a^2/(2*a^2*x^2-2)-I*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*dilog(1-I*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)))*a^2/(2*a^2*x^2-2)","A"
143,-2,0,74,180.000000," ","int((f*x)^(3/2)*(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(f x \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((f*x)^(3/2)*(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
144,-2,0,111,180.000000," ","int((f*x)^(3/2)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((f*x)^(3/2)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","F"
145,-2,0,407,180.000000," ","int((f*x)^m*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x)","F"
146,-2,0,289,180.000000," ","int((f*x)^m*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x)","F"
147,-2,0,170,180.000000," ","int((f*x)^m*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x)","F"
148,0,0,29,0.785000," ","int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x)","F"
149,0,0,144,1.249000," ","int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x)","F"
150,0,0,263,1.367000," ","int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x)","F"
151,0,0,655,2.216000," ","int((f*x)^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","F"
152,0,0,407,1.954000," ","int((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","F"
153,0,0,244,1.878000," ","int((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x)),x)","F"
154,0,0,152,0.652000," ","int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","F"
155,0,0,266,0.993000," ","int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","F"
156,0,0,394,0.911000," ","int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x)","F"
157,0,0,727,2.966000," ","int((f*x)^m*(c*d1*x+d1)^(5/2)*(-c*d2*x+d2)^(5/2)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(c \mathit{d1} x +\mathit{d1} \right)^{\frac{5}{2}} \left(-c \mathit{d2} x +\mathit{d2} \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(c*d1*x+d1)^(5/2)*(-c*d2*x+d2)^(5/2)*(a+b*arccosh(c*x)),x)","F"
158,0,0,441,2.599000," ","int((f*x)^m*(c*d1*x+d1)^(3/2)*(-c*d2*x+d2)^(3/2)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(c \mathit{d1} x +\mathit{d1} \right)^{\frac{3}{2}} \left(-c \mathit{d2} x +\mathit{d2} \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(c*d1*x+d1)^(3/2)*(-c*d2*x+d2)^(3/2)*(a+b*arccosh(c*x)),x)","F"
159,0,0,260,2.004000," ","int((f*x)^m*(c*d1*x+d1)^(1/2)*(-c*d2*x+d2)^(1/2)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \sqrt{c \mathit{d1} x +\mathit{d1}}\, \sqrt{-c \mathit{d2} x +\mathit{d2}}\, \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(c*d1*x+d1)^(1/2)*(-c*d2*x+d2)^(1/2)*(a+b*arccosh(c*x)),x)","F"
160,0,0,160,0.701000," ","int((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(1/2)/(-c*d2*x+d2)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\sqrt{c \mathit{d1} x +\mathit{d1}}\, \sqrt{-c \mathit{d2} x +\mathit{d2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(1/2)/(-c*d2*x+d2)^(1/2),x)","F"
161,0,0,294,0.957000," ","int((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(3/2)/(-c*d2*x+d2)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(c \mathit{d1} x +\mathit{d1} \right)^{\frac{3}{2}} \left(-c \mathit{d2} x +\mathit{d2} \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(3/2)/(-c*d2*x+d2)^(3/2),x)","F"
162,0,0,436,0.971000," ","int((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(5/2)/(-c*d2*x+d2)^(5/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(c \mathit{d1} x +\mathit{d1} \right)^{\frac{5}{2}} \left(-c \mathit{d2} x +\mathit{d2} \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(5/2)/(-c*d2*x+d2)^(5/2),x)","F"
163,0,0,110,0.573000," ","int((f*x)^m*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{\left(f x \right)^{m} \mathrm{arccosh}\left(a x \right)}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((f*x)^m*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
164,1,188,226,0.207000," ","int((-a^2*c*x^2+c)^3*arccosh(a*x)^2,x)","-\frac{c^{3} \left(55125 \mathrm{arccosh}\left(a x \right)^{2} a^{7} x^{7}-15750 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{6} x^{6}-231525 \mathrm{arccosh}\left(a x \right)^{2} a^{5} x^{5}+73710 \,\mathrm{arccosh}\left(a x \right) a^{4} x^{4} \sqrt{a x -1}\, \sqrt{a x +1}+2250 x^{7} a^{7}+385875 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)^{2}-158970 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{2} x^{2}-14742 x^{5} a^{5}-385875 a x \mathrm{arccosh}\left(a x \right)^{2}+453810 \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)+52990 x^{3} a^{3}-453810 a x \right)}{385875 a}"," ",0,"-1/385875/a*c^3*(55125*arccosh(a*x)^2*a^7*x^7-15750*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^6*x^6-231525*arccosh(a*x)^2*a^5*x^5+73710*arccosh(a*x)*a^4*x^4*(a*x-1)^(1/2)*(a*x+1)^(1/2)+2250*x^7*a^7+385875*a^3*x^3*arccosh(a*x)^2-158970*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^2*x^2-14742*x^5*a^5-385875*a*x*arccosh(a*x)^2+453810*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)+52990*x^3*a^3-453810*a*x)","A"
165,1,140,165,0.090000," ","int((-a^2*c*x^2+c)^2*arccosh(a*x)^2,x)","\frac{c^{2} \left(675 \mathrm{arccosh}\left(a x \right)^{2} a^{5} x^{5}-270 \,\mathrm{arccosh}\left(a x \right) a^{4} x^{4} \sqrt{a x -1}\, \sqrt{a x +1}-2250 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)^{2}+1140 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{2} x^{2}+54 x^{5} a^{5}+3375 a x \mathrm{arccosh}\left(a x \right)^{2}-4470 \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)-380 x^{3} a^{3}+4470 a x \right)}{3375 a}"," ",0,"1/3375/a*c^2*(675*arccosh(a*x)^2*a^5*x^5-270*arccosh(a*x)*a^4*x^4*(a*x-1)^(1/2)*(a*x+1)^(1/2)-2250*a^3*x^3*arccosh(a*x)^2+1140*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^2*x^2+54*x^5*a^5+3375*a*x*arccosh(a*x)^2-4470*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)-380*x^3*a^3+4470*a*x)","A"
166,1,90,92,0.072000," ","int((-a^2*c*x^2+c)*arccosh(a*x)^2,x)","-\frac{c \left(9 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)^{2}-6 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{2} x^{2}-27 a x \mathrm{arccosh}\left(a x \right)^{2}+42 \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)+2 x^{3} a^{3}-42 a x \right)}{27 a}"," ",0,"-1/27/a*c*(9*a^3*x^3*arccosh(a*x)^2-6*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^2*x^2-27*a*x*arccosh(a*x)^2+42*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)+2*x^3*a^3-42*a*x)","A"
167,1,201,163,0.084000," ","int(arccosh(a*x)^2/(-a^2*c*x^2+c),x)","-\frac{\mathrm{arccosh}\left(a x \right)^{2} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}-\frac{2 \,\mathrm{arccosh}\left(a x \right) \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{2 \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{\mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{2 \,\mathrm{arccosh}\left(a x \right) \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}-\frac{2 \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}"," ",0,"-1/a/c*arccosh(a*x)^2*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-2*arccosh(a*x)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c+2*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c+1/a/c*arccosh(a*x)^2*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+2*arccosh(a*x)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c-2*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c","A"
168,1,288,222,0.254000," ","int(arccosh(a*x)^2/(-a^2*c*x^2+c)^2,x)","-\frac{\mathrm{arccosh}\left(a x \right)^{2} x}{2 \left(a^{2} x^{2}-1\right) c^{2}}-\frac{\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}}{a \left(a^{2} x^{2}-1\right) c^{2}}-\frac{\mathrm{arccosh}\left(a x \right)^{2} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}-\frac{\mathrm{arccosh}\left(a x \right) \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}+\frac{\polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}+\frac{\mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}+\frac{\mathrm{arccosh}\left(a x \right) \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}-\frac{\polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}-\frac{2 \arctanh \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}"," ",0,"-1/2/(a^2*x^2-1)*arccosh(a*x)^2/c^2*x-1/a/(a^2*x^2-1)*arccosh(a*x)/c^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-1/2/a/c^2*arccosh(a*x)^2*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-arccosh(a*x)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2+polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2+1/2/a/c^2*arccosh(a*x)^2*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+arccosh(a*x)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2-polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2-2/a/c^2*arctanh(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))","A"
169,1,443,293,0.381000," ","int(arccosh(a*x)^2/(-a^2*c*x^2+c)^3,x)","-\frac{3 a^{2} \mathrm{arccosh}\left(a x \right)^{2} x^{3}}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{3 a \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, x^{2}}{4 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{a^{2} x^{3}}{12 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{5 \mathrm{arccosh}\left(a x \right)^{2} x}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{11 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}}{12 a \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{x}{12 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{5 \arctanh \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{3 a \,c^{3}}-\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}-\frac{3 \,\mathrm{arccosh}\left(a x \right) \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}+\frac{3 \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}+\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}+\frac{3 \,\mathrm{arccosh}\left(a x \right) \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}-\frac{3 \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}"," ",0,"-3/8*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)^2*x^3-3/4*a/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*x^2+1/12*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*x^3+5/8/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)^2*x+11/12/a/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)-1/12/(a^4*x^4-2*a^2*x^2+1)/c^3*x-5/3/a/c^3*arctanh(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-3/8/a/c^3*arccosh(a*x)^2*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-3/4*arccosh(a*x)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3+3/4*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3+3/8/a/c^3*arccosh(a*x)^2*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+3/4*arccosh(a*x)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3-3/4*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3","A"
170,1,1284,315,0.727000," ","int(x^3*(a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","a^{2} \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}-10 \,\mathrm{arccosh}\left(c x \right)+2\right)}{4000 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{864 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{864 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}+10 \,\mathrm{arccosh}\left(c x \right)+2\right)}{4000 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)"," ",0,"a^2*(-1/5*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(-c^2*d*x^2+d)^(3/2))+b^2*(1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(25*arccosh(c*x)^2-10*arccosh(c*x)+2)/(c*x+1)/c^4/(c*x-1)+1/864*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)/(c*x+1)/c^4/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)/(c*x+1)/c^4/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)/(c*x+1)/c^4/(c*x-1)+1/864*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)/(c*x+1)/c^4/(c*x-1)+1/4000*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(25*arccosh(c*x)^2+10*arccosh(c*x)+2)/(c*x+1)/c^4/(c*x-1))+2*a*b*(1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))/(c*x+1)/c^4/(c*x-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/(c*x+1)/c^4/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/(c*x+1)/c^4/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/(c*x+1)/c^4/(c*x-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/(c*x+1)/c^4/(c*x-1)+1/800*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))/(c*x+1)/c^4/(c*x-1))","B"
171,1,767,271,0.641000," ","int(x^2*(a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{8 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,\mathrm{arccosh}\left(c x \right) x^{4}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3}}{24 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{64 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{5}}{32 \left(c x +1\right) \left(c x -1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{64 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{64 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,x^{4}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{8 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{4 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}}{64 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}"," ",0,"-1/4*a^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*a^2/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*a^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*arccosh(c*x)*x^2-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*arccosh(c*x)*x^4-1/24*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^3+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)^2*x^5-3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^3+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)^2*x-1/64*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*arccosh(c*x)+1/32*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)*c^2/(c*x-1)*x^5-3/64*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*x^3+1/64*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/c^2/(c*x-1)*x-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^2-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5-3/4*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x-1/64*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)","B"
172,1,726,158,0.357000," ","int(x*(a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{216 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{216 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)"," ",0,"-1/3*a^2/c^2/d*(-c^2*d*x^2+d)^(3/2)+b^2*(1/216*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)/(c*x+1)/c^2/(c*x-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)/(c*x+1)/c^2/(c*x-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)/(c*x+1)/c^2/(c*x-1)+1/216*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)/(c*x+1)/c^2/(c*x-1))+2*a*b*(1/72*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/(c*x+1)/c^2/(c*x-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/(c*x+1)/c^2/(c*x-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/(c*x+1)/c^2/(c*x-1)+1/72*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/(c*x+1)/c^2/(c*x-1))","B"
173,1,528,172,0.296000," ","int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,\mathrm{arccosh}\left(c x \right) x^{2}}{2 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{3}}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3}}{6 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{4 \sqrt{c x +1}\, \sqrt{c x -1}\, c}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{2 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{\left(c x +1\right) \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \,x^{2}}{2 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{\left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}}{4 \sqrt{c x +1}\, \sqrt{c x -1}\, c}"," ",0,"1/2*a^2*x*(-c^2*d*x^2+d)^(1/2)+1/2*a^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*arccosh(c*x)*x^2+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*c^2*x^3-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*x-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^3+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)^2*x^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c*arccosh(c*x)-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^2+a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2-a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)/(c*x-1)*arccosh(c*x)*x+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c","B"
174,0,0,413,0.655000," ","int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \sqrt{-c^{2} d \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x,x)","F"
175,1,582,232,0.619000," ","int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{d x}-a^{2} c^{2} x \sqrt{-c^{2} d \,x^{2}+d}-\frac{a^{2} c^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} c}{3 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c}{\sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x \,c^{2}}{\left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{\left(c x +1\right) \left(c x -1\right) x}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2}}{\left(c x +1\right) \left(c x -1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{\left(c x +1\right) \left(c x -1\right) x}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{\sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-a^2/d/x*(-c^2*d*x^2+d)^(3/2)-a^2*c^2*x*(-c^2*d*x^2+d)^(1/2)-a^2*c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^3*c-b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/(c*x+1)/(c*x-1)*x*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/(c*x+1)/(c*x-1)/x+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c+b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c+a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x+1)/(c*x-1)*x*c^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x+1)/(c*x-1)/x+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c","B"
176,0,0,434,0.870000," ","int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^3,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \sqrt{-c^{2} d \,x^{2}+d}}{x^{3}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^3,x)","F"
177,1,2633,314,0.902000," ","int((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^4,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 d \,x^{3}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right)^{2} c^{8}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right)^{2} c^{6}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c^{2}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}+\frac{10 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \mathrm{arccosh}\left(c x \right)^{2} c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right)^{2} c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{2} \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right)^{2} c^{7}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{9 c^{4} x^{4}-9 c^{2} x^{2}+3}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \mathrm{arccosh}\left(c x \right) c^{7}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{20 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{10 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{3} \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c^{3}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{3}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} c^{7}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{9 c^{4} x^{4}-9 c^{2} x^{2}+3}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{9 c^{4} x^{4}-9 c^{2} x^{2}+3}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 \sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(3/2)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^8+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)-3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^6-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^2+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^4-a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^5-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^7+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3*c^6-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3*c^6+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x*c^4+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*c^3-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-6*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+20/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3*arccosh(c*x)*c^6+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x*arccosh(c*x)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^3+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*c^3-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3","B"
178,1,1952,423,0.771000," ","int(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x)","a^{2} \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}\right)+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(49 \mathrm{arccosh}\left(c x \right)^{2}-14 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{43904 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}-10 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{16000 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{1152 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{1152 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}+10 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{16000 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(49 \mathrm{arccosh}\left(c x \right)^{2}+14 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{43904 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{6272 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{3200 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{384 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d}{128 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{384 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{3200 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d}{6272 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)"," ",0,"a^2*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2))+b^2*(-1/43904*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(49*arccosh(c*x)^2-14*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)+1/16000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(25*arccosh(c*x)^2-10*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)+1/16000*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(25*arccosh(c*x)^2+10*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1)-1/43904*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(49*arccosh(c*x)^2+14*arccosh(c*x)+2)*d/(c*x+1)/c^4/(c*x-1))+2*a*b*(-1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1)-1/6272*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d/(c*x+1)/c^4/(c*x-1))","B"
179,1,1021,377,0.957000," ","int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x)","\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x}{8 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{3 \left(c x +1\right) \left(c x -1\right)}+\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{12 \left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} x^{6}}{18 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{7 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,x^{4}}{48 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2}}{16 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right)^{2} x^{7}}{6 \left(c x +1\right) \left(c x -1\right)}+\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{24 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \mathrm{arccosh}\left(c x \right)^{2} x}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{17 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{3}}{24 \left(c x +1\right) \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \mathrm{arccosh}\left(c x \right) x^{6}}{18 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{7 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,\mathrm{arccosh}\left(c x \right) x^{4}}{48 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{2}}{16 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{a^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6 c^{2} d}+\frac{a^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{2}}+\frac{a^{2} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 c^{2} \sqrt{c^{2} d}}+\frac{a^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}+\frac{7 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d}{1152 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{7 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right)}{1152 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} d}{48 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}-\frac{17 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{48 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} x^{7}}{108 \left(c x +1\right) \left(c x -1\right)}+\frac{59 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} x^{5}}{1728 \left(c x +1\right) \left(c x -1\right)}-\frac{7 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x}{1152 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{65 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3}}{3456 \left(c x +1\right) \left(c x -1\right)}"," ",0,"1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^7+11/12*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5+1/18*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6-7/48*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+1/16*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)^2*x^7+11/24*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)^2*x^5+1/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)^2*x-17/24*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-1/16*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^2*d+1/18*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*arccosh(c*x)*x^6-7/48*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*arccosh(c*x)*x^4+1/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*arccosh(c*x)*x^2-1/6*a^2*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/16*a^2/c^2*d*x*(-c^2*d*x^2+d)^(1/2)+1/16*a^2/c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/24*a^2/c^2*x*(-c^2*d*x^2+d)^(3/2)+7/1152*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)+7/1152*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*arccosh(c*x)-1/48*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^3*d-17/48*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^3-1/108*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^4/(c*x-1)*x^7+59/1728*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^2/(c*x-1)*x^5-7/1152*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/c^2/(c*x-1)*x-65/3456*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*x^3","B"
180,1,1270,308,0.450000," ","int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}-10 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{4000 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{288 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{288 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}+10 \,\mathrm{arccosh}\left(c x \right)+2\right) d}{4000 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{800 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{96 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d}{96 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d}{800 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)"," ",0,"-1/5*a^2/c^2/d*(-c^2*d*x^2+d)^(5/2)+b^2*(-1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(25*arccosh(c*x)^2-10*arccosh(c*x)+2)*d/(c*x+1)/c^2/(c*x-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)*d/(c*x+1)/c^2/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)*d/(c*x+1)/c^2/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)*d/(c*x+1)/c^2/(c*x-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)*d/(c*x+1)/c^2/(c*x-1)-1/4000*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(25*arccosh(c*x)^2+10*arccosh(c*x)+2)*d/(c*x+1)/c^2/(c*x-1))+2*a*b*(-1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)+1/96*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)+1/96*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1)-1/800*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d/(c*x+1)/c^2/(c*x-1))","B"
181,1,775,288,0.385000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x)","\frac{x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a^{2}}{4}+\frac{3 a^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{3 a^{2} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \mathrm{arccosh}\left(c x \right) x^{4}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,\mathrm{arccosh}\left(c x \right) x^{2}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} d}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{17 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right)}{64 \sqrt{c x +1}\, \sqrt{c x -1}\, c}-\frac{17 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x}{64 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{7 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \mathrm{arccosh}\left(c x \right)^{2} x}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} x^{5}}{32 \left(c x +1\right) \left(c x -1\right)}+\frac{19 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} x^{3}}{64 \left(c x +1\right) \left(c x -1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} x^{4}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \,x^{2}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{5}}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{7 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{17 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d}{64 \sqrt{c x +1}\, \sqrt{c x -1}\, c}"," ",0,"1/4*x*(-c^2*d*x^2+d)^(3/2)*a^2+3/8*a^2*d*x*(-c^2*d*x^2+d)^(1/2)+3/8*a^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3*arccosh(c*x)*x^4-5/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*arccosh(c*x)*x^2-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^3*d+17/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c*arccosh(c*x)-17/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*x-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^4*arccosh(c*x)^2*x^5+7/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)^2*x^3-5/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x-1/32*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^4*x^5+19/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^2*x^3-3/8*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^2*d+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3*x^4-5/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^4*arccosh(c*x)*x^5+7/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3-5/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x+17/64*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c","B"
182,0,0,558,0.652000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x,x)","F"
183,1,942,421,0.677000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{d x}-a^{2} c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}-\frac{3 a^{2} c^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{2}-\frac{3 a^{2} c^{2} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} c d}{2 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c d}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \,x^{3}}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d x}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c d \mathrm{arccosh}\left(c x \right)^{2}}{\sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c d \,\mathrm{arccosh}\left(c x \right)}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \mathrm{arccosh}\left(c x \right)^{2} x}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d \,\mathrm{arccosh}\left(c x \right) x^{2}}{2 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c d}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d}{\left(c x +1\right) \left(c x -1\right) x}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c d}{2 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \,\mathrm{arccosh}\left(c x \right) x^{3}}{\left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d \,x^{2}}{2 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c d \,\mathrm{arccosh}\left(c x \right)}{\sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \,\mathrm{arccosh}\left(c x \right) x}{\left(c x +1\right) \left(c x -1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c d}{4 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d}{\left(c x +1\right) \left(c x -1\right) x}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c d}{\sqrt{c x -1}\, \sqrt{c x +1}}"," ",0,"-a^2/d/x*(-c^2*d*x^2+d)^(5/2)-a^2*c^2*x*(-c^2*d*x^2+d)^(3/2)-3/2*a^2*c^2*d*x*(-c^2*d*x^2+d)^(1/2)-3/2*a^2*c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^3*c*d+b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c*d-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c*x+1)/(c*x-1)*x^3+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c*x+1)/(c*x-1)*x-b^2*(-d*(c^2*x^2-1))^(1/2)*c*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*c*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*x^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c*d+b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2*d/(c*x+1)/(c*x-1)/x+3/2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*c*d-a*b*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*c*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)-a*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*c*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*d/(c*x+1)/(c*x-1)/x+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c*d","B"
184,0,0,613,0.892000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^3,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x^{3}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^3,x)","F"
185,1,2879,394,0.935000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^4,x)","\text{output too large to display}"," ",0,"16/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8-20/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-16/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3*arccosh(c*x)*c^6+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x*arccosh(c*x)*c^4-16/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3*c^6+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^3*d*c^3-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^3+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d*c^3+a^2*c^4*d*x*(-c^2*d*x^2+d)^(1/2)+a^2*c^4*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3*c^6+3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3-a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d*c^3+16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d*c^3-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^3+20/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8-29/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)^2-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d*c^3+3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3-8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^3-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(5/2)+2/3*a^2*c^4*x*(-c^2*d*x^2+d)^(3/2)+2/3*a^2*c^2/d/x*(-c^2*d*x^2+d)^(5/2)-28/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2+64*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8+146/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-64*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+24*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5-104*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6-52*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^6-32*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^7-8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5+12*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^5-8*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c-20/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+73/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^4+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-14/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^2+32*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^8+16/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8","B"
186,1,2224,776,0.858000," ","int(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x)","a^{2} \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(81 \mathrm{arccosh}\left(c x \right)^{2}-18 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{373248 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(49 \mathrm{arccosh}\left(c x \right)^{2}-14 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{175616 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{1728 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{1728 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(49 \mathrm{arccosh}\left(c x \right)^{2}+14 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{175616 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(81 \mathrm{arccosh}\left(c x \right)^{2}+18 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{373248 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+688 c^{6} x^{6}-576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-280 c^{4} x^{4}+432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+41 c^{2} x^{2}-120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{41472 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{25088 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{576 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{256 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{576 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{25088 \left(c x +1\right) c^{4} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{9} c^{9}+256 c^{10} x^{10}+576 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}-704 c^{8} x^{8}-432 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+688 c^{6} x^{6}+120 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-280 c^{4} x^{4}-9 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +41 c^{2} x^{2}-1\right) \left(1+9 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{41472 \left(c x +1\right) c^{4} \left(c x -1\right)}\right)"," ",0,"a^2*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2))+b^2*(1/373248*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(81*arccosh(c*x)^2-18*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)-3/175616*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(49*arccosh(c*x)^2-14*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)+1/1728*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)+1/1728*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)-3/175616*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(49*arccosh(c*x)^2+14*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1)+1/373248*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(81*arccosh(c*x)^2+18*arccosh(c*x)+2)*d^2/(c*x+1)/c^4/(c*x-1))+2*a*b*(1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+688*c^6*x^6-576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-280*c^4*x^4+432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+41*c^2*x^2-120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+9*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1)+1/41472*(-d*(c^2*x^2-1))^(1/2)*(-256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^9*c^9+256*c^10*x^10+576*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7-704*c^8*x^8-432*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+688*c^6*x^6+120*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-280*c^4*x^4-9*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+41*c^2*x^2-1)*(1+9*arccosh(c*x))*d^2/(c*x+1)/c^4/(c*x-1))","B"
187,1,1312,741,0.911000," ","int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x)","\frac{359 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2}}{36864 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{359 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)}{36864 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{9}}{256 \left(c x +1\right) \left(c x -1\right)}-\frac{263 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{7}}{13824 \left(c x +1\right) \left(c x -1\right)}+\frac{1915 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} x^{5}}{55296 \left(c x +1\right) \left(c x -1\right)}-\frac{359 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x}{36864 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} d^{2}}{384 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}-\frac{133 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{384 \left(c x +1\right) \left(c x -1\right)}+\frac{5 a^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{128 c^{2}}+\frac{5 a^{2} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{128 c^{2} \sqrt{c^{2} d}}-\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}-\frac{133 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{192 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right)^{2} x^{9}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{23 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right)^{2} x^{7}}{48 \left(c x +1\right) \left(c x -1\right)}+\frac{127 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{192 \left(c x +1\right) \left(c x -1\right)}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)^{2} x}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \mathrm{arccosh}\left(c x \right) x^{8}}{32 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{17 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \mathrm{arccosh}\left(c x \right) x^{6}}{144 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{59 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,\mathrm{arccosh}\left(c x \right) x^{4}}{384 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x^{2}}{128 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{8}}{32 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{17 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{6}}{144 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{59 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,x^{4}}{384 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2}}{128 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{1081 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3}}{110592 \left(c x +1\right) \left(c x -1\right)}-\frac{a^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 c^{2} d}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{9}}{4 \left(c x +1\right) \left(c x -1\right)}-\frac{23 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{24 \left(c x +1\right) \left(c x -1\right)}+\frac{127 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{96 \left(c x +1\right) \left(c x -1\right)}+\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x}{64 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{5 a^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{192 c^{2}}+\frac{a^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{48 c^{2}}"," ",0,"359/36864*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)+359/36864*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*arccosh(c*x)+1/256*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^6/(c*x-1)*x^9-263/13824*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^4/(c*x-1)*x^7+1915/55296*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^2/(c*x-1)*x^5-359/36864*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/c^2/(c*x-1)*x-5/384*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^3*d^2-133/384*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^3+5/128*a^2/c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/128*a^2/c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-5/128*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*arccosh(c*x)^2*d^2-133/192*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)^2*x^9-23/48*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)^2*x^7+127/192*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)^2*x^5+5/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)^2*x-1/32*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*arccosh(c*x)*x^8+17/144*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*arccosh(c*x)*x^6-59/384*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*arccosh(c*x)*x^4+5/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*arccosh(c*x)*x^2-1/32*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^8+17/144*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6-59/384*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+5/128*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2-1081/110592*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*x^3-1/8*a^2*x*(-c^2*d*x^2+d)^(7/2)/c^2/d+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^9-23/24*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^7+127/96*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5+5/64*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x+5/192*a^2/c^2*d*x*(-c^2*d*x^2+d)^(3/2)+1/48*a^2/c^2*x*(-c^2*d*x^2+d)^(5/2)","A"
