1,1,351,161,0.033000," ","int((e*x+d)^3*arccosh(c*x),x)","\frac{e^{3} \mathrm{arccosh}\left(c x \right) x^{4}}{4}+e^{2} \mathrm{arccosh}\left(c x \right) x^{3} d +\frac{3 e \,\mathrm{arccosh}\left(c x \right) x^{2} d^{2}}{2}+\mathrm{arccosh}\left(c x \right) x \,d^{3}+\frac{\mathrm{arccosh}\left(c x \right) d^{4}}{4 e}-\frac{e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{16 c}-\frac{e^{2} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} d}{3 c}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, d^{4} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{4 e \sqrt{c^{2} x^{2}-1}}-\frac{3 e \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} x}{4 c}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, d^{3}}{c}-\frac{3 e \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{3 e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, x}{32 c^{3}}-\frac{2 e^{2} \sqrt{c x -1}\, \sqrt{c x +1}\, d}{3 c^{3}}-\frac{3 e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{32 c^{4} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/4*e^3*arccosh(c*x)*x^4+e^2*arccosh(c*x)*x^3*d+3/2*e*arccosh(c*x)*x^2*d^2+arccosh(c*x)*x*d^3+1/4/e*arccosh(c*x)*d^4-1/16/c*e^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-1/3/c*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*d-1/4/e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^4*ln(c*x+(c^2*x^2-1)^(1/2))-3/4/c*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^2*x-1/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^3-3/4/c^2*e*(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))-3/32/c^3*e^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x-2/3/c^3*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d-3/32/c^4*e^3*(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))","B"
2,1,233,106,0.011000," ","int((e*x+d)^2*arccosh(c*x),x)","\frac{e^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{3}+e \,\mathrm{arccosh}\left(c x \right) x^{2} d +\mathrm{arccosh}\left(c x \right) x \,d^{2}+\frac{\mathrm{arccosh}\left(c x \right) d^{3}}{3 e}-\frac{e^{2} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{9 c}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, d^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 e \sqrt{c^{2} x^{2}-1}}-\frac{e \sqrt{c x -1}\, \sqrt{c x +1}\, d x}{2 c}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, d^{2}}{c}-\frac{e \sqrt{c x -1}\, \sqrt{c x +1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{2 e^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{9 c^{3}}"," ",0,"1/3*e^2*arccosh(c*x)*x^3+e*arccosh(c*x)*x^2*d+arccosh(c*x)*x*d^2+1/3/e*arccosh(c*x)*d^3-1/9/c*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2-1/3/e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^3*ln(c*x+(c^2*x^2-1)^(1/2))-1/2/c*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*x-1/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^2-1/2/c^2*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-2/9/c^3*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)","B"
3,1,107,81,0.013000," ","int((e*x+d)*arccosh(c*x),x)","\frac{\mathrm{arccosh}\left(c x \right) x^{2} e}{2}+\mathrm{arccosh}\left(c x \right) x d -\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, e x}{4 c}-\frac{d \sqrt{c x -1}\, \sqrt{c x +1}}{c}-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{4 c^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/2*arccosh(c*x)*x^2*e+arccosh(c*x)*x*d-1/4/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e*x-d*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/4/c^2*(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"
4,1,295,220,0.164000," ","int(arccosh(c*x)/(e*x+d),x)","-\frac{\mathrm{arccosh}\left(c x \right)^{2}}{2 e}+\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}+\frac{\mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}+\frac{\dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}+\frac{\dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}"," ",0,"-1/2*arccosh(c*x)^2/e+1/e*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))+1/e*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))+1/e*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))+1/e*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))","A"
5,1,126,71,0.030000," ","int(arccosh(c*x)/(e*x+d)^2,x)","-\frac{c \,\mathrm{arccosh}\left(c x \right)}{\left(c x e +c d \right) e}-\frac{c \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right)}{e^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{c^{2} x^{2}-1}}"," ",0,"-c/(c*e*x+c*d)/e*arccosh(c*x)-c/e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*x^2-1)^(1/2)","A"
6,1,338,112,0.023000," ","int(arccosh(c*x)/(e*x+d)^3,x)","-\frac{c^{2} \mathrm{arccosh}\left(c x \right)}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x d}{2 e \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right) \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{4} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{2}}{2 e^{2} \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right) \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{2} \sqrt{c x +1}\, \sqrt{c x -1}}{2 \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}"," ",0,"-1/2*c^2/(c*e*x+c*d)^2/e*arccosh(c*x)-1/2*c^4/e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d-1/2*c^4/e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^2-1/2*c^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)","B"
7,1,1108,166,0.025000," ","int(arccosh(c*x)/(e*x+d)^4,x)","-\frac{c^{3} \mathrm{arccosh}\left(c x \right)}{3 \left(c x e +c d \right)^{3} e}-\frac{c^{7} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x^{2} d^{2}}{3 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{2 c^{7} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x \,d^{3}}{3 e \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} e \sqrt{c x +1}\, \sqrt{c x -1}\, x d}{2 \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}-\frac{c^{5} e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x^{2}}{6 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{7} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{4}}{3 e^{2} \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{2 c^{5} \sqrt{c x +1}\, \sqrt{c x -1}\, d^{2}}{3 \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}-\frac{c^{5} e \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x d}{3 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{2}}{6 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{c^{3} e^{2} \sqrt{c x +1}\, \sqrt{c x -1}}{6 \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}"," ",0,"-1/3*c^3/(c*e*x+c*d)^3/e*arccosh(c*x)-1/3*c^7*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x^2*d^2-2/3*c^7/e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d^3-1/2*c^5*e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x*d-1/6*c^5*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x^2-1/3*c^7/e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^4-2/3*c^5*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*d^2-1/3*c^5*e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d-1/6*c^5*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^2+1/6*c^3*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2","B"
8,1,329,282,0.127000," ","int((e*x+d)^3*arccosh(c*x)^2,x)","\frac{72 \mathrm{arccosh}\left(c x \right)^{2} c^{4} x^{4} e^{3}+288 \mathrm{arccosh}\left(c x \right)^{2} c^{4} x^{3} d \,e^{2}+432 \mathrm{arccosh}\left(c x \right)^{2} c^{4} x^{2} d^{2} e +288 \mathrm{arccosh}\left(c x \right)^{2} c^{4} x \,d^{3}-36 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x^{3} e^{3}-192 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x^{2} d \,e^{2}-432 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} x \,d^{2} e -576 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3} d^{3}-216 \mathrm{arccosh}\left(c x \right)^{2} c^{2} d^{2} e -54 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c x \,e^{3}-384 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c d \,e^{2}+9 c^{4} e^{3} x^{4}+64 c^{4} d \,e^{2} x^{3}+216 c^{4} d^{2} e \,x^{2}+576 x \,c^{4} d^{3}-27 \mathrm{arccosh}\left(c x \right)^{2} e^{3}+27 c^{2} x^{2} e^{3}+384 x \,c^{2} d \,e^{2}}{288 c^{4}}"," ",0,"1/288/c^4*(72*arccosh(c*x)^2*c^4*x^4*e^3+288*arccosh(c*x)^2*c^4*x^3*d*e^2+432*arccosh(c*x)^2*c^4*x^2*d^2*e+288*arccosh(c*x)^2*c^4*x*d^3-36*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x^3*e^3-192*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x^2*d*e^2-432*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*x*d^2*e-576*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^3*d^3-216*arccosh(c*x)^2*c^2*d^2*e-54*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c*x*e^3-384*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c*d*e^2+9*c^4*e^3*x^4+64*c^4*d*e^2*x^3+216*c^4*d^2*e*x^2+576*x*c^4*d^3-27*arccosh(c*x)^2*e^3+27*c^2*x^2*e^3+384*x*c^2*d*e^2)","A"
9,1,207,183,0.113000," ","int((e*x+d)^2*arccosh(c*x)^2,x)","\frac{18 \mathrm{arccosh}\left(c x \right)^{2} c^{3} x^{3} e^{2}+54 \mathrm{arccosh}\left(c x \right)^{2} c^{3} x^{2} d e +54 \mathrm{arccosh}\left(c x \right)^{2} c^{3} x \,d^{2}-12 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x^{2} e^{2}-54 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} x d e -108 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, c^{2} d^{2}-27 \mathrm{arccosh}\left(c x \right)^{2} c d e -24 \,\mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2}+4 e^{2} c^{3} x^{3}+27 c^{3} x^{2} d e +108 x \,c^{3} d^{2}+24 c x \,e^{2}}{54 c^{3}}"," ",0,"1/54/c^3*(18*arccosh(c*x)^2*c^3*x^3*e^2+54*arccosh(c*x)^2*c^3*x^2*d*e+54*arccosh(c*x)^2*c^3*x*d^2-12*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x^2*e^2-54*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*x*d*e-108*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*c^2*d^2-27*arccosh(c*x)^2*c*d*e-24*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2+4*e^2*c^3*x^3+27*c^3*x^2*d*e+108*x*c^3*d^2+24*c*x*e^2)","A"
10,1,100,104,0.097000," ","int((e*x+d)*arccosh(c*x)^2,x)","\frac{\frac{e \left(2 \mathrm{arccosh}\left(c x \right)^{2} c^{2} x^{2}-2 \,\mathrm{arccosh}\left(c x \right) c x \sqrt{c x -1}\, \sqrt{c x +1}-\mathrm{arccosh}\left(c x \right)^{2}+c^{2} x^{2}\right)}{4 c}+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)}{c}"," ",0,"1/c*(1/4*e*(2*arccosh(c*x)^2*c^2*x^2-2*arccosh(c*x)*c*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)-arccosh(c*x)^2+c^2*x^2)/c+d*(arccosh(c*x)^2*c*x-2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*c*x))","A"
11,0,0,336,0.265000," ","int(arccosh(c*x)^2/(e*x+d),x)","\int \frac{\mathrm{arccosh}\left(c x \right)^{2}}{e x +d}\, dx"," ",0,"int(arccosh(c*x)^2/(e*x+d),x)","F"
12,1,374,295,0.355000," ","int(arccosh(c*x)^2/(e*x+d)^2,x)","-\frac{c \mathrm{arccosh}\left(c x \right)^{2}}{e \left(c x e +c d \right)}+\frac{2 c \,\mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}-\frac{2 c \,\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}+\frac{2 c \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}-\frac{2 c \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}"," ",0,"-c*arccosh(c*x)^2/e/(c*e*x+c*d)+2*c/e*arccosh(c*x)/(c^2*d^2-e^2)^(1/2)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))-2*c/e*arccosh(c*x)/(c^2*d^2-e^2)^(1/2)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))+2*c/e/(c^2*d^2-e^2)^(1/2)*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))-2*c/e/(c^2*d^2-e^2)^(1/2)*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))","A"
13,1,766,382,0.516000," ","int(arccosh(c*x)^2/(e*x+d)^3,x)","-\frac{c^{3} \mathrm{arccosh}\left(c x \right) e \sqrt{c x +1}\, \sqrt{c x -1}\, x}{\left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{4} \mathrm{arccosh}\left(c x \right) e \,x^{2}}{\left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{4} \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{2 e \left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{3} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, d}{\left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 c^{4} \mathrm{arccosh}\left(c x \right) d x}{\left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{4} \mathrm{arccosh}\left(c x \right) d^{2}}{e \left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} \mathrm{arccosh}\left(c x \right)^{2} e}{2 \left(c x e +c d \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{3} \mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}-\frac{c^{3} \mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}+\frac{c^{3} \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}-\frac{c^{3} \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}+\frac{c^{2} \ln \left(2 c d \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +e \right)}{\left(c^{2} d^{2}-e^{2}\right) e}-\frac{2 c^{2} \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{\left(c^{2} d^{2}-e^{2}\right) e}"," ",0,"-c^3*arccosh(c*x)*e/(c*e*x+c*d)^2/(c^2*d^2-e^2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x+c^4*arccosh(c*x)*e/(c*e*x+c*d)^2/(c^2*d^2-e^2)*x^2-1/2*c^4*arccosh(c*x)^2/e/(c*e*x+c*d)^2/(c^2*d^2-e^2)*d^2-c^3*arccosh(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*d+2*c^4*arccosh(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)*d*x+c^4*arccosh(c*x)/e/(c*e*x+c*d)^2/(c^2*d^2-e^2)*d^2+1/2*c^2*arccosh(c*x)^2*e/(c*e*x+c*d)^2/(c^2*d^2-e^2)+c^3/(c^2*d^2-e^2)^(3/2)/e*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))*d-c^3/(c^2*d^2-e^2)^(3/2)/e*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))*d+c^3/(c^2*d^2-e^2)^(3/2)/e*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))*d-c^3/(c^2*d^2-e^2)^(3/2)/e*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))*d+c^2/(c^2*d^2-e^2)/e*ln(2*c*d*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+e)-2*c^2/(c^2*d^2-e^2)/e*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))","B"
14,1,408,169,0.006000," ","int((e*x+d)^3*(a+b*arccosh(c*x)),x)","\frac{a \,x^{4} e^{3}}{4}+a d \,e^{2} x^{3}+\frac{3 a \,d^{2} e \,x^{2}}{2}+a x \,d^{3}+\frac{a \,d^{4}}{4 e}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{4} e^{3}}{4}+b \,\mathrm{arccosh}\left(c x \right) d \,e^{2} x^{3}+\frac{3 b \,\mathrm{arccosh}\left(c x \right) d^{2} e \,x^{2}}{2}+b \,\mathrm{arccosh}\left(c x \right) x \,d^{3}+\frac{b \,\mathrm{arccosh}\left(c x \right) d^{4}}{4 e}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{4} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{4 e \sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x^{3}}{16 c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} d \,e^{2}}{3 c}-\frac{3 b \,d^{2} e x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}-\frac{b \,d^{3} \sqrt{c x -1}\, \sqrt{c x +1}}{c}-\frac{3 b e \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{3 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{3} x}{32 c^{3}}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}\, d \,e^{2}}{3 c^{3}}-\frac{3 b \,e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, \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^3+a*d*e^2*x^3+3/2*a*d^2*e*x^2+a*x*d^3+1/4*a/e*d^4+1/4*b*arccosh(c*x)*x^4*e^3+b*arccosh(c*x)*d*e^2*x^3+3/2*b*arccosh(c*x)*d^2*e*x^2+b*arccosh(c*x)*x*d^3+1/4*b/e*arccosh(c*x)*d^4-1/4*b/e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^4*ln(c*x+(c^2*x^2-1)^(1/2))-1/16/c*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x^3-1/3*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*d*e^2-3/4*b*d^2*e*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-b*d^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-3/4/c^2*b*e*(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))-3/32/c^3*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^3*x-2/3*b/c^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e^2-3/32/c^4*b*e^3*(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))","B"
15,1,274,115,0.006000," ","int((e*x+d)^2*(a+b*arccosh(c*x)),x)","\frac{a \,x^{3} e^{2}}{3}+a d e \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,\mathrm{arccosh}\left(c x \right) x^{3} e^{2}}{3}+b \,\mathrm{arccosh}\left(c x \right) d e \,x^{2}+b \,\mathrm{arccosh}\left(c x \right) x \,d^{2}+\frac{b \,\mathrm{arccosh}\left(c x \right) d^{3}}{3 e}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 e \sqrt{c^{2} x^{2}-1}}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} e^{2}}{9 c}-\frac{b d e x \sqrt{c x -1}\, \sqrt{c x +1}}{2 c}-\frac{b \,d^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{c}-\frac{b e \sqrt{c x -1}\, \sqrt{c x +1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{2 b \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2}}{9 c^{3}}"," ",0,"1/3*a*x^3*e^2+a*d*e*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*arccosh(c*x)*x^3*e^2+b*arccosh(c*x)*d*e*x^2+b*arccosh(c*x)*x*d^2+1/3*b/e*arccosh(c*x)*d^3-1/3*b/e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^3*ln(c*x+(c^2*x^2-1)^(1/2))-1/9*b/c*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*e^2-1/2*b*d*e*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-b*d^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-1/2/c^2*b*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-2/9*b/c^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2","B"
16,1,123,90,0.006000," ","int((e*x+d)*(a+b*arccosh(c*x)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \,\mathrm{arccosh}\left(c x \right) x^{2} e}{2}+b \,\mathrm{arccosh}\left(c x \right) x d -\frac{b e x \sqrt{c x -1}\, \sqrt{c x +1}}{4 c}-\frac{b d \sqrt{c x -1}\, \sqrt{c x +1}}{c}-\frac{b \sqrt{c x -1}\, \sqrt{c x +1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{4 c^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arccosh(c*x)*x^2*e+b*arccosh(c*x)*x*d-1/4*b*e*x*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c-b*d*(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)*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
17,1,314,237,0.043000," ","int((a+b*arccosh(c*x))/(e*x+d),x)","\frac{a \ln \left(c x e +c d \right)}{e}-\frac{b \mathrm{arccosh}\left(c x \right)^{2}}{2 e}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}+\frac{b \,\mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}+\frac{b \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}+\frac{b \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e}"," ",0,"a*ln(c*e*x+c*d)/e-1/2*b*arccosh(c*x)^2/e+b/e*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))+b/e*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))+b/e*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))+b/e*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))","A"
18,1,145,78,0.006000," ","int((a+b*arccosh(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c x e +c d \right) e}-\frac{c b \,\mathrm{arccosh}\left(c x \right)}{\left(c x e +c d \right) e}-\frac{c b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right)}{e^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{c^{2} x^{2}-1}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arccosh(c*x)-c*b/e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*x^2-1)^(1/2)","A"
19,1,361,121,0.006000," ","int((a+b*arccosh(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{2} b \,\mathrm{arccosh}\left(c x \right)}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{4} b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x d}{2 e \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right) \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{4} b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{2}}{2 e^{2} \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right) \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{2} b \sqrt{c x +1}\, \sqrt{c x -1}}{2 \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arccosh(c*x)-1/2*c^4*b/e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d-1/2*c^4*b/e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^2-1/2*c^2*b*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)","B"
20,1,1137,176,0.005000," ","int((a+b*arccosh(c*x))/(e*x+d)^4,x)","-\frac{c^{3} a}{3 \left(c x e +c d \right)^{3} e}-\frac{c^{3} b \,\mathrm{arccosh}\left(c x \right)}{3 \left(c x e +c d \right)^{3} e}-\frac{c^{7} b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x^{2} d^{2}}{3 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{2 c^{7} b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x \,d^{3}}{3 e \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{7} b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{4}}{3 e^{2} \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} b e \sqrt{c x +1}\, \sqrt{c x -1}\, x d}{2 \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}-\frac{2 c^{5} b \sqrt{c x +1}\, \sqrt{c x -1}\, d^{2}}{3 \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}-\frac{c^{5} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x^{2}}{6 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} b e \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x d}{3 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{2}}{6 \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{c^{3} b \,e^{2} \sqrt{c x +1}\, \sqrt{c x -1}}{6 \left(c d +e \right) \left(c d -e \right) \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}"," ",0,"-1/3*c^3*a/(c*e*x+c*d)^3/e-1/3*c^3*b/(c*e*x+c*d)^3/e*arccosh(c*x)-1/3*c^7*b*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x^2*d^2-2/3*c^7*b/e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d^3-1/3*c^7*b/e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^4-1/2*c^5*b*e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x*d-2/3*c^5*b*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*d^2-1/6*c^5*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x^2-1/3*c^5*b*e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d-1/6*c^5*b*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^2+1/6*c^3*b*e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c^2*d^2-e^2)/(c*e*x+c*d)^2","B"
21,1,791,346,0.084000," ","int((e*x+d)^3*(a+b*arccosh(c*x))^2,x)","2 b^{2} d^{3} x +\frac{a^{2} d^{4}}{4 e}-\frac{3 b^{2} \mathrm{arccosh}\left(c x \right)^{2} e^{3}}{32 c^{4}}+b^{2} \mathrm{arccosh}\left(c x \right)^{2} x \,d^{3}+\frac{b^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{4} e^{3}}{4}+a^{2} e^{2} x^{3} d +\frac{3 a^{2} e \,x^{2} d^{2}}{2}-\frac{3 a b e \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{2 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, d^{3}}{c}-\frac{2 a b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{3}}{c}+2 a b \,e^{2} \mathrm{arccosh}\left(c x \right) x^{3} d +3 a b e \,\mathrm{arccosh}\left(c x \right) x^{2} d^{2}-\frac{2 a b \,e^{2} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} d}{3 c}-\frac{a b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{4} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 e \sqrt{c^{2} x^{2}-1}}-\frac{2 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} d \,e^{2}}{3 c}-\frac{3 a b e \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2} x}{2 c}-\frac{3 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x \,d^{2} e}{2 c}-\frac{3 a b \,e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{16 c^{4} \sqrt{c^{2} x^{2}-1}}+\frac{a b \,\mathrm{arccosh}\left(c x \right) d^{4}}{2 e}+b^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{3} d \,e^{2}+\frac{3 b^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{2} d^{2} e}{2}+\frac{a b \,e^{3} \mathrm{arccosh}\left(c x \right) x^{4}}{2}+2 a b \,\mathrm{arccosh}\left(c x \right) x \,d^{3}+\frac{3 b^{2} d^{2} e \,x^{2}}{4}+\frac{3 b^{2} e^{3} x^{2}}{32 c^{2}}+\frac{2 b^{2} d \,e^{2} x^{3}}{9}-\frac{4 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, d \,e^{2}}{3 c^{3}}-\frac{a b \,e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3}}{8 c}-\frac{4 a b \,e^{2} \sqrt{c x -1}\, \sqrt{c x +1}\, d}{3 c^{3}}-\frac{3 a b \,e^{3} \sqrt{c x -1}\, \sqrt{c x +1}\, x}{16 c^{3}}-\frac{b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{3} e^{3}}{8 c}-\frac{3 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x \,e^{3}}{16 c^{3}}+\frac{b^{2} e^{3} x^{4}}{32}-\frac{3 b^{2} \mathrm{arccosh}\left(c x \right)^{2} d^{2} e}{4 c^{2}}+a^{2} x \,d^{3}+\frac{a^{2} e^{3} x^{4}}{4}+\frac{4 b^{2} d \,e^{2} x}{3 c^{2}}"," ",0,"2*b^2*d^3*x+1/4*a^2/e*d^4-3/32/c^4*b^2*arccosh(c*x)^2*e^3+b^2*arccosh(c*x)^2*x*d^3+1/4*b^2*arccosh(c*x)^2*x^4*e^3+a^2*e^2*x^3*d+3/2*a^2*e*x^2*d^2-3/2/c^2*a*b*e*(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))-2/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^3-2/c*a*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^3+2*a*b*e^2*arccosh(c*x)*x^3*d+3*a*b*e*arccosh(c*x)*x^2*d^2-2/3/c*a*b*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*d-1/2*a*b/e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^4*ln(c*x+(c^2*x^2-1)^(1/2))-2/3/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*d*e^2-3/2/c*a*b*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^2*x-3/2/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d^2*e-3/16/c^4*a*b*e^3*(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))+1/2*a*b/e*arccosh(c*x)*d^4+b^2*arccosh(c*x)^2*x^3*d*e^2+3/2*b^2*arccosh(c*x)^2*x^2*d^2*e+1/2*a*b*e^3*arccosh(c*x)*x^4+2*a*b*arccosh(c*x)*x*d^3+3/4*b^2*d^2*e*x^2+3/32*b^2*e^3*x^2/c^2+2/9*b^2*d*e^2*x^3-4/3/c^3*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*e^2-1/8/c*a*b*e^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3-4/3/c^3*a*b*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d-3/16/c^3*a*b*e^3*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x-1/8/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^3*e^3-3/16/c^3*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*e^3+1/32*b^2*e^3*x^4-3/4/c^2*b^2*arccosh(c*x)^2*d^2*e+a^2*x*d^3+1/4*a^2*e^3*x^4+4/3*b^2*d*e^2*x/c^2","B"
22,1,517,227,0.074000," ","int((e*x+d)^2*(a+b*arccosh(c*x))^2,x)","2 b^{2} d^{2} x -\frac{2 a b \,e^{2} \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2}}{9 c}-\frac{2 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x^{2} e^{2}}{9 c}-\frac{a b e \sqrt{c x -1}\, \sqrt{c x +1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{c^{2} x^{2}-1}}-\frac{4 a b \,e^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{9 c^{3}}-\frac{4 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, e^{2}}{9 c^{3}}+2 a b e \,\mathrm{arccosh}\left(c x \right) x^{2} d -\frac{2 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2}}{c}-\frac{2 a b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{2}}{c}+b^{2} \mathrm{arccosh}\left(c x \right)^{2} x \,d^{2}+a^{2} e \,x^{2} d +\frac{a^{2} d^{3}}{3 e}+\frac{b^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{3} e^{2}}{3}+\frac{2 b^{2} e^{2} x^{3}}{27}-\frac{b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x d e}{c}-\frac{2 a b \sqrt{c x -1}\, \sqrt{c x +1}\, d^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 e \sqrt{c^{2} x^{2}-1}}-\frac{a b e \sqrt{c x -1}\, \sqrt{c x +1}\, d x}{c}+\frac{4 b^{2} e^{2} x}{9 c^{2}}+\frac{b^{2} d e \,x^{2}}{2}+b^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{2} d e -\frac{b^{2} \mathrm{arccosh}\left(c x \right)^{2} d e}{2 c^{2}}+2 a b \,\mathrm{arccosh}\left(c x \right) x \,d^{2}+\frac{2 a b \,\mathrm{arccosh}\left(c x \right) d^{3}}{3 e}+\frac{2 a b \,e^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{3}+a^{2} x \,d^{2}+\frac{a^{2} e^{2} x^{3}}{3}"," ",0,"2*b^2*d^2*x-2/9/c*a*b*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2-2/9/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x^2*e^2-1/c^2*a*b*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-4/9/c^3*a*b*e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)-4/9/c^3*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e^2+2*a*b*e*arccosh(c*x)*x^2*d-2/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^2-2/c*a*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d^2+b^2*arccosh(c*x)^2*x*d^2+a^2*e*x^2*d+1/3*a^2/e*d^3+1/3*b^2*arccosh(c*x)^2*x^3*e^2+2/27*b^2*e^2*x^3-1/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*d*e-2/3*a*b/e*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*d^3*ln(c*x+(c^2*x^2-1)^(1/2))-1/c*a*b*e*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d*x+4/9*b^2*e^2*x/c^2+1/2*b^2*d*e*x^2+b^2*arccosh(c*x)^2*x^2*d*e-1/2/c^2*b^2*arccosh(c*x)^2*d*e+2*a*b*arccosh(c*x)*x*d^2+2/3*a*b/e*arccosh(c*x)*d^3+2/3*a*b*e^2*arccosh(c*x)*x^3+a^2*x*d^2+1/3*a^2*e^2*x^3","B"