188,1,1958,418,0.569000," ","int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(49 \mathrm{arccosh}\left(c x \right)^{2}-14 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{43904 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}-10 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{3200 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{384 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{384 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}+10 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{3200 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(49 \mathrm{arccosh}\left(c x \right)^{2}+14 \,\mathrm{arccosh}\left(c x \right)+2\right) d^{2}}{43904 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}+64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+104 c^{4} x^{4}-112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-25 c^{2} x^{2}+56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{6272 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{640 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{640 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right) \left(1+7 \,\mathrm{arccosh}\left(c x \right)\right) d^{2}}{6272 \left(c x +1\right) c^{2} \left(c x -1\right)}\right)"," ",0,"-1/7*a^2/c^2/d*(-c^2*d*x^2+d)^(7/2)+b^2*(1/43904*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(49*arccosh(c*x)^2-14*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)-1/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(25*arccosh(c*x)^2-10*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)-1/3200*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(25*arccosh(c*x)^2+10*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1)+1/43904*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(49*arccosh(c*x)^2+14*arccosh(c*x)+2)*d^2/(c*x+1)/c^2/(c*x-1))+2*a*b*(1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6+64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+104*c^4*x^4-112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-25*c^2*x^2+56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+7*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-1/640*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)+1/128*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)+1/128*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)-1/640*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1)+1/6272*(-d*(c^2*x^2-1))^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)*(1+7*arccosh(c*x))*d^2/(c*x+1)/c^2/(c*x-1))","B"
189,1,1053,422,0.465000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x)","\frac{x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a^{2}}{6}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right)^{2} x^{7}}{6 \left(c x +1\right) \left(c x -1\right)}+\frac{5 a^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{16}+\frac{5 a^{2} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 \sqrt{c^{2} d}}-\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,x^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{6}}{18 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{17 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{24 \left(c x +1\right) \left(c x -1\right)}+\frac{59 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{48 \left(c x +1\right) \left(c x -1\right)}-\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right) x}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{13 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \mathrm{arccosh}\left(c x \right) x^{4}}{48 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,\mathrm{arccosh}\left(c x \right) x^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \mathrm{arccosh}\left(c x \right) x^{6}}{18 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{13 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{4}}{48 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{299 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x}{1152 \left(c x +1\right) \left(c x -1\right)}-\frac{17 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{5}}{12 \left(c x +1\right) \left(c x -1\right)}+\frac{59 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{24 \left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{7}}{3 \left(c x +1\right) \left(c x -1\right)}+\frac{299 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2}}{1152 \sqrt{c x +1}\, \sqrt{c x -1}\, c}+\frac{299 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)}{1152 \sqrt{c x +1}\, \sqrt{c x -1}\, c}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} d^{2}}{48 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{7}}{108 \left(c x +1\right) \left(c x -1\right)}-\frac{113 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{5}}{1728 \left(c x +1\right) \left(c x -1\right)}+\frac{1091 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} x^{3}}{3456 \left(c x +1\right) \left(c x -1\right)}-\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \mathrm{arccosh}\left(c x \right)^{2} x}{16 \left(c x +1\right) \left(c x -1\right)}"," ",0,"1/6*x*(-c^2*d*x^2+d)^(5/2)*a^2+1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^6*arccosh(c*x)^2*x^7+5/24*a^2*d*x*(-c^2*d*x^2+d)^(3/2)+5/16*a^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/16*a^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-11/16*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2-1/18*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5*x^6-17/24*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^4*arccosh(c*x)^2*x^5+59/48*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)^2*x^3-11/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x+13/48*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3*arccosh(c*x)*x^4-11/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*arccosh(c*x)*x^2-1/18*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5*arccosh(c*x)*x^6-5/16*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^2*d^2+13/48*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3*x^4-299/1152*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*x-17/12*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^4*arccosh(c*x)*x^5+59/24*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^6*arccosh(c*x)*x^7+299/1152*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c+299/1152*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c*arccosh(c*x)-5/48*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*arccosh(c*x)^3*d^2+1/108*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^6*x^7-113/1728*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^4*x^5+1091/3456*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*c^2*x^3-11/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x","B"
190,0,0,797,0.770000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x,x)","F"
191,1,1227,559,0.755000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^2,x)","-\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{3}}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{9 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \mathrm{arccosh}\left(c x \right) x^{2}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \mathrm{arccosh}\left(c x \right) x^{4}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) d^{2}}{\left(c x +1\right) \left(c x -1\right) x}+\frac{15 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2} c}{8 \sqrt{c x -1}\, \sqrt{c x +1}}-\frac{15 a^{2} c^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \mathrm{arccosh}\left(c x \right)^{2} x}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d^{2} c}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} x^{4}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{9 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} x^{2}}{8 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,\mathrm{arccosh}\left(c x \right)}{\sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d^{2} c}{\sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{4 \left(c x +1\right) \left(c x -1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) d^{2} c}{\sqrt{c x -1}\, \sqrt{c x +1}}-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{d x}-a^{2} c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{\left(c x +1\right) \left(c x -1\right) x}-\frac{15 a^{2} c^{2} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}-\frac{5 a^{2} c^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{5}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \mathrm{arccosh}\left(c x \right)^{2}}{\sqrt{c x +1}\, \sqrt{c x -1}}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{3} d^{2} c}{8 \sqrt{c x -1}\, \sqrt{c x +1}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{5}}{32 \left(c x +1\right) \left(c x -1\right)}-\frac{35 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{3}}{64 \left(c x +1\right) \left(c x -1\right)}+\frac{33 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} x}{64 \left(c x +1\right) \left(c x -1\right)}-\frac{33 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c}{64 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{33 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \,\mathrm{arccosh}\left(c x \right)}{64 \sqrt{c x +1}\, \sqrt{c x -1}}"," ",0,"-11/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x+9/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*x^2-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*x^4+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*d^2/(c*x+1)/(c*x-1)/x+15/8*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d^2*c-15/8*a^2*c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x-11/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^3+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^4+9/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^5-a^2/d/x*(-c^2*d*x^2+d)^(7/2)-a^2*c^2*x*(-c^2*d*x^2+d)^(5/2)+b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c+b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2*d^2/(c*x+1)/(c*x-1)/x-15/8*a^2*c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-5/4*a^2*c^2*d*x*(-c^2*d*x^2+d)^(3/2)+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)*x^5-b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2+5/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^3*d^2*c+1/32*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*x^5-35/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*x^3+33/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c*x+1)/(c*x-1)*x-33/64*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c*x+1)^(1/2)/(c*x-1)^(1/2)-33/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)","B"
192,0,0,849,1.010000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^3,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x^{3}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^3,x)","F"
193,1,3431,580,1.027000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^4,x)","\text{output too large to display}"," ",0,"70*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5-294*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^7+294*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-406*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+380/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-46/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^2+16/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)^2-7/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^3+5*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*x^2-21*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^7+5*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+28/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*d^2*c^3-5/2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d^2*c^3-14/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c^3-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c*x+1)^(1/2)/(c*x-1)^(1/2)*x^2+5*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+5/3*a^2*c^4*d*x*(-c^2*d*x^2+d)^(3/2)+5/2*a^2*c^4*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/2*a^2*c^4*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)^2*x+56/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8-14/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c^3-71/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+4/3*a^2*c^2/d/x*(-c^2*d*x^2+d)^(7/2)+7/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3*c^6-49/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3*arccosh(c*x)*c^6+7/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x*arccosh(c*x)*c^4-49/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3*c^6+7/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x*c^4+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^3+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c*x+1)^(1/2)/(c*x-1)^(1/2)+14/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^2*d^2*c^3-5/6*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*arccosh(c*x)^3*d^2*c^3-7/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*d^2*c^3+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*x^3-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*x-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(7/2)+4/3*a^2*c^4*x*(-c^2*d*x^2+d)^(5/2)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c-147*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^7+35*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)^2*c^5-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c-14/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^3-21*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c^5+190/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^4+7/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*arccosh(c*x)*c^4-23/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^2+147*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^8+49/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*arccosh(c*x)*c^8-203*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)^2*c^6-56/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*arccosh(c*x)*c^6+a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c*x+1)/(c*x-1)*arccosh(c*x)*x+49/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c*x+1)/(c*x-1)*c^8+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^3/(c*x+1)/(c*x-1)*arccosh(c*x)-56/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c*x+1)/(c*x-1)*c^6+7/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c*x+1)/(c*x-1)*c^4-21*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*arccosh(c*x)*c^5","B"
194,1,1314,365,0.796000," ","int(x^5*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","a^{2} \left(-\frac{x^{4} \sqrt{-c^{2} d \,x^{2}+d}}{5 c^{2} d}+\frac{-\frac{4 x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{15 c^{2} d}-\frac{8 \sqrt{-c^{2} d \,x^{2}+d}}{15 d \,c^{4}}}{c^{2}}\right)+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}-10 \,\mathrm{arccosh}\left(c x \right)+2\right)}{4000 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{864 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{864 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(25 \mathrm{arccosh}\left(c x \right)^{2}+10 \,\mathrm{arccosh}\left(c x \right)+2\right)}{4000 c^{6} d \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+13 c^{2} x^{2}-20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -1\right) \left(-1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right) \left(1+5 \,\mathrm{arccosh}\left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/5*x^4/c^2/d*(-c^2*d*x^2+d)^(1/2)+4/5/c^2*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2)))+b^2*(-1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(25*arccosh(c*x)^2-10*arccosh(c*x)+2)/c^6/d/(c^2*x^2-1)-5/864*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)/c^6/d/(c^2*x^2-1)-5/864*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)/c^6/d/(c^2*x^2-1)-1/4000*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(25*arccosh(c*x)^2+10*arccosh(c*x)+2)/c^6/d/(c^2*x^2-1))+2*a*b*(-1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+13*c^2*x^2-20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-1)*(-1+5*arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/288*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/c^6/d/(c^2*x^2-1)-5/288*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/c^6/d/(c^2*x^2-1)-1/800*(-d*(c^2*x^2-1))^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)*(1+5*arccosh(c*x))/c^6/d/(c^2*x^2-1))","B"
195,1,887,307,0.954000," ","int(x^4*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} x^{3} \sqrt{-c^{2} d \,x^{2}+d}}{4 c^{2} d}-\frac{3 a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{4} d}+\frac{3 a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{4} \sqrt{c^{2} d}}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{8 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5}}{32 d \left(c^{2} x^{2}-1\right)}-\frac{13 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{64 d \,c^{2} \left(c^{2} x^{2}-1\right)}+\frac{15 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{64 d \,c^{4} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{3}}{8 d \,c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{4}}{8 d c \left(c^{2} x^{2}-1\right)}-\frac{15 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}}{64 d \,c^{5} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{5}}{4 d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{8 d \,c^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{8 d \,c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{8 d \,c^{5} \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{8 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{5}}{2 d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{4 d \,c^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{4 d \,c^{4} \left(c^{2} x^{2}-1\right)}-\frac{15 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{64 d \,c^{5} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4}}{8 d c \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a^2*x^3/c^2/d*(-c^2*d*x^2+d)^(1/2)-3/8*a^2/c^4*x/d*(-c^2*d*x^2+d)^(1/2)+3/8*a^2/c^4/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^3/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2-1/32*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*x^5-13/64*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*x^3+15/64*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^4/(c^2*x^2-1)*x-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c^5/(c^2*x^2-1)*arccosh(c*x)^3+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^4-15/64*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^5/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)^2*x^5-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*arccosh(c*x)^2*x^3+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^4/(c^2*x^2-1)*arccosh(c*x)^2*x-3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c^5/(c^2*x^2-1)*arccosh(c*x)^2+3/8*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c^3/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*x^5-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*arccosh(c*x)*x^3+3/4*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c^4/(c^2*x^2-1)*arccosh(c*x)*x-15/64*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c^5/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4","B"
196,1,752,252,0.698000," ","int(x^3*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","a^{2} \left(-\frac{x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}-6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{216 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(9 \mathrm{arccosh}\left(c x \right)^{2}+6 \,\mathrm{arccosh}\left(c x \right)+2\right)}{216 c^{4} d \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}+4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +1\right) \left(-1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right) \left(1+3 \,\mathrm{arccosh}\left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2))+b^2*(-1/216*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(9*arccosh(c*x)^2-6*arccosh(c*x)+2)/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)/c^4/d/(c^2*x^2-1)-1/216*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(9*arccosh(c*x)^2+6*arccosh(c*x)+2)/c^4/d/(c^2*x^2-1))+2*a*b*(-1/72*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+1)*(-1+3*arccosh(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/c^4/d/(c^2*x^2-1)-1/72*(-d*(c^2*x^2-1))^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)*(1+3*arccosh(c*x))/c^4/d/(c^2*x^2-1))","B"
197,1,624,194,0.718000," ","int(x^2*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{3}}{6 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{2 d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{2 d \,c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{2 d c \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{4 d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{4 d \,c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}}{4 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{2 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{2 d c \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{d \,c^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{4 d \,c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+1/2*a^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c^3/(c^2*x^2-1)*arccosh(c*x)^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)^2*x^3+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*arccosh(c*x)^2*x+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*x^3+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*x-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d/c^3/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c^3/(c^2*x^2-1)*arccosh(c*x)^2-a*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*x^3+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+a*b*(-d*(c^2*x^2-1))^(1/2)/d/c^2/(c^2*x^2-1)*arccosh(c*x)*x-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/d/c^3/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)","B"
198,1,314,139,0.307000," ","int(x*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}-2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(c x \right)^{2}+2 \,\mathrm{arccosh}\left(c x \right)+2\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(-1+\mathrm{arccosh}\left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \left(1+\mathrm{arccosh}\left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-a^2/c^2/d*(-c^2*d*x^2+d)^(1/2)+b^2*(-1/2*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2-2*arccosh(c*x)+2)/c^2/d/(c^2*x^2-1)-1/2*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(arccosh(c*x)^2+2*arccosh(c*x)+2)/c^2/d/(c^2*x^2-1))+2*a*b*(-1/2*(-d*(c^2*x^2-1))^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-1+arccosh(c*x))/c^2/d/(c^2*x^2-1)-1/2*(-d*(c^2*x^2-1))^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(1+arccosh(c*x))/c^2/d/(c^2*x^2-1))","B"
199,1,149,45,0.086000," ","int((a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-\left(c x -1\right) \left(c x +1\right) d}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{3}}{3 c d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-\left(c x -1\right) \left(c x +1\right) d}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{c d \left(c^{2} x^{2}-1\right)}"," ",0,"a^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/3*b^2*(-(c*x-1)*(c*x+1)*d)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/d/(c^2*x^2-1)*arccosh(c*x)^3-a*b*(-(c*x-1)*(c*x+1)*d)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/d/(c^2*x^2-1)*arccosh(c*x)^2","B"
200,0,0,300,0.508000," ","int((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x \sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(1/2),x)","F"
201,1,513,192,0.485000," ","int((a+b*arccosh(c*x))^2/x^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{d x}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2} c}{d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x \,c^{2}}{\left(c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{x \left(c^{2} x^{2}-1\right) d}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{d \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c}{d \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{x \left(c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a^2/d/x*(-c^2*d*x^2+d)^(1/2)-b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)^2*c-b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2*x/(c^2*x^2-1)/d*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/x/(c^2*x^2-1)/d+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c+b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*x/(c^2*x^2-1)/d*c^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/x/(c^2*x^2-1)/d+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c","B"
202,0,0,437,0.806000," ","int((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x^{3} \sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(1/2),x)","F"
203,1,2198,310,0.898000," ","int((a+b*arccosh(c*x))^2/x^4/(-c^2*d*x^2+d)^(1/2),x)","\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) \left(c x +1\right) \left(c x -1\right) c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x^{2}}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(c x +1\right) \left(c x -1\right) c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(c x +1\right) \left(c x -1\right) c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x^{2}}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x^{3}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} c^{2}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x^{3}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(c x +1\right) \left(c x -1\right) c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2} c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,\mathrm{arccosh}\left(c x \right) c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, c^{3}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c^{2}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) x}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{2 a^{2} c^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 d x}-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,x^{3}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) \left(c x +1\right) \left(c x -1\right) c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \mathrm{arccosh}\left(c x \right)^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, c^{5}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \mathrm{arccosh}\left(c x \right) c^{8}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right)^{2} c^{6}}{d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \mathrm{arccosh}\left(c x \right) c^{6}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \mathrm{arccosh}\left(c x \right)^{2} c^{4}}{3 d \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right)}"," ",0,"2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^5*c^8+4*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*arccosh(c*x)*(c*x+1)*(c*x-1)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*(c*x+1)*(c*x-1)*c^6-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*(c*x+1)*(c*x-1)*c^4+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x^3*arccosh(c*x)^2-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*arccosh(c*x)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x*arccosh(c*x)^2*c^2+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^5*c^8-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*c^6-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*c^4+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x^3*arccosh(c*x)-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*(c*x+1)*(c*x-1)*c^6-b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)^2*c^3+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-4*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*arccosh(c*x)*c^6+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*arccosh(c*x)*c^4-a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)/x*arccosh(c*x)*c^2-2/3*a^2*c^2/d/x*(-c^2*d*x^2+d)^(1/2)-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(1/2)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*c^6-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*c^4-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^2*x^2-1)*arccosh(c*x)*c^3-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*arccosh(c*x)*(c*x+1)*(c*x-1)*c^6+2*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^2*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^5*arccosh(c*x)*c^8-2*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*arccosh(c*x)^2*c^6-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x^3*arccosh(c*x)*c^6+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d/(3*c^4*x^4-2*c^2*x^2-1)*x*arccosh(c*x)^2*c^4","B"
204,1,1099,529,0.862000," ","int(x^5*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x^{4}}{3 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a^{2} x^{2}}{3 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{8 a^{2}}{3 c^{6} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{8 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{3 c^{6} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{9 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{10 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x}{3 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4}}{27 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{92 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{27 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{94 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{27 c^{6} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{4}}{3 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{2}}{3 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3}}{9 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{10 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{16 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 c^{6} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{4}}{3 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{3 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{c^{6} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a^2*x^4/c^2/d/(-c^2*d*x^2+d)^(1/2)-4/3*a^2/c^4*x^2/d/(-c^2*d*x^2+d)^(1/2)+8/3*a^2/c^6/d/(-c^2*d*x^2+d)^(1/2)-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/c^6/d^2/(c^2*x^2-1)*arccosh(c*x)^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2/9*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-10/3*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2/27*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*x^4+92/27*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*x^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-94/27*b^2*(-d*(c^2*x^2-1))^(1/2)/c^6/d^2/(c^2*x^2-1)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)^2*x^4+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)^2*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2/9*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^2/(c^2*x^2-1)*arccosh(c*x)+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)*x^4+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)*x^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)","B"
205,1,1141,414,1.011000," ","int(x^4*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x^{3}}{2 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a^{2} x}{2 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{4} d \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{2 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}}{4 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{3}}{2 d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{2 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{3}}{2 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{4 d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{4 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{2 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3}}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{2 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{d^{2} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{4 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{d^{2} c^{5} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a^2*x^3/c^2/d/(-c^2*d*x^2+d)^(1/2)+3/2*a^2/c^4*x/d/(-c^2*d*x^2+d)^(1/2)-3/2*a^2/c^4/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^2/(c^2*x^2-1)*arccosh(c*x)^2*x^3-3/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*arccosh(c*x)^2*x+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)^3+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^2/(c^2*x^2-1)*x^3-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*x-b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+3/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)^2+a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^2/(c^2*x^2-1)*arccosh(c*x)*x^3-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^3/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*arccosh(c*x)*x+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^5/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
206,1,836,410,0.693000," ","int(x^3*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a^{2}}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a^2*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*a^2/d/c^4/(-c^2*d*x^2+d)^(1/2)+b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)^2*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)*x^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
207,1,738,255,0.658000," ","int(x^2*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{3}}{3 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)^3-b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)^2-b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/d^2/c^2/(c^2*x^2-1)*x+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arccosh(c*x)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/c^2/(c^2*x^2-1)*x+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
208,1,542,215,0.345000," ","int(x*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2/c^2/d/(-c^2*d*x^2+d)^(1/2)-b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arccosh(c*x)+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
209,1,578,204,0.308000," ","int((a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2}}{d^{2} c \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2} c \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)}{d^{2} c \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}-1\right)}{d^{2} c \left(c^{2} x^{2}-1\right)}"," ",0,"a^2/d*x/(-c^2*d*x^2+d)^(1/2)-b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*arccosh(c*x)^2-b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/d^2/(c^2*x^2-1)*x+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*arccosh(c*x)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
210,0,0,517,0.597000," ","int((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(3/2),x)","F"
211,1,826,359,0.487000," ","int((a+b*arccosh(c*x))^2/x^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2}}{d x \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a^{2} c^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right)^{2} c}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x \,c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{x \left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) c}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{x \left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{4}-1\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}"," ",0,"-a^2/d/x/(-c^2*d*x^2+d)^(1/2)+2*a^2*c^2/d*x/(-c^2*d*x^2+d)^(1/2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)^2*c-2*b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2*x/(c^2*x^2-1)/d^2*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)^2/x/(c^2*x^2-1)/d^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c+b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))*c+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))*c-4*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*arccosh(c*x)*c-4*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)*x/(c^2*x^2-1)/d^2*c^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/x/(c^2*x^2-1)/d^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/d^2*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^4-1)*c","B"
212,0,0,674,0.924000," ","int((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(3/2),x)","F"
213,1,2868,486,0.946000," ","int((a+b*arccosh(c*x))^2/x^4/(-c^2*d*x^2+d)^(3/2),x)","\text{output too large to display}"," ",0,"40/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*c^8+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)*c^3-128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*arccosh(c*x)*c^6+16*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*arccosh(c*x)*c^4-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+8*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x*arccosh(c*x)*c^2-16/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)^2*c^3+32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*(c*x-1)*(c*x+1)*c^8-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*(c*x-1)*(c*x+1)*c^6-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))*c^3+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c^3+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*arccosh(c*x)^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3+5/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-1/3*a^2/d/x^3/(-c^2*d*x^2+d)^(1/2)-4/3*a^2*c^2/d/x/(-c^2*d*x^2+d)^(1/2)+128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^5-7/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x^3*arccosh(c*x)^2-32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^7*c^10+8/3*a^2*c^4/d*x/(-c^2*d*x^2+d)^(1/2)-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*arccosh(c*x)*c^4+4*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x*arccosh(c*x)^2*c^2-64/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^7*c^10+32*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*c^8-8*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*c^6-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*c^4+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x^3*arccosh(c*x)-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c-32/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*c^3+64/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*(c*x-1)*(c*x+1)*c^8-32/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*(c*x-1)*(c*x+1)*c^6-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*(c*x-1)*(c*x+1)*c^4+16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3+64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*arccosh(c*x)*(c*x-1)*(c*x+1)*c^8-32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*arccosh(c*x)*(c*x-1)*(c*x+1)*c^6+64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^2*arccosh(c*x)^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^5-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*arccosh(c*x)*(c*x-1)*(c*x+1)*c^4-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)/x^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c^3+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))*c^3+10/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c^3-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^7*arccosh(c*x)*c^10+32*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^5*arccosh(c*x)*c^8-64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*arccosh(c*x)^2*c^6-8*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x^3*arccosh(c*x)*c^6+8*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(8*c^4*x^4-7*c^2*x^2-1)*x*arccosh(c*x)^2*c^4","B"
214,1,1211,531,0.890000," ","int(x^5*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{4 a^{2} x^{2}}{c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{10 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{8 a^{2}}{3 c^{6} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}+\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}-\frac{a^{2} x^{4}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{5}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{5}}"," ",0,"4*a^2/c^4*x^2/d/(-c^2*d*x^2+d)^(3/2)+2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)+2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arccosh(c*x)-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6*arccosh(c*x)-b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arccosh(c*x)^2*x^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arccosh(c*x)^2*x^2-8/3*a^2/c^6/d/(-c^2*d*x^2+d)^(3/2)+11/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-11/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arccosh(c*x)*x^2+4*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arccosh(c*x)*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*x^2+b^2*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arccosh(c*x)^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*x^2-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6*arccosh(c*x)^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6-a^2*x^4/c^2/d/(-c^2*d*x^2+d)^(3/2)-11/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^5*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x+2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x+11/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+11/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-11/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)+2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x","B"