23,1,245,132,0.099000," ","int((e*x+d)*(a+b*arccosh(c*x))^2,x)","\frac{a^{2} x^{2} e}{2}+a^{2} d x +\frac{b^{2} \mathrm{arccosh}\left(c x \right)^{2} x^{2} e}{2}-\frac{b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, x e}{2 c}+\frac{b^{2} e \,x^{2}}{4}-\frac{b^{2} \mathrm{arccosh}\left(c x \right)^{2} e}{4 c^{2}}+b^{2} \mathrm{arccosh}\left(c x \right)^{2} x d -\frac{2 b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x -1}\, \sqrt{c x +1}\, d}{c}+2 b^{2} d x +a b \,\mathrm{arccosh}\left(c x \right) x^{2} e +2 a b \,\mathrm{arccosh}\left(c x \right) x d -\frac{a b \sqrt{c x -1}\, \sqrt{c x +1}\, e x}{2 c}-\frac{2 a b \sqrt{c x -1}\, \sqrt{c x +1}\, d}{c}-\frac{a b \sqrt{c x -1}\, \sqrt{c x +1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{2} \sqrt{c^{2} x^{2}-1}}"," ",0,"1/2*a^2*x^2*e+a^2*d*x+1/2*b^2*arccosh(c*x)^2*x^2*e-1/2/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*x*e+1/4*b^2*e*x^2-1/4/c^2*b^2*arccosh(c*x)^2*e+b^2*arccosh(c*x)^2*x*d-2/c*b^2*arccosh(c*x)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d+2*b^2*d*x+a*b*arccosh(c*x)*x^2*e+2*a*b*arccosh(c*x)*x*d-1/2/c*a*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*e*x-2/c*a*b*(c*x-1)^(1/2)*(c*x+1)^(1/2)*d-1/2/c^2*a*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"
24,0,0,367,0.033000," ","int((a+b*arccosh(c*x))^2/(e*x+d),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}{e x +d}\, dx"," ",0,"int((a+b*arccosh(c*x))^2/(e*x+d),x)","F"
25,1,536,315,0.072000," ","int((a+b*arccosh(c*x))^2/(e*x+d)^2,x)","-\frac{c \,a^{2}}{\left(c x e +c d \right) e}-\frac{c \,b^{2} \mathrm{arccosh}\left(c x \right)^{2}}{e \left(c x e +c d \right)}+\frac{2 c \,b^{2} \mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}-\frac{2 c \,b^{2} \mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}+\frac{2 c \,b^{2} \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}-\frac{2 c \,b^{2} \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}-\frac{2 c a b \,\mathrm{arccosh}\left(c x \right)}{\left(c x e +c d \right) e}-\frac{2 c a b \sqrt{c x -1}\, \sqrt{c x +1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right)}{e^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{c^{2} x^{2}-1}}"," ",0,"-c*a^2/(c*e*x+c*d)/e-c*b^2*arccosh(c*x)^2/e/(c*e*x+c*d)+2*c*b^2/e*arccosh(c*x)/(c^2*d^2-e^2)^(1/2)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))-2*c*b^2/e*arccosh(c*x)/(c^2*d^2-e^2)^(1/2)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))+2*c*b^2/e/(c^2*d^2-e^2)^(1/2)*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))-2*c*b^2/e/(c^2*d^2-e^2)^(1/2)*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))-2*c*a*b/(c*e*x+c*d)/e*arccosh(c*x)-2*c*a*b/e^2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*x^2-1)^(1/2)","A"
26,1,1170,410,0.161000," ","int((a+b*arccosh(c*x))^2/(e*x+d)^3,x)","-\frac{c^{2} a^{2}}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{4} b^{2} \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{2 e \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}-\frac{c^{3} b^{2} \mathrm{arccosh}\left(c x \right) e \sqrt{c x +1}\, \sqrt{c x -1}\, x}{\left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}-\frac{c^{3} b^{2} \mathrm{arccosh}\left(c x \right) \sqrt{c x +1}\, \sqrt{c x -1}\, d}{\left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}+\frac{c^{4} b^{2} \mathrm{arccosh}\left(c x \right) e \,x^{2}}{\left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}+\frac{2 c^{4} b^{2} \mathrm{arccosh}\left(c x \right) x d}{\left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}+\frac{c^{4} b^{2} \mathrm{arccosh}\left(c x \right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}+\frac{c^{2} b^{2} \mathrm{arccosh}\left(c x \right)^{2} e}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c x e +c d \right)^{2}}+\frac{c^{3} b^{2} \mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}-\frac{c^{3} b^{2} \mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}+\frac{c^{3} b^{2} \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e -c d +\sqrt{c^{2} d^{2}-e^{2}}}{-c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}-\frac{c^{3} b^{2} \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) e +c d +\sqrt{c^{2} d^{2}-e^{2}}}{c d +\sqrt{c^{2} d^{2}-e^{2}}}\right) d}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}} e}+\frac{c^{2} b^{2} \ln \left(2 c d \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)+\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} e +e \right)}{\left(c^{2} d^{2}-e^{2}\right) e}-\frac{2 c^{2} b^{2} \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{\left(c^{2} d^{2}-e^{2}\right) e}-\frac{c^{2} a b \,\mathrm{arccosh}\left(c x \right)}{\left(c x e +c d \right)^{2} e}-\frac{c^{4} a b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) x d}{e \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right) \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{4} a b \sqrt{c x +1}\, \sqrt{c x -1}\, \ln \left(-\frac{2 \left(c^{2} d x -\sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e +e \right)}{c x e +c d}\right) d^{2}}{e^{2} \sqrt{c^{2} x^{2}-1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right) \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{2} a b \sqrt{c x +1}\, \sqrt{c x -1}}{\left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}"," ",0,"-1/2*c^2*a^2/(c*e*x+c*d)^2/e-1/2*c^4*b^2*arccosh(c*x)^2/e/(c^2*d^2-e^2)/(c*e*x+c*d)^2*d^2-c^3*b^2*arccosh(c*x)*e/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-c^3*b^2*arccosh(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*d+c^4*b^2*arccosh(c*x)*e/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x^2+2*c^4*b^2*arccosh(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x*d+c^4*b^2*arccosh(c*x)/e/(c^2*d^2-e^2)/(c*e*x+c*d)^2*d^2+1/2*c^2*b^2*arccosh(c*x)^2*e/(c^2*d^2-e^2)/(c*e*x+c*d)^2+c^3*b^2/(c^2*d^2-e^2)^(3/2)/e*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))*d-c^3*b^2/(c^2*d^2-e^2)^(3/2)/e*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))*d+c^3*b^2/(c^2*d^2-e^2)^(3/2)/e*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e-c*d+(c^2*d^2-e^2)^(1/2))/(-c*d+(c^2*d^2-e^2)^(1/2)))*d-c^3*b^2/(c^2*d^2-e^2)^(3/2)/e*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*e+c*d+(c^2*d^2-e^2)^(1/2))/(c*d+(c^2*d^2-e^2)^(1/2)))*d+c^2*b^2/(c^2*d^2-e^2)/e*ln(2*c*d*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*e+e)-2*c^2*b^2/(c^2*d^2-e^2)/e*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-c^2*a*b/(c*e*x+c*d)^2/e*arccosh(c*x)-c^4*a*b/e*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*x*d-c^4*a*b/e^2*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^2*x^2-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)/((c^2*d^2-e^2)/e^2)^(1/2)*ln(-2*(c^2*d*x-(c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e+e)/(c*e*x+c*d))*d^2-c^2*a*b*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)","B"
27,1,394,374,0.565000," ","int((e*x+d)^3/(a+b*arccosh(c*x)),x)","\frac{-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \,\mathrm{arccosh}\left(c x \right)-\frac{4 a}{b}\right)}{16 c^{3} b}+\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \,\mathrm{arccosh}\left(c x \right)+\frac{4 a}{b}\right)}{16 c^{3} b}+\frac{3 e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right) d^{2}}{4 c b}+\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right)}{8 c^{3} b}-\frac{3 e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right) d^{2}}{4 c b}-\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right)}{8 c^{3} b}-\frac{3 d \,e^{2} {\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{d^{3} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right)}{2 b}+\frac{3 d \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) e^{2}}{8 c^{2} b}-\frac{d^{3} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right)}{2 b}-\frac{3 d \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) e^{2}}{8 c^{2} b}+\frac{3 d \,e^{2} {\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}}{c}"," ",0,"1/c*(-1/16/c^3*e^3/b*exp(-4*a/b)*Ei(1,-4*arccosh(c*x)-4*a/b)+1/16/c^3*e^3/b*exp(4*a/b)*Ei(1,4*arccosh(c*x)+4*a/b)+3/4/c*e/b*exp(2*a/b)*Ei(1,2*arccosh(c*x)+2*a/b)*d^2+1/8/c^3*e^3/b*exp(2*a/b)*Ei(1,2*arccosh(c*x)+2*a/b)-3/4/c*e/b*exp(-2*a/b)*Ei(1,-2*arccosh(c*x)-2*a/b)*d^2-1/8/c^3*e^3/b*exp(-2*a/b)*Ei(1,-2*arccosh(c*x)-2*a/b)-3/8/c^2*d*e^2/b*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b)+1/2*d^3/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)+3/8/c^2*d/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*e^2-1/2*d^3/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)-3/8/c^2*d/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*e^2+3/8/c^2*d*e^2/b*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b))","A"
28,1,254,237,0.421000," ","int((e*x+d)^2/(a+b*arccosh(c*x)),x)","\frac{-\frac{e^{2} {\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^{2} {\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}}{2 b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) e^{2}}{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}}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) e^{2}}{8 c^{2} b}-\frac{d e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right)}{2 c b}+\frac{d e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right)}{2 c b}}{c}"," ",0,"1/c*(-1/8/c^2*e^2/b*exp(-3*a/b)*Ei(1,-3*arccosh(c*x)-3*a/b)+1/8/c^2*e^2/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^2+1/8/c^2/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^2-1/8/c^2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*e^2-1/2/c*d*e/b*exp(-2*a/b)*Ei(1,-2*arccosh(c*x)-2*a/b)+1/2/c*d*e/b*exp(2*a/b)*Ei(1,2*arccosh(c*x)+2*a/b))","A"
29,1,120,112,0.286000," ","int((e*x+d)/(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) d}{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{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right)}{4 c b}+\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right)}{4 c b}}{c}"," ",0,"1/c*(1/2/b*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*d-1/2/b*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*d-1/4/c*e/b*exp(-2*a/b)*Ei(1,-2*arccosh(c*x)-2*a/b)+1/4/c*e/b*exp(2*a/b)*Ei(1,2*arccosh(c*x)+2*a/b))","A"
30,0,0,20,0.285000," ","int(1/(e*x+d)/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(e x +d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arccosh(c*x)),x)","F"
31,0,0,20,0.458000," ","int(1/(e*x+d)^2/(a+b*arccosh(c*x)),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)^2/(a+b*arccosh(c*x)),x)","F"
32,1,649,354,0.494000," ","int((e*x+d)^2/(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^{2}}{8 c^{2} b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\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)}{8 c^{2} b^{2}}-\frac{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)}{8 b \,c^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\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)}{8 b^{2} c^{2}}+\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) e^{2}}{8 c^{2} 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)}{8 c^{2} 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{e^{2} \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{8 c^{2} 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)}{8 c^{2} b^{2}}+\frac{\left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +2 c^{2} x^{2}-1\right) d e}{2 c \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{e d \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right)}{c \,b^{2}}-\frac{e d \left(2 c^{2} x^{2}-1+2 \sqrt{c x +1}\, \sqrt{c x -1}\, x c \right)}{2 b c \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{e d \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right)}{b^{2} c}}{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^2/c^2/b/(a+b*arccosh(c*x))-3/8*e^2/c^2/b^2*exp(3*a/b)*Ei(1,3*arccosh(c*x)+3*a/b)-1/8/b*e^2/c^2*(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/b^2*e^2/c^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^2/b/(a+b*arccosh(c*x))-1/2*d^2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)+1/8*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*e^2/c^2/b/(a+b*arccosh(c*x))-1/8/c^2*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)-1/8/c^2/b*e^2*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))-1/8/c^2/b^2*e^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)+1/2*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+2*c^2*x^2-1)*d*e/c/(a+b*arccosh(c*x))/b-e*d/c/b^2*exp(2*a/b)*Ei(1,2*arccosh(c*x)+2*a/b)-1/2/b*e*d/c*(2*c^2*x^2-1+2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c)/(a+b*arccosh(c*x))-1/b^2*e*d/c*exp(-2*a/b)*Ei(1,-2*arccosh(c*x)-2*a/b))","A"
33,1,285,182,0.327000," ","int((e*x+d)/(a+b*arccosh(c*x))^2,x)","\frac{\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{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(c x \right)+\frac{a}{b}\right) d}{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{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(c x \right)-\frac{a}{b}\right) d}{2 b^{2}}+\frac{\left(-2 \sqrt{c x +1}\, \sqrt{c x -1}\, x c +2 c^{2} x^{2}-1\right) e}{4 c \left(a +b \,\mathrm{arccosh}\left(c x \right)\right) b}-\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(c x \right)+\frac{2 a}{b}\right)}{2 c \,b^{2}}-\frac{e \left(2 c^{2} x^{2}-1+2 \sqrt{c x +1}\, \sqrt{c x -1}\, x c \right)}{4 c b \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(c x \right)-\frac{2 a}{b}\right)}{2 c \,b^{2}}}{c}"," ",0,"1/c*(1/2*(-(c*x-1)^(1/2)*(c*x+1)^(1/2)+c*x)*d/b/(a+b*arccosh(c*x))-1/2/b^2*exp(a/b)*Ei(1,arccosh(c*x)+a/b)*d-1/2/b*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))/(a+b*arccosh(c*x))*d-1/2/b^2*exp(-a/b)*Ei(1,-arccosh(c*x)-a/b)*d+1/4*(-2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c+2*c^2*x^2-1)*e/c/(a+b*arccosh(c*x))/b-1/2/c*e/b^2*exp(2*a/b)*Ei(1,2*arccosh(c*x)+2*a/b)-1/4/c*e/b*(2*c^2*x^2-1+2*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c)/(a+b*arccosh(c*x))-1/2/c*e/b^2*exp(-2*a/b)*Ei(1,-2*arccosh(c*x)-2*a/b))","A"
34,0,0,20,0.284000," ","int(1/(e*x+d)/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(e x +d \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arccosh(c*x))^2,x)","F"
35,0,0,20,0.446000," ","int(1/(e*x+d)^2/(a+b*arccosh(c*x))^2,x)","\int \frac{1}{\left(e x +d \right)^{2} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x+d)^2/(a+b*arccosh(c*x))^2,x)","F"
36,0,0,77,4.036000," ","int((e*x+d)^m*(a+b*arccosh(c*x))^3,x)","\int \left(e x +d \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{3}\, dx"," ",0,"int((e*x+d)^m*(a+b*arccosh(c*x))^3,x)","F"
37,0,0,75,4.226000," ","int((e*x+d)^m*(a+b*arccosh(c*x))^2,x)","\int \left(e x +d \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}\, dx"," ",0,"int((e*x+d)^m*(a+b*arccosh(c*x))^2,x)","F"
38,0,0,111,4.839000," ","int((e*x+d)^m*(a+b*arccosh(c*x)),x)","\int \left(e x +d \right)^{m} \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)\, dx"," ",0,"int((e*x+d)^m*(a+b*arccosh(c*x)),x)","F"
39,0,0,20,1.755000," ","int((e*x+d)^m/(a+b*arccosh(c*x)),x)","\int \frac{\left(e x +d \right)^{m}}{a +b \,\mathrm{arccosh}\left(c x \right)}\, dx"," ",0,"int((e*x+d)^m/(a+b*arccosh(c*x)),x)","F"
40,0,0,20,1.498000," ","int((e*x+d)^m/(a+b*arccosh(c*x))^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(a+b*arccosh(c*x))^2,x)","F"
41,1,255,332,0.031000," ","int((d*x^2+c)^4*arccosh(a*x),x)","\frac{\frac{a \,\mathrm{arccosh}\left(a x \right) d^{4} x^{9}}{9}+\frac{4 a \,\mathrm{arccosh}\left(a x \right) c \,d^{3} x^{7}}{7}+\frac{6 a \,\mathrm{arccosh}\left(a x \right) c^{2} d^{2} x^{5}}{5}+\frac{4 a \,\mathrm{arccosh}\left(a x \right) c^{3} d \,x^{3}}{3}+\mathrm{arccosh}\left(a x \right) c^{4} a x -\frac{\sqrt{a x -1}\, \sqrt{a x +1}\, \left(1225 a^{8} d^{4} x^{8}+8100 a^{8} c \,d^{3} x^{6}+23814 a^{8} c^{2} d^{2} x^{4}+1400 a^{6} d^{4} x^{6}+44100 a^{8} c^{3} d \,x^{2}+9720 a^{6} c \,d^{3} x^{4}+99225 a^{8} c^{4}+31752 a^{6} c^{2} d^{2} x^{2}+1680 a^{4} d^{4} x^{4}+88200 a^{6} c^{3} d +12960 a^{4} c \,d^{3} x^{2}+63504 a^{4} c^{2} d^{2}+2240 a^{2} d^{4} x^{2}+25920 a^{2} c \,d^{3}+4480 d^{4}\right)}{99225 a^{8}}}{a}"," ",0,"1/a*(1/9*a*arccosh(a*x)*d^4*x^9+4/7*a*arccosh(a*x)*c*d^3*x^7+6/5*a*arccosh(a*x)*c^2*d^2*x^5+4/3*a*arccosh(a*x)*c^3*d*x^3+arccosh(a*x)*c^4*a*x-1/99225/a^8*(a*x-1)^(1/2)*(a*x+1)^(1/2)*(1225*a^8*d^4*x^8+8100*a^8*c*d^3*x^6+23814*a^8*c^2*d^2*x^4+1400*a^6*d^4*x^6+44100*a^8*c^3*d*x^2+9720*a^6*c*d^3*x^4+99225*a^8*c^4+31752*a^6*c^2*d^2*x^2+1680*a^4*d^4*x^4+88200*a^6*c^3*d+12960*a^4*c*d^3*x^2+63504*a^4*c^2*d^2+2240*a^2*d^4*x^2+25920*a^2*c*d^3+4480*d^4))","A"
42,1,176,239,0.013000," ","int((d*x^2+c)^3*arccosh(a*x),x)","\frac{\frac{a \,\mathrm{arccosh}\left(a x \right) d^{3} x^{7}}{7}+\frac{3 a \,\mathrm{arccosh}\left(a x \right) c \,d^{2} x^{5}}{5}+a \,\mathrm{arccosh}\left(a x \right) c^{2} d \,x^{3}+\mathrm{arccosh}\left(a x \right) c^{3} a x -\frac{\sqrt{a x -1}\, \sqrt{a x +1}\, \left(75 a^{6} d^{3} x^{6}+441 a^{6} c \,d^{2} x^{4}+1225 a^{6} c^{2} d \,x^{2}+90 a^{4} d^{3} x^{4}+3675 a^{6} c^{3}+588 a^{4} c \,d^{2} x^{2}+2450 a^{4} c^{2} d +120 a^{2} d^{3} x^{2}+1176 a^{2} c \,d^{2}+240 d^{3}\right)}{3675 a^{6}}}{a}"," ",0,"1/a*(1/7*a*arccosh(a*x)*d^3*x^7+3/5*a*arccosh(a*x)*c*d^2*x^5+a*arccosh(a*x)*c^2*d*x^3+arccosh(a*x)*c^3*a*x-1/3675/a^6*(a*x-1)^(1/2)*(a*x+1)^(1/2)*(75*a^6*d^3*x^6+441*a^6*c*d^2*x^4+1225*a^6*c^2*d*x^2+90*a^4*d^3*x^4+3675*a^6*c^3+588*a^4*c*d^2*x^2+2450*a^4*c^2*d+120*a^2*d^3*x^2+1176*a^2*c*d^2+240*d^3))","A"
43,1,113,159,0.011000," ","int((d*x^2+c)^2*arccosh(a*x),x)","\frac{\frac{a \,\mathrm{arccosh}\left(a x \right) d^{2} x^{5}}{5}+\frac{2 a \,\mathrm{arccosh}\left(a x \right) c d \,x^{3}}{3}+\mathrm{arccosh}\left(a x \right) c^{2} a x -\frac{\sqrt{a x -1}\, \sqrt{a x +1}\, \left(9 a^{4} d^{2} x^{4}+50 a^{4} c d \,x^{2}+225 a^{4} c^{2}+12 a^{2} d^{2} x^{2}+100 a^{2} c d +24 d^{2}\right)}{225 a^{4}}}{a}"," ",0,"1/a*(1/5*a*arccosh(a*x)*d^2*x^5+2/3*a*arccosh(a*x)*c*d*x^3+arccosh(a*x)*c^2*a*x-1/225/a^4*(a*x-1)^(1/2)*(a*x+1)^(1/2)*(9*a^4*d^2*x^4+50*a^4*c*d*x^2+225*a^4*c^2+12*a^2*d^2*x^2+100*a^2*c*d+24*d^2))","A"
44,1,62,70,0.010000," ","int((d*x^2+c)*arccosh(a*x),x)","\frac{\frac{a \,\mathrm{arccosh}\left(a x \right) d \,x^{3}}{3}+\mathrm{arccosh}\left(a x \right) c a x -\frac{\sqrt{a x -1}\, \sqrt{a x +1}\, \left(a^{2} d \,x^{2}+9 a^{2} c +2 d \right)}{9 a^{2}}}{a}"," ",0,"1/a*(1/3*a*arccosh(a*x)*d*x^3+arccosh(a*x)*c*a*x-1/9/a^2*(a*x-1)^(1/2)*(a*x+1)^(1/2)*(a^2*d*x^2+9*a^2*c+2*d))","A"
45,1,214,489,1.503000," ","int(arccosh(a*x)/(d*x^2+c),x)","\frac{a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} d +2 a^{2} c +d}\right)}{2}-\frac{a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{\mathrm{arccosh}\left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} d +2 a^{2} c +d \right)}\right)}{2}"," ",0,"1/2*a*sum(_R1/(_R1^2*d+2*a^2*c+d)*(arccosh(a*x)*ln((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)+dilog((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))-1/2*a*sum(1/_R1/(_R1^2*d+2*a^2*c+d)*(arccosh(a*x)*ln((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)+dilog((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))","C"
46,1,1632,702,3.402000," ","int(arccosh(a*x)/(d*x^2+c)^2,x)","\frac{a^{2} \mathrm{arccosh}\left(a x \right) x}{2 c \left(a^{2} d \,x^{2}+a^{2} c \right)}+\frac{a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{\textit{\_R1} \left(\mathrm{arccosh}\left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} d +2 a^{2} c +d}\right)}{4 c}+\frac{a^{5} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) c}{\left(a^{2} c +d \right) d^{3}}-\frac{a^{3} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{\left(a^{2} c +d \right) d^{3}}+\frac{a^{3} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right)}{\left(a^{2} c +d \right) d^{2}}-\frac{a \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{2 c \left(a^{2} c +d \right) d^{2}}-\frac{a^{3} \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right)}{d^{3}}+\frac{a \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{c \,d^{3}}-\frac{a \sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctan \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}}\right)}{2 c \,d^{2}}+\frac{a^{5} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) c}{\left(a^{2} c +d \right) d^{3}}+\frac{a^{3} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{\left(a^{2} c +d \right) d^{3}}+\frac{a^{3} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right)}{\left(a^{2} c +d \right) d^{2}}+\frac{a \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{2 c \left(a^{2} c +d \right) d^{2}}-\frac{a^{3} \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right)}{d^{3}}-\frac{a \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right) \sqrt{a^{2} c \left(a^{2} c +d \right)}}{c \,d^{3}}-\frac{a \sqrt{-\left(2 a^{2} c -2 \sqrt{a^{2} c \left(a^{2} c +d \right)}+d \right) d}\, \arctanh \left(\frac{d \left(a x +\sqrt{a x -1}\, \sqrt{a x +1}\right)}{\sqrt{\left(-2 a^{2} c +2 \sqrt{a^{2} c \left(a^{2} c +d \right)}-d \right) d}}\right)}{2 c \,d^{2}}-\frac{a \left(\munderset{\textit{\_R1} =\RootOf \left(d \,\textit{\_Z}^{4}+\left(4 a^{2} c +2 d \right) \textit{\_Z}^{2}+d \right)}{\sum}\frac{\mathrm{arccosh}\left(a x \right) \ln \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -a x -\sqrt{a x -1}\, \sqrt{a x +1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} d +2 a^{2} c +d \right)}\right)}{4 c}"," ",0,"1/2*a^2*arccosh(a*x)*x/c/(a^2*d*x^2+a^2*c)+1/4*a/c*sum(_R1/(_R1^2*d+2*a^2*c+d)*(arccosh(a*x)*ln((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)+dilog((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))+a^5*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))*c/(a^2*c+d)/d^3-a^3*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/(a^2*c+d)/d^3*(a^2*c*(a^2*c+d))^(1/2)+a^3*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/(a^2*c+d)/d^2-1/2*a*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/c/(a^2*c+d)/d^2*(a^2*c*(a^2*c+d))^(1/2)-a^3*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/d^3+a*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/c/d^3*(a^2*c*(a^2*c+d))^(1/2)-1/2*a*((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctan(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2))/c/d^2+a^5*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))*c/(a^2*c+d)/d^3+a^3*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/(a^2*c+d)/d^3*(a^2*c*(a^2*c+d))^(1/2)+a^3*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/(a^2*c+d)/d^2+1/2*a*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/c/(a^2*c+d)/d^2*(a^2*c*(a^2*c+d))^(1/2)-a^3*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/d^3-a*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/c/d^3*(a^2*c*(a^2*c+d))^(1/2)-1/2*a*(-(2*a^2*c-2*(a^2*c*(a^2*c+d))^(1/2)+d)*d)^(1/2)*arctanh(d*(a*x+(a*x-1)^(1/2)*(a*x+1)^(1/2))/((-2*a^2*c+2*(a^2*c*(a^2*c+d))^(1/2)-d)*d)^(1/2))/c/d^2-1/4*a/c*sum(1/_R1/(_R1^2*d+2*a^2*c+d)*(arccosh(a*x)*ln((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)+dilog((_R1-a*x-(a*x-1)^(1/2)*(a*x+1)^(1/2))/_R1)),_R1=RootOf(d*_Z^4+(4*a^2*c+2*d)*_Z^2+d))","C"
47,0,0,16,0.312000," ","int((d*x^2+c)^(1/2)*arccosh(a*x),x)","\int \sqrt{d \,x^{2}+c}\, \mathrm{arccosh}\left(a x \right)\, dx"," ",0,"int((d*x^2+c)^(1/2)*arccosh(a*x),x)","F"
48,0,0,16,0.386000," ","int(arccosh(a*x)/(d*x^2+c)^(1/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)}{\sqrt{d \,x^{2}+c}}\, dx"," ",0,"int(arccosh(a*x)/(d*x^2+c)^(1/2),x)","F"
49,0,0,80,0.326000," ","int(arccosh(a*x)/(d*x^2+c)^(3/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccosh(a*x)/(d*x^2+c)^(3/2),x)","F"
50,0,0,148,0.322000," ","int(arccosh(a*x)/(d*x^2+c)^(5/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arccosh(a*x)/(d*x^2+c)^(5/2),x)","F"
51,0,0,225,0.346000," ","int(arccosh(a*x)/(d*x^2+c)^(7/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(arccosh(a*x)/(d*x^2+c)^(7/2),x)","F"
52,0,0,313,0.323000," ","int(arccosh(a*x)/(d*x^2+c)^(9/2),x)","\int \frac{\mathrm{arccosh}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{9}{2}}}\, dx"," ",0,"int(arccosh(a*x)/(d*x^2+c)^(9/2),x)","F"
53,1,1213,613,1.085000," ","int((g*x+f)^3*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{2 a \,g^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} 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)}\, f \,g^{2} \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)}\, g \,c^{2} \mathrm{arccosh}\left(c x \right) x^{4} f^{2}}{\left(c x +1\right) \left(c x -1\right)}+\frac{a \,f^{3} x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a \,f^{3} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{3 a f \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}-\frac{a \,f^{2} g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{c^{2} d}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g c \,x^{3} f^{2}}{3 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g x \,f^{2}}{\sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} c \,x^{4}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} x^{2}}{16 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right) x^{2} f^{2}}{\left(c x +1\right) \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \mathrm{arccosh}\left(c x \right)^{2} g^{2}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} c^{2} \mathrm{arccosh}\left(c x \right) x^{6}}{5 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right) x^{2}}{15 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right) f^{2}}{\left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{2 \left(c x +1\right) \left(c x -1\right)}-\frac{a \,g^{3} x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3}}{8 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{3 a f \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{3 a f \,g^{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 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} x^{3}}{45 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} x}{15 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} c \,x^{5}}{25 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} c \,x^{2}}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2}}{128 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \mathrm{arccosh}\left(c x \right)^{2}}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right)}{15 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right) x^{4}}{15 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \mathrm{arccosh}\left(c x \right) x}{2 \left(c x +1\right) \left(c x -1\right)}"," ",0,"-2/15*a*g^3/d/c^4*(-c^2*d*x^2+d)^(3/2)+3/4*b*(-d*(c^2*x^2-1))^(1/2)*f*g^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)*f*g^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x+b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4*f^2+1/2*a*f^3*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*f^3*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/8*a*f*g^2/c^2*x*(-c^2*d*x^2+d)^(1/2)-a*f^2*g/c^2/d*(-c^2*d*x^2+d)^(3/2)-1/3*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3*f^2+b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x*f^2-3/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+3/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2-9/8*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-2*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2*f^2-3/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*f*arccosh(c*x)^2*g^2+1/5*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^6-1/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x^2+b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*f^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^3-1/5*a*g^3*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*b*(-d*(c^2*x^2-1))^(1/2)*f^3/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)-3/4*a*f*g^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+3/8*a*f*g^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/45*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^3+2/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*x-1/25*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^5-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^3/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^2-3/128*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)-1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*f^3*arccosh(c*x)^2+2/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)/c^4/(c*x-1)*arccosh(c*x)-4/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c*x+1)/(c*x-1)*arccosh(c*x)*x^4-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3/(c*x+1)/(c*x-1)*arccosh(c*x)*x","A"