215,1,4074,446,1.007000," ","int(x^4*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-44/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*x^5-76*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*arccosh(c*x)^2*x^5-44/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*arccosh(c*x)*x^5+20/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*x^7+43/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*x^3-4*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*x-32*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6-4*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*x+64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)+16/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-16/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x^5-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)^3-8*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*(c*x+1)*(c*x-1)*x^3+21*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)^2-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+64*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*arccosh(c*x)*x^7-16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*(c*x+1)*(c*x-1)*x^5+362/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*arccosh(c*x)*x^3-32*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*arccosh(c*x)*x+16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*(c*x+1)*(c*x-1)*x-55/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+1/3*a^2*x^3/c^2/d/(-c^2*d*x^2+d)^(3/2)+a^2/c^4/d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-17*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*x^5+16/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)+28/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*(c*x+1)*(c*x-1)*x^3+8*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-4*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*(c*x+1)*(c*x-1)*x-13*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+84*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+28/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x^3-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)-a^2/c^4/d^2*x/(-c^2*d*x^2+d)^(1/2)-64*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6+168*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-440/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)^2+16/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^5/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*(c*x+1)*(c*x-1)*x^5+32*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*arccosh(c*x)^2*x^7+16/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*arccosh(c*x)*x^7+181/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*arccosh(c*x)^2*x^3+40/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*arccosh(c*x)*x^3-16*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*arccosh(c*x)^2*x-4*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*arccosh(c*x)*x+16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)*c^2/d^3*x^7-152*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/d^3*arccosh(c*x)*x^5+40/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^2/d^3*x^3-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^5/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-13*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+8*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-220/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^3/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-4*b^2*(-d*(c^2*x^2-1))^(1/2)/(24*c^8*x^8-87*c^6*x^6+118*c^4*x^4-71*c^2*x^2+16)/c^4/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x","B"
216,1,835,331,0.744000," ","int(x^3*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{a^{2} x^{2}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a^{2}}{3 d \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{3}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{3}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{3 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{4} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2*x^2/c^2/d/(-c^2*d*x^2+d)^(3/2)-2/3*a^2/d/c^4/(-c^2*d*x^2+d)^(3/2)+b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arccosh(c*x)^2*x^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^3*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*x^2-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arccosh(c*x)^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+5/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+5/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arccosh(c*x)*x^2+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arccosh(c*x)-5/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)+5/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^4/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
217,1,3445,363,0.756000," ","int(x^2*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*x^7-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*x^5+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*arccosh(c*x)*x^3+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*arccosh(c*x)^2*x^7+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*arccosh(c*x)*x^7-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*arccosh(c*x)^2*x^5-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*arccosh(c*x)*x^5+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*(c*x+1)*(c*x-1)*x^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*arccosh(c*x)*x^7-2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*arccosh(c*x)*x^5+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*(c*x+1)*(c*x-1)*x^3+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*arccosh(c*x)^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*(c*x+1)*(c*x-1)*x^5-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^2/d^3*(c*x+1)*(c*x-1)*x-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*arccosh(c*x)^2*x^3+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*x^3+4*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6+1/3*a^2/c^2/d*x/(-c^2*d*x^2+d)^(3/2)-1/3*a^2/c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*x^3+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/d^3*arccosh(c*x)*x^3+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4/d^3*x^7-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*x^5+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*arccosh(c*x)-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x^5+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2/d^3*(c*x+1)*(c*x-1)*x^5+a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2","B"
218,1,720,297,0.434000," ","int(x*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{a^{2}}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1-c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \polylog \left(2, -c x -\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right)}{3 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d^{3} c^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a^2/c^2/d/(-c^2*d*x^2+d)^(3/2)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*x^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arccosh(c*x)^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arccosh(c*x)+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c^2/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
219,1,3050,313,0.439000," ","int((a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6/d^3*x^7+14/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*x^5-16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*x^3-8*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*arccosh(c*x)*x+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*(c*x+1)*(c*x-1)*x-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6/d^3*arccosh(c*x)*x^7-2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*arccosh(c*x)^2*x^5+14/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*arccosh(c*x)*x^5+17/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*arccosh(c*x)^2*x^3-16/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*arccosh(c*x)*x^3-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*x-28/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+4*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+34/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*arccosh(c*x)*x^3+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*(c*x+1)*(c*x-1)*x-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x+7/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*(c*x+1)*(c*x-1)*x^3-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*arccosh(c*x)^2-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*(c*x+1)*(c*x-1)*x^5+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))-4*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*arccosh(c*x)*x^5+1/3*a^2/d*x/(-c^2*d*x^2+d)^(3/2)+2/3*a^2/d^2*x/(-c^2*d*x^2+d)^(1/2)-4*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*arccosh(c*x)^2*x+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*arccosh(c*x)*x-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6/d^3*x^7+3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*x^5-13/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*x^3+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/d^3*x+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x^5+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4-10/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*arccosh(c*x)*(c*x+1)*(c*x-1)*x^3-14/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*arccosh(c*x)+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4/d^3*(c*x+1)*(c*x-1)*x^5-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2/d^3*(c*x+1)*(c*x-1)*x^3+a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c/d^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+16/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c/d^3*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/c/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)","B"
220,0,0,621,0.634000," ","int((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(5/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(5/2),x)","F"
221,1,3798,470,0.597000," ","int((a+b*arccosh(c*x))^2/x^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-160/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*c^6-64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^9*arccosh(c*x)*c^10+224/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*arccosh(c*x)*c^8-64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*arccosh(c*x)^2*c^6-3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5+17/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3-272/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+24*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*polylog(2,-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))*c+b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c-16/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)^2*c+80/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*(c*x+1)*(c*x-1)*c^4-a^2/d/x/(-c^2*d*x^2+d)^(3/2)+29*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*c^4-5*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*c^2+9*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/x*arccosh(c*x)^2-32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^9*c^10+40*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*c^8+112*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*arccosh(c*x)*c^4-88*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*arccosh(c*x)*c^2-88/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*(c*x+1)*(c*x-1)*c^6-128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*arccosh(c*x)*c^6-3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+8/3*a^2*c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)-3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*arccosh(c*x)*(c*x+1)*(c*x-1)*c^8-160/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*arccosh(c*x)*(c*x+1)*(c*x-1)*c^6+64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^4*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))*c+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c-8*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*arccosh(c*x)*(c*x+1)*(c*x-1)*c^2-32/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*arccosh(c*x)*c+64/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*(c*x+1)*(c*x-1)*c^8-160/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*(c*x+1)*(c*x-1)*c^6+40*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*(c*x+1)*(c*x-1)*c^4-8*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*(c*x+1)*(c*x-1)*c^2+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+48*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c+10/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2-1)*c+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)*c+32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*(c*x+1)*(c*x-1)*c^8+4/3*a^2*c^2/d*x/(-c^2*d*x^2+d)^(3/2)-8*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*(c*x+1)*(c*x-1)*c^2+40*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*arccosh(c*x)*(c*x+1)*(c*x-1)*c^4+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d^3/(c^2*x^2-1)*polylog(2,c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c-64/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^9*c^10+224/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^7*c^8-280/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*arccosh(c*x)*c^6-280/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^5*c^6+48*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*c^4-8*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*c^2+18*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/x*arccosh(c*x)+56*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*arccosh(c*x)^2*c^4+48*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^3*arccosh(c*x)*c^4-44*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*arccosh(c*x)^2*c^2-8*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x*arccosh(c*x)*c^2-136/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^2*arccosh(c*x)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^3+128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)*x^4*arccosh(c*x)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c^5","B"
222,0,0,798,0.973000," ","int((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(5/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(5/2),x)","F"
223,1,5251,544,0.885000," ","int((a+b*arccosh(c*x))^2/x^4/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
224,1,794,395,0.503000," ","int(arccosh(a*x)^2/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-20 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+15 a x +16 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-8 \sqrt{a x -1}\, \sqrt{a x +1}\right) \left(-64 \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) x^{7} a^{7}-64 \,\mathrm{arccosh}\left(a x \right) x^{8} a^{8}-32 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{7} a^{7}-32 x^{8} a^{8}+248 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{5} x^{5}+280 \,\mathrm{arccosh}\left(a x \right) x^{6} a^{6}+126 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{5} a^{5}+142 x^{6} a^{6}+80 a^{4} x^{4} \mathrm{arccosh}\left(a x \right)^{2}-340 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{3} x^{3}-456 a^{4} x^{4} \mathrm{arccosh}\left(a x \right)-156 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}-265 x^{4} a^{4}-190 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)^{2}+165 \,\mathrm{arccosh}\left(a x \right) a x \sqrt{a x -1}\, \sqrt{a x +1}+328 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)+62 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +235 a^{2} x^{2}+128 \mathrm{arccosh}\left(a x \right)^{2}-88 \,\mathrm{arccosh}\left(a x \right)-80\right)}{30 \left(40 a^{10} x^{10}-215 x^{8} a^{8}+469 x^{6} a^{6}-517 x^{4} a^{4}+287 a^{2} x^{2}-64\right) a \,c^{4}}-\frac{16 \sqrt{a x +1}\, \sqrt{a x -1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(a x \right)^{2}}{15 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{16 \sqrt{a x +1}\, \sqrt{a x -1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(a x \right) \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{15 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{16 \sqrt{a x +1}\, \sqrt{a x -1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{15 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{16 \sqrt{a x +1}\, \sqrt{a x -1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(a x \right) \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{15 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{16 \sqrt{a x +1}\, \sqrt{a x -1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{15 c^{4} a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/30*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-20*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+15*a*x+16*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-8*(a*x-1)^(1/2)*(a*x+1)^(1/2))*(-64*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)*x^7*a^7-64*arccosh(a*x)*x^8*a^8-32*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^7*a^7-32*x^8*a^8+248*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^5*x^5+280*arccosh(a*x)*x^6*a^6+126*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^5*a^5+142*x^6*a^6+80*a^4*x^4*arccosh(a*x)^2-340*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^3*x^3-456*a^4*x^4*arccosh(a*x)-156*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)-265*x^4*a^4-190*a^2*x^2*arccosh(a*x)^2+165*arccosh(a*x)*a*x*(a*x-1)^(1/2)*(a*x+1)^(1/2)+328*a^2*x^2*arccosh(a*x)+62*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+235*a^2*x^2+128*arccosh(a*x)^2-88*arccosh(a*x)-80)/(40*a^10*x^10-215*a^8*x^8+469*a^6*x^6-517*a^4*x^4+287*a^2*x^2-64)/a/c^4-16/15*(a*x+1)^(1/2)*(a*x-1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)^2+16/15*(a*x+1)^(1/2)*(a*x-1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))+16/15*(a*x+1)^(1/2)*(a*x-1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c^4/a/(a^2*x^2-1)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+16/15*(a*x+1)^(1/2)*(a*x-1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+16/15*(a*x+1)^(1/2)*(a*x-1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c^4/a/(a^2*x^2-1)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))","B"
225,1,488,199,0.769000," ","int(x^4*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3}}{8 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}+8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x -8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(8 \mathrm{arccosh}\left(a x \right)^{2}-4 \,\mathrm{arccosh}\left(a x \right)+1\right)}{512 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(2 \mathrm{arccosh}\left(a x \right)^{2}-2 \,\mathrm{arccosh}\left(a x \right)+1\right)}{16 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(2 \mathrm{arccosh}\left(a x \right)^{2}+2 \,\mathrm{arccosh}\left(a x \right)+1\right)}{16 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x +8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(8 \mathrm{arccosh}\left(a x \right)^{2}+4 \,\mathrm{arccosh}\left(a x \right)+1\right)}{512 a^{5} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*arccosh(a*x)^3-1/512*(-a^2*x^2+1)^(1/2)*(8*x^5*a^5-12*x^3*a^3+8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x-8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(8*arccosh(a*x)^2-4*arccosh(a*x)+1)/a^5/(a^2*x^2-1)-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(2*arccosh(a*x)^2-2*arccosh(a*x)+1)/a^5/(a^2*x^2-1)-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(2*arccosh(a*x)^2+2*arccosh(a*x)+1)/a^5/(a^2*x^2-1)-1/512*(-a^2*x^2+1)^(1/2)*(8*x^5*a^5-12*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x+8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(8*arccosh(a*x)^2+4*arccosh(a*x)+1)/a^5/(a^2*x^2-1)","B"
226,1,343,145,0.501000," ","int(x^3*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 x^{4} a^{4}-5 a^{2} x^{2}+4 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}-3 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +1\right) \left(9 \mathrm{arccosh}\left(a x \right)^{2}-6 \,\mathrm{arccosh}\left(a x \right)+2\right)}{216 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{a x +1}\, \sqrt{a x -1}\, a x +a^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(a x \right)^{2}-2 \,\mathrm{arccosh}\left(a x \right)+2\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \left(\mathrm{arccosh}\left(a x \right)^{2}+2 \,\mathrm{arccosh}\left(a x \right)+2\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 x^{4} a^{4}-5 a^{2} x^{2}-4 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}+3 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +1\right) \left(9 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+2\right)}{216 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/216*(-a^2*x^2+1)^(1/2)*(4*x^4*a^4-5*a^2*x^2+4*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)-3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+1)*(9*arccosh(a*x)^2-6*arccosh(a*x)+2)/a^4/(a^2*x^2-1)-3/8*(-a^2*x^2+1)^(1/2)*((a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+a^2*x^2-1)*(arccosh(a*x)^2-2*arccosh(a*x)+2)/a^4/(a^2*x^2-1)-3/8*(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*(arccosh(a*x)^2+2*arccosh(a*x)+2)/a^4/(a^2*x^2-1)-1/216*(-a^2*x^2+1)^(1/2)*(4*x^4*a^4-5*a^2*x^2-4*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+1)*(9*arccosh(a*x)^2+6*arccosh(a*x)+2)/a^4/(a^2*x^2-1)","B"
227,1,239,123,0.462000," ","int(x^2*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3}}{6 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(2 \mathrm{arccosh}\left(a x \right)^{2}-2 \,\mathrm{arccosh}\left(a x \right)+1\right)}{16 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(2 \mathrm{arccosh}\left(a x \right)^{2}+2 \,\mathrm{arccosh}\left(a x \right)+1\right)}{16 a^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/6*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^3/(a^2*x^2-1)*arccosh(a*x)^3-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(2*arccosh(a*x)^2-2*arccosh(a*x)+1)/a^3/(a^2*x^2-1)-1/16*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(2*arccosh(a*x)^2+2*arccosh(a*x)+1)/a^3/(a^2*x^2-1)","A"
228,1,139,69,0.200000," ","int(x*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{a x +1}\, \sqrt{a x -1}\, a x +a^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(a x \right)^{2}-2 \,\mathrm{arccosh}\left(a x \right)+2\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \left(\mathrm{arccosh}\left(a x \right)^{2}+2 \,\mathrm{arccosh}\left(a x \right)+2\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*((a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+a^2*x^2-1)*(arccosh(a*x)^2-2*arccosh(a*x)+2)/a^2/(a^2*x^2-1)-1/2*(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*(arccosh(a*x)^2+2*arccosh(a*x)+2)/a^2/(a^2*x^2-1)","A"
229,1,51,26,0.058000," ","int(arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3}}{3 a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/3*(-(a*x-1)*(a*x+1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a/(a^2*x^2-1)*arccosh(a*x)^3","A"
230,0,0,220,0.343000," ","int(arccosh(a*x)^2/x/(-a^2*x^2+1)^(1/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)^{2}}{x \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arccosh(a*x)^2/x/(-a^2*x^2+1)^(1/2),x)","F"
231,1,241,136,0.358000," ","int(arccosh(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \mathrm{arccosh}\left(a x \right)^{2}}{x \left(a^{2} x^{2}-1\right)}-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} a}{a^{2} x^{2}-1}+\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \ln \left(1+\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}\right) a}{a^{2} x^{2}-1}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(2, -\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}\right) a}{a^{2} x^{2}-1}"," ",0,"-(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*arccosh(a*x)^2/x/(a^2*x^2-1)-2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)^2*a+2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)*ln(1+(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2)*a+(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*polylog(2,-(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2)*a","A"
232,0,0,317,0.667000," ","int(arccosh(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)^{2}}{x^{3} \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arccosh(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x)","F"
233,0,0,1079,2.232000," ","int((f*x)^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x)","F"
234,0,0,541,1.753000," ","int((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x)","F"
235,0,0,221,1.542000," ","int((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x))^2,x)","\int \left(f x \right)^{m} \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x))^2,x)","F"
236,0,0,31,0.594000," ","int((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","F"
237,0,0,31,0.834000," ","int((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","F"
238,0,0,31,0.862000," ","int((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","F"
239,0,0,26,0.524000," ","int((f*x)^m*arccosh(c*x)^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(f x \right)^{m} \mathrm{arccosh}\left(c x \right)^{2}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((f*x)^m*arccosh(c*x)^2/(-c^2*x^2+1)^(1/2),x)","F"
240,1,294,429,0.132000," ","int((-a^2*c*x^2+c)^3*arccosh(a*x)^3,x)","-\frac{c^{3} \left(1929375 \mathrm{arccosh}\left(a x \right)^{3} a^{7} x^{7}-826875 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}\, a^{6} x^{6}-8103375 \mathrm{arccosh}\left(a x \right)^{3} a^{5} x^{5}+3869775 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}\, a^{4} x^{4}+236250 \,\mathrm{arccosh}\left(a x \right) a^{7} x^{7}-33750 \sqrt{a x -1}\, \sqrt{a x +1}\, a^{6} x^{6}+13505625 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)^{3}-8345925 \mathrm{arccosh}\left(a x \right)^{2} a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-1547910 \,\mathrm{arccosh}\left(a x \right) a^{5} x^{5}+269082 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}-13505625 a x \mathrm{arccosh}\left(a x \right)^{3}+23825025 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}+5563950 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)-1495874 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-47650050 a x \,\mathrm{arccosh}\left(a x \right)+44658302 \sqrt{a x -1}\, \sqrt{a x +1}\right)}{13505625 a}"," ",0,"-1/13505625/a*c^3*(1929375*arccosh(a*x)^3*a^7*x^7-826875*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^6*x^6-8103375*arccosh(a*x)^3*a^5*x^5+3869775*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^4*x^4+236250*arccosh(a*x)*a^7*x^7-33750*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^6*x^6+13505625*a^3*x^3*arccosh(a*x)^3-8345925*arccosh(a*x)^2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-1547910*arccosh(a*x)*a^5*x^5+269082*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4-13505625*a*x*arccosh(a*x)^3+23825025*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+5563950*a^3*x^3*arccosh(a*x)-1495874*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-47650050*a*x*arccosh(a*x)+44658302*(a*x-1)^(1/2)*(a*x+1)^(1/2))","A"
241,1,218,328,0.102000," ","int((-a^2*c*x^2+c)^2*arccosh(a*x)^3,x)","\frac{c^{2} \left(3375 \mathrm{arccosh}\left(a x \right)^{3} a^{5} x^{5}-2025 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}\, a^{4} x^{4}-11250 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)^{3}+8550 \mathrm{arccosh}\left(a x \right)^{2} a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+810 \,\mathrm{arccosh}\left(a x \right) a^{5} x^{5}-162 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+16875 a x \mathrm{arccosh}\left(a x \right)^{3}-33525 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}-5700 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)+1684 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+67050 a x \,\mathrm{arccosh}\left(a x \right)-63682 \sqrt{a x -1}\, \sqrt{a x +1}\right)}{16875 a}"," ",0,"1/16875/a*c^2*(3375*arccosh(a*x)^3*a^5*x^5-2025*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^4*x^4-11250*a^3*x^3*arccosh(a*x)^3+8550*arccosh(a*x)^2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+810*arccosh(a*x)*a^5*x^5-162*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+16875*a*x*arccosh(a*x)^3-33525*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-5700*a^3*x^3*arccosh(a*x)+1684*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+67050*a*x*arccosh(a*x)-63682*(a*x-1)^(1/2)*(a*x+1)^(1/2))","A"
242,1,140,145,0.092000," ","int((-a^2*c*x^2+c)*arccosh(a*x)^3,x)","-\frac{c \left(-9 \mathrm{arccosh}\left(a x \right)^{2} a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+9 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)^{3}+63 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}-2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-27 a x \mathrm{arccosh}\left(a x \right)^{3}+6 a^{3} x^{3} \mathrm{arccosh}\left(a x \right)+122 \sqrt{a x -1}\, \sqrt{a x +1}-126 a x \,\mathrm{arccosh}\left(a x \right)\right)}{27 a}"," ",0,"-1/27/a*c*(-9*arccosh(a*x)^2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+9*a^3*x^3*arccosh(a*x)^3+63*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-27*a*x*arccosh(a*x)^3+6*a^3*x^3*arccosh(a*x)+122*(a*x-1)^(1/2)*(a*x+1)^(1/2)-126*a*x*arccosh(a*x))","A"
243,1,273,235,0.090000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c),x)","-\frac{\mathrm{arccosh}\left(a x \right)^{3} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}-\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{6 \,\mathrm{arccosh}\left(a x \right) \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}-\frac{6 \polylog \left(4, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{\mathrm{arccosh}\left(a x \right)^{3} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}-\frac{6 \,\mathrm{arccosh}\left(a x \right) \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}+\frac{6 \polylog \left(4, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a c}"," ",0,"-1/a/c*arccosh(a*x)^3*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-3*arccosh(a*x)^2*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c+6*arccosh(a*x)*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c-6*polylog(4,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c+1/a/c*arccosh(a*x)^3*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+3*arccosh(a*x)^2*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c-6*arccosh(a*x)*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c+6*polylog(4,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c","A"
244,1,464,378,0.269000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c)^2,x)","-\frac{\mathrm{arccosh}\left(a x \right)^{3} x}{2 \left(a^{2} x^{2}-1\right) c^{2}}-\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}}{2 a \left(a^{2} x^{2}-1\right) c^{2}}-\frac{\mathrm{arccosh}\left(a x \right)^{3} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}-\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}+\frac{3 \,\mathrm{arccosh}\left(a x \right) \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}-\frac{3 \polylog \left(4, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}+\frac{\mathrm{arccosh}\left(a x \right)^{3} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}+\frac{3 \mathrm{arccosh}\left(a x \right)^{2} \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{2}}-\frac{3 \,\mathrm{arccosh}\left(a x \right) \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}+\frac{3 \polylog \left(4, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}+\frac{3 \,\mathrm{arccosh}\left(a x \right) \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}+\frac{3 \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}-\frac{3 \,\mathrm{arccosh}\left(a x \right) \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}-\frac{3 \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{a \,c^{2}}"," ",0,"-1/2/(a^2*x^2-1)*arccosh(a*x)^3/c^2*x-3/2/a/(a^2*x^2-1)*arccosh(a*x)^2/c^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-1/2/a/c^2*arccosh(a*x)^3*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-3/2*arccosh(a*x)^2*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2+3*arccosh(a*x)*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2-3*polylog(4,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2+1/2/a/c^2*arccosh(a*x)^3*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+3/2*arccosh(a*x)^2*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2-3*arccosh(a*x)*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2+3*polylog(4,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2+3/a/c^2*arccosh(a*x)*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))+3*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2-3/a/c^2*arccosh(a*x)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-3*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^2","A"
245,1,710,475,0.404000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c)^3,x)","-\frac{3 a^{2} \mathrm{arccosh}\left(a x \right)^{3} x^{3}}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{9 a \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}\, x^{2}}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{a^{2} x^{3} \mathrm{arccosh}\left(a x \right)}{4 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{a \sqrt{a x +1}\, \sqrt{a x -1}\, x^{2}}{4 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{5 \mathrm{arccosh}\left(a x \right)^{3} x}{8 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{11 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x -1}\, \sqrt{a x +1}}{8 a \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{x \,\mathrm{arccosh}\left(a x \right)}{4 \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{\sqrt{a x -1}\, \sqrt{a x +1}}{4 a \left(x^{4} a^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{5 \,\mathrm{arccosh}\left(a x \right) \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{3}}+\frac{5 \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{3}}-\frac{5 \,\mathrm{arccosh}\left(a x \right) \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{3}}-\frac{5 \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{2 a \,c^{3}}-\frac{3 \mathrm{arccosh}\left(a x \right)^{3} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}-\frac{9 \mathrm{arccosh}\left(a x \right)^{2} \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}+\frac{9 \,\mathrm{arccosh}\left(a x \right) \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}-\frac{9 \polylog \left(4, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}+\frac{3 \mathrm{arccosh}\left(a x \right)^{3} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}+\frac{9 \mathrm{arccosh}\left(a x \right)^{2} \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{8 a \,c^{3}}-\frac{9 \,\mathrm{arccosh}\left(a x \right) \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}+\frac{9 \polylog \left(4, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{4 a \,c^{3}}"," ",0,"-3/8*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)^3*x^3-9/8*a/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)*x^2+1/4*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*x^3*arccosh(a*x)+1/4*a/(a^4*x^4-2*a^2*x^2+1)/c^3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^2+5/8/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)^3*x+11/8/a/(a^4*x^4-2*a^2*x^2+1)/c^3*arccosh(a*x)^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-1/4/(a^4*x^4-2*a^2*x^2+1)/c^3*x*arccosh(a*x)-1/4/a/(a^4*x^4-2*a^2*x^2+1)/c^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+5/2/a/c^3*arccosh(a*x)*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))+5/2*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3-5/2/a/c^3*arccosh(a*x)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-5/2*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3-3/8/a/c^3*arccosh(a*x)^3*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-9/8*arccosh(a*x)^2*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3+9/4*arccosh(a*x)*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3-9/4*polylog(4,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3+3/8/a/c^3*arccosh(a*x)^3*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+9/8*arccosh(a*x)^2*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3-9/4*arccosh(a*x)*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3+9/4*polylog(4,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/a/c^3","A"
246,1,887,517,0.508000," ","int((-a^2*c*x^2+c)^(5/2)*arccosh(a*x)^3,x)","-\frac{5 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(a x \right)^{4} c^{2}}{64 \sqrt{a x -1}\, \sqrt{a x +1}\, a}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(32 x^{7} a^{7}-64 x^{5} a^{5}+32 \sqrt{a x -1}\, \sqrt{a x +1}\, a^{6} x^{6}+38 x^{3} a^{3}-48 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}-6 a x +18 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(36 \mathrm{arccosh}\left(a x \right)^{3}-18 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-1\right) c^{2}}{13824 \left(a x -1\right) \left(a x +1\right) a}-\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}+8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x -8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(32 \mathrm{arccosh}\left(a x \right)^{3}-24 \mathrm{arccosh}\left(a x \right)^{2}+12 \,\mathrm{arccosh}\left(a x \right)-3\right) c^{2}}{4096 \left(a x -1\right) \left(a x +1\right) a}+\frac{15 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}-6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-3\right) c^{2}}{512 \left(a x -1\right) \left(a x +1\right) a}+\frac{15 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}+6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+3\right) c^{2}}{512 \left(a x -1\right) \left(a x +1\right) a}-\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x +8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(32 \mathrm{arccosh}\left(a x \right)^{3}+24 \mathrm{arccosh}\left(a x \right)^{2}+12 \,\mathrm{arccosh}\left(a x \right)+3\right) c^{2}}{4096 \left(a x -1\right) \left(a x +1\right) a}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-32 \sqrt{a x -1}\, \sqrt{a x +1}\, a^{6} x^{6}+32 x^{7} a^{7}+48 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}-64 x^{5} a^{5}-18 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+38 x^{3} a^{3}+\sqrt{a x -1}\, \sqrt{a x +1}-6 a x \right) \left(36 \mathrm{arccosh}\left(a x \right)^{3}+18 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+1\right) c^{2}}{13824 \left(a x -1\right) \left(a x +1\right) a}"," ",0,"-5/64*(-c*(a^2*x^2-1))^(1/2)/(a*x-1)^(1/2)/(a*x+1)^(1/2)/a*arccosh(a*x)^4*c^2+1/13824*(-c*(a^2*x^2-1))^(1/2)*(32*x^7*a^7-64*x^5*a^5+32*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^6*x^6+38*x^3*a^3-48*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4-6*a*x+18*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(36*arccosh(a*x)^3-18*arccosh(a*x)^2+6*arccosh(a*x)-1)*c^2/(a*x-1)/(a*x+1)/a-3/4096*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-12*x^3*a^3+8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x-8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(32*arccosh(a*x)^3-24*arccosh(a*x)^2+12*arccosh(a*x)-3)*c^2/(a*x-1)/(a*x+1)/a+15/512*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3-6*arccosh(a*x)^2+6*arccosh(a*x)-3)*c^2/(a*x-1)/(a*x+1)/a+15/512*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3+6*arccosh(a*x)^2+6*arccosh(a*x)+3)*c^2/(a*x-1)/(a*x+1)/a-3/4096*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-12*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x+8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(32*arccosh(a*x)^3+24*arccosh(a*x)^2+12*arccosh(a*x)+3)*c^2/(a*x-1)/(a*x+1)/a+1/13824*(-c*(a^2*x^2-1))^(1/2)*(-32*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^6*x^6+32*x^7*a^7+48*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4-64*x^5*a^5-18*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+38*x^3*a^3+(a*x-1)^(1/2)*(a*x+1)^(1/2)-6*a*x)*(36*arccosh(a*x)^3+18*arccosh(a*x)^2+6*arccosh(a*x)+1)*c^2/(a*x-1)/(a*x+1)/a","A"
247,1,536,338,0.347000," ","int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^3,x)","-\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(a x \right)^{4} c}{32 \sqrt{a x -1}\, \sqrt{a x +1}\, a}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}+8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x -8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(32 \mathrm{arccosh}\left(a x \right)^{3}-24 \mathrm{arccosh}\left(a x \right)^{2}+12 \,\mathrm{arccosh}\left(a x \right)-3\right) c}{2048 \left(a x -1\right) \left(a x +1\right) a}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}-6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-3\right) c}{32 \left(a x -1\right) \left(a x +1\right) a}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}+6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+3\right) c}{32 \left(a x -1\right) \left(a x +1\right) a}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x +8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(32 \mathrm{arccosh}\left(a x \right)^{3}+24 \mathrm{arccosh}\left(a x \right)^{2}+12 \,\mathrm{arccosh}\left(a x \right)+3\right) c}{2048 \left(a x -1\right) \left(a x +1\right) a}"," ",0,"-3/32*(-c*(a^2*x^2-1))^(1/2)/(a*x-1)^(1/2)/(a*x+1)^(1/2)/a*arccosh(a*x)^4*c-1/2048*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-12*x^3*a^3+8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x-8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(32*arccosh(a*x)^3-24*arccosh(a*x)^2+12*arccosh(a*x)-3)*c/(a*x-1)/(a*x+1)/a+1/32*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3-6*arccosh(a*x)^2+6*arccosh(a*x)-3)*c/(a*x-1)/(a*x+1)/a+1/32*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3+6*arccosh(a*x)^2+6*arccosh(a*x)+3)*c/(a*x-1)/(a*x+1)/a-1/2048*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-12*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x+8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(32*arccosh(a*x)^3+24*arccosh(a*x)^2+12*arccosh(a*x)+3)*c/(a*x-1)/(a*x+1)/a","A"
248,1,256,191,0.329000," ","int(arccosh(a*x)^3*(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(a x \right)^{4}}{8 \sqrt{a x -1}\, \sqrt{a x +1}\, a}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}-6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-3\right)}{32 \left(a x -1\right) \left(a x +1\right) a}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}+6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+3\right)}{32 \left(a x -1\right) \left(a x +1\right) a}"," ",0,"-1/8*(-c*(a^2*x^2-1))^(1/2)/(a*x-1)^(1/2)/(a*x+1)^(1/2)/a*arccosh(a*x)^4+1/32*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3-6*arccosh(a*x)^2+6*arccosh(a*x)-3)/(a*x-1)/(a*x+1)/a+1/32*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3+6*arccosh(a*x)^2+6*arccosh(a*x)+3)/(a*x-1)/(a*x+1)/a","A"
249,1,55,38,0.059000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{4}}{4 a c \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a/c/(a^2*x^2-1)*arccosh(a*x)^4","A"
250,1,548,252,0.393000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-\sqrt{a x -1}\, \sqrt{a x +1}+a x \right) \mathrm{arccosh}\left(a x \right)^{3}}{c^{2} a \left(a^{2} x^{2}-1\right)}-\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3}}{c^{2} a \left(a^{2} x^{2}-1\right)}+\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}+\frac{6 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}-\frac{6 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}+\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}+\frac{6 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}-\frac{6 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(-(a*x-1)^(1/2)*(a*x+1)^(1/2)+a*x)*arccosh(a*x)^3/c^2/a/(a^2*x^2-1)-2*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*arccosh(a*x)^3+3*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*arccosh(a*x)^2*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))+6*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*arccosh(a*x)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-6*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+3*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*arccosh(a*x)^2*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+6*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*arccosh(a*x)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-6*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^2/a/(a^2*x^2-1)*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))","B"