54,1,855,407,0.943000," ","int((g*x+f)^2*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{a \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a \,g^{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{2 a f g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+\frac{a \,f^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a \,f^{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 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} f^{2}}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} g^{2}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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)}\, g^{2} \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)}\, g^{2} \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)}\, g^{2}}{128 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,\mathrm{arccosh}\left(c x \right)}{3 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} 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)}\, f^{2} \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)}\, f^{2}}{8 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c \,x^{2}}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c \,x^{4}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} x^{2}}{16 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,c^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{3 \left(c x +1\right) \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,\mathrm{arccosh}\left(c x \right) x^{2}}{3 \left(c x +1\right) \left(c x -1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g c \,x^{3}}{9 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g x}{3 \sqrt{c x +1}\, c \sqrt{c x -1}}"," ",0,"-1/4*a*g^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*a*g^2/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*a*g^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2/3*a*f*g/c^2/d*(-c^2*d*x^2+d)^(3/2)+1/2*a*f^2*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*f^2*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*f^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*g^2+1/4*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3+1/8*b*(-d*(c^2*x^2-1))^(1/2)*g^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x-1/128*b*(-d*(c^2*x^2-1))^(1/2)*g^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)+2/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^3-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x+1/8*b*(-d*(c^2*x^2-1))^(1/2)*f^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^2-1/16*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2+2/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4-4/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2-2/9*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3+2/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x","B"
55,1,461,215,0.728000," ","int((g*x+f)*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+\frac{a f x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a f 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)}\, g \,\mathrm{arccosh}\left(c x \right)}{3 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,c^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{3 \left(c x +1\right) \left(c x -1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right) x^{2}}{3 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,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)}\, f \,\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)}\, f}{8 \sqrt{c x +1}\, \sqrt{c x -1}\, c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g c \,x^{3}}{9 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g x}{3 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f c \,x^{2}}{4 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \mathrm{arccosh}\left(c x \right)^{2}}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, c}"," ",0,"-1/3*a*g/c^2/d*(-c^2*d*x^2+d)^(3/2)+1/2*a*f*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*f*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/3*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)+1/3*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4-2/3*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f/(c*x+1)/(c*x-1)*c^2*arccosh(c*x)*x^3-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f/(c*x+1)/(c*x-1)*arccosh(c*x)*x+1/8*b*(-d*(c^2*x^2-1))^(1/2)*f/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c-1/9*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3+1/3*b*(-d*(c^2*x^2-1))^(1/2)*g/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2-1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*f*arccosh(c*x)^2","B"
56,1,1072,753,0.623000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/(g*x+f),x)","\frac{a \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{g}+\frac{a \,c^{2} d f \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{g^{2} \sqrt{c^{2} d}}+\frac{a d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right) c^{2} f^{2}}{g^{3} \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{a d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \mathrm{arccosh}\left(c x \right)^{2} c}{2 \sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}+\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) g}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c x}{\sqrt{c x -1}\, \sqrt{c x +1}\, g}-\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) g}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}"," ",0,"a/g*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)+a/g^2*c^2*d*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+a/g^3*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2-a/g*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*f*arccosh(c*x)^2*c/g^2+b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)/(c*x+1)/g*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)/g*c*x-b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)/(c*x+1)/g*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))-b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))-b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))","A"
57,1,1956,864,0.933000," ","int((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/(g*x+f)^2,x)","\frac{a \left(-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}\right)^{\frac{3}{2}}}{d \left(c^{2} f^{2}-g^{2}\right) \left(x +\frac{f}{g}\right)}-\frac{a \,c^{2} f \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{g \left(c^{2} f^{2}-g^{2}\right)}-\frac{a \,c^{4} f^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{g^{2} \left(c^{2} f^{2}-g^{2}\right) \sqrt{c^{2} d}}-\frac{a \,c^{4} f^{3} d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g^{3} \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a \,c^{2} f d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a \,c^{2} \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, x}{c^{2} f^{2}-g^{2}}+\frac{a \,c^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{\left(c^{2} f^{2}-g^{2}\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}\, g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2} f}{g^{2} \left(g x +f \right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3} c^{4} f}{\left(c x -1\right) \left(c x +1\right) g^{2} \left(g x +f \right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x c}{\sqrt{c x -1}\, \sqrt{c x +1}\, g \left(g x +f \right)}-\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) g \left(g x +f \right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) c f}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \left(g x +f \right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2} f}{\left(c x -1\right) \left(c x +1\right) g^{2} \left(g x +f \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) g \left(g x +f \right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} f \,\mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \sqrt{c^{2} f^{2}-g^{2}}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} f \,\mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \sqrt{c^{2} f^{2}-g^{2}}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) f^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \left(c^{2} f^{2}-g^{2}\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} g +2 c f \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)+g \right) f^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \left(c^{2} f^{2}-g^{2}\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} f \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \sqrt{c^{2} f^{2}-g^{2}}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} f \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{2} \sqrt{c^{2} f^{2}-g^{2}}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(c^{2} f^{2}-g^{2}\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \ln \left(\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)^{2} g +2 c f \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)+g \right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(c^{2} f^{2}-g^{2}\right)}"," ",0,"a/d/(c^2*f^2-g^2)/(x+f/g)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)-a/g*c^2*f/(c^2*f^2-g^2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-a/g^2*c^4*f^2/(c^2*f^2-g^2)*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-a/g^3*c^4*f^3/(c^2*f^2-g^2)*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+a/g*c^2*f/(c^2*f^2-g^2)*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+a*c^2/(c^2*f^2-g^2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x+a*c^2/(c^2*f^2-g^2)*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(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/g^2+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/g^2/(g*x+f)*x*c^2*f-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x-1)/(c*x+1)/g^2/(g*x+f)*x^3*c^4*f+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g/(g*x+f)*x*c-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x-1)/(c*x+1)/g/(g*x+f)*x^2*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(g*x+f)*c*f+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x-1)/(c*x+1)/g^2/(g*x+f)*x*c^2*f+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/(c*x-1)/(c*x+1)/g/(g*x+f)-b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(c^2*f^2-g^2)^(1/2)*f*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(c^2*f^2-g^2)^(1/2)*f*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-2*b*(-d*(c^2*x^2-1))^(1/2)*c^3/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(c^2*f^2-g^2)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*f^2+b*(-d*(c^2*x^2-1))^(1/2)*c^3/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(c^2*f^2-g^2)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*g+2*c*f*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+g)*f^2-b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(c^2*f^2-g^2)^(1/2)*f*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2/(c^2*f^2-g^2)^(1/2)*f*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))+2*b*(-d*(c^2*x^2-1))^(1/2)*c/(c*x-1)^(1/2)/(c*x+1)^(1/2)/(c^2*f^2-g^2)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))-b*(-d*(c^2*x^2-1))^(1/2)*c/(c*x-1)^(1/2)/(c*x+1)^(1/2)/(c^2*f^2-g^2)*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*g+2*c*f*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+g)","B"
58,1,1638,885,1.149000," ","int((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{2 \left(c x +1\right) \left(c x -1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{8 \left(c x +1\right) \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d \,\mathrm{arccosh}\left(c x \right) x}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{6} f^{2}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{4} f^{2}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{3 a \,f^{3} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}-\frac{2 a \,g^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}-\frac{3 a \,f^{2} g \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}-\frac{a \,g^{3} x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}+\frac{a f \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8 c^{2}}+\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{6}}{35 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,\mathrm{arccosh}\left(c x \right) x^{2}}{35 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,\mathrm{arccosh}\left(c x \right) f^{2}}{5 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} 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)}\, f^{3} d \,c^{2} \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)}\, f \,g^{2} d \,c^{3} x^{6}}{12 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d c \,x^{4}}{32 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d \,x^{2}}{32 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{3} x^{5} f^{2}}{25 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d c \,x^{3} f^{2}}{5 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d x \,f^{2}}{5 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,\mathrm{arccosh}\left(c x \right) x^{2} f^{2}}{5 \left(c x +1\right) \left(c x -1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d \,\mathrm{arccosh}\left(c x \right) x^{3}}{16 \left(c x +1\right) \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \mathrm{arccosh}\left(c x \right)^{2} d \,g^{2}}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{3 a \,f^{3} d x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} 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)}\, f^{3} d c \,x^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,c^{3} x^{7}}{49 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d c \,x^{5}}{175 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \mathrm{arccosh}\left(c x \right)^{2} d}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,\mathrm{arccosh}\left(c x \right)}{35 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} d \,\mathrm{arccosh}\left(c x \right) x}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,\mathrm{arccosh}\left(c x \right) x^{4}}{35 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,x^{3}}{105 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d x}{35 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d}{768 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{a \,f^{3} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{8}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{a f \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2 c^{2} d}+\frac{3 a f \,g^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{2}}+\frac{3 a f \,g^{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{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} d}{128 \sqrt{c x +1}\, c \sqrt{c x -1}}"," ",0,"-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^7+11/8*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5+3/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x-3/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^6*f^2+9/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4*f^2+3/8*a*f^3*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2/35*a*g^3/d/c^4*(-c^2*d*x^2+d)^(5/2)-3/5*a*f^2*g/c^2/d*(-c^2*d*x^2+d)^(5/2)-1/7*a*g^3*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/8*a*f*g^2/c^2*x*(-c^2*d*x^2+d)^(3/2)+13/35*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^6-1/35*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x^2+3/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*f^2-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^5+7/8*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^3+1/12*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6-7/32*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+3/32*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2+3/25*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^5*f^2-2/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3*f^2+3/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x*f^2-9/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2*f^2-17/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-3/32*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*f*arccosh(c*x)^2*d*g^2+3/8*a*f^3*d*x*(-c^2*d*x^2+d)^(1/2)+1/16*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^4-5/16*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^2+1/49*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^7-8/175*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^5-3/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*f^3*arccosh(c*x)^2*d+2/35*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)/c^4/(c*x-1)*arccosh(c*x)-5/8*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x-9/35*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^4+1/105*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^3+2/35*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*x+7/768*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)+1/4*a*f^3*x*(-c^2*d*x^2+d)^(3/2)-1/7*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^8-1/2*a*f*g^2*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+3/16*a*f*g^2/c^2*d*x*(-c^2*d*x^2+d)^(1/2)+3/16*a*f*g^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))+17/128*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)","A"
59,1,1177,621,1.039000," ","int((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","\frac{a \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}+\frac{a \,f^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d \,\mathrm{arccosh}\left(c x \right)}{5 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{5} f^{2}}{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} f^{2}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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)}\, g^{2} d \,c^{2} \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)}\, g^{2} d \,\mathrm{arccosh}\left(c x \right) x}{16 \left(c x +1\right) c^{2} \left(c x -1\right)}-\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d \,\mathrm{arccosh}\left(c x \right) x^{2}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d \,c^{3} x^{5}}{25 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d c \,x^{3}}{15 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d x}{5 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x \,f^{2}}{8 \left(c x +1\right) \left(c x -1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} d \,\mathrm{arccosh}\left(c x \right) x^{3}}{48 \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)^{2} d \,f^{2}}{16 \sqrt{c x -1}\, \sqrt{c x +1}\, c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d \,g^{2}}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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^{3} x^{4} f^{2}}{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} f^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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)}\, g^{2} d c \,x^{4}}{96 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{a \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6 c^{2} d}+\frac{a \,g^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{2}}+\frac{a \,g^{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{2 a f g \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+\frac{3 a \,f^{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{3 a \,f^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{8}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{6}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,f^{2}}{128 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} d}{2304 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}"," ",0,"1/24*a*g^2/c^2*x*(-c^2*d*x^2+d)^(3/2)+1/4*a*f^2*x*(-c^2*d*x^2+d)^(3/2)+2/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)-1/4*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^5*f^2+7/8*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^3*f^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^2*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5+1/16*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x-6/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2+2/25*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^5-4/15*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3+2/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x-5/8*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x*f^2-17/48*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-3/16*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*f^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*g^2+1/32*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2+1/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^4*f^2-5/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^2*f^2+1/36*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^2*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4-1/6*a*g^2*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/16*a*g^2/c^2*d*x*(-c^2*d*x^2+d)^(1/2)+1/16*a*g^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))-2/5*a*f*g/c^2/d*(-c^2*d*x^2+d)^(5/2)+3/8*a*f^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/8*a*f^2*d*x*(-c^2*d*x^2+d)^(1/2)-2/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^6+6/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4+17/128*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*f^2+7/2304*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)","A"
60,1,656,338,0.768000," ","int((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x)","-\frac{a g \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+\frac{a f x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{3 a f d x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{3 a f \,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 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d x}{5 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f 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)}\, f d c \,x^{2}}{16 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f 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)}\, f 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)}\, f 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)}\, f d}{128 \sqrt{c x +1}\, \sqrt{c x -1}\, c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{4} \mathrm{arccosh}\left(c x \right) x^{6}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{5 \left(c x +1\right) \left(c x -1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,\mathrm{arccosh}\left(c x \right) x^{2}}{5 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{3} x^{5}}{25 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d c \,x^{3}}{15 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \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)}\, g d \,\mathrm{arccosh}\left(c x \right)}{5 \left(c x +1\right) c^{2} \left(c x -1\right)}"," ",0,"-1/5*a*g/c^2/d*(-c^2*d*x^2+d)^(5/2)+1/4*a*f*x*(-c^2*d*x^2+d)^(3/2)+3/8*a*f*d*x*(-c^2*d*x^2+d)^(1/2)+3/8*a*f*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x+1/16*b*(-d*(c^2*x^2-1))^(1/2)*f*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)*f*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)*f*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)*f*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)*f*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x+17/128*b*(-d*(c^2*x^2-1))^(1/2)*f*d/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c-1/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^6+3/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4-3/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2+1/25*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^5-2/15*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3-3/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*f*arccosh(c*x)^2*d+1/5*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)","A"
61,1,1965,1178,0.637000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/(g*x+f),x)","-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{2} d \,\mathrm{arccosh}\left(c x \right) x}{2 \left(c x -1\right) \left(c x +1\right) g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{4} d \,\mathrm{arccosh}\left(c x \right) x^{3}}{2 \left(c x -1\right) \left(c x +1\right) g^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) x^{2} c^{4} f^{2}}{\left(c x -1\right) \left(c x +1\right) g^{3}}+\frac{a \left(-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}\right)^{\frac{3}{2}}}{3 g}+\frac{a d \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{g}-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\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}\, g}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c x}{3 \sqrt{c x -1}\, \sqrt{c x +1}\, g}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f c d}{8 \sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}+\frac{b \left(c^{2} f^{2}-g^{2}\right)^{\frac{3}{2}} d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{4}}-\frac{b \left(c^{2} f^{2}-g^{2}\right)^{\frac{3}{2}} d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{4}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,\mathrm{arccosh}\left(c x \right) c^{2} f^{2}}{\left(c x -1\right) \left(c x +1\right) g^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \mathrm{arccosh}\left(c x \right)^{2} c^{3} d}{2 \sqrt{c x -1}\, \sqrt{c x +1}\, g^{4}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \mathrm{arccosh}\left(c x \right)^{2} c d}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}-\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) g}+\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) g}-\frac{b \left(c^{2} f^{2}-g^{2}\right)^{\frac{3}{2}} d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{4}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{3} d \,x^{2}}{4 \sqrt{c x -1}\, \sqrt{c x +1}\, g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{3} f^{2}}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{3}}+\frac{b \left(c^{2} f^{2}-g^{2}\right)^{\frac{3}{2}} d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\sqrt{c x -1}\, \sqrt{c x +1}\, g^{4}}-\frac{a d \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, c^{2} f^{2}}{g^{3}}+\frac{2 a \,d^{2} \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right) c^{2} f^{2}}{g^{3} \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a \,c^{2} d f \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, x}{2 g^{2}}+\frac{3 a \,c^{2} d^{2} f \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{2 g^{2} \sqrt{c^{2} d}}-\frac{a \,d^{2} c^{4} f^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{g^{4} \sqrt{c^{2} d}}-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right) c^{4} f^{4}}{g^{5} \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\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) g}"," ",0,"-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f*c^2*d/(c*x-1)/(c*x+1)/g^2*arccosh(c*x)*x+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f*c^4*d/(c*x-1)/(c*x+1)/g^2*arccosh(c*x)*x^3-b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x-1)/(c*x+1)/g^3*arccosh(c*x)*x^2*c^4*f^2+1/3*a/g*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)+a/g*d*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-a/g*d^2/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+1/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g*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)/g*c*x+b*(c^2*f^2-g^2)^(3/2)*d*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-b*(c^2*f^2-g^2)^(3/2)*d*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+1/8*b*(-d*(c^2*x^2-1))^(1/2)*f*c*d/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2+b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x-1)/(c*x+1)/g^3*arccosh(c*x)*c^2*f^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*f^3*arccosh(c*x)^2*c^3*d/g^4-3/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*f*arccosh(c*x)^2*c*d/g^2-1/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x-1)/(c*x+1)/g*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)/g*arccosh(c*x)*x^2*c^2-b*(c^2*f^2-g^2)^(3/2)*d*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f*c^3*d/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*x^2+b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^3*x*c^3*f^2+b*(c^2*f^2-g^2)^(3/2)*d*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-a/g^3*d*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^2*f^2+2*a/g^3*d^2/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2+1/2*a/g^2*c^2*d*f*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x+3/2*a/g^2*c^2*d^2*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-a/g^4*d^2*c^4*f^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-a/g^5*d^2/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^4*f^4-4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c*x-1)/(c*x+1)/g*arccosh(c*x)","A"