251,1,955,400,0.565000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}-3 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+2 \sqrt{a x -1}\, \sqrt{a x +1}\right) \mathrm{arccosh}\left(a x \right) \left(6 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{3} x^{3}+6 a^{4} x^{4} \mathrm{arccosh}\left(a x \right)+6 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}+6 x^{4} a^{4}+6 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)^{2}-9 \,\mathrm{arccosh}\left(a x \right) a x \sqrt{a x -1}\, \sqrt{a x +1}-12 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)-6 \sqrt{a x +1}\, \sqrt{a x -1}\, a x -18 a^{2} x^{2}-8 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+12\right)}{6 \left(3 x^{6} a^{6}-10 x^{4} a^{4}+11 a^{2} x^{2}-4\right) a \,c^{3}}+\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}-1\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}-\frac{4 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3}}{3 c^{3} a \left(a^{2} x^{2}-1\right)}+\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}+\frac{4 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}-\frac{4 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}+\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}+\frac{4 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}-\frac{4 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{3} a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/6*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3-3*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+2*(a*x-1)^(1/2)*(a*x+1)^(1/2))*arccosh(a*x)*(6*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^3*x^3+6*a^4*x^4*arccosh(a*x)+6*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+6*x^4*a^4+6*a^2*x^2*arccosh(a*x)^2-9*arccosh(a*x)*a*x*(a*x-1)^(1/2)*(a*x+1)^(1/2)-12*a^2*x^2*arccosh(a*x)-6*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-18*a^2*x^2-8*arccosh(a*x)^2+6*arccosh(a*x)+12)/(3*a^6*x^6-10*a^4*x^4+11*a^2*x^2-4)/a/c^3+2*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*ln(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*ln(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)-1)-(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-4/3*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*arccosh(a*x)^3+2*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*arccosh(a*x)^2*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))+4*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*arccosh(a*x)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-4*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+2*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*arccosh(a*x)^2*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+4*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*arccosh(a*x)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-4*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^3/a/(a^2*x^2-1)*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))","B"
252,1,1319,564,0.586000," ","int(arccosh(a*x)^3/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}-20 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+15 a x +16 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-8 \sqrt{a x -1}\, \sqrt{a x +1}\right) \left(24+24 x^{8} a^{8}-96 x^{6} a^{6}+144 x^{4} a^{4}-96 a^{2} x^{2}-192 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x +1}\, \sqrt{a x -1}\, x^{7} a^{7}-192 \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) x^{7} a^{7}-1368 a^{4} x^{4} \mathrm{arccosh}\left(a x \right)^{2}-192 \,\mathrm{arccosh}\left(a x \right) x^{8} a^{8}+105 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}-45 \sqrt{a x +1}\, \sqrt{a x -1}\, a x -192 \mathrm{arccosh}\left(a x \right)^{2} x^{8} a^{8}-380 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)^{3}+984 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)^{2}+744 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x +1}\, \sqrt{a x -1}\, x^{5} a^{5}-1020 \mathrm{arccosh}\left(a x \right)^{2} \sqrt{a x +1}\, \sqrt{a x -1}\, x^{3} a^{3}+852 \,\mathrm{arccosh}\left(a x \right) x^{6} a^{6}-1590 a^{4} x^{4} \mathrm{arccosh}\left(a x \right)+1410 a^{2} x^{2} \mathrm{arccosh}\left(a x \right)+372 \,\mathrm{arccosh}\left(a x \right) a x \sqrt{a x -1}\, \sqrt{a x +1}-936 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{3} x^{3}+24 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{7} a^{7}-84 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{5} a^{5}-480 \,\mathrm{arccosh}\left(a x \right)-264 \mathrm{arccosh}\left(a x \right)^{2}+256 \mathrm{arccosh}\left(a x \right)^{3}+756 \,\mathrm{arccosh}\left(a x \right) \sqrt{a x -1}\, \sqrt{a x +1}\, a^{5} x^{5}+495 \mathrm{arccosh}\left(a x \right)^{2} a x \sqrt{a x -1}\, \sqrt{a x +1}+840 \mathrm{arccosh}\left(a x \right)^{2} a^{6} x^{6}+160 \mathrm{arccosh}\left(a x \right)^{3} x^{4} a^{4}\right)}{60 \left(40 a^{10} x^{10}-215 x^{8} a^{8}+469 x^{6} a^{6}-517 x^{4} a^{4}+287 a^{2} x^{2}-64\right) a \,c^{4}}+\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{4} a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}-1\right)}{c^{4} a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{c^{4} a \left(a^{2} x^{2}-1\right)}-\frac{16 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3}}{15 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{8 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1-a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{5 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{16 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{5 c^{4} a \left(a^{2} x^{2}-1\right)}-\frac{16 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{5 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{8 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{5 c^{4} a \left(a^{2} x^{2}-1\right)}+\frac{16 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{5 c^{4} a \left(a^{2} x^{2}-1\right)}-\frac{16 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, -a x -\sqrt{a x -1}\, \sqrt{a x +1}\right)}{5 c^{4} a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/60*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5-20*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+15*a*x+16*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-8*(a*x-1)^(1/2)*(a*x+1)^(1/2))*(24+24*x^8*a^8-96*x^6*a^6+144*x^4*a^4-96*a^2*x^2-192*arccosh(a*x)^2*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^7*a^7-192*(a*x-1)^(1/2)*(a*x+1)^(1/2)*arccosh(a*x)*x^7*a^7-1368*a^4*x^4*arccosh(a*x)^2-192*arccosh(a*x)*x^8*a^8+105*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)-45*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-192*arccosh(a*x)^2*x^8*a^8-380*a^2*x^2*arccosh(a*x)^3+984*a^2*x^2*arccosh(a*x)^2+744*arccosh(a*x)^2*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^5*a^5-1020*arccosh(a*x)^2*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^3*a^3+852*arccosh(a*x)*x^6*a^6-1590*a^4*x^4*arccosh(a*x)+1410*a^2*x^2*arccosh(a*x)+372*arccosh(a*x)*a*x*(a*x-1)^(1/2)*(a*x+1)^(1/2)-936*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^3*x^3+24*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^7*a^7-84*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^5*a^5-480*arccosh(a*x)-264*arccosh(a*x)^2+256*arccosh(a*x)^3+756*arccosh(a*x)*(a*x-1)^(1/2)*(a*x+1)^(1/2)*a^5*x^5+495*arccosh(a*x)^2*a*x*(a*x-1)^(1/2)*(a*x+1)^(1/2)+840*arccosh(a*x)^2*a^6*x^6+160*arccosh(a*x)^3*x^4*a^4)/(40*a^10*x^10-215*a^8*x^8+469*a^6*x^6-517*a^4*x^4+287*a^2*x^2-64)/a/c^4+2*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*ln(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*ln(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2)-1)-(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-16/15*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)^3+8/5*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)^2*ln(1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))+16/5*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)*polylog(2,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))-16/5*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*polylog(3,a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+8/5*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)^2*ln(1+a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))+16/5*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*arccosh(a*x)*polylog(2,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))-16/5*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/c^4/a/(a^2*x^2-1)*polylog(3,-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))","B"
253,1,520,259,0.711000," ","int(x^4*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{4}}{32 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}+8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x -8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(32 \mathrm{arccosh}\left(a x \right)^{3}-24 \mathrm{arccosh}\left(a x \right)^{2}+12 \,\mathrm{arccosh}\left(a x \right)-3\right)}{2048 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}-6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-3\right)}{32 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}+6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+3\right)}{32 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(8 x^{5} a^{5}-12 x^{3} a^{3}-8 \sqrt{a x +1}\, \sqrt{a x -1}\, x^{4} a^{4}+4 a x +8 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(32 \mathrm{arccosh}\left(a x \right)^{3}+24 \mathrm{arccosh}\left(a x \right)^{2}+12 \,\mathrm{arccosh}\left(a x \right)+3\right)}{2048 a^{5} \left(a^{2} x^{2}-1\right)}"," ",0,"-3/32*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*arccosh(a*x)^4-1/2048*(-a^2*x^2+1)^(1/2)*(8*x^5*a^5-12*x^3*a^3+8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x-8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(32*arccosh(a*x)^3-24*arccosh(a*x)^2+12*arccosh(a*x)-3)/a^5/(a^2*x^2-1)-1/32*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3-6*arccosh(a*x)^2+6*arccosh(a*x)-3)/a^5/(a^2*x^2-1)-1/32*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3+6*arccosh(a*x)^2+6*arccosh(a*x)+3)/a^5/(a^2*x^2-1)-1/2048*(-a^2*x^2+1)^(1/2)*(8*x^5*a^5-12*x^3*a^3-8*(a*x+1)^(1/2)*(a*x-1)^(1/2)*x^4*a^4+4*a*x+8*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(32*arccosh(a*x)^3+24*arccosh(a*x)^2+12*arccosh(a*x)+3)/a^5/(a^2*x^2-1)","B"
254,1,375,201,0.491000," ","int(x^3*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 x^{4} a^{4}-5 a^{2} x^{2}+4 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}-3 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +1\right) \left(9 \mathrm{arccosh}\left(a x \right)^{3}-9 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-2\right)}{216 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{a x +1}\, \sqrt{a x -1}\, a x +a^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(a x \right)^{3}-3 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-6\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \left(\mathrm{arccosh}\left(a x \right)^{3}+3 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+6\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 x^{4} a^{4}-5 a^{2} x^{2}-4 a^{3} x^{3} \sqrt{a x -1}\, \sqrt{a x +1}+3 \sqrt{a x +1}\, \sqrt{a x -1}\, a x +1\right) \left(9 \mathrm{arccosh}\left(a x \right)^{3}+9 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+2\right)}{216 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/216*(-a^2*x^2+1)^(1/2)*(4*x^4*a^4-5*a^2*x^2+4*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)-3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+1)*(9*arccosh(a*x)^3-9*arccosh(a*x)^2+6*arccosh(a*x)-2)/a^4/(a^2*x^2-1)-3/8*(-a^2*x^2+1)^(1/2)*((a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+a^2*x^2-1)*(arccosh(a*x)^3-3*arccosh(a*x)^2+6*arccosh(a*x)-6)/a^4/(a^2*x^2-1)-3/8*(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*(arccosh(a*x)^3+3*arccosh(a*x)^2+6*arccosh(a*x)+6)/a^4/(a^2*x^2-1)-1/216*(-a^2*x^2+1)^(1/2)*(4*x^4*a^4-5*a^2*x^2-4*a^3*x^3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+3*(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+1)*(9*arccosh(a*x)^3+9*arccosh(a*x)^2+6*arccosh(a*x)+2)/a^4/(a^2*x^2-1)","A"
255,1,255,154,0.450000," ","int(x^2*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{4}}{8 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x +2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}-\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}-6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-3\right)}{32 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-2 a x -2 a^{2} x^{2} \sqrt{a x -1}\, \sqrt{a x +1}+\sqrt{a x -1}\, \sqrt{a x +1}\right) \left(4 \mathrm{arccosh}\left(a x \right)^{3}+6 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+3\right)}{32 a^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^3/(a^2*x^2-1)*arccosh(a*x)^4-1/32*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x+2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)-(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3-6*arccosh(a*x)^2+6*arccosh(a*x)-3)/a^3/(a^2*x^2-1)-1/32*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3-2*a*x-2*a^2*x^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)+(a*x-1)^(1/2)*(a*x+1)^(1/2))*(4*arccosh(a*x)^3+6*arccosh(a*x)^2+6*arccosh(a*x)+3)/a^3/(a^2*x^2-1)","A"
256,1,155,96,0.197000," ","int(x*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{a x +1}\, \sqrt{a x -1}\, a x +a^{2} x^{2}-1\right) \left(\mathrm{arccosh}\left(a x \right)^{3}-3 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)-6\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \left(\mathrm{arccosh}\left(a x \right)^{3}+3 \mathrm{arccosh}\left(a x \right)^{2}+6 \,\mathrm{arccosh}\left(a x \right)+6\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*((a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x+a^2*x^2-1)*(arccosh(a*x)^3-3*arccosh(a*x)^2+6*arccosh(a*x)-6)/a^2/(a^2*x^2-1)-1/2*(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*(arccosh(a*x)^3+3*arccosh(a*x)^2+6*arccosh(a*x)+6)/a^2/(a^2*x^2-1)","A"
257,1,51,26,0.055000," ","int(arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{4}}{4 a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(-(a*x-1)*(a*x+1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a/(a^2*x^2-1)*arccosh(a*x)^4","A"
258,0,0,316,0.329000," ","int(arccosh(a*x)^3/x/(-a^2*x^2+1)^(1/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)^{3}}{x \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arccosh(a*x)^3/x/(-a^2*x^2+1)^(1/2),x)","F"
259,1,313,185,0.375000," ","int(arccosh(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-\sqrt{a x +1}\, \sqrt{a x -1}\, a x -1\right) \mathrm{arccosh}\left(a x \right)^{3}}{x \left(a^{2} x^{2}-1\right)}-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{3} a}{a^{2} x^{2}-1}+\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right)^{2} \ln \left(1+\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}\right) a}{a^{2} x^{2}-1}+\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \mathrm{arccosh}\left(a x \right) \polylog \left(2, -\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}\right) a}{a^{2} x^{2}-1}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \polylog \left(3, -\left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)^{2}\right) a}{2 \left(a^{2} x^{2}-1\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)*(a^2*x^2-(a*x+1)^(1/2)*(a*x-1)^(1/2)*a*x-1)*arccosh(a*x)^3/x/(a^2*x^2-1)-2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)^3*a+3*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)^2*ln(1+(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2)*a+3*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*arccosh(a*x)*polylog(2,-(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2)*a-3/2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/(a^2*x^2-1)*polylog(3,-(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))^2)*a","A"
260,0,0,520,0.605000," ","int(arccosh(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)^{3}}{x^{3} \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arccosh(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x)","F"
261,0,0,30,0.582000," ","int((f*x)^m*(a+b*arccosh(c*x))^3/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{3}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^3/(-c^2*x^2+1)^(1/2),x)","F"
262,1,44,59,0.147000," ","int((-a^2*c*x^2+c)^3/arccosh(a*x),x)","\frac{c^{3} \left(35 \Shi \left(\mathrm{arccosh}\left(a x \right)\right)-21 \Shi \left(3 \,\mathrm{arccosh}\left(a x \right)\right)+7 \Shi \left(5 \,\mathrm{arccosh}\left(a x \right)\right)-\Shi \left(7 \,\mathrm{arccosh}\left(a x \right)\right)\right)}{64 a}"," ",0,"1/64/a*c^3*(35*Shi(arccosh(a*x))-21*Shi(3*arccosh(a*x))+7*Shi(5*arccosh(a*x))-Shi(7*arccosh(a*x)))","A"
263,1,33,44,0.064000," ","int((-a^2*c*x^2+c)^2/arccosh(a*x),x)","\frac{c^{2} \left(10 \Shi \left(\mathrm{arccosh}\left(a x \right)\right)-5 \Shi \left(3 \,\mathrm{arccosh}\left(a x \right)\right)+\Shi \left(5 \,\mathrm{arccosh}\left(a x \right)\right)\right)}{16 a}"," ",0,"1/16/a*c^2*(10*Shi(arccosh(a*x))-5*Shi(3*arccosh(a*x))+Shi(5*arccosh(a*x)))","A"
264,1,24,25,0.065000," ","int((-a^2*c*x^2+c)/arccosh(a*x),x)","\frac{c \left(3 \Shi \left(\mathrm{arccosh}\left(a x \right)\right)-\Shi \left(3 \,\mathrm{arccosh}\left(a x \right)\right)\right)}{4 a}"," ",0,"1/4/a*c*(3*Shi(arccosh(a*x))-Shi(3*arccosh(a*x)))","A"
265,0,0,22,0.161000," ","int(1/(-a^2*c*x^2+c)/arccosh(a*x),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right) \mathrm{arccosh}\left(a x \right)}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)/arccosh(a*x),x)","F"
266,0,0,22,0.398000," ","int(1/(-a^2*c*x^2+c)^2/arccosh(a*x),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{2} \mathrm{arccosh}\left(a x \right)}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^2/arccosh(a*x),x)","F"
267,1,591,297,0.661000," ","int(x^4*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{64 \left(c x +1\right) c^{5} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-6 a}{b}}}{64 \left(c x +1\right) c^{5} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{5} b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{32 \left(c x +1\right) c^{5} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{64 \left(c x +1\right) c^{5} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{64 \left(c x +1\right) c^{5} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{32 \left(c x +1\right) c^{5} \left(c x -1\right) b}"," ",0,"1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/c^5/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-6*arccosh(c*x)-6*a/b)*exp((b*arccosh(c*x)-6*a)/b)/(c*x+1)/c^5/(c*x-1)/b-1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^5*ln(a+b*arccosh(c*x))/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/c^5/(c*x-1)/b-1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/c^5/(c*x-1)/b-1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp((b*arccosh(c*x)-2*a)/b)/(c*x+1)/c^5/(c*x-1)/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp((b*arccosh(c*x)-4*a)/b)/(c*x+1)/c^5/(c*x-1)/b","A"
268,1,543,261,0.424000," ","int(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{32 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{32 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{32 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-5 a}{b}}}{32 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{16 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{16 \left(c x +1\right) c^{4} \left(c x -1\right) b}"," ",0,"1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp((b*arccosh(c*x)-3*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-5*arccosh(c*x)-5*a/b)*exp((b*arccosh(c*x)-5*a)/b)/(c*x+1)/c^4/(c*x-1)/b-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp((b*arccosh(c*x)-a)/b)/(c*x+1)/c^4/(c*x-1)/b-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^4/(c*x-1)/b","B"
269,1,227,121,0.334000," ","int(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{16 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{16 \left(c x +1\right) c^{3} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b}"," ",0,"1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp((b*arccosh(c*x)-4*a)/b)/(c*x+1)/c^3/(c*x-1)/b-1/8*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*ln(a+b*arccosh(c*x))/b","A"
270,1,361,173,0.198000," ","int(x*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{8 \left(c x +1\right) c^{2} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{8 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{8 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{8 \left(c x +1\right) c^{2} \left(c x -1\right) b}"," ",0,"1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^2/(c*x-1)/b+1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp((b*arccosh(c*x)-3*a)/b)/(c*x+1)/c^2/(c*x-1)/b-1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp((b*arccosh(c*x)-a)/b)/(c*x+1)/c^2/(c*x-1)/b-1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^2/(c*x-1)/b","B"
271,1,227,121,0.184000," ","int((-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{4 \left(c x +1\right) \left(c x -1\right) c b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{4 \left(c x +1\right) \left(c x -1\right) c b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{2 \sqrt{c x -1}\, \sqrt{c x +1}\, c b}"," ",0,"1/4*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c/b+1/4*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp((b*arccosh(c*x)-2*a)/b)/(c*x+1)/(c*x-1)/c/b-1/2*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*ln(a+b*arccosh(c*x))/b","A"
272,0,0,106,0.414000," ","int((-c^2*x^2+1)^(1/2)/x/(a+b*arccosh(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x/(a+b*arccosh(c*x)),x)","F"
273,0,0,59,0.368000," ","int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arccosh(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arccosh(c*x)),x)","F"
274,0,0,28,0.737000," ","int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arccosh(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arccosh(c*x)),x)","F"
275,0,0,28,0.840000," ","int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arccosh(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arccosh(c*x)),x)","F"
276,1,725,349,0.442000," ","int(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 7 \,\mathrm{arccosh}\left(c x \right)+\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+7 a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -7 \,\mathrm{arccosh}\left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-7 a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-5 a}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{128 \left(c x +1\right) c^{4} \left(c x -1\right) b}"," ",0,"-1/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,7*arccosh(c*x)+7*a/b)*exp((b*arccosh(c*x)+7*a)/b)/(c*x+1)/c^4/(c*x-1)/b-1/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-7*arccosh(c*x)-7*a/b)*exp((b*arccosh(c*x)-7*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^4/(c*x-1)/b+3/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^4/(c*x-1)/b-3/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp((b*arccosh(c*x)-a)/b)/(c*x+1)/c^4/(c*x-1)/b+3/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp((b*arccosh(c*x)-3*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-5*arccosh(c*x)-5*a/b)*exp((b*arccosh(c*x)-5*a)/b)/(c*x+1)/c^4/(c*x-1)/b-3/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^4/(c*x-1)/b","B"
277,1,591,297,0.516000," ","int(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-6 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{32 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{32 \left(c x +1\right) c^{3} \left(c x -1\right) b}"," ",0,"-1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/c^3/(c*x-1)/b-1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-6*arccosh(c*x)-6*a/b)*exp((b*arccosh(c*x)-6*a)/b)/(c*x+1)/c^3/(c*x-1)/b-1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*ln(a+b*arccosh(c*x))/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp((b*arccosh(c*x)-2*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp((b*arccosh(c*x)-4*a)/b)/(c*x+1)/c^3/(c*x-1)/b","A"
278,1,543,261,0.231000," ","int(x*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{32 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-5 a}{b}}}{32 \left(c x +1\right) c^{2} \left(c x -1\right) b}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{32 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{16 \left(c x +1\right) c^{2} \left(c x -1\right) b}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{32 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{16 \left(c x +1\right) c^{2} \left(c x -1\right) b}"," ",0,"-1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^2/(c*x-1)/b-1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-5*arccosh(c*x)-5*a/b)*exp((b*arccosh(c*x)-5*a)/b)/(c*x+1)/c^2/(c*x-1)/b+3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^2/(c*x-1)/b-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp((b*arccosh(c*x)-a)/b)/(c*x+1)/c^2/(c*x-1)/b+3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp((b*arccosh(c*x)-3*a)/b)/(c*x+1)/c^2/(c*x-1)/b-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^2/(c*x-1)/b","B"
279,1,409,209,0.208000," ","int((-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{16 \left(c x +1\right) \left(c x -1\right) c b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{16 \left(c x +1\right) \left(c x -1\right) c b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{4 \left(c x +1\right) \left(c x -1\right) c b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{4 \left(c x +1\right) \left(c x -1\right) c b}"," ",0,"-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c/b-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp((b*arccosh(c*x)-4*a)/b)/(c*x+1)/(c*x-1)/c/b-3/8*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*ln(a+b*arccosh(c*x))/b+1/4*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c/b+1/4*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp((b*arccosh(c*x)-2*a)/b)/(c*x+1)/(c*x-1)/c/b","A"
280,0,0,189,0.420000," ","int((-c^2*x^2+1)^(3/2)/x/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x/(a+b*arccosh(c*x)),x)","F"
281,0,0,143,0.469000," ","int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arccosh(c*x)),x)","F"
282,0,0,28,0.705000," ","int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arccosh(c*x)),x)","F"
283,0,0,28,0.832000," ","int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arccosh(c*x)),x)","F"
284,1,725,349,0.450000," ","int(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 9 \,\mathrm{arccosh}\left(c x \right)+\frac{9 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+9 a}{b}}}{512 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -9 \,\mathrm{arccosh}\left(c x \right)-\frac{9 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-9 a}{b}}}{512 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 7 \,\mathrm{arccosh}\left(c x \right)+\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+7 a}{b}}}{512 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{64 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{256 \left(c x +1\right) c^{4} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{64 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -7 \,\mathrm{arccosh}\left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-7 a}{b}}}{512 \left(c x +1\right) c^{4} \left(c x -1\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{256 \left(c x +1\right) c^{4} \left(c x -1\right) b}"," ",0,"1/512*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,9*arccosh(c*x)+9*a/b)*exp((b*arccosh(c*x)+9*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/512*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-9*arccosh(c*x)-9*a/b)*exp((b*arccosh(c*x)-9*a)/b)/(c*x+1)/c^4/(c*x-1)/b-3/512*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,7*arccosh(c*x)+7*a/b)*exp((b*arccosh(c*x)+7*a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^4/(c*x-1)/b-3/256*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp((b*arccosh(c*x)-a)/b)/(c*x+1)/c^4/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp((b*arccosh(c*x)-3*a)/b)/(c*x+1)/c^4/(c*x-1)/b-3/512*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-7*arccosh(c*x)-7*a/b)*exp((b*arccosh(c*x)-7*a)/b)/(c*x+1)/c^4/(c*x-1)/b-3/256*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^4/(c*x-1)/b","B"
285,1,773,385,0.561000," ","int(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 8 \,\mathrm{arccosh}\left(c x \right)+\frac{8 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+8 a}{b}}}{256 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -8 \,\mathrm{arccosh}\left(c x \right)-\frac{8 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-8 a}{b}}}{256 \left(c x +1\right) c^{3} \left(c x -1\right) b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-6 a}{b}}}{64 \left(c x +1\right) c^{3} \left(c x -1\right) b}"," ",0,"1/256*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,8*arccosh(c*x)+8*a/b)*exp((b*arccosh(c*x)+8*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/256*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-8*arccosh(c*x)-8*a/b)*exp((b*arccosh(c*x)-8*a)/b)/(c*x+1)/c^3/(c*x-1)/b-5/128*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*ln(a+b*arccosh(c*x))/b-1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp((b*arccosh(c*x)-2*a)/b)/(c*x+1)/c^3/(c*x-1)/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp((b*arccosh(c*x)-4*a)/b)/(c*x+1)/c^3/(c*x-1)/b-1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-6*arccosh(c*x)-6*a/b)*exp((b*arccosh(c*x)-6*a)/b)/(c*x+1)/c^3/(c*x-1)/b","B"
286,1,725,349,0.259000," ","int(x*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 7 \,\mathrm{arccosh}\left(c x \right)+\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+7 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -7 \,\mathrm{arccosh}\left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-7 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}+\frac{9 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}+\frac{9 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-5 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b}"," ",0,"1/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,7*arccosh(c*x)+7*a/b)*exp((b*arccosh(c*x)+7*a)/b)/(c*x+1)/c^2/(c*x-1)/b+1/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-7*arccosh(c*x)-7*a/b)*exp((b*arccosh(c*x)-7*a)/b)/(c*x+1)/c^2/(c*x-1)/b-5/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^2/(c*x-1)/b+9/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^2/(c*x-1)/b-5/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp((b*arccosh(c*x)-a)/b)/(c*x+1)/c^2/(c*x-1)/b+9/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp((b*arccosh(c*x)-3*a)/b)/(c*x+1)/c^2/(c*x-1)/b-5/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-5*arccosh(c*x)-5*a/b)*exp((b*arccosh(c*x)-5*a)/b)/(c*x+1)/c^2/(c*x-1)/b-5/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^2/(c*x-1)/b","B"
287,1,591,297,0.243000," ","int((-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{64 \left(c x +1\right) \left(c x -1\right) c b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-6 a}{b}}}{64 \left(c x +1\right) \left(c x -1\right) c b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c b}+\frac{15 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{64 \left(c x +1\right) \left(c x -1\right) c b}+\frac{15 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{64 \left(c x +1\right) \left(c x -1\right) c b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c b}"," ",0,"1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/(c*x-1)/c/b+1/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-6*arccosh(c*x)-6*a/b)*exp((b*arccosh(c*x)-6*a)/b)/(c*x+1)/(c*x-1)/c/b-5/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*ln(a+b*arccosh(c*x))/b-3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c/b+15/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c/b+15/64*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp((b*arccosh(c*x)-2*a)/b)/(c*x+1)/(c*x-1)/c/b-3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp((b*arccosh(c*x)-4*a)/b)/(c*x+1)/(c*x-1)/c/b","A"
288,0,0,271,0.457000," ","int((-c^2*x^2+1)^(5/2)/x/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x/(a+b*arccosh(c*x)),x)","F"
289,0,0,226,0.493000," ","int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arccosh(c*x)),x)","F"
290,0,0,28,0.743000," ","int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arccosh(c*x)),x)","F"
291,0,0,28,0.884000," ","int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arccosh(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arccosh(c*x)),x)","F"
292,1,249,80,0.712000," ","int(x^4/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, 4 \,\mathrm{arccosh}\left(a x \right)\right)}{16 a^{5} \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, -4 \,\mathrm{arccosh}\left(a x \right)\right)}{16 a^{5} \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(\mathrm{arccosh}\left(a x \right)\right)}{8 a^{5} \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, 2 \,\mathrm{arccosh}\left(a x \right)\right)}{4 a^{5} \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, -2 \,\mathrm{arccosh}\left(a x \right)\right)}{4 a^{5} \left(a^{2} x^{2}-1\right)}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*Ei(1,4*arccosh(a*x))+1/16*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*Ei(1,-4*arccosh(a*x))-3/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*ln(arccosh(a*x))+1/4*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*Ei(1,2*arccosh(a*x))+1/4*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^5/(a^2*x^2-1)*Ei(1,-2*arccosh(a*x))","B"
293,1,200,53,0.612000," ","int(x^3/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, 3 \,\mathrm{arccosh}\left(a x \right)\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, -3 \,\mathrm{arccosh}\left(a x \right)\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}+\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, \mathrm{arccosh}\left(a x \right)\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}+\frac{3 \sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, -\mathrm{arccosh}\left(a x \right)\right)}{8 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"1/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^4/(a^2*x^2-1)*Ei(1,3*arccosh(a*x))+1/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^4/(a^2*x^2-1)*Ei(1,-3*arccosh(a*x))+3/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^4/(a^2*x^2-1)*Ei(1,arccosh(a*x))+3/8*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^4/(a^2*x^2-1)*Ei(1,-arccosh(a*x))","B"
294,1,149,53,0.470000," ","int(x^2/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, 2 \,\mathrm{arccosh}\left(a x \right)\right)}{4 a^{3} \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, -2 \,\mathrm{arccosh}\left(a x \right)\right)}{4 a^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(\mathrm{arccosh}\left(a x \right)\right)}{2 a^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"1/4*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^3/(a^2*x^2-1)*Ei(1,2*arccosh(a*x))+1/4*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^3/(a^2*x^2-1)*Ei(1,-2*arccosh(a*x))-1/2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^3/(a^2*x^2-1)*ln(arccosh(a*x))","B"
295,1,100,24,0.257000," ","int(x/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, \mathrm{arccosh}\left(a x \right)\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \Ei \left(1, -\mathrm{arccosh}\left(a x \right)\right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^2/(a^2*x^2-1)*Ei(1,arccosh(a*x))+1/2*(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a^2/(a^2*x^2-1)*Ei(1,-arccosh(a*x))","B"
296,1,48,24,0.172000," ","int(1/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{a x -1}\, \sqrt{a x +1}\, \ln \left(\mathrm{arccosh}\left(a x \right)\right)}{a \left(a^{2} x^{2}-1\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a/(a^2*x^2-1)*ln(arccosh(a*x))","A"
297,0,0,24,0.330000," ","int(1/x/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{1}{x \,\mathrm{arccosh}\left(a x \right) \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
298,0,0,24,0.372000," ","int(1/x^2/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \mathrm{arccosh}\left(a x \right) \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
299,1,349,173,0.451000," ","int(x^3/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{8 b \left(c^{2} x^{2}-1\right) c^{4}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{8 b \left(c^{2} x^{2}-1\right) c^{4}}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{-\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{8 b \left(c^{2} x^{2}-1\right) c^{4}}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{8 b \left(c^{2} x^{2}-1\right) c^{4}}"," ",0,"1/8*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp(-(b*arccosh(c*x)-3*a)/b)/b/(c^2*x^2-1)/c^4+1/8*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-(b*arccosh(c*x)+3*a)/b)/b/(c^2*x^2-1)/c^4+3/8*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp(-(a+b*arccosh(c*x))/b)/b/(c^2*x^2-1)/c^4+3/8*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp(-(b*arccosh(c*x)-a)/b)/b/(c^2*x^2-1)/c^4","B"
300,1,232,121,0.570000," ","int(x^2/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{4 b \left(c^{2} x^{2}-1\right) c^{3}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{4 b \left(c^{2} x^{2}-1\right) c^{3}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{2 \left(c^{2} x^{2}-1\right) c^{3} b}"," ",0,"1/4*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp(-(b*arccosh(c*x)-2*a)/b)/b/(c^2*x^2-1)/c^3+1/4*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-(b*arccosh(c*x)+2*a)/b)/b/(c^2*x^2-1)/c^3-1/2*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^3*ln(a+b*arccosh(c*x))/b","A"
301,1,173,84,0.194000," ","int(x/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) {\mathrm e}^{-\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{2 b \left(c^{2} x^{2}-1\right) c^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{2 b \left(c^{2} x^{2}-1\right) c^{2}}"," ",0,"1/2*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,-arccosh(c*x)-a/b)*exp(-(a+b*arccosh(c*x))/b)/b/(c^2*x^2-1)/c^2+1/2*(-c^2*x^2+1)^(1/2)*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp(-(b*arccosh(c*x)-a)/b)/b/(c^2*x^2-1)/c^2","B"
302,1,55,31,0.177000," ","int(1/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{c \left(c^{2} x^{2}-1\right) b}"," ",0,"-(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/(c^2*x^2-1)*ln(a+b*arccosh(c*x))/b","A"
303,0,0,28,0.377000," ","int(1/x/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
304,0,0,28,0.435000," ","int(1/x^2/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
305,0,0,28,0.553000," ","int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
306,0,0,26,0.279000," ","int(x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
307,0,0,25,0.247000," ","int(1/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
308,0,0,28,0.496000," ","int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
309,0,0,28,0.407000," ","int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
310,0,0,28,1.169000," ","int(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{x^{m} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
311,0,0,28,1.186000," ","int(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\int \frac{x^{m} \sqrt{-c^{2} x^{2}+1}}{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","F"
312,0,0,28,0.500000," ","int(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","\int \frac{x^{m}}{\sqrt{-c^{2} x^{2}+1}\, \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x)","F"
313,0,0,28,0.706000," ","int(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{x^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x)","F"
314,0,0,28,0.670000," ","int(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x)","\int \frac{x^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x)","F"
315,1,107,86,0.250000," ","int((-a^2*c*x^2+c)^3/arccosh(a*x)^2,x)","\frac{c^{3} \left(35 \Chi \left(\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-63 \Chi \left(3 \,\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)+35 \Chi \left(5 \,\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-7 \Chi \left(7 \,\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-35 \sqrt{a x -1}\, \sqrt{a x +1}+21 \sinh \left(3 \,\mathrm{arccosh}\left(a x \right)\right)-7 \sinh \left(5 \,\mathrm{arccosh}\left(a x \right)\right)+\sinh \left(7 \,\mathrm{arccosh}\left(a x \right)\right)\right)}{64 a \,\mathrm{arccosh}\left(a x \right)}"," ",0,"1/64/a*c^3*(35*Chi(arccosh(a*x))*arccosh(a*x)-63*Chi(3*arccosh(a*x))*arccosh(a*x)+35*Chi(5*arccosh(a*x))*arccosh(a*x)-7*Chi(7*arccosh(a*x))*arccosh(a*x)-35*(a*x-1)^(1/2)*(a*x+1)^(1/2)+21*sinh(3*arccosh(a*x))-7*sinh(5*arccosh(a*x))+sinh(7*arccosh(a*x)))/arccosh(a*x)","A"
316,1,87,72,0.135000," ","int((-a^2*c*x^2+c)^2/arccosh(a*x)^2,x)","\frac{c^{2} \left(10 \Chi \left(\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-15 \Chi \left(3 \,\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)+5 \Chi \left(5 \,\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-10 \sqrt{a x -1}\, \sqrt{a x +1}+5 \sinh \left(3 \,\mathrm{arccosh}\left(a x \right)\right)-\sinh \left(5 \,\mathrm{arccosh}\left(a x \right)\right)\right)}{16 a \,\mathrm{arccosh}\left(a x \right)}"," ",0,"1/16/a*c^2*(10*Chi(arccosh(a*x))*arccosh(a*x)-15*Chi(3*arccosh(a*x))*arccosh(a*x)+5*Chi(5*arccosh(a*x))*arccosh(a*x)-10*(a*x-1)^(1/2)*(a*x+1)^(1/2)+5*sinh(3*arccosh(a*x))-sinh(5*arccosh(a*x)))/arccosh(a*x)","A"
317,1,63,50,0.115000," ","int((-a^2*c*x^2+c)/arccosh(a*x)^2,x)","-\frac{c \left(3 \sqrt{a x -1}\, \sqrt{a x +1}+3 \Chi \left(3 \,\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-3 \Chi \left(\mathrm{arccosh}\left(a x \right)\right) \mathrm{arccosh}\left(a x \right)-\sinh \left(3 \,\mathrm{arccosh}\left(a x \right)\right)\right)}{4 a \,\mathrm{arccosh}\left(a x \right)}"," ",0,"-1/4/a*c*(3*(a*x-1)^(1/2)*(a*x+1)^(1/2)+3*Chi(3*arccosh(a*x))*arccosh(a*x)-3*Chi(arccosh(a*x))*arccosh(a*x)-sinh(3*arccosh(a*x)))/arccosh(a*x)","A"
318,0,0,57,0.158000," ","int(1/(-a^2*c*x^2+c)/arccosh(a*x)^2,x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right) \mathrm{arccosh}\left(a x \right)^{2}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)/arccosh(a*x)^2,x)","F"
319,0,0,59,0.356000," ","int(1/(-a^2*c*x^2+c)^2/arccosh(a*x)^2,x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{2} \mathrm{arccosh}\left(a x \right)^{2}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^2/arccosh(a*x)^2,x)","F"
320,1,1029,308,0.735000," ","int(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right)}{32 \left(c x +1\right) c^{4} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{32 \left(c x +1\right) c^{4} \left(c x -1\right) b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right)}{32 \left(c x +1\right) c^{4} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{32 \left(c x +1\right) c^{4} \left(c x -1\right) b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+4 x^{3} b \,c^{3}+3 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} b +3 \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -3 x b c \right)}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{4} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} b \,c^{4}+16 x^{5} b \,c^{5}-12 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}-20 x^{3} b \,c^{3}+5 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) a +5 x b c \right)}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{4} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{4} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{16 \left(c x +1\right) c^{4} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{16 \left(c x +1\right) c^{4} \left(c x -1\right) b^{2}}"," ",0,"1/32*(-c^2*x^2+1)^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)/(c*x+1)/c^4/(c*x-1)/(a+b*arccosh(c*x))/b-5/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^4/(c*x-1)/b^2+1/32*(-c^2*x^2+1)^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)/(c*x+1)/c^4/(c*x-1)/(a+b*arccosh(c*x))/b-3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^4/(c*x-1)/b^2-1/32*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+4*x^3*b*c^3+3*arccosh(c*x)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*b+3*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-3*x*b*c)/c^4/b^2/(a+b*arccosh(c*x))-1/32*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*b*c^4+16*x^5*b*c^5-12*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2-20*x^3*b*c^3+5*arccosh(c*x)*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+5*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*a+5*x*b*c)/c^4/b^2/(a+b*arccosh(c*x))+1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/c^4/b^2/(a+b*arccosh(c*x))-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/(c*x+1)/c^4/(c*x-1)/(a+b*arccosh(c*x))/b+1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^4/(c*x-1)/b^2","B"