62,1,2116,1201,1.233000," ","int((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","-\frac{2 a \,g^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} d^{2} \mathrm{arccosh}\left(c x \right) x}{16 \left(c x +1\right) \left(c x -1\right)}-\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{63 \left(c x +1\right) \left(c x -1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \mathrm{arccosh}\left(c x \right)^{2} d^{2}}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} \mathrm{arccosh}\left(c x \right)}{63 \left(c x +1\right) c^{4} \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} 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)}\, f^{3} 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)}\, f^{3} 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)}\, g^{3} d^{2} c^{5} x^{9}}{81 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{19 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} c^{3} x^{7}}{441 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} c \,x^{5}}{21 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} x^{3}}{189 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} x}{63 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{359 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2}}{24576 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{a \,f^{3} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}-\frac{a \,g^{3} x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}+\frac{a f \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{16 c^{2}}-\frac{3 a \,f^{2} g \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} c^{3} x^{6}}{96 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{5} x^{7} f^{2}}{49 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{3} x^{5} f^{2}}{35 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c \,x^{3} f^{2}}{7 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} x \,f^{2}}{7 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} c^{5} x^{8}}{64 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{59 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} c \,x^{4}}{256 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} x^{2}}{256 \sqrt{c x +1}\, c \sqrt{c x -1}}+\frac{5 a \,f^{3} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,f^{3} 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 a \,f^{3} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}-\frac{133 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{128 \left(c x +1\right) \left(c x -1\right)}-\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} \mathrm{arccosh}\left(c x \right) x^{2} f^{2}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} 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)}\, f^{3} d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{48 \left(c x +1\right) \left(c x -1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \mathrm{arccosh}\left(c x \right)^{2} d^{2} g^{2}}{256 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{10}}{9 \left(c x +1\right) \left(c x -1\right)}-\frac{26 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{8}}{63 \left(c x +1\right) \left(c x -1\right)}+\frac{34 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{6}}{63 \left(c x +1\right) \left(c x -1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} d^{2} \mathrm{arccosh}\left(c x \right) x^{2}}{63 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} \mathrm{arccosh}\left(c x \right) f^{2}}{7 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{7}}{6 \left(c x +1\right) \left(c x -1\right)}+\frac{18 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{4} f^{2}}{7 \left(c x +1\right) \left(c x -1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} 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)}\, f \,g^{2} d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{7}}{16 \left(c x +1\right) \left(c x -1\right)}+\frac{127 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{64 \left(c x +1\right) \left(c x -1\right)}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} d^{2} \mathrm{arccosh}\left(c x \right) x}{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)}\, g \,d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{8} f^{2}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{6} f^{2}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{3 a f \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 c^{2} d}+\frac{5 a f \,g^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{64 c^{2}}+\frac{15 a f \,g^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{128 c^{2}}+\frac{15 a f \,g^{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{299 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} d^{2}}{2304 \sqrt{c x +1}\, c \sqrt{c x -1}}"," ",0,"-2/63*a*g^3/d/c^4*(-c^2*d*x^2+d)^(7/2)-11/16*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x-16/63*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^4-5/32*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c*f^3*arccosh(c*x)^2*d^2+2/63*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)/c^4/(c*x-1)*arccosh(c*x)-1/36*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^6+13/96*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^4-11/32*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^2-1/81*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^9+19/441*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^7-1/21*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^5+1/189*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^3+2/63*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)*x+359/24576*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)+1/6*a*f^3*x*(-c^2*d*x^2+d)^(5/2)-1/9*a*g^3*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d+1/16*a*f*g^2/c^2*x*(-c^2*d*x^2+d)^(5/2)-3/7*a*f^2*g/c^2/d*(-c^2*d*x^2+d)^(7/2)+17/96*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6-3/49*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^7*f^2+9/35*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^5*f^2-3/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3*f^2+3/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x*f^2-3/64*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^8-59/256*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^4+15/256*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2+5/16*a*f^3*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/16*a*f^3*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+5/24*a*f^3*d*x*(-c^2*d*x^2+d)^(3/2)-133/128*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^3-12/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2*f^2-17/24*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^5+59/48*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^3-15/256*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/c^3*f*arccosh(c*x)^2*d^2*g^2+1/9*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^10-26/63*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^8+34/63*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^6-1/63*b*(-d*(c^2*x^2-1))^(1/2)*g^3*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x^2+3/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*f^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^7+18/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4*f^2+3/8*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^9-23/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^7+127/64*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5+15/128*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x+3/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^8*f^2-12/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^6*f^2-3/8*a*f*g^2*x*(-c^2*d*x^2+d)^(7/2)/c^2/d+5/64*a*f*g^2/c^2*d*x*(-c^2*d*x^2+d)^(3/2)+15/128*a*f*g^2/c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+15/128*a*f*g^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))+299/2304*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)","A"
63,1,1540,879,1.130000," ","int((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","\frac{a \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{48 c^{2}}-\frac{133 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} d^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{384 \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 \,f^{2}}{16 \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)^{2} d^{2} f^{2}}{32 \sqrt{c x -1}\, \sqrt{c x +1}\, c}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right)^{2} d^{2} g^{2}}{256 \sqrt{c x -1}\, \sqrt{c x +1}\, c^{3}}-\frac{59 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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)}\, g^{2} 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^{5} x^{6} f^{2}}{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} f^{2}}{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} f^{2}}{32 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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)}\, g^{2} d^{2} c^{3} x^{6}}{288 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{5 a \,f^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a \,g^{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{2 a f g \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}-\frac{a \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 c^{2} d}+\frac{5 a \,g^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{192 c^{2}}+\frac{5 a \,g^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{128 c^{2}}+\frac{a \,f^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}+\frac{5 a \,f^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,f^{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{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{8}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{6}}{7 \left(c x +1\right) \left(c x -1\right)}+\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{7 \left(c x +1\right) \left(c x -1\right)}+\frac{359 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} d^{2}}{73728 \sqrt{c x +1}\, c^{3} \sqrt{c x -1}}+\frac{299 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} f^{2}}{2304 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} c \,x^{3}}{7 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} x}{7 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} c^{5} x^{7}}{49 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} c^{3} x^{5}}{35 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} 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)}\, g^{2} 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)}\, g^{2} d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{5}}{192 \left(c x +1\right) \left(c x -1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} d^{2} \mathrm{arccosh}\left(c x \right) x}{128 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} \mathrm{arccosh}\left(c x \right)}{7 \left(c x +1\right) c^{2} \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{7} f^{2}}{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} f^{2}}{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} f^{2}}{48 \left(c x +1\right) \left(c x -1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,d^{2} \mathrm{arccosh}\left(c x \right) x^{2}}{7 \left(c x +1\right) \left(c x -1\right)}"," ",0,"1/48*a*g^2/c^2*x*(-c^2*d*x^2+d)^(5/2)-133/384*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d^2/(c*x+1)/(c*x-1)*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*f^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*f^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*g^2-59/768*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^2*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x^2-1/36*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^6*f^2+13/96*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^4*f^2-11/32*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^2*f^2-1/64*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^2*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^6+5/24*a*f^2*d*x*(-c^2*d*x^2+d)^(3/2)+5/128*a*g^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))-2/7*a*f*g/c^2/d*(-c^2*d*x^2+d)^(7/2)-1/8*a*g^2*x*(-c^2*d*x^2+d)^(7/2)/c^2/d+5/192*a*g^2/c^2*d*x*(-c^2*d*x^2+d)^(3/2)+5/128*a*g^2/c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+1/6*a*f^2*x*(-c^2*d*x^2+d)^(5/2)+5/16*a*f^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/16*a*f^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+2/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^8-8/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^6+12/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4+359/73728*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d^2/(c*x+1)^(1/2)/c^3/(c*x-1)^(1/2)+299/2304*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*f^2-2/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3+2/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x-2/49*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^7+6/35*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^5+1/8*b*(-d*(c^2*x^2-1))^(1/2)*g^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)*g^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)*g^2*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^5+5/128*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)*x+2/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)+1/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^7*f^2-17/24*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^5*f^2+59/48*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^3*f^2-8/7*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2","A"