321,1,422,136,0.567000," ","int(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+8 c^{5} x^{5}+8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-12 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+4 c x \right)}{16 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{4 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(8 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+8 x^{4} b \,c^{4}-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -8 x^{2} b \,c^{2}+4 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"1/16*(-c^2*x^2+1)^(1/2)*(-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+8*c^5*x^5+8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-12*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))-1/4*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2-1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+8*x^4*b*c^4-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-8*x^2*b*c^2+4*arccosh(c*x)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/c^3/b^2/(a+b*arccosh(c*x))+1/8*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3/b/(a+b*arccosh(c*x))","B"
322,1,622,218,0.319000," ","int(x*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{8 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+4 x^{3} b \,c^{3}+3 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} b +3 \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -3 x b c \right)}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{8 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{8 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}"," ",0,"1/8*(-c^2*x^2+1)^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b-3/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^2/(c*x-1)/b^2-1/8*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+4*x^3*b*c^3+3*arccosh(c*x)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*b+3*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-3*x*b*c)/c^2/b^2/(a+b*arccosh(c*x))+1/8*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/c^2/b^2/(a+b*arccosh(c*x))-1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b+1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^2/(c*x-1)/b^2","B"
323,1,361,132,0.296000," ","int((-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{4 \left(c x +1\right) \left(c x -1\right) c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{2 \left(c x +1\right) \left(c x -1\right) c \,b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, c \,b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}}{2 \sqrt{c x -1}\, \sqrt{c x +1}\, c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"1/4*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c*x+1)/(c*x-1)/c/b/(a+b*arccosh(c*x))-1/2*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c/b^2-1/4*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/c/b^2/(a+b*arccosh(c*x))+1/2*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c/b/(a+b*arccosh(c*x))","B"
324,0,0,163,0.563000," ","int((-c^2*x^2+1)^(1/2)/x/(a+b*arccosh(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x/(a+b*arccosh(c*x))^2,x)","F"
325,0,0,87,0.356000," ","int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arccosh(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arccosh(c*x))^2,x)","F"
326,0,0,28,0.693000," ","int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arccosh(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arccosh(c*x))^2,x)","F"
327,0,0,28,0.859000," ","int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arccosh(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arccosh(c*x))^2,x)","F"
328,1,1176,312,0.751000," ","int(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-32 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{6} c^{6}+32 c^{7} x^{7}+48 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}-64 c^{5} x^{5}-18 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+38 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-6 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(32 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} b \,c^{5}+32 x^{6} b \,c^{6}-32 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}-48 x^{4} b \,c^{4}+6 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +18 x^{2} b \,c^{2}+6 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) b +6 \,{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) a -b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+8 c^{5} x^{5}+8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-12 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+4 c x \right)}{32 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{8 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(8 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+8 x^{4} b \,c^{4}-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -8 x^{2} b \,c^{2}+4 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"-1/64*(-c^2*x^2+1)^(1/2)*(-32*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6*c^6+32*c^7*x^7+48*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4-64*c^5*x^5-18*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+38*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-6*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))+3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2+1/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(32*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*b*c^5+32*x^6*b*c^6-32*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3-48*x^4*b*c^4+6*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+18*x^2*b*c^2+6*arccosh(c*x)*exp(-6*a/b)*Ei(1,-6*arccosh(c*x)-6*a/b)*b+6*exp(-6*a/b)*Ei(1,-6*arccosh(c*x)-6*a/b)*a-b)/c^3/b^2/(a+b*arccosh(c*x))+1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3/b/(a+b*arccosh(c*x))+1/32*(-c^2*x^2+1)^(1/2)*(-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+8*c^5*x^5+8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-12*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))-1/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2+1/64*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))-1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2-1/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/c^3/b^2/(a+b*arccosh(c*x))-1/32*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+8*x^4*b*c^4-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-8*x^2*b*c^2+4*arccosh(c*x)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/c^3/b^2/(a+b*arccosh(c*x))","B"
329,1,1029,306,0.408000," ","int(x*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right)}{32 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}+\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{32 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} b \,c^{4}+16 x^{5} b \,c^{5}-12 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}-20 x^{3} b \,c^{3}+5 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) a +5 x b c \right)}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right)}{32 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{9 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{32 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+4 x^{3} b \,c^{3}+3 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} b +3 \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -3 x b c \right)}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{16 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{16 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}"," ",0,"-1/32*(-c^2*x^2+1)^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b+5/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^2/(c*x-1)/b^2+1/32*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*b*c^4+16*x^5*b*c^5-12*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2-20*x^3*b*c^3+5*arccosh(c*x)*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+5*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*a+5*x*b*c)/c^2/b^2/(a+b*arccosh(c*x))+3/32*(-c^2*x^2+1)^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b-9/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^2/(c*x-1)/b^2+1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/c^2/b^2/(a+b*arccosh(c*x))-3/32*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+4*x^3*b*c^3+3*arccosh(c*x)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*b+3*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-3*x*b*c)/c^2/b^2/(a+b*arccosh(c*x))-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b+1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^2/(c*x-1)/b^2","B"
330,1,737,220,0.336000," ","int((-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+8 c^{5} x^{5}+8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-12 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+4 c x \right)}{16 \left(c x +1\right) \left(c x -1\right) c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{4 \left(c x +1\right) \left(c x -1\right) c \,b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(8 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+8 x^{4} b \,c^{4}-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -8 x^{2} b \,c^{2}+4 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c \,b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{4 \left(c x +1\right) \left(c x -1\right) c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{2 \left(c x +1\right) \left(c x -1\right) c \,b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, c \,b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"-1/16*(-c^2*x^2+1)^(1/2)*(-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+8*c^5*x^5+8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-12*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c*x)/(c*x+1)/(c*x-1)/c/b/(a+b*arccosh(c*x))+1/4*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c/b^2+1/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+8*x^4*b*c^4-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-8*x^2*b*c^2+4*arccosh(c*x)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/c/b^2/(a+b*arccosh(c*x))+3/8*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c/b/(a+b*arccosh(c*x))+1/4*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c*x+1)/(c*x-1)/c/b/(a+b*arccosh(c*x))-1/2*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c/b^2-1/4*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/c/b^2/(a+b*arccosh(c*x))","B"
331,0,0,256,0.647000," ","int((-c^2*x^2+1)^(3/2)/x/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x/(a+b*arccosh(c*x))^2,x)","F"
332,0,0,142,0.696000," ","int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arccosh(c*x))^2,x)","F"
333,0,0,28,1.043000," ","int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arccosh(c*x))^2,x)","F"
334,0,0,96,0.826000," ","int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arccosh(c*x))^2,x)","F"
335,1,1676,400,0.867000," ","int(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-128 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{8} c^{8}+128 x^{9} c^{9}+256 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{6} c^{6}-320 c^{7} x^{7}-160 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+272 c^{5} x^{5}+32 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-88 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+8 c x \right)}{256 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 8 \,\mathrm{arccosh}\left(c x \right)+\frac{8 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+8 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(128 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{7} b \,c^{7}+128 x^{8} b \,c^{8}-192 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} b \,c^{5}-256 x^{6} b \,c^{6}+80 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+160 x^{4} b \,c^{4}-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -32 x^{2} b \,c^{2}+8 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -8 \,\mathrm{arccosh}\left(c x \right)-\frac{8 a}{b}\right) {\mathrm e}^{-\frac{8 a}{b}} b +8 \Ei \left(1, -8 \,\mathrm{arccosh}\left(c x \right)-\frac{8 a}{b}\right) {\mathrm e}^{-\frac{8 a}{b}} a +b \right)}{256 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{5 \sqrt{-c^{2} x^{2}+1}}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-32 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{6} c^{6}+32 c^{7} x^{7}+48 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}-64 c^{5} x^{5}-18 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+38 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-6 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+8 c^{5} x^{5}+8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-12 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+4 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{16 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c^{3} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c^{3} b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(8 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+8 x^{4} b \,c^{4}-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -8 x^{2} b \,c^{2}+4 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \left(32 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} b \,c^{5}+32 x^{6} b \,c^{6}-32 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}-48 x^{4} b \,c^{4}+6 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +18 x^{2} b \,c^{2}+6 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) b +6 \,{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) a -b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"1/256*(-c^2*x^2+1)^(1/2)*(-128*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^8*c^8+128*x^9*c^9+256*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6*c^6-320*c^7*x^7-160*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+272*c^5*x^5+32*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-88*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+8*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))-1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,8*arccosh(c*x)+8*a/b)*exp((b*arccosh(c*x)+8*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2-1/256*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(128*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^7*b*c^7+128*x^8*b*c^8-192*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*b*c^5-256*x^6*b*c^6+80*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+160*x^4*b*c^4-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-32*x^2*b*c^2+8*arccosh(c*x)*Ei(1,-8*arccosh(c*x)-8*a/b)*exp(-8*a/b)*b+8*Ei(1,-8*arccosh(c*x)-8*a/b)*exp(-8*a/b)*a+b)/c^3/b^2/(a+b*arccosh(c*x))+5/128*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3/b/(a+b*arccosh(c*x))-1/64*(-c^2*x^2+1)^(1/2)*(-32*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6*c^6+32*c^7*x^7+48*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4-64*c^5*x^5-18*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+38*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-6*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))+3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2+1/64*(-c^2*x^2+1)^(1/2)*(-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+8*c^5*x^5+8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-12*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))-1/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2+1/64*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c*x+1)/(c*x-1)/c^3/b/(a+b*arccosh(c*x))-1/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c^3/b^2-1/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/c^3/b^2/(a+b*arccosh(c*x))-1/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+8*x^4*b*c^4-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-8*x^2*b*c^2+4*arccosh(c*x)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/c^3/b^2/(a+b*arccosh(c*x))+1/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(32*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*b*c^5+32*x^6*b*c^6-32*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3-48*x^4*b*c^4+6*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+18*x^2*b*c^2+6*arccosh(c*x)*exp(-6*a/b)*Ei(1,-6*arccosh(c*x)-6*a/b)*b+6*exp(-6*a/b)*Ei(1,-6*arccosh(c*x)-6*a/b)*a-b)/c^3/b^2/(a+b*arccosh(c*x))","B"
336,1,1499,394,0.562000," ","int(x*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{7} c^{7}+64 c^{8} x^{8}+112 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}-144 c^{6} x^{6}-56 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+104 c^{4} x^{4}+7 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -25 c^{2} x^{2}+1\right)}{128 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{7 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 7 \,\mathrm{arccosh}\left(c x \right)+\frac{7 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+7 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(64 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{6} b \,c^{6}+64 x^{7} b \,c^{7}-80 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} b \,c^{4}-112 x^{5} b \,c^{5}+24 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+56 x^{3} b \,c^{3}+7 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -7 \,\mathrm{arccosh}\left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} b +7 \Ei \left(1, -7 \,\mathrm{arccosh}\left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -7 x b c \right)}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right)}{128 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}+\frac{25 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+5 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}+\frac{9 \sqrt{-c^{2} x^{2}+1}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right)}{128 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{27 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+3 a}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}+\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{9 \sqrt{-c^{2} x^{2}+1}\, \left(4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+4 x^{3} b \,c^{3}+3 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} b +3 \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -3 x b c \right)}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} b \,c^{4}+16 x^{5} b \,c^{5}-12 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}-20 x^{3} b \,c^{3}+5 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) a +5 x b c \right)}{128 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{128 \left(c x +1\right) c^{2} \left(c x -1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}+\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{\frac{a +b \,\mathrm{arccosh}\left(c x \right)}{b}}}{128 \left(c x +1\right) c^{2} \left(c x -1\right) b^{2}}"," ",0,"1/128*(-c^2*x^2+1)^(1/2)*(-64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^7*c^7+64*c^8*x^8+112*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5-144*c^6*x^6-56*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+104*c^4*x^4+7*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-25*c^2*x^2+1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b-7/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,7*arccosh(c*x)+7*a/b)*exp((b*arccosh(c*x)+7*a)/b)/(c*x+1)/c^2/(c*x-1)/b^2-1/128*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(64*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6*b*c^6+64*x^7*b*c^7-80*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*b*c^4-112*x^5*b*c^5+24*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+56*x^3*b*c^3+7*arccosh(c*x)*Ei(1,-7*arccosh(c*x)-7*a/b)*exp(-7*a/b)*b+7*Ei(1,-7*arccosh(c*x)-7*a/b)*exp(-7*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-7*x*b*c)/c^2/b^2/(a+b*arccosh(c*x))-5/128*(-c^2*x^2+1)^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b+25/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,5*arccosh(c*x)+5*a/b)*exp((b*arccosh(c*x)+5*a)/b)/(c*x+1)/c^2/(c*x-1)/b^2+9/128*(-c^2*x^2+1)^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b-27/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,3*arccosh(c*x)+3*a/b)*exp((b*arccosh(c*x)+3*a)/b)/(c*x+1)/c^2/(c*x-1)/b^2+5/128*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/c^2/b^2/(a+b*arccosh(c*x))-9/128*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+4*x^3*b*c^3+3*arccosh(c*x)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*b+3*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-3*x*b*c)/c^2/b^2/(a+b*arccosh(c*x))+5/128*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*b*c^4+16*x^5*b*c^5-12*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2-20*x^3*b*c^3+5*arccosh(c*x)*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+5*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*a+5*x*b*c)/c^2/b^2/(a+b*arccosh(c*x))-5/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/(c*x+1)/c^2/(c*x-1)/(a+b*arccosh(c*x))/b+5/128*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,arccosh(c*x)+a/b)*exp((a+b*arccosh(c*x))/b)/(c*x+1)/c^2/(c*x-1)/b^2","B"
337,1,1176,309,0.432000," ","int((-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-32 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{6} c^{6}+32 c^{7} x^{7}+48 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}-64 c^{5} x^{5}-18 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+38 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-6 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 6 \,\mathrm{arccosh}\left(c x \right)+\frac{6 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+6 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c \,b^{2}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(32 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} b \,c^{5}+32 x^{6} b \,c^{6}-32 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}-48 x^{4} b \,c^{4}+6 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +18 x^{2} b \,c^{2}+6 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) b +6 \,{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \,\mathrm{arccosh}\left(c x \right)-\frac{6 a}{b}\right) a -b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c \,b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{5 \sqrt{-c^{2} x^{2}+1}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+8 c^{5} x^{5}+8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-12 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+4 c x \right)}{32 \left(c x +1\right) \left(c x -1\right) c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+4 a}{b}}}{8 \left(c x +1\right) \left(c x -1\right) c \,b^{2}}+\frac{15 \sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{64 \left(c x +1\right) \left(c x -1\right) c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{15 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{\frac{b \,\mathrm{arccosh}\left(c x \right)+2 a}{b}}}{32 \left(c x +1\right) \left(c x -1\right) c \,b^{2}}-\frac{15 \sqrt{-c^{2} x^{2}+1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{64 \sqrt{c x -1}\, \sqrt{c x +1}\, c \,b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(8 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+8 x^{4} b \,c^{4}-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -8 x^{2} b \,c^{2}+4 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c \,b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"1/64*(-c^2*x^2+1)^(1/2)*(-32*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^6*c^6+32*c^7*x^7+48*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4-64*c^5*x^5-18*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+38*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-6*c*x)/(c*x+1)/(c*x-1)/c/b/(a+b*arccosh(c*x))-3/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,6*arccosh(c*x)+6*a/b)*exp((b*arccosh(c*x)+6*a)/b)/(c*x+1)/(c*x-1)/c/b^2-1/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(32*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*b*c^5+32*x^6*b*c^6-32*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3-48*x^4*b*c^4+6*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+18*x^2*b*c^2+6*arccosh(c*x)*exp(-6*a/b)*Ei(1,-6*arccosh(c*x)-6*a/b)*b+6*exp(-6*a/b)*Ei(1,-6*arccosh(c*x)-6*a/b)*a-b)/c/b^2/(a+b*arccosh(c*x))+5/16*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c/b/(a+b*arccosh(c*x))-3/32*(-c^2*x^2+1)^(1/2)*(-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+8*c^5*x^5+8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-12*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c*x)/(c*x+1)/(c*x-1)/c/b/(a+b*arccosh(c*x))+3/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,4*arccosh(c*x)+4*a/b)*exp((b*arccosh(c*x)+4*a)/b)/(c*x+1)/(c*x-1)/c/b^2+15/64*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c*x+1)/(c*x-1)/c/b/(a+b*arccosh(c*x))-15/32*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*Ei(1,2*arccosh(c*x)+2*a/b)*exp((b*arccosh(c*x)+2*a)/b)/(c*x+1)/(c*x-1)/c/b^2-15/64*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/c/b^2/(a+b*arccosh(c*x))+3/32*(-c^2*x^2+1)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*(8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+8*x^4*b*c^4-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-8*x^2*b*c^2+4*arccosh(c*x)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/c/b^2/(a+b*arccosh(c*x))","B"
338,0,0,339,0.738000," ","int((-c^2*x^2+1)^(5/2)/x/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x/(a+b*arccosh(c*x))^2,x)","F"
339,0,0,146,0.795000," ","int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arccosh(c*x))^2,x)","F"
340,0,0,28,1.080000," ","int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arccosh(c*x))^2,x)","F"
341,0,0,28,1.249000," ","int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arccosh(c*x))^2,x)","F"
342,1,1046,297,0.838000," ","int(x^5/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{5} c^{5}+16 c^{6} x^{6}+20 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}-28 c^{4} x^{4}-5 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +13 c^{2} x^{2}-1\right)}{32 \left(c^{2} x^{2}-1\right) c^{6} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-5 a}{b}}}{32 b^{2} \left(c^{2} x^{2}-1\right) c^{6}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} b \,c^{4}+16 x^{5} b \,c^{5}-12 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}-20 x^{3} b \,c^{3}+5 \,\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right) a +5 x b c \right)}{32 \left(c^{2} x^{2}-1\right) c^{6} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right)}{32 \left(c^{2} x^{2}-1\right) c^{6} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{15 \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{32 b^{2} \left(c^{2} x^{2}-1\right) c^{6}}+\frac{5 \sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{16 \left(c^{2} x^{2}-1\right) c^{6} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{5 \sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+4 x^{3} b \,c^{3}+3 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} b +3 \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -3 x b c \right)}{32 \left(c^{2} x^{2}-1\right) c^{6} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{16 \left(c^{2} x^{2}-1\right) c^{6} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{16 b^{2} \left(c^{2} x^{2}-1\right) c^{6}}"," ",0,"-1/32*(-c^2*x^2+1)^(1/2)*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^5*c^5+16*c^6*x^6+20*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3-28*c^4*x^4-5*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+13*c^2*x^2-1)/(c^2*x^2-1)/c^6/b/(a+b*arccosh(c*x))-5/32*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,5*arccosh(c*x)+5*a/b)*exp(-(b*arccosh(c*x)-5*a)/b)/b^2/(c^2*x^2-1)/c^6+1/32*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^6*(16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*b*c^4+16*x^5*b*c^5-12*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2-20*x^3*b*c^3+5*arccosh(c*x)*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+5*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)*a+5*x*b*c)/b^2/(a+b*arccosh(c*x))-5/32*(-c^2*x^2+1)^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)/(c^2*x^2-1)/c^6/b/(a+b*arccosh(c*x))-15/32*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,3*arccosh(c*x)+3*a/b)*exp(-(b*arccosh(c*x)-3*a)/b)/b^2/(c^2*x^2-1)/c^6+5/16*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^6*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/b^2/(a+b*arccosh(c*x))+5/32*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^6*(4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+4*x^3*b*c^3+3*arccosh(c*x)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*b+3*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-3*x*b*c)/b^2/(a+b*arccosh(c*x))-5/16*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/(c^2*x^2-1)/c^6/b/(a+b*arccosh(c*x))-5/16*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,arccosh(c*x)+a/b)*exp(-(b*arccosh(c*x)-a)/b)/b^2/(c^2*x^2-1)/c^6","B"
343,1,758,212,0.874000," ","int(x^4/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+8 c^{5} x^{5}+8 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-12 c^{3} x^{3}-\sqrt{c x -1}\, \sqrt{c x +1}+4 c x \right)}{16 \left(c^{2} x^{2}-1\right) c^{5} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{\left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-4 a}{b}}}{4 b^{2} \left(c^{2} x^{2}-1\right) c^{5}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(8 \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} b \,c^{3}+8 x^{4} b \,c^{4}-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c -8 x^{2} b \,c^{2}+4 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{16 \left(c^{2} x^{2}-1\right) c^{5} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}}{8 \left(c^{2} x^{2}-1\right) c^{5} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{4 \left(c^{2} x^{2}-1\right) c^{5} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{\left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{2 b^{2} \left(c^{2} x^{2}-1\right) c^{5}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{4 \left(c^{2} x^{2}-1\right) c^{5} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}"," ",0,"-1/16*(-c^2*x^2+1)^(1/2)*(-8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+8*c^5*x^5+8*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-12*c^3*x^3-(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c*x)/(c^2*x^2-1)/c^5/(a+b*arccosh(c*x))/b-1/4*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,4*arccosh(c*x)+4*a/b)*exp(-(b*arccosh(c*x)-4*a)/b)/b^2/(c^2*x^2-1)/c^5+1/16*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^5*(8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*b*c^3+8*x^4*b*c^4-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c-8*x^2*b*c^2+4*arccosh(c*x)*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arccosh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/b^2/(a+b*arccosh(c*x))+3/8*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^5/(a+b*arccosh(c*x))/b-1/4*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c^2*x^2-1)/c^5/(a+b*arccosh(c*x))/b-1/2*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,2*arccosh(c*x)+2*a/b)*exp(-(b*arccosh(c*x)-2*a)/b)/b^2/(c^2*x^2-1)/c^5+1/4*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^5*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/b^2/(a+b*arccosh(c*x))","B"
344,1,634,209,0.651000," ","int(x^3/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3} c^{3}+4 c^{4} x^{4}+3 \sqrt{c x +1}\, \sqrt{c x -1}\, x c -5 c^{2} x^{2}+1\right)}{8 \left(c^{2} x^{2}-1\right) c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-3 a}{b}}}{8 b^{2} \left(c^{2} x^{2}-1\right) c^{4}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} b \,c^{2}+4 x^{3} b \,c^{3}+3 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} b +3 \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) {\mathrm e}^{-\frac{3 a}{b}} a -\sqrt{c x +1}\, \sqrt{c x -1}\, b -3 x b c \right)}{8 \left(c^{2} x^{2}-1\right) c^{4} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{8 \left(c^{2} x^{2}-1\right) c^{4} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 \sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{8 \left(c^{2} x^{2}-1\right) c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 \left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{8 b^{2} \left(c^{2} x^{2}-1\right) c^{4}}"," ",0,"-1/8*(-c^2*x^2+1)^(1/2)*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3*c^3+4*c^4*x^4+3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c-5*c^2*x^2+1)/(c^2*x^2-1)/c^4/b/(a+b*arccosh(c*x))-3/8*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,3*arccosh(c*x)+3*a/b)*exp(-(b*arccosh(c*x)-3*a)/b)/b^2/(c^2*x^2-1)/c^4+1/8*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^4*(4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*b*c^2+4*x^3*b*c^3+3*arccosh(c*x)*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*b+3*Ei(1,-3*arccosh(c*x)-3*a/b)*exp(-3*a/b)*a-(c*x+1)^(1/2)*(c*x-1)^(1/2)*b-3*x*b*c)/b^2/(a+b*arccosh(c*x))+3/8*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^4*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/b^2/(a+b*arccosh(c*x))-3/8*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/(c^2*x^2-1)/c^4/b/(a+b*arccosh(c*x))-3/8*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,arccosh(c*x)+a/b)*exp(-(b*arccosh(c*x)-a)/b)/b^2/(c^2*x^2-1)/c^4","B"
345,1,377,124,0.538000," ","int(x^2/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+2 c^{3} x^{3}+\sqrt{c x -1}\, \sqrt{c x +1}-2 c x \right)}{4 \left(c^{2} x^{2}-1\right) c^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{\left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-2 a}{b}}}{2 b^{2} \left(c^{2} x^{2}-1\right) c^{3}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(2 \sqrt{c x +1}\, \sqrt{c x -1}\, x b c +2 x^{2} b \,c^{2}+2 \,\mathrm{arccosh}\left(c x \right) \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} b +2 \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) {\mathrm e}^{-\frac{2 a}{b}} a -b \right)}{4 \left(c^{2} x^{2}-1\right) c^{3} b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}}{2 \left(c^{2} x^{2}-1\right) c^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}"," ",0,"-1/4*(-c^2*x^2+1)^(1/2)*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+2*c^3*x^3+(c*x-1)^(1/2)*(c*x+1)^(1/2)-2*c*x)/(c^2*x^2-1)/c^3/(a+b*arccosh(c*x))/b-1/2*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,2*arccosh(c*x)+2*a/b)*exp(-(b*arccosh(c*x)-2*a)/b)/b^2/(c^2*x^2-1)/c^3+1/4*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^3*(2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*b*c+2*x^2*b*c^2+2*arccosh(c*x)*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*b+2*Ei(1,-2*arccosh(c*x)-2*a/b)*exp(-2*a/b)*a-b)/b^2/(a+b*arccosh(c*x))+1/2*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)/c^3/(a+b*arccosh(c*x))/b","B"
346,1,283,118,0.280000," ","int(x/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \left(\mathrm{arccosh}\left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) b +\sqrt{c x +1}\, \sqrt{c x -1}\, b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) a +x b c \right)}{2 c^{2} \left(c^{2} x^{2}-1\right) b^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\sqrt{-c^{2} x^{2}+1}\, \left(-\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right)}{2 c^{2} \left(c^{2} x^{2}-1\right) b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\left(\sqrt{c x +1}\, \sqrt{c x -1}\, x c +c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}\, \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) {\mathrm e}^{-\frac{b \,\mathrm{arccosh}\left(c x \right)-a}{b}}}{2 b^{2} c^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"1/2*(-c^2*x^2+1)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^2/(c^2*x^2-1)*(arccosh(c*x)*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*b+(c*x+1)^(1/2)*(c*x-1)^(1/2)*b+exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*a+x*b*c)/b^2/(a+b*arccosh(c*x))-1/2*(-c^2*x^2+1)^(1/2)*(-(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)/c^2/(c^2*x^2-1)/b/(a+b*arccosh(c*x))-1/2*((c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*Ei(1,arccosh(c*x)+a/b)*exp(-(b*arccosh(c*x)-a)/b)/b^2/c^2/(c^2*x^2-1)","B"
347,1,57,33,0.058000," ","int(1/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(c x -1\right) \left(c x +1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}}{c \left(c^{2} x^{2}-1\right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}"," ",0,"(-(c*x-1)*(c*x+1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/(c^2*x^2-1)/(a+b*arccosh(c*x))/b","A"
348,0,0,76,0.375000," ","int(1/x/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","F"
349,0,0,76,0.388000," ","int(1/x^2/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x)","F"
350,0,0,28,0.896000," ","int(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x^{3}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
351,0,0,96,0.589000," ","int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
352,0,0,26,0.287000," ","int(x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
353,0,0,91,0.265000," ","int(1/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
354,0,0,28,0.622000," ","int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
355,0,0,28,0.438000," ","int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
356,0,0,98,0.897000," ","int(x^4/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x^{4}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^4/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
357,0,0,28,0.868000," ","int(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x^{3}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
358,0,0,28,0.894000," ","int(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
359,0,0,26,0.540000," ","int(x/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
360,0,0,91,0.436000," ","int(1/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
361,0,0,28,0.988000," ","int(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
362,0,0,28,1.124000," ","int(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
363,0,0,30,1.327000," ","int((f*x)^m*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(f x \right)^{m} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((f*x)^m*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
364,0,0,30,1.263000," ","int((f*x)^m*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(f x \right)^{m} \sqrt{-c^{2} x^{2}+1}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((f*x)^m*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","F"
365,0,0,83,0.532000," ","int((f*x)^m/(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(f x \right)^{m}}{\sqrt{-c^{2} x^{2}+1}\, \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((f*x)^m/(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x)","F"
366,0,0,30,0.744000," ","int((f*x)^m/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(f x \right)^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((f*x)^m/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
367,0,0,30,0.764000," ","int((f*x)^m/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(f x \right)^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((f*x)^m/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
368,1,51,26,0.070000," ","int(1/arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a x -1}\, \sqrt{a x +1}}{2 a \left(a^{2} x^{2}-1\right) \mathrm{arccosh}\left(a x \right)^{2}}"," ",0,"1/2*(-(a*x-1)*(a*x+1))^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)/a/(a^2*x^2-1)/arccosh(a*x)^2","A"
369,-2,0,201,180.000000," ","int(x^3*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{x^{3} \left(-c^{2} d \,x^{2}+d \right)}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","F"
370,-2,0,269,180.000000," ","int(x^2*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","F"
371,-2,0,189,180.000000," ","int(x*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{x \left(-c^{2} d \,x^{2}+d \right)}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","F"
372,-2,0,184,180.000000," ","int((-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{-c^{2} d \,x^{2}+d}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","F"
373,-2,0,152,180.000000," ","int((-c^2*d*x^2+d)/x/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{-c^{2} d \,x^{2}+d}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c^2*d*x^2+d)/x/(a+b*arccosh(c*x))^(3/2),x)","F"
374,-2,0,375,180.000000," ","int(x^3*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{x^{3} \left(-c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","F"
375,-2,0,369,180.000000," ","int(x^2*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","F"
376,-2,0,285,180.000000," ","int(x*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{x \left(-c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","F"
377,-2,0,280,180.000000," ","int((-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","F"
378,-2,0,230,180.000000," ","int((-c^2*d*x^2+d)^2/x/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{2}}{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c^2*d*x^2+d)^2/x/(a+b*arccosh(c*x))^(3/2),x)","F"
379,0,0,275,0.799000," ","int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(1/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\mathrm{arccosh}\left(a x \right)}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(1/2),x)","F"
380,0,0,159,0.713000," ","int((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(1/2),x)","\int \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\mathrm{arccosh}\left(a x \right)}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(1/2),x)","F"
381,1,41,38,0.082000," ","int(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{2 \mathrm{arccosh}\left(a x \right)^{\frac{3}{2}} \sqrt{a x -1}\, \sqrt{a x +1}}{3 a \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}"," ",0,"2/3*arccosh(a*x)^(3/2)/a/(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)","A"
382,0,0,80,0.773000," ","int(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\sqrt{\mathrm{arccosh}\left(a x \right)}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","F"
383,0,0,160,0.759000," ","int(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{\sqrt{\mathrm{arccosh}\left(a x \right)}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","F"
384,0,0,405,0.617000," ","int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(3/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(3/2),x)","F"
385,0,0,236,0.703000," ","int((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(3/2),x)","\int \sqrt{-a^{2} c \,x^{2}+c}\, \mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(3/2),x)","F"
386,1,41,38,0.080000," ","int(arccosh(a*x)^(3/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{2 \mathrm{arccosh}\left(a x \right)^{\frac{5}{2}} \sqrt{a x -1}\, \sqrt{a x +1}}{5 a \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}"," ",0,"2/5*arccosh(a*x)^(5/2)/a/(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)","A"
387,0,0,80,0.641000," ","int(arccosh(a*x)^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccosh(a*x)^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","F"
388,0,0,462,0.627000," ","int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(5/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(5/2),x)","F"
389,0,0,258,0.688000," ","int((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(5/2),x)","\int \sqrt{-a^{2} c \,x^{2}+c}\, \mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(5/2),x)","F"
390,1,41,38,0.084000," ","int(arccosh(a*x)^(5/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{2 \mathrm{arccosh}\left(a x \right)^{\frac{7}{2}} \sqrt{a x -1}\, \sqrt{a x +1}}{7 a \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}"," ",0,"2/7*arccosh(a*x)^(7/2)/a/(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)","A"
391,0,0,80,0.632000," ","int(arccosh(a*x)^(5/2)/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccosh(a*x)^(5/2)/(-a^2*c*x^2+c)^(3/2),x)","F"
392,0,0,292,0.704000," ","int((a^2-x^2)^(3/2)*arccosh(x/a)^(1/2),x)","\int \left(a^{2}-x^{2}\right)^{\frac{3}{2}} \sqrt{\mathrm{arccosh}\left(\frac{x}{a}\right)}\, dx"," ",0,"int((a^2-x^2)^(3/2)*arccosh(x/a)^(1/2),x)","F"
393,0,0,165,0.687000," ","int((a^2-x^2)^(1/2)*arccosh(x/a)^(1/2),x)","\int \sqrt{a^{2}-x^{2}}\, \sqrt{\mathrm{arccosh}\left(\frac{x}{a}\right)}\, dx"," ",0,"int((a^2-x^2)^(1/2)*arccosh(x/a)^(1/2),x)","F"
394,1,44,40,0.089000," ","int(arccosh(x/a)^(1/2)/(a^2-x^2)^(1/2),x)","\frac{2 \mathrm{arccosh}\left(\frac{x}{a}\right)^{\frac{3}{2}} a \sqrt{\frac{-a +x}{a}}\, \sqrt{\frac{a +x}{a}}}{3 \sqrt{-\left(-a +x \right) \left(a +x \right)}}"," ",0,"2/3*arccosh(x/a)^(3/2)*a/(-(-a+x)*(a+x))^(1/2)*((-a+x)/a)^(1/2)*((a+x)/a)^(1/2)","A"
395,0,0,83,0.648000," ","int(arccosh(x/a)^(1/2)/(a^2-x^2)^(3/2),x)","\int \frac{\sqrt{\mathrm{arccosh}\left(\frac{x}{a}\right)}}{\left(a^{2}-x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccosh(x/a)^(1/2)/(a^2-x^2)^(3/2),x)","F"
396,0,0,166,0.762000," ","int(arccosh(x/a)^(1/2)/(a^2-x^2)^(5/2),x)","\int \frac{\sqrt{\mathrm{arccosh}\left(\frac{x}{a}\right)}}{\left(a^{2}-x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(arccosh(x/a)^(1/2)/(a^2-x^2)^(5/2),x)","F"
397,0,0,419,0.602000," ","int((a^2-x^2)^(3/2)*arccosh(x/a)^(3/2),x)","\int \left(a^{2}-x^{2}\right)^{\frac{3}{2}} \mathrm{arccosh}\left(\frac{x}{a}\right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2-x^2)^(3/2)*arccosh(x/a)^(3/2),x)","F"
398,0,0,250,0.696000," ","int(arccosh(x/a)^(3/2)*(a^2-x^2)^(1/2),x)","\int \mathrm{arccosh}\left(\frac{x}{a}\right)^{\frac{3}{2}} \sqrt{a^{2}-x^{2}}\, dx"," ",0,"int(arccosh(x/a)^(3/2)*(a^2-x^2)^(1/2),x)","F"
399,1,44,40,0.083000," ","int(arccosh(x/a)^(3/2)/(a^2-x^2)^(1/2),x)","\frac{2 \mathrm{arccosh}\left(\frac{x}{a}\right)^{\frac{5}{2}} a \sqrt{\frac{-a +x}{a}}\, \sqrt{\frac{a +x}{a}}}{5 \sqrt{-\left(-a +x \right) \left(a +x \right)}}"," ",0,"2/5*arccosh(x/a)^(5/2)*a/(-(-a+x)*(a+x))^(1/2)*((-a+x)/a)^(1/2)*((a+x)/a)^(1/2)","A"
400,0,0,83,0.617000," ","int(arccosh(x/a)^(3/2)/(a^2-x^2)^(3/2),x)","\int \frac{\mathrm{arccosh}\left(\frac{x}{a}\right)^{\frac{3}{2}}}{\left(a^{2}-x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccosh(x/a)^(3/2)/(a^2-x^2)^(3/2),x)","F"
401,0,0,45,0.450000," ","int(x/(-x^2+1)^(1/2)/arccosh(x)^(1/2),x)","\int \frac{x}{\sqrt{-x^{2}+1}\, \sqrt{\mathrm{arccosh}\left(x \right)}}\, dx"," ",0,"int(x/(-x^2+1)^(1/2)/arccosh(x)^(1/2),x)","F"
402,0,0,344,0.663000," ","int((-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(1/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\sqrt{\mathrm{arccosh}\left(a x \right)}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(1/2),x)","F"
403,0,0,230,0.631000," ","int((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(1/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\sqrt{\mathrm{arccosh}\left(a x \right)}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(1/2),x)","F"
404,0,0,137,0.708000," ","int((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(1/2),x)","\int \frac{\sqrt{-a^{2} c \,x^{2}+c}}{\sqrt{\mathrm{arccosh}\left(a x \right)}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(1/2),x)","F"
405,1,41,38,0.076000," ","int(1/(-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(1/2),x)","\frac{2 \sqrt{\mathrm{arccosh}\left(a x \right)}\, \sqrt{a x -1}\, \sqrt{a x +1}}{a \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}"," ",0,"2*arccosh(a*x)^(1/2)/a/(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)","A"
406,0,0,22,0.661000," ","int(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(1/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\mathrm{arccosh}\left(a x \right)}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(1/2),x)","F"
407,0,0,22,0.737000," ","int(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(1/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\mathrm{arccosh}\left(a x \right)}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(1/2),x)","F"
408,0,0,341,0.599000," ","int((-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(3/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(3/2),x)","F"
409,0,0,229,0.603000," ","int((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(3/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(3/2),x)","F"
410,0,0,137,0.691000," ","int((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(3/2),x)","\int \frac{\sqrt{-a^{2} c \,x^{2}+c}}{\mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(3/2),x)","F"
411,1,41,38,0.082000," ","int(1/(-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(3/2),x)","-\frac{2 \sqrt{a x -1}\, \sqrt{a x +1}}{\sqrt{\mathrm{arccosh}\left(a x \right)}\, a \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}"," ",0,"-2/arccosh(a*x)^(1/2)/a/(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)","A"
412,0,0,93,0.640000," ","int(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(3/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(3/2),x)","F"
413,0,0,93,0.726000," ","int(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(3/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \mathrm{arccosh}\left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(3/2),x)","F"
414,0,0,263,0.611000," ","int((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(5/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(5/2),x)","F"
415,0,0,159,0.688000," ","int((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(5/2),x)","\int \frac{\sqrt{-a^{2} c \,x^{2}+c}}{\mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(5/2),x)","F"
416,1,41,38,0.082000," ","int(1/(-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(5/2),x)","-\frac{2 \sqrt{a x -1}\, \sqrt{a x +1}}{3 \mathrm{arccosh}\left(a x \right)^{\frac{3}{2}} a \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}"," ",0,"-2/3/arccosh(a*x)^(3/2)/a/(-(a*x-1)*(a*x+1)*c)^(1/2)*(a*x-1)^(1/2)*(a*x+1)^(1/2)","A"
417,0,0,93,0.653000," ","int(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(5/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(5/2),x)","F"
418,0,0,93,0.749000," ","int(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(5/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \mathrm{arccosh}\left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(5/2),x)","F"
419,-2,0,239,180.000000," ","int(x^2*(a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x)","\int x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n} \sqrt{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x)","F"
420,0,0,352,0.341000," ","int(x*(a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x)","\int x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n} \sqrt{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x)","F"
421,0,0,235,0.293000," ","int((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n} \sqrt{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x)","F"
422,0,0,196,0.544000," ","int((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n} \sqrt{-c^{2} d \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2)/x,x)","F"
423,0,0,83,0.551000," ","int((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n} \sqrt{-c^{2} d \,x^{2}+d}}{x^{2}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2)/x^2,x)","F"
424,-2,0,620,180.000000," ","int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","\int x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","F"
425,0,0,537,0.277000," ","int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","\int x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","F"
426,0,0,426,0.239000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","\int \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","F"
427,0,0,385,0.490000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n/x,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n/x,x)","F"
428,0,0,271,0.585000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n/x^2,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n/x^2,x)","F"
429,-2,0,826,180.000000," ","int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x)","\int x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x)","F"
430,0,0,738,0.279000," ","int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x)","\int x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x)","F"
431,0,0,636,0.245000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x)","\int \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x)","F"
432,0,0,747,0.491000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n/x,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n/x,x)","F"
433,0,0,459,0.540000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n/x^2,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n/x^2,x)","F"
434,-2,0,304,180.000000," ","int(x^3*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(x^3*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","F"
435,-2,0,199,180.000000," ","int(x^2*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(x^2*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","F"
436,0,0,145,0.307000," ","int(x*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","\int \frac{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(x*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","F"
437,1,53,39,0.055000," ","int((a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","\frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{1+n} \sqrt{c x -1}\, \sqrt{c x +1}}{b \left(1+n \right) c \sqrt{-\left(c x -1\right) \left(c x +1\right)}}"," ",0,"(a+b*arccosh(c*x))^(1+n)/b/(1+n)/c/(-(c*x-1)*(c*x+1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)","A"
438,0,0,28,0.404000," ","int((a+b*arccosh(c*x))^n/x/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/x/(-c^2*x^2+1)^(1/2),x)","F"
439,0,0,28,0.417000," ","int((a+b*arccosh(c*x))^n/x^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x^{2} \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/x^2/(-c^2*x^2+1)^(1/2),x)","F"
440,-2,0,352,180.000000," ","int(x^3*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x^3*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","F"
441,-2,0,235,180.000000," ","int(x^2*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x^2*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","F"
442,0,0,169,0.319000," ","int(x*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","F"
443,1,54,51,0.056000," ","int((a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","\frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{1+n} \sqrt{c x -1}\, \sqrt{c x +1}}{b \left(1+n \right) c \sqrt{-\left(c x -1\right) \left(c x +1\right) d}}"," ",0,"(a+b*arccosh(c*x))^(1+n)/b/(1+n)/c/(-(c*x-1)*(c*x+1)*d)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)","A"
444,0,0,29,0.416000," ","int((a+b*arccosh(c*x))^n/x/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x \sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/x/(-c^2*d*x^2+d)^(1/2),x)","F"
445,0,0,29,0.441000," ","int((a+b*arccosh(c*x))^n/x^2/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x^{2} \sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/x^2/(-c^2*d*x^2+d)^(1/2),x)","F"
446,-2,0,29,180.000000," ","int(x^2*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","F"
447,0,0,27,0.309000," ","int(x*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{x \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","F"
448,0,0,26,0.253000," ","int((a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","F"
449,0,0,29,0.425000," ","int((a+b*arccosh(c*x))^n/x/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/x/(-c^2*d*x^2+d)^(3/2),x)","F"
450,0,0,29,0.438000," ","int((a+b*arccosh(c*x))^n/x^2/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n/x^2/(-c^2*d*x^2+d)^(3/2),x)","F"
451,0,0,30,0.453000," ","int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","F"
452,-2,0,31,180.000000," ","int((f*x)^m*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))^n,x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))^n,x)","F"
453,-2,0,29,180.000000," ","int((f*x)^m*(-c^2*d*x^2+d)*(a+b*arccosh(c*x))^n,x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)*(a+b*arccosh(c*x))^n,x)","F"
454,0,0,18,0.127000," ","int((f*x)^m*(a+b*arccosh(c*x))^n,x)","\int \left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^n,x)","F"
455,0,0,31,0.275000," ","int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d),x)","F"
456,0,0,31,0.482000," ","int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\left(-c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^2,x)","F"
457,0,0,31,0.506000," ","int((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","\int \left(f x \right)^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x)","F"
458,0,0,31,0.537000," ","int((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x))^n,x)","\int \left(f x \right)^{m} \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}\, dx"," ",0,"int((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x))^n,x)","F"
459,0,0,31,0.451000," ","int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x)","F"
460,0,0,31,0.436000," ","int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x)","F"
461,1,133,149,0.029000," ","int(x^4*(e*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e \,c^{7} x^{7}+\frac{1}{5} c^{7} x^{5} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e \,c^{7} x^{7}}{7}+\frac{\mathrm{arccosh}\left(c x \right) c^{7} x^{5} d}{5}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(75 c^{6} e \,x^{6}+147 c^{6} d \,x^{4}+90 c^{4} e \,x^{4}+196 c^{4} d \,x^{2}+120 c^{2} x^{2} e +392 c^{2} d +240 e \right)}{3675}\right)}{c^{2}}}{c^{5}}"," ",0,"1/c^5*(a/c^2*(1/7*e*c^7*x^7+1/5*c^7*x^5*d)+b/c^2*(1/7*arccosh(c*x)*e*c^7*x^7+1/5*arccosh(c*x)*c^7*x^5*d-1/3675*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(75*c^6*e*x^6+147*c^6*d*x^4+90*c^4*e*x^4+196*c^4*d*x^2+120*c^2*e*x^2+392*c^2*d+240*e)))","A"
462,1,250,137,0.017000," ","int(x^3*(e*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{a e \,x^{6}}{6}+\frac{a \,x^{4} d}{4}+\frac{b \,\mathrm{arccosh}\left(c x \right) e \,x^{6}}{6}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{4} d}{4}-\frac{b e \,x^{5} \sqrt{c x -1}\, \sqrt{c x +1}}{36 c}-\frac{b d \,x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{16 c}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, e \,x^{3}}{144 c^{3}}-\frac{3 b d x \sqrt{c x -1}\, \sqrt{c x +1}}{32 c^{3}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d}{32 c^{4} \sqrt{c^{2} x^{2}-1}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, e x}{96 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{96 c^{6} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/6*a*e*x^6+1/4*a*x^4*d+1/6*b*arccosh(c*x)*e*x^6+1/4*b*arccosh(c*x)*x^4*d-1/36*b*e*x^5*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/16*b*d*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-5/144/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e*x^3-3/32*b*d*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-3/32/c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d-5/96/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e*x-5/96/c^6*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
463,1,115,116,0.012000," ","int(x^2*(e*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} c^{5} x^{5} e +\frac{1}{3} c^{5} x^{3} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{5} e}{5}+\frac{\mathrm{arccosh}\left(c x \right) c^{5} x^{3} d}{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(9 c^{4} e \,x^{4}+25 c^{4} d \,x^{2}+12 c^{2} x^{2} e +50 c^{2} d +24 e \right)}{225}\right)}{c^{2}}}{c^{3}}"," ",0,"1/c^3*(a/c^2*(1/5*c^5*x^5*e+1/3*c^5*x^3*d)+b/c^2*(1/5*arccosh(c*x)*c^5*x^5*e+1/3*arccosh(c*x)*c^5*x^3*d-1/225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(9*c^4*e*x^4+25*c^4*d*x^2+12*c^2*e*x^2+50*c^2*d+24*e)))","A"
464,1,202,104,0.013000," ","int(x*(e*x^2+d)*(a+b*arccosh(c*x)),x)","\frac{a \,x^{4} e}{4}+\frac{a \,x^{2} d}{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{4} e}{4}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{2} d}{2}-\frac{b e \,x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{16 c}-\frac{b d x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d}{4 c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, e x}{32 c^{3}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{32 c^{4} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/4*a*x^4*e+1/2*a*x^2*d+1/4*b*arccosh(c*x)*x^4*e+1/2*b*arccosh(c*x)*x^2*d-1/16*b*e*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/4*b*d*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/4/c^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d-3/32/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e*x-3/32/c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
465,1,90,80,0.010000," ","int((e*x^2+d)*(a+b*arccosh(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{\mathrm{arccosh}\left(c x \right) c^{3} x^{3} e}{3}+\mathrm{arccosh}\left(c x \right) c^{3} d x -\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(c^{2} x^{2} e +9 c^{2} d +2 e \right)}{9}\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*arccosh(c*x)*c^3*x^3*e+arccosh(c*x)*c^3*d*x-1/9*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(c^2*e*x^2+9*c^2*d+2*e)))","A"
466,1,130,244,0.316000," ","int((e*x^2+d)*(a+b*arccosh(c*x))/x,x)","\frac{a \,x^{2} e}{2}+d a \ln \left(c x \right)-\frac{b \mathrm{arccosh}\left(c x \right)^{2} d}{2}-\frac{b e x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{2} e}{2}-\frac{b e \,\mathrm{arccosh}\left(c x \right)}{4 c^{2}}+b d \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)+\frac{b d \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}"," ",0,"1/2*a*x^2*e+d*a*ln(c*x)-1/2*b*arccosh(c*x)^2*d-1/4*b*e*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c+1/2*b*arccosh(c*x)*x^2*e-1/4*b*e*arccosh(c*x)/c^2+b*d*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*b*d*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
467,1,95,67,0.018000," ","int((e*x^2+d)*(a+b*arccosh(c*x))/x^2,x)","a x e -\frac{a d}{x}+b \,\mathrm{arccosh}\left(c x \right) x e -\frac{b \,\mathrm{arccosh}\left(c x \right) d}{x}-\frac{c b \sqrt{c x -1}\, \sqrt{c x +1}\, d \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{\sqrt{c^{2} x^{2}-1}}-\frac{b e \sqrt{c x -1}\, \sqrt{c x +1}}{c}"," ",0,"a*x*e-a*d/x+b*arccosh(c*x)*x*e-b*arccosh(c*x)*d/x-c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d*arctan(1/(c^2*x^2-1)^(1/2))-b*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c","A"
468,1,126,233,0.607000," ","int((e*x^2+d)*(a+b*arccosh(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{a d}{2 x^{2}}-\frac{b \mathrm{arccosh}\left(c x \right)^{2} e}{2}+\frac{b c d \sqrt{c x -1}\, \sqrt{c x +1}}{2 x}-\frac{c^{2} b d}{2}-\frac{b \,\mathrm{arccosh}\left(c x \right) d}{2 x^{2}}+b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)+\frac{b e \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}"," ",0,"a*e*ln(c*x)-1/2*a*d/x^2-1/2*b*arccosh(c*x)^2*e+1/2*b*c*d*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x-1/2*c^2*b*d-1/2*b*arccosh(c*x)*d/x^2+b*e*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/2*b*e*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
469,1,146,80,0.019000," ","int((e*x^2+d)*(a+b*arccosh(c*x))/x^4,x)","-\frac{a e}{x}-\frac{d a}{3 x^{3}}-\frac{b \,\mathrm{arccosh}\left(c x \right) e}{x}-\frac{d b \,\mathrm{arccosh}\left(c x \right)}{3 x^{3}}-\frac{c^{3} d b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{6 \sqrt{c^{2} x^{2}-1}}+\frac{b c d \sqrt{c x -1}\, \sqrt{c x +1}}{6 x^{2}}-\frac{c b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) e}{\sqrt{c^{2} x^{2}-1}}"," ",0,"-a*e/x-1/3*d*a/x^3-b*arccosh(c*x)*e/x-1/3*d*b*arccosh(c*x)/x^3-1/6*c^3*d*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))+1/6*b*c*d*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x^2-c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))*e","A"
470,1,227,283,0.013000," ","int(x^4*(e*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{2} c^{9} x^{9}+\frac{2}{7} c^{9} d e \,x^{7}+\frac{1}{5} c^{9} x^{5} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{2} c^{9} x^{9}}{9}+\frac{2 \,\mathrm{arccosh}\left(c x \right) c^{9} d e \,x^{7}}{7}+\frac{\mathrm{arccosh}\left(c x \right) c^{9} x^{5} d^{2}}{5}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(1225 c^{8} e^{2} x^{8}+4050 c^{8} d e \,x^{6}+3969 c^{8} d^{2} x^{4}+1400 c^{6} e^{2} x^{6}+4860 c^{6} d e \,x^{4}+5292 c^{6} d^{2} x^{2}+1680 c^{4} e^{2} x^{4}+6480 c^{4} d e \,x^{2}+10584 d^{2} c^{4}+2240 c^{2} e^{2} x^{2}+12960 c^{2} d e +4480 e^{2}\right)}{99225}\right)}{c^{4}}}{c^{5}}"," ",0,"1/c^5*(a/c^4*(1/9*e^2*c^9*x^9+2/7*c^9*d*e*x^7+1/5*c^9*x^5*d^2)+b/c^4*(1/9*arccosh(c*x)*e^2*c^9*x^9+2/7*arccosh(c*x)*c^9*d*e*x^7+1/5*arccosh(c*x)*c^9*x^5*d^2-1/99225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(1225*c^8*e^2*x^8+4050*c^8*d*e*x^6+3969*c^8*d^2*x^4+1400*c^6*e^2*x^6+4860*c^6*d*e*x^4+5292*c^6*d^2*x^2+1680*c^4*e^2*x^4+6480*c^4*d*e*x^2+10584*c^4*d^2+2240*c^2*e^2*x^2+12960*c^2*d*e+4480*e^2)))","A"
471,1,440,301,0.017000," ","int(x^3*(e*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{a \,e^{2} x^{8}}{8}+\frac{a d e \,x^{6}}{3}+\frac{a \,x^{4} d^{2}}{4}+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{2} x^{8}}{8}+\frac{b \,\mathrm{arccosh}\left(c x \right) d e \,x^{6}}{3}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{4} d^{2}}{4}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x^{7}}{64 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} d e}{18 c}-\frac{b \,d^{2} x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{16 c}-\frac{7 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x^{5}}{384 c^{3}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, d e \,x^{3}}{72 c^{3}}-\frac{3 b \,d^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{32 c^{3}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{32 c^{4} \sqrt{c^{2} x^{2}-1}}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x^{3}}{1536 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, d e x}{48 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, d e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{48 c^{6} \sqrt{c^{2} x^{2}-1}}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x}{1024 c^{7}}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{1024 c^{8} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/8*a*e^2*x^8+1/3*a*d*e*x^6+1/4*a*x^4*d^2+1/8*b*arccosh(c*x)*e^2*x^8+1/3*b*arccosh(c*x)*d*e*x^6+1/4*b*arccosh(c*x)*x^4*d^2-1/64/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x^7-1/18/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*d*e-1/16*b*d^2*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-7/384/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x^5-5/72/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e*x^3-3/32*b*d^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-3/32/c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^2*ln(c*x+(c^2*x^2-1)^(1/2))-35/1536/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x^3-5/48/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e*x-5/48/c^6*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d*e*ln(c*x+(c^2*x^2-1)^(1/2))-35/1024/c^7*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x-35/1024/c^8*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","A"
472,1,195,230,0.013000," ","int(x^2*(e*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{2} c^{7} x^{7}+\frac{2}{5} c^{7} d e \,x^{5}+\frac{1}{3} x^{3} c^{7} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{2} c^{7} x^{7}}{7}+\frac{2 \,\mathrm{arccosh}\left(c x \right) c^{7} d e \,x^{5}}{5}+\frac{\mathrm{arccosh}\left(c x \right) c^{7} x^{3} d^{2}}{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(225 c^{6} e^{2} x^{6}+882 c^{6} d e \,x^{4}+1225 c^{6} d^{2} x^{2}+270 c^{4} e^{2} x^{4}+1176 c^{4} d e \,x^{2}+2450 d^{2} c^{4}+360 c^{2} e^{2} x^{2}+2352 c^{2} d e +720 e^{2}\right)}{11025}\right)}{c^{4}}}{c^{3}}"," ",0,"1/c^3*(a/c^4*(1/7*e^2*c^7*x^7+2/5*c^7*d*e*x^5+1/3*x^3*c^7*d^2)+b/c^4*(1/7*arccosh(c*x)*e^2*c^7*x^7+2/5*arccosh(c*x)*c^7*d*e*x^5+1/3*arccosh(c*x)*c^7*x^3*d^2-1/11025*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(225*c^6*e^2*x^6+882*c^6*d*e*x^4+1225*c^6*d^2*x^2+270*c^4*e^2*x^4+1176*c^4*d*e*x^2+2450*c^4*d^2+360*c^2*e^2*x^2+2352*c^2*d*e+720*e^2)))","A"
473,1,363,239,0.016000," ","int(x*(e*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{a \,e^{2} x^{6}}{6}+\frac{a d e \,x^{4}}{2}+\frac{a \,x^{2} d^{2}}{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{2} x^{6}}{6}+\frac{b \,\mathrm{arccosh}\left(c x \right) d e \,x^{4}}{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{2} d^{2}}{2}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x^{5}}{36 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, d e \,x^{3}}{8 c}-\frac{b \,d^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{4 c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x^{3}}{144 c^{3}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, d e x}{16 c^{3}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, d e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{16 c^{4} \sqrt{c^{2} x^{2}-1}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} x}{96 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{96 c^{6} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/6*a*e^2*x^6+1/2*a*d*e*x^4+1/2*a*x^2*d^2+1/6*b*arccosh(c*x)*e^2*x^6+1/2*b*arccosh(c*x)*d*e*x^4+1/2*b*arccosh(c*x)*x^2*d^2-1/36/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x^5-1/8/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e*x^3-1/4*b*d^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/4/c^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^2*ln(c*x+(c^2*x^2-1)^(1/2))-5/144/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x^3-3/16/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e*x-3/16/c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d*e*ln(c*x+(c^2*x^2-1)^(1/2))-5/96/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2*x-5/96/c^6*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","A"
474,1,157,174,0.011000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} d e \,x^{3}+x \,c^{5} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \,\mathrm{arccosh}\left(c x \right) c^{5} d e \,x^{3}}{3}+\mathrm{arccosh}\left(c x \right) c^{5} x \,d^{2}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(9 c^{4} e^{2} x^{4}+50 c^{4} d e \,x^{2}+225 d^{2} c^{4}+12 c^{2} e^{2} x^{2}+100 c^{2} d e +24 e^{2}\right)}{225}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*d*e*x^3+x*c^5*d^2)+b/c^4*(1/5*arccosh(c*x)*e^2*c^5*x^5+2/3*arccosh(c*x)*c^5*d*e*x^3+arccosh(c*x)*c^5*x*d^2-1/225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(9*c^4*e^2*x^4+50*c^4*d*e*x^2+225*c^4*d^2+12*c^2*e^2*x^2+100*c^2*d*e+24*e^2)))","A"
475,1,225,316,0.338000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x))/x,x)","\frac{a \,e^{2} x^{4}}{4}+a d e \,x^{2}+a \,d^{2} \ln \left(c x \right)+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{2} x^{4}}{4}-\frac{b d e x \sqrt{c x -1}\, \sqrt{c x +1}}{2 c}+b \,\mathrm{arccosh}\left(c x \right) d e \,x^{2}+\frac{b \,d^{2} \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}-\frac{b d e \,\mathrm{arccosh}\left(c x \right)}{2 c^{2}}-\frac{b \,e^{2} x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{16 c}-\frac{3 b \,e^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{32 c^{3}}-\frac{b \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{2}+b \,d^{2} \mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)-\frac{3 b \,e^{2} \mathrm{arccosh}\left(c x \right)}{32 c^{4}}"," ",0,"1/4*a*e^2*x^4+a*d*e*x^2+a*d^2*ln(c*x)+1/4*b*arccosh(c*x)*e^2*x^4-1/2*b*d*e*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c+b*arccosh(c*x)*d*e*x^2+1/2*b*d^2*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-1/2*b*d*e*arccosh(c*x)/c^2-1/16*b*e^2*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-3/32*b*e^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-1/2*b*arccosh(c*x)^2*d^2+b*d^2*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-3/32*b*e^2*arccosh(c*x)/c^4","A"
476,1,177,142,0.017000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x))/x^2,x)","\frac{a \,x^{3} e^{2}}{3}+2 a d e x -\frac{d^{2} a}{x}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{3} e^{2}}{3}+2 b \,\mathrm{arccosh}\left(c x \right) d e x -\frac{d^{2} b \,\mathrm{arccosh}\left(c x \right)}{x}-\frac{c \,d^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{\sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} e^{2}}{9 c}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}\, d e}{c}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2}}{9 c^{3}}"," ",0,"1/3*a*x^3*e^2+2*a*d*e*x-d^2*a/x+1/3*b*arccosh(c*x)*x^3*e^2+2*b*arccosh(c*x)*d*e*x-d^2*b*arccosh(c*x)/x-c*d^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))-1/9*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*e^2-2*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e-2/9*b/c^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2","A"
477,1,198,297,0.537000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x))/x^3,x)","\frac{a \,x^{2} e^{2}}{2}+2 a d e \ln \left(c x \right)-\frac{a \,d^{2}}{2 x^{2}}-b d e \mathrm{arccosh}\left(c x \right)^{2}-\frac{b \,e^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{2} e^{2}}{2}-\frac{b \,e^{2} \mathrm{arccosh}\left(c x \right)}{4 c^{2}}+\frac{b c \,d^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{2 x}-\frac{c^{2} b \,d^{2}}{2}-\frac{b \,\mathrm{arccosh}\left(c x \right) d^{2}}{2 x^{2}}+2 b d e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)+b d e \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)"," ",0,"1/2*a*x^2*e^2+2*a*d*e*ln(c*x)-1/2*a*d^2/x^2-b*d*e*arccosh(c*x)^2-1/4*b*e^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c+1/2*b*arccosh(c*x)*x^2*e^2-1/4*b*e^2*arccosh(c*x)/c^2+1/2*b*c*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x-1/2*c^2*b*d^2-1/2*b*arccosh(c*x)*d^2/x^2+2*b*d*e*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+b*d*e*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)","A"
478,1,196,162,0.019000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x))/x^4,x)","a x \,e^{2}-\frac{2 a d e}{x}-\frac{a \,d^{2}}{3 x^{3}}+b \,\mathrm{arccosh}\left(c x \right) x \,e^{2}-\frac{2 b \,\mathrm{arccosh}\left(c x \right) d e}{x}-\frac{b \,\mathrm{arccosh}\left(c x \right) d^{2}}{3 x^{3}}-\frac{c^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{6 \sqrt{c^{2} x^{2}-1}}+\frac{b c \,d^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{6 x^{2}}-\frac{2 c b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) d e}{\sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2}}{c}"," ",0,"a*x*e^2-2*a*d*e/x-1/3*a*d^2/x^3+b*arccosh(c*x)*x*e^2-2*b*arccosh(c*x)*d*e/x-1/3*b*arccosh(c*x)*d^2/x^3-1/6*c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^2*arctan(1/(c^2*x^2-1)^(1/2))+1/6*b*c*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x^2-2*c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))*d*e-1/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2","A"
479,1,335,391,0.016000," ","int(x^4*(e*x^2+d)^3*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{11} e^{3} c^{11} x^{11}+\frac{1}{3} d \,e^{2} c^{11} x^{9}+\frac{3}{7} c^{11} d^{2} e \,x^{7}+\frac{1}{5} c^{11} x^{5} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{3} c^{11} x^{11}}{11}+\frac{\mathrm{arccosh}\left(c x \right) d \,e^{2} c^{11} x^{9}}{3}+\frac{3 \,\mathrm{arccosh}\left(c x \right) c^{11} d^{2} e \,x^{7}}{7}+\frac{\mathrm{arccosh}\left(c x \right) c^{11} x^{5} d^{3}}{5}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(33075 c^{10} e^{3} x^{10}+148225 c^{10} d \,e^{2} x^{8}+245025 c^{10} d^{2} e \,x^{6}+36750 c^{8} e^{3} x^{8}+160083 c^{10} d^{3} x^{4}+169400 c^{8} d \,e^{2} x^{6}+294030 c^{8} d^{2} e \,x^{4}+42000 c^{6} e^{3} x^{6}+213444 c^{8} d^{3} x^{2}+203280 c^{6} d \,e^{2} x^{4}+392040 c^{6} d^{2} e \,x^{2}+50400 c^{4} e^{3} x^{4}+426888 d^{3} c^{6}+271040 c^{4} d \,e^{2} x^{2}+784080 c^{4} d^{2} e +67200 c^{2} e^{3} x^{2}+542080 d \,e^{2} c^{2}+134400 e^{3}\right)}{4002075}\right)}{c^{6}}}{c^{5}}"," ",0,"1/c^5*(a/c^6*(1/11*e^3*c^11*x^11+1/3*d*e^2*c^11*x^9+3/7*c^11*d^2*e*x^7+1/5*c^11*x^5*d^3)+b/c^6*(1/11*arccosh(c*x)*e^3*c^11*x^11+1/3*arccosh(c*x)*d*e^2*c^11*x^9+3/7*arccosh(c*x)*c^11*d^2*e*x^7+1/5*arccosh(c*x)*c^11*x^5*d^3-1/4002075*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(33075*c^10*e^3*x^10+148225*c^10*d*e^2*x^8+245025*c^10*d^2*e*x^6+36750*c^8*e^3*x^8+160083*c^10*d^3*x^4+169400*c^8*d*e^2*x^6+294030*c^8*d^2*e*x^4+42000*c^6*e^3*x^6+213444*c^8*d^3*x^2+203280*c^6*d*e^2*x^4+392040*c^6*d^2*e*x^2+50400*c^4*e^3*x^4+426888*c^6*d^3+271040*c^4*d*e^2*x^2+784080*c^4*d^2*e+67200*c^2*e^3*x^2+542080*c^2*d*e^2+134400*e^3)))","A"
480,1,659,450,0.023000," ","int(x^3*(e*x^2+d)^3*(a+b*arccosh(c*x)),x)","-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} d^{3}}{16 c}-\frac{9 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{7}}{800 c^{3}}-\frac{21 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{5}}{1600 c^{5}}-\frac{21 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{3}}{1280 c^{7}}-\frac{63 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x}{2560 c^{9}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{9}}{100 c}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{7} d \,e^{2}}{64 c}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} d \,e^{2}}{512 c^{5}}-\frac{63 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2560 c^{10} \sqrt{c^{2} x^{2}-1}}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d^{3}}{32 c^{4} \sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} d^{2} e}{12 c}-\frac{7 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} d \,e^{2}}{128 c^{3}}-\frac{105 b \sqrt{c x -1}\, \sqrt{c x +1}\, x d \,e^{2}}{1024 c^{7}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, x \,d^{2} e}{32 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} d^{2} e}{48 c^{3}}+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{3} x^{10}}{10}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{4} d^{3}}{4}+\frac{3 a d \,e^{2} x^{8}}{8}+\frac{a \,d^{2} e \,x^{6}}{2}-\frac{3 b \,d^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{32 c^{3}}+\frac{b \,\mathrm{arccosh}\left(c x \right) d^{2} e \,x^{6}}{2}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d^{2} e}{32 c^{6} \sqrt{c^{2} x^{2}-1}}+\frac{a \,e^{3} x^{10}}{10}+\frac{a \,x^{4} d^{3}}{4}-\frac{105 b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d \,e^{2}}{1024 c^{8} \sqrt{c^{2} x^{2}-1}}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) d \,e^{2} x^{8}}{8}"," ",0,"-1/16/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*d^3-9/800/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^7-21/1600/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^5-21/1280/c^7*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^3-63/2560/c^9*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x-1/100/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^9-3/64/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^7*d*e^2-35/512/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*d*e^2-63/2560/c^10*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*e^3*ln(c*x+(c^2*x^2-1)^(1/2))-3/32/c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d^3-1/12/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*d^2*e-7/128/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*d*e^2-105/1024/c^7*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d*e^2-5/32/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d^2*e-5/48/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*d^2*e+1/10*b*arccosh(c*x)*e^3*x^10+1/4*b*arccosh(c*x)*x^4*d^3+3/8*a*d*e^2*x^8+1/2*a*d^2*e*x^6-3/32*b*d^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3+1/2*b*arccosh(c*x)*d^2*e*x^6-5/32/c^6*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d^2*e+1/10*a*e^3*x^10+1/4*a*x^4*d^3-105/1024/c^8*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d*e^2+3/8*b*arccosh(c*x)*d*e^2*x^8","A"
481,1,289,327,0.013000," ","int(x^2*(e*x^2+d)^3*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{3} c^{9} x^{9}+\frac{3}{7} d \,e^{2} c^{9} x^{7}+\frac{3}{5} c^{9} d^{2} e \,x^{5}+\frac{1}{3} x^{3} c^{9} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{3} c^{9} x^{9}}{9}+\frac{3 \,\mathrm{arccosh}\left(c x \right) d \,e^{2} c^{9} x^{7}}{7}+\frac{3 \,\mathrm{arccosh}\left(c x \right) c^{9} d^{2} e \,x^{5}}{5}+\frac{\mathrm{arccosh}\left(c x \right) c^{9} x^{3} d^{3}}{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(1225 c^{8} e^{3} x^{8}+6075 c^{8} d \,e^{2} x^{6}+11907 c^{8} d^{2} e \,x^{4}+1400 c^{6} e^{3} x^{6}+11025 c^{8} d^{3} x^{2}+7290 c^{6} d \,e^{2} x^{4}+15876 c^{6} d^{2} e \,x^{2}+1680 c^{4} e^{3} x^{4}+22050 d^{3} c^{6}+9720 c^{4} d \,e^{2} x^{2}+31752 c^{4} d^{2} e +2240 c^{2} e^{3} x^{2}+19440 d \,e^{2} c^{2}+4480 e^{3}\right)}{99225}\right)}{c^{6}}}{c^{3}}"," ",0,"1/c^3*(a/c^6*(1/9*e^3*c^9*x^9+3/7*d*e^2*c^9*x^7+3/5*c^9*d^2*e*x^5+1/3*x^3*c^9*d^3)+b/c^6*(1/9*arccosh(c*x)*e^3*c^9*x^9+3/7*arccosh(c*x)*d*e^2*c^9*x^7+3/5*arccosh(c*x)*c^9*d^2*e*x^5+1/3*arccosh(c*x)*c^9*x^3*d^3-1/99225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(1225*c^8*e^3*x^8+6075*c^8*d*e^2*x^6+11907*c^8*d^2*e*x^4+1400*c^6*e^3*x^6+11025*c^8*d^3*x^2+7290*c^6*d*e^2*x^4+15876*c^6*d^2*e*x^2+1680*c^4*e^3*x^4+22050*c^6*d^3+9720*c^4*d*e^2*x^2+31752*c^4*d^2*e+2240*c^2*e^3*x^2+19440*c^2*d*e^2+4480*e^3)))","A"
482,1,553,322,0.016000," ","int(x*(e*x^2+d)^3*(a+b*arccosh(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{d^{3} a \,x^{2}}{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{3} x^{8}}{8}+\frac{b \,\mathrm{arccosh}\left(c x \right) d \,e^{2} x^{6}}{2}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) d^{2} e \,x^{4}}{4}+\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right) x^{2}}{2}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{7}}{64 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{5} d \,e^{2}}{12 c}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} d^{2} e}{16 c}-\frac{b \,d^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}-\frac{d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{4 c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{7 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{5}}{384 c^{3}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} d \,e^{2}}{48 c^{3}}-\frac{9 b \sqrt{c x -1}\, \sqrt{c x +1}\, x \,d^{2} e}{32 c^{3}}-\frac{9 b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d^{2} e}{32 c^{4} \sqrt{c^{2} x^{2}-1}}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{3}}{1536 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, x d \,e^{2}}{32 c^{5}}-\frac{5 b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right) d \,e^{2}}{32 c^{6} \sqrt{c^{2} x^{2}-1}}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x}{1024 c^{7}}-\frac{35 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{1024 c^{8} \sqrt{c^{2} x^{2}-1}}"," ",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*d^3*a*x^2+1/8*b*arccosh(c*x)*e^3*x^8+1/2*b*arccosh(c*x)*d*e^2*x^6+3/4*b*arccosh(c*x)*d^2*e*x^4+1/2*d^3*b*arccosh(c*x)*x^2-1/64/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^7-1/12/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^5*d*e^2-3/16/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*d^2*e-1/4*b*d^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/4/c^2*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))-7/384/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^5-5/48/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*d*e^2-9/32/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d^2*e-9/32/c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d^2*e-35/1536/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^3-5/32/c^5*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d*e^2-5/32/c^6*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*ln(c*x+(c^2*x^2-1)^(1/2))*d*e^2-35/1024/c^7*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x-35/1024/c^8*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*e^3*ln(c*x+(c^2*x^2-1)^(1/2))","A"
483,1,235,259,0.013000," ","int((e*x^2+d)^3*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{3} c^{7} x^{7}+\frac{3}{5} c^{7} d \,e^{2} x^{5}+c^{7} d^{2} e \,x^{3}+x \,c^{7} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{3} c^{7} x^{7}}{7}+\frac{3 \,\mathrm{arccosh}\left(c x \right) d \,e^{2} c^{7} x^{5}}{5}+\mathrm{arccosh}\left(c x \right) c^{7} d^{2} e \,x^{3}+\mathrm{arccosh}\left(c x \right) c^{7} x \,d^{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(75 c^{6} e^{3} x^{6}+441 c^{6} d \,e^{2} x^{4}+1225 c^{6} d^{2} e \,x^{2}+90 c^{4} e^{3} x^{4}+3675 d^{3} c^{6}+588 c^{4} d \,e^{2} x^{2}+2450 c^{4} d^{2} e +120 c^{2} e^{3} x^{2}+1176 d \,e^{2} c^{2}+240 e^{3}\right)}{3675}\right)}{c^{6}}}{c}"," ",0,"1/c*(a/c^6*(1/7*e^3*c^7*x^7+3/5*c^7*d*e^2*x^5+c^7*d^2*e*x^3+x*c^7*d^3)+b/c^6*(1/7*arccosh(c*x)*e^3*c^7*x^7+3/5*arccosh(c*x)*d*e^2*c^7*x^5+arccosh(c*x)*c^7*d^2*e*x^3+arccosh(c*x)*c^7*x*d^3-1/3675*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(75*c^6*e^3*x^6+441*c^6*d*e^2*x^4+1225*c^6*d^2*e*x^2+90*c^4*e^3*x^4+3675*c^6*d^3+588*c^4*d*e^2*x^2+2450*c^4*d^2*e+120*c^2*e^3*x^2+1176*c^2*d*e^2+240*e^3)))","A"
484,1,351,451,0.305000," ","int((e*x^2+d)^3*(a+b*arccosh(c*x))/x,x)","\frac{a \,e^{3} x^{6}}{6}+\frac{3 a d \,e^{2} x^{4}}{4}+\frac{3 a \,d^{2} e \,x^{2}}{2}+d^{3} a \ln \left(c x \right)+\frac{3 b \,\mathrm{arccosh}\left(c x \right) d \,e^{2} x^{4}}{4}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) d^{2} e \,x^{2}}{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{3} x^{6}}{6}+\frac{d^{3} b \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}-\frac{3 b \,d^{2} e \,\mathrm{arccosh}\left(c x \right)}{4 c^{2}}-\frac{9 b d \,e^{2} \mathrm{arccosh}\left(c x \right)}{32 c^{4}}-\frac{d^{3} b \mathrm{arccosh}\left(c x \right)^{2}}{2}+d^{3} b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)-\frac{b \,e^{3} x^{5} \sqrt{c x -1}\, \sqrt{c x +1}}{36 c}-\frac{5 b \,e^{3} x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{144 c^{3}}-\frac{5 b \,e^{3} x \sqrt{c x -1}\, \sqrt{c x +1}}{96 c^{5}}-\frac{3 b d \,e^{2} x^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{16 c}-\frac{9 b d \,e^{2} x \sqrt{c x -1}\, \sqrt{c x +1}}{32 c^{3}}-\frac{3 b \,d^{2} e x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}-\frac{5 b \,e^{3} \mathrm{arccosh}\left(c x \right)}{96 c^{6}}"," ",0,"1/6*a*e^3*x^6+3/4*a*d*e^2*x^4+3/2*a*d^2*e*x^2+d^3*a*ln(c*x)+3/4*b*arccosh(c*x)*d*e^2*x^4+3/2*b*arccosh(c*x)*d^2*e*x^2+1/6*b*arccosh(c*x)*e^3*x^6+1/2*d^3*b*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-3/4*b*d^2*e*arccosh(c*x)/c^2-9/32*b*d*e^2*arccosh(c*x)/c^4-1/2*d^3*b*arccosh(c*x)^2+d^3*b*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-1/36*b*e^3*x^5*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-5/144*b*e^3*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-5/96*b*e^3*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^5-3/16*b*d*e^2*x^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-9/32*b*d*e^2*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3-3/4*b*d^2*e*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-5/96*b*e^3*arccosh(c*x)/c^6","A"
485,1,282,237,0.020000," ","int((e*x^2+d)^3*(a+b*arccosh(c*x))/x^2,x)","\frac{a \,e^{3} x^{5}}{5}+a d \,e^{2} x^{3}+3 a \,d^{2} e x -\frac{d^{3} a}{x}+\frac{b \,\mathrm{arccosh}\left(c x \right) e^{3} x^{5}}{5}+b \,\mathrm{arccosh}\left(c x \right) d \,e^{2} x^{3}+3 b \,\mathrm{arccosh}\left(c x \right) d^{2} e x -\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right)}{x}-\frac{c \,d^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{\sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{4} e^{3}}{25 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} d \,e^{2}}{3 c}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} e}{c}-\frac{4 b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} e^{3}}{75 c^{3}}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}\, d \,e^{2}}{3 c^{3}}-\frac{8 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3}}{75 c^{5}}"," ",0,"1/5*a*e^3*x^5+a*d*e^2*x^3+3*a*d^2*e*x-d^3*a/x+1/5*b*arccosh(c*x)*e^3*x^5+b*arccosh(c*x)*d*e^2*x^3+3*b*arccosh(c*x)*d^2*e*x-d^3*b*arccosh(c*x)/x-c*d^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))-1/25*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^4*e^3-1/3*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*d*e^2-3*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^2*e-4/75*b/c^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*e^3-2/3*b/c^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e^2-8/75*b/c^5*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3","A"
486,1,296,432,0.428000," ","int((e*x^2+d)^3*(a+b*arccosh(c*x))/x^3,x)","\frac{a \,x^{4} e^{3}}{4}+\frac{3 a \,x^{2} d \,e^{2}}{2}+3 a \,d^{2} e \ln \left(c x \right)-\frac{d^{3} a}{2 x^{2}}-\frac{d^{3} b \,\mathrm{arccosh}\left(c x \right)}{2 x^{2}}-\frac{3 b \,d^{2} e \mathrm{arccosh}\left(c x \right)^{2}}{2}+3 b \,d^{2} e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)-\frac{3 b \,\mathrm{arccosh}\left(c x \right) e^{3}}{32 c^{4}}+\frac{c \,d^{3} b \sqrt{c x +1}\, \sqrt{c x -1}}{2 x}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{3}}{16 c}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x}{32 c^{3}}+\frac{3 b \,d^{2} e \polylog \left(2, -\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2}\right)}{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{4} e^{3}}{4}-\frac{d^{3} b \,c^{2}}{2}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) x^{2} d \,e^{2}}{2}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, x d \,e^{2}}{4 c}-\frac{3 b \,\mathrm{arccosh}\left(c x \right) d \,e^{2}}{4 c^{2}}"," ",0,"1/4*a*x^4*e^3+3/2*a*x^2*d*e^2+3*a*d^2*e*ln(c*x)-1/2*d^3*a/x^2-1/2*d^3*b*arccosh(c*x)/x^2-3/2*b*d^2*e*arccosh(c*x)^2+3*b*d^2*e*arccosh(c*x)*ln(1+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)-3/32/c^4*b*arccosh(c*x)*e^3+1/2*c*d^3*b/x*(c*x+1)^(1/2)*(c*x-1)^(1/2)-1/16/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^3-3/32/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x+3/2*b*d^2*e*polylog(2,-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2)+1/4*b*arccosh(c*x)*x^4*e^3-1/2*d^3*b*c^2+3/2*b*arccosh(c*x)*x^2*d*e^2-3/4/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d*e^2-3/4/c^2*b*arccosh(c*x)*d*e^2","A"
487,1,278,228,0.022000," ","int((e*x^2+d)^3*(a+b*arccosh(c*x))/x^4,x)","\frac{a \,x^{3} e^{3}}{3}+3 a x d \,e^{2}-\frac{3 a \,d^{2} e}{x}-\frac{a \,d^{3}}{3 x^{3}}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{3} e^{3}}{3}+3 b \,\mathrm{arccosh}\left(c x \right) x d \,e^{2}-\frac{3 b \,\mathrm{arccosh}\left(c x \right) d^{2} e}{x}-\frac{b \,\mathrm{arccosh}\left(c x \right) d^{3}}{3 x^{3}}-\frac{c^{3} b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{3} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{6 \sqrt{c^{2} x^{2}-1}}+\frac{b c \,d^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{6 x^{2}}-\frac{3 c b \sqrt{c x -1}\, \sqrt{c x +1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) d^{2} e}{\sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} e^{3}}{9 c}-\frac{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, d \,e^{2}}{c}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3}}{9 c^{3}}"," ",0,"1/3*a*x^3*e^3+3*a*x*d*e^2-3*a*d^2*e/x-1/3*a*d^3/x^3+1/3*b*arccosh(c*x)*x^3*e^3+3*b*arccosh(c*x)*x*d*e^2-3*b*arccosh(c*x)*d^2*e/x-1/3*b*arccosh(c*x)*d^3/x^3-1/6*c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^3*arctan(1/(c^2*x^2-1)^(1/2))+1/6*b*c*d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/x^2-3*c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*arctan(1/(c^2*x^2-1)^(1/2))*d^2*e-1/9/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*e^3-3/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e^2-2/9/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3","A"
488,1,331,357,0.013000," ","int((e*x^2+d)^4*(a+b*arccosh(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{4} c^{9} x^{9}+\frac{4}{7} c^{9} d \,e^{3} x^{7}+\frac{6}{5} c^{9} d^{2} e^{2} x^{5}+\frac{4}{3} c^{9} d^{3} e \,x^{3}+c^{9} d^{4} x \right)}{c^{8}}+\frac{b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{4} c^{9} x^{9}}{9}+\frac{4 \,\mathrm{arccosh}\left(c x \right) c^{9} d \,e^{3} x^{7}}{7}+\frac{6 \,\mathrm{arccosh}\left(c x \right) c^{9} d^{2} e^{2} x^{5}}{5}+\frac{4 \,\mathrm{arccosh}\left(c x \right) c^{9} d^{3} e \,x^{3}}{3}+\mathrm{arccosh}\left(c x \right) c^{9} d^{4} x -\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(1225 c^{8} e^{4} x^{8}+8100 c^{8} d \,e^{3} x^{6}+23814 c^{8} d^{2} e^{2} x^{4}+1400 c^{6} e^{4} x^{6}+44100 c^{8} d^{3} e \,x^{2}+9720 c^{6} d \,e^{3} x^{4}+99225 c^{8} d^{4}+31752 c^{6} d^{2} e^{2} x^{2}+1680 c^{4} e^{4} x^{4}+88200 c^{6} d^{3} e +12960 c^{4} d \,e^{3} x^{2}+63504 c^{4} d^{2} e^{2}+2240 c^{2} e^{4} x^{2}+25920 c^{2} d \,e^{3}+4480 e^{4}\right)}{99225}\right)}{c^{8}}}{c}"," ",0,"1/c*(a/c^8*(1/9*e^4*c^9*x^9+4/7*c^9*d*e^3*x^7+6/5*c^9*d^2*e^2*x^5+4/3*c^9*d^3*e*x^3+c^9*d^4*x)+b/c^8*(1/9*arccosh(c*x)*e^4*c^9*x^9+4/7*arccosh(c*x)*c^9*d*e^3*x^7+6/5*arccosh(c*x)*c^9*d^2*e^2*x^5+4/3*arccosh(c*x)*c^9*d^3*e*x^3+arccosh(c*x)*c^9*d^4*x-1/99225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(1225*c^8*e^4*x^8+8100*c^8*d*e^3*x^6+23814*c^8*d^2*e^2*x^4+1400*c^6*e^4*x^6+44100*c^8*d^3*e*x^2+9720*c^6*d*e^3*x^4+99225*c^8*d^4+31752*c^6*d^2*e^2*x^2+1680*c^4*e^4*x^4+88200*c^6*d^3*e+12960*c^4*d*e^3*x^2+63504*c^4*d^2*e^2+2240*c^2*e^4*x^2+25920*c^2*d*e^3+4480*e^4)))","A"
489,1,364,617,9.447000," ","int(x^4*(a+b*arccosh(c*x))/(e*x^2+d),x)","\frac{a \,x^{3}}{3 e}-\frac{a d x}{e^{2}}+\frac{a \,d^{2} \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{e^{2} \sqrt{d e}}-\frac{b \,x^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{9 c e}+\frac{c b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{2 e^{2}}-\frac{c b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{2 e^{2}}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{3}}{3 e}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}}{9 c^{3} e}+\frac{b d \sqrt{c x -1}\, \sqrt{c x +1}}{c \,e^{2}}-\frac{b d x \,\mathrm{arccosh}\left(c x \right)}{e^{2}}"," ",0,"1/3*a*x^3/e-a*d*x/e^2+a*d^2/e^2/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-1/9*b*x^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/e+1/2*c*b*d^2/e^2*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-1/2*c*b*d^2/e^2*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/3*b/e*arccosh(c*x)*x^3-2/9*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3/e+b*d*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/e^2-b*d*x*arccosh(c*x)/e^2","C"
490,1,2912,549,0.682000," ","int(x^3*(a+b*arccosh(c*x))/(e*x^2+d),x)","\text{output too large to display}"," ",0,"-1/4*b*arccosh(c*x)/c^2/e+1/2*a*x^2/e-3*c^2*b*d^2/e^3/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)-2*c^4*b*d^3/e^4/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+1/2*b*arccosh(c*x)*x^2/e+b*arccosh(c*x)^2*d/e^2-1/4*b/e^2*d*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-1/2*a*d/e^2*ln(c^2*e*x^2+c^2*d)-1/2*b*d/e^2*sum((_R1^2*e+4*c^2*d+2*e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-1/8/c^2*b/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+5/4*c^2*b/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*d^2-2*c^2*b/e^4*d^2*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)+c^6*b*d^4/e^4/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+2*c^4*b*d^3/e^3/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-5/2*c^2*b/e^2/(c^2*d+e)*arccosh(c*x)^2*d^2+1/8/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))-2*c^6*b*d^4/e^4/(c^2*d+e)*arccosh(c*x)^2-4*c^4*b*d^3/e^3/(c^2*d+e)*arccosh(c*x)^2+c^2*b/e^4*d^2*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-2*c^2*b/e^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d^2-2*c^4*b/e^4*d^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-3/4*b/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)*d+1/4*b*(c^2*d*(c^2*d+e))^(1/2)*d/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))+b*(c^2*d*(c^2*d+e))^(1/2)*d/e^2/(c^2*d+e)*arccosh(c*x)^2+b/e^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d*(c^2*d*(c^2*d+e))^(1/2)+1/2*b/e/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d+1/4*b/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*d-1/2*b/e/(c^2*d+e)*arccosh(c*x)^2*d-b/e^3*d*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)+1/2*b/e^3*d*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-1/2*b/e^2*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d-c^2*b/e^3*d^2*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-c^4*b/e^4*d^3*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+2*c^4*b/e^4*d^3*arccosh(c*x)^2+2*c^2*b/e^3*d^2*arccosh(c*x)^2-1/4*b*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/e-3/2*b/e^2/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)*d+1/2*b*(c^2*d*(c^2*d+e))^(1/2)*d/e^2/(c^2*d+e)*arccosh(c*x)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))+3*c^2*b*d^2/e^3/(c^2*d+e)*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)-c^4*b*d^3/e^4/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-3/2*c^2*b*d^2/e^3/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+1/4/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arccosh(c*x)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))+2*c^4*b*d^3/e^4/(c^2*d+e)*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)-1/4/c^2*b/e/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+2*c^2*b/e^4*d^2*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+2*c^6*b*d^4/e^4/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)+4*c^4*b*d^3/e^3/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)+5/2*c^2*b/e^2/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d^2","C"
491,1,284,548,1.360000," ","int(x^2*(a+b*arccosh(c*x))/(e*x^2+d),x)","\frac{a x}{e}-\frac{a d \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{e \sqrt{d e}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}}{c e}+\frac{b x \,\mathrm{arccosh}\left(c x \right)}{e}-\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{2 e}+\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{2 e}"," ",0,"a*x/e-a*d/e/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/e+b*x*arccosh(c*x)/e-1/2*c*b*d/e*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/2*c*b*d/e*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
492,1,2805,487,0.372000," ","int(x*(a+b*arccosh(c*x))/(e*x^2+d),x)","\text{output too large to display}"," ",0,"3/2*b/e/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/2*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arccosh(c*x)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))+3/4*b/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-1/8/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))+1/8/c^2*b/d/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-2*c^4*b/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*d^2-5/4*c^2*b/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*d-c^6*b*d^3/e^3/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+4*c^4*b/e^2/(c^2*d+e)*arccosh(c*x)^2*d^2+5/2*c^2*b/e/(c^2*d+e)*arccosh(c*x)^2*d+1/2*a/e*ln(c^2*e*x^2+c^2*d)+1/2*b/(c^2*d+e)*arccosh(c*x)^2-1/4*b/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-b*arccosh(c*x)^2/e+2*c^4*b*d^2/e^3/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+3*c^2*b/e^2/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)*d-1/2*b/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)+b/e^2*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)-1/2*b/e^2*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+1/2*b/e*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-1/4*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))-b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arccosh(c*x)^2-b/e^2*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)-2*c^2*b*arccosh(c*x)^2*d/e^2+c^4*b/e^3*d^2*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+c^2*b/e^2*d*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-2*c^4*b/e^3*d^2*arccosh(c*x)^2+1/4*b/e*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+1/2*b*sum((_R1^2*e+4*c^2*d+2*e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))/e+2*c^6*b*d^3/e^3/(c^2*d+e)*arccosh(c*x)^2+2*c^4*b/e^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d^2+2*c^2*b/e^2*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d+2*c^2*b/e^3*d*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)-c^2*b/e^3*d*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-4*c^4*b/e^2/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d^2-5/2*c^2*b/e/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d+1/4/c^2*b/d/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/4/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arccosh(c*x)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))-2*c^4*b*d^2/e^3/(c^2*d+e)*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)+3/2*c^2*b/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)*d+c^4*b*d^2/e^3/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-3*c^2*b*(c^2*d*(c^2*d+e))^(1/2)*d/e^2/(c^2*d+e)*arccosh(c*x)^2-2*c^6*b*d^3/e^3/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-2*c^2*b/e^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d*(c^2*d*(c^2*d+e))^(1/2)","C"
493,1,232,509,0.127000," ","int((a+b*arccosh(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{2}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{2}"," ",0,"a/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/2*c*b*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-1/2*c*b*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
494,1,393,553,0.355000," ","int((a+b*arccosh(c*x))/x/(e*x^2+d),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 d}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right) e}{4 d}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d}+\frac{b \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d}+\frac{b \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d}"," ",0,"a/d*ln(c*x)-1/2*a/d*ln(c^2*e*x^2+c^2*d)-1/4*b*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))*e/d+b/d*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-1/4*b*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))/d","C"
495,1,329,549,1.575000," ","int((a+b*arccosh(c*x))/x^2/(e*x^2+d),x)","-\frac{a}{d x}-\frac{a e \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{d \sqrt{d e}}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{d x}-\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(4 \textit{\_R1}^{2} c^{2} d +\textit{\_R1}^{2} e +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{8 c \,d^{2}}+\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{8 c \,d^{2}}+\frac{2 c b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d}"," ",0,"-a/d/x-a*e/d/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-b*arccosh(c*x)/d/x-1/8*b/c/d^2*e*sum((4*_R1^2*c^2*d+_R1^2*e+e)/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/8*b/c/d^2*e*sum((_R1^2*e+4*c^2*d+e)/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+2*c*b/d*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","C"
496,1,462,609,0.420000," ","int((a+b*arccosh(c*x))/x^3/(e*x^2+d),x)","-\frac{a}{2 d \,x^{2}}-\frac{a e \ln \left(c x \right)}{d^{2}}+\frac{a e \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 d^{2}}+\frac{b c \sqrt{c x -1}\, \sqrt{c x +1}}{2 d x}-\frac{c^{2} b}{2 d}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{2 d \,x^{2}}+\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{2}}-\frac{b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}-\frac{b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}-\frac{b e \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}-\frac{b e \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}+\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{2}}"," ",0,"-1/2*a/d/x^2-a/d^2*e*ln(c*x)+1/2*a*e/d^2*ln(c^2*e*x^2+c^2*d)+1/2*b*c*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/x-1/2*c^2*b/d-1/2*b*arccosh(c*x)/d/x^2+1/4*b/d^2*e^2*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-b/d^2*e*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-b/d^2*e*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-b/d^2*e*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-b/d^2*e*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+1/4*b/d^2*e*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
497,1,410,617,1.793000," ","int((a+b*arccosh(c*x))/x^4/(e*x^2+d),x)","-\frac{a}{3 d \,x^{3}}+\frac{a e}{d^{2} x}+\frac{a \,e^{2} \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{d^{2} \sqrt{d e}}+\frac{b c \sqrt{c x -1}\, \sqrt{c x +1}}{6 d \,x^{2}}+\frac{b \,\mathrm{arccosh}\left(c x \right) e}{d^{2} x}-\frac{b \,\mathrm{arccosh}\left(c x \right)}{3 d \,x^{3}}-\frac{2 c b e \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{8 c \,d^{3}}+\frac{c^{3} b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{3 d}+\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(4 \textit{\_R1}^{2} c^{2} d +\textit{\_R1}^{2} e +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{8 c \,d^{3}}"," ",0,"-1/3*a/d/x^3+a/d^2*e/x+a*e^2/d^2/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/6*b*c*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/x^2+b*arccosh(c*x)/d^2*e/x-1/3*b/d*arccosh(c*x)/x^3-2*c*b/d^2*e*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-1/8/c*b/d^3*e^2*sum((_R1^2*e+4*c^2*d+e)/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/3*c^3*b/d*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+1/8/c*b/d^3*e^2*sum((4*_R1^2*c^2*d+_R1^2*e+e)/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
498,1,2964,580,0.929000," ","int(x^3*(a+b*arccosh(c*x))/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"1/2*a/e^2*ln(c^2*e*x^2+c^2*d)+1/4*b/e^2*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-b*arccosh(c*x)^2/e^2+1/2*b/e^2*sum((_R1^2*e+4*c^2*d+2*e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/4/c^2*b/d/e/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+2*c^4*b*d^2/e^4/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/4/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d/e/(c^2*d+e)*arccosh(c*x)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))+3*c^2*b*d/e^3/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+1/2*c^2*a/e^2*d/(c^2*e*x^2+c^2*d)+c^2*b/e^3*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*d-2*c^2*b/e^3*arccosh(c*x)^2*d-2*c^4*b/e^4*d^2*arccosh(c*x)^2+c^4*b/e^4*d^2*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-1/2*b/e/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-b/e^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)+3/4*b/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+1/2*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))-1/4*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))-b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arccosh(c*x)^2+1/2*b/e^2*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-1/2*b/e^3*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+b/e^3*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)+1/2*b/e/(c^2*d+e)*arccosh(c*x)^2-1/4*b/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+1/2*c^2*b*arccosh(c*x)/e^2*d/(c^2*e*x^2+c^2*d)+2*c^2*b/e^3*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d+2*c^4*b/e^4*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d^2-c^2*b/e^4*d*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+4*c^4*b/e^3/(c^2*d+e)*arccosh(c*x)^2*d^2-c^6*b*d^3/e^4/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))+2*c^2*b/e^4*d*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)+2*c^6*b*d^3/e^4/(c^2*d+e)*arccosh(c*x)^2+5/2*c^2*b*d/e^2/(c^2*d+e)*arccosh(c*x)^2-5/4*c^2*b*d/e^2/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))-2*c^4*b/e^3/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*d^2+3/2*b/e^2/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/2*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arccosh(c*x)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))-1/8/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e))-2*c^6*b*d^3/e^4/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-4*c^4*b*d^2/e^3/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-5/2*c^2*b*d/e^2/(c^2*d+e)*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)-2*c^2*b/e^4*ln(1-e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*arccosh(c*x)*d*(c^2*d*(c^2*d+e))^(1/2)+1/8/c^2*b/d/e/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)+3/2*c^2*b/e^3/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)*d-3*c^2*b/e^3/(c^2*d+e)*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)*d+c^4*b*d^2/e^4/(c^2*d+e)*polylog(2,e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2/(-2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)-e))*(c^2*d*(c^2*d+e))^(1/2)-2*c^4*b*d^2/e^4/(c^2*d+e)*arccosh(c*x)^2*(c^2*d*(c^2*d+e))^(1/2)","C"
499,1,638,96,0.039000," ","int(x*(a+b*arccosh(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right)}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{4} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) d}{4 \sqrt{c^{2} x^{2}-1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}}+\frac{c^{4} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) d}{4 \sqrt{c^{2} x^{2}-1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}}-\frac{c^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) e}{4 \sqrt{c^{2} x^{2}-1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}}+\frac{c^{2} b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) e}{4 \sqrt{c^{2} x^{2}-1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{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)*arccosh(c*x)-1/4*c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)/((-c^2*d*e)^(1/2)+e)/(e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*d+1/4*c^4*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)/((-c^2*d*e)^(1/2)+e)/(e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*d-1/4*c^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)/((-c^2*d*e)^(1/2)+e)/(e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*e+1/4*c^2*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)/((-c^2*d*e)^(1/2)+e)/(e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*e","B"
500,1,529,642,0.444000," ","int((a+b*arccosh(c*x))/x/(e*x^2+d)^2,x)","\frac{a \ln \left(c x \right)}{d^{2}}+\frac{a \,c^{2}}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{a \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 d^{2}}+\frac{b \,c^{2} \mathrm{arccosh}\left(c x \right)}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +4 c^{2} d +2 e}{4 \sqrt{d^{2} c^{4}+c^{2} d e}}\right)}{2 d^{2} \left(c^{2} d +e \right)}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{2}}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}+\frac{b \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}+\frac{b \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2}}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right) e}{4 d^{2}}"," ",0,"a/d^2*ln(c*x)+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)+1/2*b*c^2*arccosh(c*x)/d/(c^2*e*x^2+c^2*d)+1/2*b*(c^2*d*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))-1/4*b/d^2*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+b/d^2*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d^2*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d^2*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d^2*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-1/4*b/d^2*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))*e","C"
501,1,723,691,0.639000," ","int((a+b*arccosh(c*x))/x^3/(e*x^2+d)^2,x)","-\frac{a}{2 d^{2} x^{2}}-\frac{2 a e \ln \left(c x \right)}{d^{3}}-\frac{c^{2} a e}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a e \ln \left(c^{2} x^{2} e +c^{2} d \right)}{d^{3}}+\frac{c^{3} b x \sqrt{c x -1}\, \sqrt{c x +1}\, e}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{c^{3} b \sqrt{c x -1}\, \sqrt{c x +1}}{2 x d \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{4} b \,x^{2} e}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{4} b}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) e}{d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right)}{2 x^{2} d \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, e \arctanh \left(\frac{2 \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +4 c^{2} d +2 e}{4 \sqrt{d^{2} c^{4}+c^{2} d e}}\right)}{2 d^{3} \left(c^{2} d +e \right)}+\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{2 d^{3}}-\frac{2 b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3}}-\frac{2 b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3}}-\frac{2 b e \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3}}-\frac{2 b e \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3}}+\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{2 d^{3}}"," ",0,"-1/2*a/d^2/x^2-2*a/d^3*e*ln(c*x)-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)+1/2*c^3*b*x/d^2/(c^2*e*x^2+c^2*d)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e+1/2*c^3*b/x/d/(c^2*e*x^2+c^2*d)*(c*x-1)^(1/2)*(c*x+1)^(1/2)-1/2*c^4*b*x^2/d^2/(c^2*e*x^2+c^2*d)*e-1/2*c^4*b/d/(c^2*e*x^2+c^2*d)-c^2*b*arccosh(c*x)*e/d^2/(c^2*e*x^2+c^2*d)-1/2*c^2*b/x^2/d/(c^2*e*x^2+c^2*d)*arccosh(c*x)-1/2*b*(c^2*d*(c^2*d+e))^(1/2)/d^3/(c^2*d+e)*e*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))+1/2*b/d^3*e*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-2*b/d^3*e*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-2*b/d^3*e*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-2*b/d^3*e*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-2*b/d^3*e*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+1/2*b/d^3*e^2*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
502,1,1749,763,7.079000," ","int(x^4*(a+b*arccosh(c*x))/(e*x^2+d)^2,x)","\frac{a x}{e^{2}}+\frac{c^{2} a d x}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{3 a d \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 e^{2} \sqrt{d e}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d^{2}}{e^{5}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{2 e^{4}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d^{2}}{e^{5}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{2 e^{4}}+\frac{3 c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{4 e^{2}}-\frac{3 c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 e^{2}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}}{c \,e^{2}}+\frac{b x \,\mathrm{arccosh}\left(c x \right)}{e^{2}}+\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) d x}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{3} \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{5} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5}}+\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{3} \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{5} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5}}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5} \left(c^{2} d +e \right)}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{4} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5} \left(c^{2} d +e \right)}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{4} \left(c^{2} d +e \right)}"," ",0,"a*x/e^2+1/2*c^2*a/e^2*d*x/(c^2*e*x^2+c^2*d)-3/2*a/e^2*d/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d^2/e^5-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^4-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d^2/e^5-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^4+3/4*c*b/e^2*d*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-3/4*c*b/e^2*d*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-b*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/e^2+b*x*arccosh(c*x)/e^2+1/2*c^2*b*arccosh(c*x)*d*x/e^2/(c^2*e*x^2+c^2*d)+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)-c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^5*(c^2*d*(c^2*d+e))^(1/2)+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)+c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^5*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)","C"
503,1,1689,723,2.916000," ","int(x^2*(a+b*arccosh(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a x}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 e \sqrt{d e}}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) x}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{e^{4}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{2 e^{3}}-\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{e^{4}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{2 e^{3}}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 e}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{4 e}"," ",0,"-1/2*c^2*a/e*x/(c^2*e*x^2+c^2*d)+1/2*a/e/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-1/2*c^2*b*arccosh(c*x)*x/e/(c^2*e*x^2+c^2*d)-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*d-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^4+c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*d+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^4-c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3+1/4*c*b/e*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-1/4*c*b/e*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
504,1,1695,735,1.933000," ","int((a+b*arccosh(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right) x}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d}+\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d \left(c^{2} d +e \right) e^{2}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{3}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \,e^{3}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{2 d \,e^{2}}+\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d \left(c^{2} d +e \right) e^{2}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{3}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \,e^{3}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{2 d \,e^{2}}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{4 d}"," ",0,"1/2*c^2*a*x/d/(c^2*e*x^2+c^2*d)+1/2*a/d/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/2*c^2*b*arccosh(c*x)*x/d/(c^2*e*x^2+c^2*d)+1/4*c*b/d*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*d+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^2+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3-c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/e^3*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/e^2+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*d-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^2-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3+c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/e^3*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/e^2-1/4*c*b/d*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
505,1,1821,772,6.415000," ","int((a+b*arccosh(c*x))/x^2/(e*x^2+d)^2,x)","-\frac{a}{d^{2} x}-\frac{a e \,c^{2} x}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{3 a e \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 d^{2} \sqrt{d e}}-\frac{3 b \,c^{2} x \,\mathrm{arccosh}\left(c x \right) e}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{b \,c^{2} \mathrm{arccosh}\left(c x \right)}{x d \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{b \,c^{5} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}-\frac{b \,c^{3} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \left(c^{2} d +e \right) e^{2}}-\frac{b \,c^{3} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{d \left(c^{2} d +e \right) e}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d^{2} \left(c^{2} d +e \right) e}+\frac{b \,c^{3} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{d \,e^{2}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d^{2} e^{2}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{2 d^{2} e}-\frac{b \,c^{5} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}+\frac{b \,c^{3} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \left(c^{2} d +e \right) e^{2}}-\frac{b \,c^{3} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{d \left(c^{2} d +e \right) e}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d^{2} \left(c^{2} d +e \right) e}+\frac{b \,c^{3} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{d \,e^{2}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d^{2} e^{2}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{2 d^{2} e}+\frac{3 b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{16 c \,d^{3}}+\frac{2 c b \arctan \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{d^{2}}-\frac{3 b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(4 \textit{\_R1}^{2} c^{2} d +\textit{\_R1}^{2} e +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{16 c \,d^{3}}"," ",0,"-a/d^2/x-1/2*a/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)-3/2*a/d^2*e/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-3/2*b*c^2*x*arccosh(c*x)/d^2/(c^2*e*x^2+c^2*d)*e-b*c^2/x*arccosh(c*x)/d/(c^2*e*x^2+c^2*d)-b*c^5*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^2-b*c^3*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)-b*c^3*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)/e-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/(c^2*d+e)/e*(c^2*d*(c^2*d+e))^(1/2)+b*c^3*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/e^2+c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/e^2*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/e-b*c^5*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^2+b*c^3*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)-b*c^3*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)/e+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/(c^2*d+e)/e*(c^2*d*(c^2*d+e))^(1/2)+b*c^3*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/e^2-c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/e^2*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/e+3/16*b/c/d^3*e*sum((_R1^2*e+4*c^2*d+e)/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+2*c*b/d^2*arctan(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-3/16*b/c/d^3*e*sum((4*_R1^2*c^2*d+_R1^2*e+e)/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
506,1,5196,733,1.564000," ","int(x^5*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
507,1,2499,197,0.035000," ","int(x^3*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","-\frac{c^{2} a}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{c^{4} a d}{4 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right)}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{c^{4} b \,\mathrm{arccosh}\left(c x \right) d}{4 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{8} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) x^{2} d^{2}}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{8} b e \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) d^{3}}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{c^{8} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) x^{2} d^{2}}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{c^{8} b e \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) d^{3}}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{c^{5} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, x d}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2}}-\frac{5 c^{6} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) x^{2} d}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{5 c^{6} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) d^{2}}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{5 c^{6} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) x^{2} d}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{5 c^{6} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) d^{2}}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{c^{3} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, x}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2}}-\frac{3 c^{4} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) x^{2}}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{3 c^{4} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) d}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{3 c^{4} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) x^{2}}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{3 c^{4} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) d}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arccosh(c*x)/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arccosh(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2-1/8*c^8*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*x^2*d^2-1/8*c^8*b*e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*d^3+1/8*c^8*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*x^2*d^2+1/8*c^8*b*e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*d^3+1/8*c^5*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2*x*d-5/16*c^6*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*x^2*d-5/16*c^6*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*d^2+5/16*c^6*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*x^2*d+5/16*c^6*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*d^2+1/8*c^3*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2*x-3/16*c^4*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*x^2-3/16*c^4*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*d+3/16*c^4*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*x^2+3/16*c^4*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*d","B"
508,1,2443,154,0.029000," ","int(x*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a}{4 e \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{4} b \,\mathrm{arccosh}\left(c x \right)}{4 e \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{c^{8} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) x^{2} d}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{c^{8} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) d^{2}}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{8} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) x^{2} d}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{8} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) d^{2}}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{5} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, x}{8 \left(c x e -\sqrt{-c^{2} d e}\right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2}}+\frac{3 c^{6} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) x^{2}}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{3 c^{6} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) d}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{3 c^{6} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) x^{2}}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{3 c^{6} b \,e^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) d}{16 \left(c x e -\sqrt{-c^{2} d e}\right) \sqrt{-c^{2} d e}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e +\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{3} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, x}{8 \left(c x e +\sqrt{-c^{2} d e}\right) \left(c x e -\sqrt{-c^{2} d e}\right) d \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2}}+\frac{c^{4} b \,e^{5} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right) x^{2}}{16 \sqrt{-c^{2} d e}\, \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e -\sqrt{-c^{2} d e}\right) d \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}+\frac{c^{4} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{-c^{2} d e}\, \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e -\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{4} b \,e^{5} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right) x^{2}}{16 \sqrt{-c^{2} d e}\, \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e -\sqrt{-c^{2} d e}\right) d \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}-\frac{c^{4} b \,e^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{-\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x -2 e}{c x e -\sqrt{-c^{2} d e}}\right)}{16 \sqrt{-c^{2} d e}\, \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c x e -\sqrt{-c^{2} d e}\right) \left(e -\sqrt{-c^{2} d e}\right)^{2} \left(\sqrt{-c^{2} d e}+e \right)^{2} \sqrt{c^{2} x^{2}-1}}"," ",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*arccosh(c*x)+1/8*c^8*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*x^2*d+1/8*c^8*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*d^2-1/8*c^8*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*x^2*d-1/8*c^8*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*d^2-1/8*c^5*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2*x+3/16*c^6*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*x^2+3/16*c^6*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*d-3/16*c^6*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*x^2-3/16*c^6*b*e^3*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(-c^2*d*e)^(1/2)/(-(c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*d-1/8*c^3*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(c*x*e-(-c^2*d*e)^(1/2))/d/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2*x+1/16*c^4*b*e^5*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(-c^2*d*e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d+e)/e)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/d/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*x^2+1/16*c^4*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(-c^2*d*e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d+e)/e)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(-2*(-(c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))-1/16*c^4*b*e^5*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(-c^2*d*e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d+e)/e)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/d/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))*x^2-1/16*c^4*b*e^4*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(-c^2*d*e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d+e)/e)^(1/2)/(c*x*e-(-c^2*d*e)^(1/2))/(e-(-c^2*d*e)^(1/2))^2/((-c^2*d*e)^(1/2)+e)^2/(c^2*x^2-1)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*(-(c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e-(-c^2*d*e)^(1/2)))","B"
509,1,1478,790,0.503000," ","int((a+b*arccosh(c*x))/x/(e*x^2+d)^3,x)","\frac{a \,c^{2}}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a \,c^{4}}{4 d \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{b \,c^{6}}{8 \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{a \ln \left(c x \right)}{d^{3}}-\frac{a \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 d^{3}}+\frac{b \,c^{5} \sqrt{c x -1}\, \sqrt{c x +1}\, x e}{8 d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{3 b \,c^{6} \mathrm{arccosh}\left(c x \right)}{4 \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{b \,c^{6} \mathrm{arccosh}\left(c x \right) x^{2} e}{2 d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{b \,c^{4} \mathrm{arccosh}\left(c x \right) x^{2} e^{2}}{2 d^{2} \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{b \,c^{5} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} e^{2}}{8 d^{2} \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{5 b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, e \arctanh \left(\frac{2 \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +4 c^{2} d +2 e}{4 \sqrt{d^{2} c^{4}+c^{2} d e}}\right)}{8 d^{3} \left(c^{2} d +e \right)^{2}}+\frac{3 b \,c^{2} \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +4 c^{2} d +2 e}{4 \sqrt{d^{2} c^{4}+c^{2} d e}}\right)}{4 d^{2} \left(c^{2} d +e \right)^{2}}-\frac{b \,c^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right) e}{4 d^{2} \left(c^{2} d +e \right)}+\frac{b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{b \,c^{2} \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} d +e \right)}+\frac{b \,c^{2} \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} d +e \right)}-\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{3} \left(c^{2} d +e \right)}-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right) e^{2}}{4 d^{3} \left(c^{2} d +e \right)}-\frac{b \,c^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{2} \left(c^{2} d +e \right)}+\frac{b e \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{b e \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{b \,c^{2} \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} d +e \right)}+\frac{b \,c^{2} \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{2} \left(c^{2} d +e \right)}-\frac{b \,c^{6} e^{2} x^{4}}{8 d^{2} \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{b \,c^{6} e \,x^{2}}{4 d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{3 b \,c^{4} \mathrm{arccosh}\left(c x \right) e}{4 d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}"," ",0,"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)^2-1/8*b*c^6/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2+a/d^3*ln(c*x)-1/2*a/d^3*ln(c^2*e*x^2+c^2*d)+1/8*b*c^5/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*e+3/4*b*c^6/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)+1/2*b*c^6/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x^2*e+1/2*b*c^4/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x^2*e^2+1/8*b*c^5/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*e^2+5/8*b*(c^2*d*(c^2*d+e))^(1/2)/d^3/(c^2*d+e)^2*e*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))+b/d^3/(c^2*d+e)*e*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d^3/(c^2*d+e)*e*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+3/4*b*c^2*(c^2*d*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)^2*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))+b*c^2/d^2/(c^2*d+e)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b*c^2/d^2/(c^2*d+e)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-1/4*b*c^2/d^2/(c^2*d+e)*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))*e-1/4*b/d^3/(c^2*d+e)*e*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+b/d^3/(c^2*d+e)*e*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b/d^3/(c^2*d+e)*e*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-1/4*b/d^3/(c^2*d+e)*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))*e^2-1/4*b*c^2/d^2/(c^2*d+e)*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+b*c^2/d^2/(c^2*d+e)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+b*c^2/d^2/(c^2*d+e)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-1/8*b*c^6/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*e^2*x^4-1/4*b*c^6/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*e*x^2+3/4*b*c^4/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*e","C"
510,1,1928,851,0.766000," ","int((a+b*arccosh(c*x))/x^3/(e*x^2+d)^3,x)","-\frac{a}{2 d^{3} x^{2}}-\frac{c^{4} b \,\mathrm{arccosh}\left(c x \right) e}{2 x^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2} d \left(c^{2} d +e \right)}-\frac{3 c^{4} b \,x^{2} \mathrm{arccosh}\left(c x \right) e^{3}}{2 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d^{3} \left(c^{2} d +e \right)}-\frac{3 c^{6} b \,\mathrm{arccosh}\left(c x \right) x^{2} e^{2}}{2 d^{2} \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{7 c^{5} b x \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2}}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d^{2} \left(c^{2} d +e \right)}+\frac{c^{5} b \sqrt{c x -1}\, \sqrt{c x +1}\, e}{2 x \left(c^{2} x^{2} e +c^{2} d \right)^{2} d \left(c^{2} d +e \right)}+\frac{3 c^{5} b \,x^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3}}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d^{3} \left(c^{2} d +e \right)}+\frac{c^{7} b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} e^{2}}{2 d^{2} \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{c^{7} b \sqrt{c x -1}\, \sqrt{c x +1}\, x e}{d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{8} b}{2 \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{3 a e \ln \left(c x \right)}{d^{4}}+\frac{3 a e \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 d^{4}}-\frac{3 c^{6} b \,x^{2} e^{2}}{4 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d^{2} \left(c^{2} d +e \right)}-\frac{c^{8} b \,e^{2} x^{4}}{2 d^{2} \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{8} b e \,x^{2}}{d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{3 c^{6} b \,x^{4} e^{3}}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d^{3} \left(c^{2} d +e \right)}+\frac{c^{7} b \sqrt{c x -1}\, \sqrt{c x +1}}{2 x \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{9 c^{6} b \,\mathrm{arccosh}\left(c x \right) e}{4 d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{9 c^{4} b \,\mathrm{arccosh}\left(c x \right) e^{2}}{4 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d^{2} \left(c^{2} d +e \right)}-\frac{c^{2} a e}{d^{3} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{4} a e}{4 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{3 b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{4} \left(c^{2} d +e \right)}+\frac{3 b \,e^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{4} \left(c^{2} d +e \right)}-\frac{3 b \,e^{2} \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 b \,e^{2} \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 c^{6} b e}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d \left(c^{2} d +e \right)}-\frac{c^{6} b \,\mathrm{arccosh}\left(c x \right)}{2 x^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{9 b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, e^{2} \arctanh \left(\frac{2 \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +4 c^{2} d +2 e}{4 \sqrt{d^{2} c^{4}+c^{2} d e}}\right)}{8 d^{4} \left(c^{2} d +e \right)^{2}}+\frac{3 c^{2} b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e +4 c^{2} d +e \right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{4 d^{3} \left(c^{2} d +e \right)}+\frac{3 c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right) e^{2}}{4 d^{3} \left(c^{2} d +e \right)}-\frac{3 b \,e^{2} \mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 b \,e^{2} \mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 c^{2} b e \dilog \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}-\frac{3 c^{2} b e \dilog \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}-\frac{5 c^{2} b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, e \arctanh \left(\frac{2 \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +4 c^{2} d +2 e}{4 \sqrt{d^{2} c^{4}+c^{2} d e}}\right)}{4 d^{3} \left(c^{2} d +e \right)^{2}}-\frac{3 c^{2} b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1+i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}-\frac{3 c^{2} b e \,\mathrm{arccosh}\left(c x \right) \ln \left(1-i \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)\right)}{d^{3} \left(c^{2} d +e \right)}"," ",0,"-1/2*a/d^3/x^2-1/2*c^4*b/x^2/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*arccosh(c*x)*e-3/2*c^4*b*x^2/(c^2*e*x^2+c^2*d)^2/d^3/(c^2*d+e)*arccosh(c*x)*e^3-3/2*c^6*b/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x^2*e^2+7/8*c^5*b*x/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2+1/2*c^5*b/x/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e+3/8*c^5*b*x^3/(c^2*e*x^2+c^2*d)^2/d^3/(c^2*d+e)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3+1/2*c^7*b/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*e^2+c^7*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*e-1/2*c^8*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2-3*a/d^4*e*ln(c*x)+3/2*a*e/d^4*ln(c^2*e*x^2+c^2*d)-3/4*c^6*b*x^2/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*e^2-1/2*c^8*b/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*e^2*x^4-c^8*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*e*x^2-3/8*c^6*b*x^4/(c^2*e*x^2+c^2*d)^2/d^3/(c^2*d+e)*e^3-5/4*c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d^3/(c^2*d+e)^2*e*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))-3*c^2*b/d^3/(c^2*d+e)*e*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-3*c^2*b/d^3/(c^2*d+e)*e*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+1/2*c^7*b/x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(c*x-1)^(1/2)*(c*x+1)^(1/2)-9/4*c^6*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*e-9/4*c^4*b/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*arccosh(c*x)*e^2-c^2*a*e/d^3/(c^2*e*x^2+c^2*d)-1/4*c^4*a*e/d^2/(c^2*e*x^2+c^2*d)^2-3*b/d^4*e^2/(c^2*d+e)*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+3/4*b/d^4*e^2/(c^2*d+e)*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-3*b/d^4*e^2/(c^2*d+e)*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+3/4*b/d^4*e^3/(c^2*d+e)*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-3/8*c^6*b/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*e-3*b/d^4*e^2/(c^2*d+e)*arccosh(c*x)*ln(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-9/8*b*(c^2*d*(c^2*d+e))^(1/2)/d^4/(c^2*d+e)^2*e^2*arctanh(1/4*(2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+4*c^2*d+2*e)/(c^4*d^2+c^2*d*e)^(1/2))-3*b/d^4*e^2/(c^2*d+e)*arccosh(c*x)*ln(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-1/2*c^6*b/x^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)+3/4*c^2*b/d^3/(c^2*d+e)*e*sum((_R1^2*e+4*c^2*d+e)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-3*c^2*b/d^3/(c^2*d+e)*e*dilog(1+I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))-3*c^2*b/d^3/(c^2*d+e)*e*dilog(1-I*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)))+3/4*c^2*b/d^3/(c^2*d+e)*sum((_R1^2+1)/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))*e^2","C"
511,1,3125,1044,4.243000," ","int(x^4*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"3/8*a/e^2/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-5/4*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-9/4*c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)^2*d^2-5/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+7/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)*d-9/4*c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)^2*d^2-5/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+7/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)*d-c^7*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)^2+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d^2/e^5/(c^2*d+e)-c^7*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)^2+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d^2/e^5/(c^2*d+e)-5/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)+5/4*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+5/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-1/8*c^5*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*d-3/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e^2*d*x+5/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)+5/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)+3/16*c^3*b/e^2/(c^2*d+e)*d*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-3/16*c^3*b/e^2/(c^2*d+e)*d*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-5/8*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)*x^3+7/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)*d-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-1/8*c^5*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*d^2-5/8*c^6*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)*x^3*d-3/8*c^6*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)*x*d^2-3/8*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)*x*d+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-7/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)*d-5/8*c^4*a/(c^2*e*x^2+c^2*d)^2*x^3/e-3/16*c*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+3/16*c*b/e/(c^2*d+e)*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))","C"
512,1,2269,1060,3.270000," ","int(x^2*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{4 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{4 e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{4 \left(c^{2} d +e \right)^{2} e^{2}}+\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{8 d e \sqrt{d e}}+\frac{c^{4} a \,x^{3}}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} d}-\frac{c^{4} a x}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} e}+\frac{c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{16 e \left(c^{2} d +e \right)}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d +e}\right)}{16 d \left(c^{2} d +e \right)}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{16 d \left(c^{2} d +e \right)}-\frac{c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d +2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c x -1}\, \sqrt{c x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d +e \right)}\right)}{16 e \left(c^{2} d +e \right)}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} d \,e^{2}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} d \left(c^{2} d +e \right)}+\frac{c^{4} b e \,\mathrm{arccosh}\left(c x \right) x^{3}}{8 d \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{c^{5} b d \sqrt{c x +1}\, \sqrt{c x -1}}{8 e \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{6} b \,\mathrm{arccosh}\left(c x \right) x d}{8 e \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} d \,e^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} d \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{4 e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{4 \left(c^{2} d +e \right)^{2} e^{2}}+\frac{c^{6} b \,\mathrm{arccosh}\left(c x \right) x^{3}}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} b \,\mathrm{arccosh}\left(c x \right) x}{8 \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{8 e^{2} d \left(c^{2} d +e \right)}+\frac{c^{5} b \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{8 \left(c^{2} d +e \right) \left(c^{2} x^{2} e +c^{2} d \right)^{2}}+\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{4 e^{3} \left(c^{2} d +e \right)^{2}}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{8 e^{2} d \left(c^{2} d +e \right)}"," ",0,"1/4*c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+1/4*c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+1/16*c^3*b/e/(c^2*d+e)*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/8*a/d/e/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/d*x^3-1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x+1/16*c*b/d/(c^2*d+e)*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-1/16*c*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-1/16*c^3*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+1/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)-1/4*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-1/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)+1/4*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/8*c^4*b*e/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x^3+1/8*c^5*b/e*d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)-1/8*c^6*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)*x*d-1/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)-1/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)+1/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/e^2+1/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/e^2+1/8*c^6*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccosh(c*x)*x^3-1/8*c^4*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x+1/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-1/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-1/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^2/d/(c^2*d+e)-1/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^2/d/(c^2*d+e)+1/8*c^5*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2","C"
513,1,3128,1057,3.127000," ","int((a+b*arccosh(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-3/16*c*b/d^2/(c^2*d+e)*e*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+3/16*c*b/d^2/(c^2*d+e)*e*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))+7/4*c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/e^2+7/4*c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/e^2-1/8*c^5*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)+5/8*c^6*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)-1/8*c^5*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*e-3/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/(c^2*d+e)^2/e*(c^2*d*(c^2*d+e))^(1/2)+3/4*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^2/d^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+3/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/(c^2*d+e)^2/e*(c^2*d*(c^2*d+e))^(1/2)+3/8*c^6*b*e/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x^3+3/8*c^4*b/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x^3*e^2+5/8*c^4*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arccosh(c*x)*x*e+5/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-5/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-3/4*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^2/d^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+3/8*a/d^2/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/4*c^4*a*x/d/(c^2*e*x^2+c^2*d)^2+3/8*c^2*a/d^2*x/(c^2*e*x^2+c^2*d)+3/16*c^3*b/d/(c^2*d+e)*sum(_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-3/16*c^3*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*e+2*c^2*d+e)*(arccosh(c*x)*ln((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)+dilog((_R1-c*x-(c*x-1)^(1/2)*(c*x+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d+2*e)*_Z^2+e))-5/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^2/d/(c^2*d+e)-5/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^2/d/(c^2*d+e)+c^7*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-3/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e/d^2/(c^2*d+e)+3/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)^2/e-3/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e/d^2/(c^2*d+e)+3/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)^2/e+c^7*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*d","C"
514,0,0,20,0.558000," ","int((a+b*arccosh(c*x))*(e*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccosh(c*x))*(e*x^2+d)^(1/2),x)","F"
515,0,0,20,0.602000," ","int((a+b*arccosh(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccosh}\left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccosh(c*x))/(e*x^2+d)^(1/2),x)","F"
516,0,0,85,0.638000," ","int((a+b*arccosh(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccosh}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))/(e*x^2+d)^(3/2),x)","F"
517,0,0,150,0.712000," ","int((a+b*arccosh(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccosh}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))/(e*x^2+d)^(5/2),x)","F"
518,0,0,240,0.832000," ","int((a+b*arccosh(c*x))/(e*x^2+d)^(7/2),x)","\int \frac{a +b \,\mathrm{arccosh}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))/(e*x^2+d)^(7/2),x)","F"
519,-2,0,536,180.000000," ","int((f*x)^m*(e*x^2+d)^3*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^3*(a+b*arccosh(c*x)),x)","F"
520,-2,0,335,180.000000," ","int((f*x)^m*(e*x^2+d)^2*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^2*(a+b*arccosh(c*x)),x)","F"
521,-2,0,184,180.000000," ","int((f*x)^m*(e*x^2+d)*(a+b*arccosh(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(a+b*arccosh(c*x)),x)","F"
522,0,0,25,1.200000," ","int((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d),x)","F"
523,0,0,25,1.233000," ","int((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d)^2,x)","F"
524,0,0,25,1.084000," ","int((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d)^3,x)","F"
525,1,632,529,0.137000," ","int((e*x^2+d)^3*(a+b*arccosh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{7} e^{3} c^{7} x^{7}+\frac{3}{5} c^{7} d \,e^{2} x^{5}+c^{7} d^{2} e \,x^{3}+x \,c^{7} d^{3}\right)}{c^{6}}+\frac{b^{2} \left(\frac{e^{3} \left(3675 \mathrm{arccosh}\left(c x \right)^{2} c^{7} x^{7}-1050 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{6} x^{6}-1260 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{4} x^{4}+150 c^{7} x^{7}-1680 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2}+252 c^{5} x^{5}-3360 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+560 c^{3} x^{3}+3360 c x \right)}{25725}+\frac{d \,e^{2} c^{2} \left(225 \mathrm{arccosh}\left(c x \right)^{2} c^{5} x^{5}-90 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{4} x^{4}-120 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2}+18 c^{5} x^{5}-240 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+40 c^{3} x^{3}+240 c x \right)}{375}+\frac{c^{4} d^{2} e \left(9 \mathrm{arccosh}\left(c x \right)^{2} c^{3} x^{3}-6 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2}-12 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c^{3} x^{3}+12 c x \right)}{9}+d^{3} c^{6} \left(\mathrm{arccosh}\left(c x \right)^{2} c x -2 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c x \right)\right)}{c^{6}}+\frac{2 a b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{3} c^{7} x^{7}}{7}+\frac{3 \,\mathrm{arccosh}\left(c x \right) d \,e^{2} c^{7} x^{5}}{5}+\mathrm{arccosh}\left(c x \right) c^{7} d^{2} e \,x^{3}+\mathrm{arccosh}\left(c x \right) c^{7} x \,d^{3}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(75 c^{6} e^{3} x^{6}+441 c^{6} d \,e^{2} x^{4}+1225 c^{6} d^{2} e \,x^{2}+90 c^{4} e^{3} x^{4}+3675 d^{3} c^{6}+588 c^{4} d \,e^{2} x^{2}+2450 c^{4} d^{2} e +120 c^{2} e^{3} x^{2}+1176 d \,e^{2} c^{2}+240 e^{3}\right)}{3675}\right)}{c^{6}}}{c}"," ",0,"1/c*(a^2/c^6*(1/7*e^3*c^7*x^7+3/5*c^7*d*e^2*x^5+c^7*d^2*e*x^3+x*c^7*d^3)+b^2/c^6*(1/25725*e^3*(3675*arccosh(c*x)^2*c^7*x^7-1050*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^6*x^6-1260*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^4*x^4+150*c^7*x^7-1680*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2+252*c^5*x^5-3360*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+560*c^3*x^3+3360*c*x)+1/375*d*e^2*c^2*(225*arccosh(c*x)^2*c^5*x^5-90*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^4*x^4-120*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2+18*c^5*x^5-240*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+40*c^3*x^3+240*c*x)+1/9*c^4*d^2*e*(9*arccosh(c*x)^2*c^3*x^3-6*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2-12*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c^3*x^3+12*c*x)+d^3*c^6*(arccosh(c*x)^2*c*x-2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c*x))+2*a*b/c^6*(1/7*arccosh(c*x)*e^3*c^7*x^7+3/5*arccosh(c*x)*d*e^2*c^7*x^5+arccosh(c*x)*c^7*d^2*e*x^3+arccosh(c*x)*c^7*x*d^3-1/3675*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(75*c^6*e^3*x^6+441*c^6*d*e^2*x^4+1225*c^6*d^2*e*x^2+90*c^4*e^3*x^4+3675*c^6*d^3+588*c^4*d*e^2*x^2+2450*c^4*d^2*e+120*c^2*e^3*x^2+1176*c^2*d*e^2+240*e^3)))","A"
526,1,402,311,0.117000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} d e \,x^{3}+x \,c^{5} d^{2}\right)}{c^{4}}+\frac{b^{2} \left(\frac{e^{2} \left(225 \mathrm{arccosh}\left(c x \right)^{2} c^{5} x^{5}-90 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{4} x^{4}-120 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2}+18 c^{5} x^{5}-240 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+40 c^{3} x^{3}+240 c x \right)}{1125}+\frac{2 c^{2} d e \left(9 \mathrm{arccosh}\left(c x \right)^{2} c^{3} x^{3}-6 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2}-12 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c^{3} x^{3}+12 c x \right)}{27}+d^{2} c^{4} \left(\mathrm{arccosh}\left(c x \right)^{2} c x -2 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c x \right)\right)}{c^{4}}+\frac{2 a b \left(\frac{\mathrm{arccosh}\left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \,\mathrm{arccosh}\left(c x \right) c^{5} d e \,x^{3}}{3}+\mathrm{arccosh}\left(c x \right) c^{5} x \,d^{2}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(9 c^{4} e^{2} x^{4}+50 c^{4} d e \,x^{2}+225 d^{2} c^{4}+12 c^{2} e^{2} x^{2}+100 c^{2} d e +24 e^{2}\right)}{225}\right)}{c^{4}}}{c}"," ",0,"1/c*(a^2/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*d*e*x^3+x*c^5*d^2)+b^2/c^4*(1/1125*e^2*(225*arccosh(c*x)^2*c^5*x^5-90*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^4*x^4-120*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2+18*c^5*x^5-240*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+40*c^3*x^3+240*c*x)+2/27*c^2*d*e*(9*arccosh(c*x)^2*c^3*x^3-6*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2-12*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c^3*x^3+12*c*x)+d^2*c^4*(arccosh(c*x)^2*c*x-2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c*x))+2*a*b/c^4*(1/5*arccosh(c*x)*e^2*c^5*x^5+2/3*arccosh(c*x)*c^5*d*e*x^3+arccosh(c*x)*c^5*x*d^2-1/225*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(9*c^4*e^2*x^4+50*c^4*d*e*x^2+225*c^4*d^2+12*c^2*e^2*x^2+100*c^2*d*e+24*e^2)))","A"
527,1,217,146,0.103000," ","int((e*x^2+d)*(a+b*arccosh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{3} c^{3} x^{3} e +c^{3} d x \right)}{c^{2}}+\frac{b^{2} \left(\frac{e \left(9 \mathrm{arccosh}\left(c x \right)^{2} c^{3} x^{3}-6 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2}-12 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c^{3} x^{3}+12 c x \right)}{27}+c^{2} d \left(\mathrm{arccosh}\left(c x \right)^{2} c x -2 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c x \right)\right)}{c^{2}}+\frac{2 a b \left(\frac{\mathrm{arccosh}\left(c x \right) c^{3} x^{3} e}{3}+\mathrm{arccosh}\left(c x \right) c^{3} d x -\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(c^{2} x^{2} e +9 c^{2} d +2 e \right)}{9}\right)}{c^{2}}}{c}"," ",0,"1/c*(a^2/c^2*(1/3*c^3*x^3*e+c^3*d*x)+b^2/c^2*(1/27*e*(9*arccosh(c*x)^2*c^3*x^3-6*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2-12*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c^3*x^3+12*c*x)+c^2*d*(arccosh(c*x)^2*c*x-2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c*x))+2*a*b/c^2*(1/3*arccosh(c*x)*c^3*x^3*e+arccosh(c*x)*c^3*d*x-1/9*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(c^2*e*x^2+9*c^2*d+2*e)))","A"
528,1,78,47,0.068000," ","int((a+b*arccosh(c*x))^2,x)","\frac{a^{2} c x +b^{2} \left(\mathrm{arccosh}\left(c x \right)^{2} c x -2 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}+2 c x \right)+2 a b \left(c x \,\mathrm{arccosh}\left(c x \right)-\sqrt{c x -1}\, \sqrt{c x +1}\right)}{c}"," ",0,"1/c*(a^2*c*x+b^2*(arccosh(c*x)^2*c*x-2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c*x)+2*a*b*(c*x*arccosh(c*x)-(c*x-1)^(1/2)*(c*x+1)^(1/2)))","A"
529,0,0,791,0.629000," ","int((a+b*arccosh(c*x))^2/(e*x^2+d),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/(e*x^2+d),x)","F"
530,0,0,22,0.378000," ","int((a+b*arccosh(c*x))^2*(e*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccosh(c*x))^2*(e*x^2+d)^(1/2),x)","F"
531,0,0,22,0.466000," ","int((a+b*arccosh(c*x))^2/(e*x^2+d)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/(e*x^2+d)^(1/2),x)","F"
532,0,0,22,0.444000," ","int((a+b*arccosh(c*x))^2/(e*x^2+d)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/(e*x^2+d)^(3/2),x)","F"
533,0,0,22,0.444000," ","int((a+b*arccosh(c*x))^2/(e*x^2+d)^(5/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/(e*x^2+d)^(5/2),x)","F"
534,1,380,368,0.443000," ","int((e*x^2+d)^2/(a+b*arccosh(c*x)),x)","\frac{-\frac{e^{2} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right)}{32 c^{4} b}+\frac{e^{2} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right)}{32 c^{4} b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) d^{2}}{2 b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) d e}{4 c^{2} b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) e^{2}}{16 c^{4} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) d^{2}}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) d e}{4 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) e^{2}}{16 c^{4} b}+\frac{e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) d}{4 c^{2} b}+\frac{3 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right)}{32 c^{4} b}-\frac{e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) d}{4 c^{2} b}-\frac{3 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right)}{32 c^{4} b}}{c}"," ",0,"1/c*(-1/32/c^4*e^2/b*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)+1/32/c^4*e^2/b*exp(5*a/b)*Ei(1,5*arccosh(c*x)+5*a/b)+1/2/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*d^2+1/4/c^2/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*d*e+1/16/c^4/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*e^2-1/2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*d^2-1/4/c^2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*d*e-1/16/c^4/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*e^2+1/4/c^2*e/b*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)*d+3/32/c^4*e^2/b*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)-1/4/c^2*e/b*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b)*d-3/32/c^4*e^2/b*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b))","A"
535,1,178,131,0.416000," ","int((e*x^2+d)/(a+b*arccosh(c*x)),x)","\frac{-\frac{e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right)}{8 c^{2} b}+\frac{e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right)}{8 c^{2} b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) d}{2 b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) e}{8 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) d}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) e}{8 c^{2} b}}{c}"," ",0,"1/c*(-1/8/c^2*e/b*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b)+1/8/c^2*e/b*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)+1/2/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*d+1/8/c^2/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*e-1/2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*d-1/8/c^2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*e)","A"
536,1,56,54,0.035000," ","int(1/(a+b*arccosh(c*x)),x)","\frac{\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right)}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right)}{2 b}}{c}"," ",0,"1/c*(1/2/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)-1/2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b))","A"
537,0,0,22,0.456000," ","int(1/(e*x^2+d)/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arccosh(c*x)),x)","F"
538,0,0,22,0.666000," ","int(1/(e*x^2+d)^2/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arccosh(c*x)),x)","F"
539,0,0,22,0.340000," ","int((e*x^2+d)^(1/2)/(a+b*arccosh(c*x)),x)","\int \frac{\sqrt{e \,x^{2}+d}}{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int((e*x^2+d)^(1/2)/(a+b*arccosh(c*x)),x)","F"
540,0,0,22,0.389000," ","int(1/(a+b*arccosh(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(1/(a+b*arccosh(c*x))/(e*x^2+d)^(1/2),x)","F"
541,0,0,22,0.375000," ","int(1/(e*x^2+d)^(3/2)/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(3/2)/(a+b*arccosh(c*x)),x)","F"
542,0,0,22,0.374000," ","int(1/(e*x^2+d)^(5/2)/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(5/2)/(a+b*arccosh(c*x)),x)","F"
543,1,1102,478,0.571000," ","int((e*x^2+d)^2/(a+b*arccosh(c*x))^2,x)","\frac{\frac{\left(-16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+12 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-\sqrt{c x -1}\, \sqrt{c x +1}+16 c^{5} x^{5}-20 c^{3} x^{3}+5 c x \right) e^{2}}{32 c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 e^{2} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \,\mathrm{arccosh}\left(c x \right)+\frac{5 a}{b}\right)}{32 c^{4} b^{2}}-\frac{e^{2} \left(16 c^{5} x^{5}-20 c^{3} x^{3}+16 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{4} c^{4}+5 c x -12 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+\sqrt{c x -1}\, \sqrt{c x +1}\right)}{32 b \,c^{4} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{5 e^{2} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(c x \right)-\frac{5 a}{b}\right)}{32 b^{2} c^{4}}+\frac{\left(-\sqrt{c x -1}\, \sqrt{c x +1}+c x \right) d^{2}}{2 b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{d^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right)}{2 b^{2}}+\frac{\left(-\sqrt{c x -1}\, \sqrt{c x +1}+c x \right) d e}{4 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{d e \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right)}{4 c^{2} b^{2}}+\frac{\left(-\sqrt{c x -1}\, \sqrt{c x +1}+c x \right) e^{2}}{16 c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right)}{16 c^{4} b^{2}}-\frac{d^{2} \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{2 b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{d^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right)}{2 b^{2}}-\frac{d e \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{4 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{d e \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right)}{4 c^{2} b^{2}}-\frac{e^{2} \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{16 c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right)}{16 c^{4} b^{2}}+\frac{\left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+\sqrt{c x -1}\, \sqrt{c x +1}+4 c^{3} x^{3}-3 c x \right) d e}{4 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{3 \left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+\sqrt{c x -1}\, \sqrt{c x +1}+4 c^{3} x^{3}-3 c x \right) e^{2}}{32 c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right) d}{4 c^{2} b^{2}}-\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right)}{32 c^{4} b^{2}}-\frac{e \left(4 c^{3} x^{3}-3 c x +4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-\sqrt{c x -1}\, \sqrt{c x +1}\right) d}{4 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 e^{2} \left(4 c^{3} x^{3}-3 c x +4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-\sqrt{c x -1}\, \sqrt{c x +1}\right)}{32 c^{4} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right) d}{4 c^{2} b^{2}}-\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right)}{32 c^{4} b^{2}}}{c}"," ",0,"1/c*(1/32*(-16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+12*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-(c*x-1)^(1/2)*(c*x+1)^(1/2)+16*c^5*x^5-20*c^3*x^3+5*c*x)*e^2/c^4/b/(a+b*arccosh(c*x))-5/32*e^2/c^4/b^2*exp(5*a/b)*Ei(1,5*arccosh(c*x)+5*a/b)-1/32/b*e^2/c^4*(16*c^5*x^5-20*c^3*x^3+16*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^4*c^4+5*c*x-12*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-5/32/b^2*e^2/c^4*exp(-5*a/b)*Ei(1,-5*arccosh(c*x)-5*a/b)+1/2*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*d^2/b/(a+b*arccosh(c*x))-1/2*d^2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)+1/4*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*d*e/c^2/b/(a+b*arccosh(c*x))-1/4/c^2*d*e/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)+1/16*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*e^2/c^4/b/(a+b*arccosh(c*x))-1/16/c^4*e^2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)-1/2/b*d^2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-1/2/b^2*d^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)-1/4/c^2/b*d*e*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-1/4/c^2/b^2*d*e*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)-1/16/c^4/b*e^2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-1/16/c^4/b^2*e^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)+1/4*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c^3*x^3-3*c*x)*d*e/c^2/b/(a+b*arccosh(c*x))+3/32*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c^3*x^3-3*c*x)*e^2/c^4/b/(a+b*arccosh(c*x))-3/4*e/c^2/b^2*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)*d-9/32*e^2/c^4/b^2*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)-1/4/c^2*e/b*(4*c^3*x^3-3*c*x+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))*d-3/32/c^4*e^2/b*(4*c^3*x^3-3*c*x+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-3/4/c^2*e/b^2*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b)*d-9/32/c^4*e^2/b^2*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b))","B"
544,1,465,241,0.474000," ","int((e*x^2+d)/(a+b*arccosh(c*x))^2,x)","\frac{\frac{\left(-4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}+\sqrt{c x -1}\, \sqrt{c x +1}+4 c^{3} x^{3}-3 c x \right) e}{8 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(c x \right)+\frac{3 a}{b}\right)}{8 c^{2} b^{2}}-\frac{e \left(4 c^{3} x^{3}-3 c x +4 \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2} c^{2}-\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{3 e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(c x \right)-\frac{3 a}{b}\right)}{8 c^{2} b^{2}}+\frac{\left(-\sqrt{c x -1}\, \sqrt{c x +1}+c x \right) d}{2 b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}+\frac{\left(-\sqrt{c x -1}\, \sqrt{c x +1}+c x \right) e}{8 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) d}{2 b^{2}}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) e}{8 c^{2} b^{2}}-\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) d}{2 b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e}{8 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) d}{2 b^{2}}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) e}{8 c^{2} b^{2}}}{c}"," ",0,"1/c*(1/8*(-4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2+(c*x-1)^(1/2)*(c*x+1)^(1/2)+4*c^3*x^3-3*c*x)*e/c^2/b/(a+b*arccosh(c*x))-3/8/c^2*e/b^2*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)-1/8/c^2*e/b*(4*c^3*x^3-3*c*x+4*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2*c^2-(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-3/8/c^2*e/b^2*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b)+1/2*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*d/b/(a+b*arccosh(c*x))+1/8*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*e/c^2/b/(a+b*arccosh(c*x))-1/2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*d-1/8/c^2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*e-1/2/b*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))*d-1/8/c^2/b*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))*e-1/2/b^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*d-1/8/c^2/b^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*e)","A"
545,1,125,86,0.052000," ","int(1/(a+b*arccosh(c*x))^2,x)","\frac{-\frac{c x +\sqrt{c x -1}\, \sqrt{c x +1}}{2 b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right)}{2 b^{2}}+\frac{-\sqrt{c x -1}\, \sqrt{c x +1}+c x}{2 b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right)}{2 b^{2}}}{c}"," ",0,"1/c*(-1/2/b*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-1/2/b^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)+1/2*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)/b/(a+b*arccosh(c*x))-1/2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b))","A"
546,0,0,22,0.455000," ","int(1/(e*x^2+d)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arccosh(c*x))^2,x)","F"
547,0,0,22,0.708000," ","int(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^2,x)","F"
548,0,0,22,0.380000," ","int((e*x^2+d)^(1/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{\sqrt{e \,x^{2}+d}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((e*x^2+d)^(1/2)/(a+b*arccosh(c*x))^2,x)","F"
549,0,0,22,0.390000," ","int(1/(a+b*arccosh(c*x))^2/(e*x^2+d)^(1/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(1/(a+b*arccosh(c*x))^2/(e*x^2+d)^(1/2),x)","F"
550,0,0,22,0.374000," ","int(1/(e*x^2+d)^(3/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(3/2)/(a+b*arccosh(c*x))^2,x)","F"
551,0,0,22,0.374000," ","int(1/(e*x^2+d)^(5/2)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(5/2)/(a+b*arccosh(c*x))^2,x)","F"
552,-2,0,521,180.000000," ","int((e*x^2+d)^2*(a+b*arccosh(c*x))^(1/2),x)","\int \left(e \,x^{2}+d \right)^{2} \sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int((e*x^2+d)^2*(a+b*arccosh(c*x))^(1/2),x)","F"
553,-2,0,248,180.000000," ","int((e*x^2+d)*(a+b*arccosh(c*x))^(1/2),x)","\int \left(e \,x^{2}+d \right) \sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int((e*x^2+d)*(a+b*arccosh(c*x))^(1/2),x)","F"
554,0,0,79,0.014000," ","int((a+b*arccosh(c*x))^(1/2),x)","\int \sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int((a+b*arccosh(c*x))^(1/2),x)","F"
555,0,0,22,0.651000," ","int((a+b*arccosh(c*x))^(1/2)/(e*x^2+d),x)","\int \frac{\sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccosh(c*x))^(1/2)/(e*x^2+d),x)","F"
556,0,0,22,1.430000," ","int((a+b*arccosh(c*x))^(1/2)/(e*x^2+d)^2,x)","\int \frac{\sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arccosh(c*x))^(1/2)/(e*x^2+d)^2,x)","F"
557,-2,0,344,180.000000," ","int((e*x^2+d)*(a+b*arccosh(c*x))^(3/2),x)","\int \left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((e*x^2+d)*(a+b*arccosh(c*x))^(3/2),x)","F"
558,0,0,109,0.000000," ","int((a+b*arccosh(c*x))^(3/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arccosh(c*x))^(3/2),x)","F"
559,0,0,22,0.625000," ","int((a+b*arccosh(c*x))^(3/2)/(e*x^2+d),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccosh(c*x))^(3/2)/(e*x^2+d),x)","F"
560,0,0,22,1.349000," ","int((a+b*arccosh(c*x))^(3/2)/(e*x^2+d)^2,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arccosh(c*x))^(3/2)/(e*x^2+d)^2,x)","F"
561,-2,0,471,180.000000," ","int((e*x^2+d)^2/(a+b*arccosh(c*x))^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right)^{2}}{\sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}\, dx"," ",0,"int((e*x^2+d)^2/(a+b*arccosh(c*x))^(1/2),x)","F"
562,-2,0,219,180.000000," ","int((e*x^2+d)/(a+b*arccosh(c*x))^(1/2),x)","\int \frac{e \,x^{2}+d}{\sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}\, dx"," ",0,"int((e*x^2+d)/(a+b*arccosh(c*x))^(1/2),x)","F"
563,0,0,67,0.000000," ","int(1/(a+b*arccosh(c*x))^(1/2),x)","\int \frac{1}{\sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}\, dx"," ",0,"int(1/(a+b*arccosh(c*x))^(1/2),x)","F"
564,0,0,22,0.641000," ","int(1/(e*x^2+d)/(a+b*arccosh(c*x))^(1/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arccosh(c*x))^(1/2),x)","F"
565,0,0,22,1.309000," ","int(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^(1/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \sqrt{a +b \,\mathrm{arccosh}\left(c x \right)}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^(1/2),x)","F"
566,-2,0,286,180.000000," ","int((e*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{e \,x^{2}+d}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","F"
567,0,0,97,0.002000," ","int(1/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(c*x))^(3/2),x)","F"
568,0,0,22,0.634000," ","int(1/(e*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arccosh(c*x))^(3/2),x)","F"
569,0,0,22,1.299000," ","int(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x)","F"