64,1,877,488,0.896000," ","int((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x)","-\frac{a g \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+\frac{a f x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}+\frac{5 a f d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a f \,d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{16}+\frac{5 a f \,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)}\, f \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)}\, g \,d^{2} c^{6} \mathrm{arccosh}\left(c x \right) x^{8}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{4} \mathrm{arccosh}\left(c x \right) x^{6}}{7 \left(c x +1\right) \left(c x -1\right)}+\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{2} \mathrm{arccosh}\left(c x \right) x^{4}}{7 \left(c x +1\right) \left(c x -1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} \mathrm{arccosh}\left(c x \right) x^{2}}{7 \left(c x +1\right) \left(c x -1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,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)}\, f \,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)}\, f \,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)}\, f \,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)}\, f \,d^{2}}{2304 \sqrt{c x +1}\, \sqrt{c x -1}\, c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{5} x^{7}}{49 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c^{3} x^{5}}{35 \sqrt{c x +1}\, \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} c \,x^{3}}{7 \sqrt{c x +1}\, \sqrt{c x -1}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,d^{2} x}{7 \sqrt{c x +1}\, c \sqrt{c x -1}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,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)}\, f \,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)}\, f \,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)}\, g \,d^{2} \mathrm{arccosh}\left(c x \right)}{7 \left(c x +1\right) c^{2} \left(c x -1\right)}"," ",0,"-1/7*a*g/c^2/d*(-c^2*d*x^2+d)^(7/2)+1/6*a*f*x*(-c^2*d*x^2+d)^(5/2)+5/24*a*f*d*x*(-c^2*d*x^2+d)^(3/2)+5/16*a*f*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/16*a*f*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*f*arccosh(c*x)^2*d^2+1/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)*c^6/(c*x-1)*arccosh(c*x)*x^8-4/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)*c^4/(c*x-1)*arccosh(c*x)*x^6+6/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)*c^2/(c*x-1)*arccosh(c*x)*x^4-4/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)*f*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)*f*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)*f*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)*f*d^2/(c*x+1)/(c*x-1)*arccosh(c*x)*x+299/2304*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)/c-1/49*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)*c^5/(c*x-1)^(1/2)*x^7+3/35*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)*c^3/(c*x-1)^(1/2)*x^5-1/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)*c/(c*x-1)^(1/2)*x^3+1/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)^(1/2)/c/(c*x-1)^(1/2)*x-1/36*b*(-d*(c^2*x^2-1))^(1/2)*f*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)*f*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)*f*d^2/(c*x+1)^(1/2)/(c*x-1)^(1/2)*c*x^2+1/7*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c*x+1)/c^2/(c*x-1)*arccosh(c*x)","A"
65,1,4234,1608,0.749000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/(g*x+f),x)","\text{output too large to display}"," ",0,"-1/8*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^3/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4-1/25*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g*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)/g*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)/g*c*x+33/128*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2+b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))-b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-a/g*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-1/3*a/g^3*d*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)*c^2*f^2+a/g^5*d^2*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^4*f^4-2*a/g^3*d^2*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^2*f^2+b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^6*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))*c^4*f^4-b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^6*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))*c^4*f^4-2*b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))*c^2*f^2+2*b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))*c^2*f^2+1/5*a/g*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(5/2)-14/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g*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)/g*arccosh(c*x)*x^2*c^2+1/3*a/g*d*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)+a/g*d^2*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-1/9*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^3*x^3*c^5*f^2+7/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^3*x*c^3*f^2+1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^5/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*x^2-b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^5*x*c^5*f^4+1/16*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^5/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*x^4-9/16*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^3/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*x^2+b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))-b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^2*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g^5*arccosh(c*x)*c^4*f^4+7/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g^3*arccosh(c*x)*c^2*f^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*f^5*arccosh(c*x)^2*d^2*c^5/g^6+5/4*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*f^3*arccosh(c*x)^2*d^2*c^3/g^4-15/16*b*(-d*(c^2*x^2-1))^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)*f*arccosh(c*x)^2*d^2*c/g^2+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g*arccosh(c*x)*x^6*c^6+3*a/g^3*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2+a/g^6*d^3*c^6*f^5/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+a/g^7*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^6*f^6-3*a/g^5*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^4*f^4-5/2*a/g^4*d^3*c^4*f^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+1/4*a/g^2*c^2*d*f*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)*x+7/8*a/g^2*c^2*d^2*f*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x+15/8*a/g^2*c^2*d^3*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-1/2*a/g^4*d^2*c^4*f^3*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x-23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g*arccosh(c*x)-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^6/(c*x-1)/(c*x+1)/g^2*arccosh(c*x)*x^5+11/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^4/(c*x-1)/(c*x+1)/g^2*arccosh(c*x)*x^3-9/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^2/(c*x-1)/(c*x+1)/g^2*arccosh(c*x)*x+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g^3*arccosh(c*x)*x^4*c^6*f^2-8/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g^3*arccosh(c*x)*x^2*c^4*f^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^6/(c*x-1)/(c*x+1)/g^4*arccosh(c*x)*x^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^4/(c*x-1)/(c*x+1)/g^4*arccosh(c*x)*x+b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c*x-1)/(c*x+1)/g^5*arccosh(c*x)*x^2*c^6*f^4+b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^6*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))*c^4*f^4-b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^6*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))*c^4*f^4-2*b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))*c^2*f^2+2*b*d^2*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)/(c*x-1)^(1/2)/(c*x+1)^(1/2)/g^4*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))*c^2*f^2","B"
66,1,859,418,1.043000," ","int((g*x+f)^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,g^{3} x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 a \,g^{3} \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}-\frac{3 a f \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{3 a f \,g^{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{3 a \,f^{2} g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a \,f^{3} \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)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, f^{3} \mathrm{arccosh}\left(c x \right)^{2}}{2 d c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, x^{3}}{9 c d \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, x}{3 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \mathrm{arccosh}\left(c x \right) x^{3}}{2 d \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \mathrm{arccosh}\left(c x \right) x}{2 d \,c^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{8 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right) x^{2} f^{2}}{d \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}\, f \mathrm{arccosh}\left(c x \right)^{2} g^{2}}{4 d \,c^{3} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{4 d c \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{c x +1}\, \sqrt{c x -1}\, x \,f^{2}}{c d \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right)}{3 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right) x^{4}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right) x^{2}}{3 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right) f^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a*g^3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3*a*g^3/d/c^4*(-c^2*d*x^2+d)^(1/2)-3/2*a*f*g^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+3/2*a*f*g^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3*a*f^2*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a*f^3/(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/c/(c^2*x^2-1)*f^3*arccosh(c*x)^2+1/9*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c/d/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^3+2/3*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-3/2*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/d/(c^2*x^2-1)*arccosh(c*x)*x^3+3/2*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/d/c^2/(c^2*x^2-1)*arccosh(c*x)*x-3/8*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/d/c^3/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)-3*b*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arccosh(c*x)*x^2*f^2-3/4*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)*f*arccosh(c*x)^2*g^2+3/4*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/d/c/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2+3*b*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*f^2+2/3*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d/(c^2*x^2-1)*arccosh(c*x)-1/3*b*(-d*(c^2*x^2-1))^(1/2)*g^3/d/(c^2*x^2-1)*arccosh(c*x)*x^4-1/3*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d/(c^2*x^2-1)*arccosh(c*x)*x^2+3*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arccosh(c*x)*f^2","B"
67,1,559,252,0.820000," ","int((g*x+f)^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a \,g^{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{2 a f g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a \,f^{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)}\, g^{2} \sqrt{c x +1}\, \sqrt{c x -1}\, x^{2}}{4 d c \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,\mathrm{arccosh}\left(c x \right) x^{2}}{\left(c^{2} x^{2}-1\right) d}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c \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}\, \mathrm{arccosh}\left(c x \right)^{2} f^{2}}{2 d c \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)^{2} g^{2}}{4 d \,c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \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)}\, g^{2} \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)}\, g^{2} \sqrt{c x -1}\, \sqrt{c x +1}}{8 d \,c^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,\mathrm{arccosh}\left(c x \right)}{c^{2} \left(c^{2} x^{2}-1\right) d}"," ",0,"-1/2*a*g^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+1/2*a*g^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2*a*f*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a*f^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)*g^2/d/c/(c^2*x^2-1)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x^2-2*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c^2*x^2-1)/d*arccosh(c*x)*x^2+2*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c/(c^2*x^2-1)/d*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/c/(c^2*x^2-1)*arccosh(c*x)^2*f^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*g^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)*g^2/d/(c^2*x^2-1)*arccosh(c*x)*x^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)*g^2/d/c^2/(c^2*x^2-1)*arccosh(c*x)*x-1/8*b*(-d*(c^2*x^2-1))^(1/2)*g^2/d/c^3/(c^2*x^2-1)*(c*x-1)^(1/2)*(c*x+1)^(1/2)+2*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/(c^2*x^2-1)/d*arccosh(c*x)","B"
68,1,239,120,0.655000," ","int((g*x+f)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a f \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)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, f \mathrm{arccosh}\left(c x \right)^{2}}{2 d c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right) x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,\mathrm{arccosh}\left(c x \right)}{c^{2} d \left(c^{2} x^{2}-1\right)}"," ",0,"-a*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a*f/(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/c/(c^2*x^2-1)*f*arccosh(c*x)^2-b*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arccosh(c*x)*x^2+b*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(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)*g/c^2/d/(c^2*x^2-1)*arccosh(c*x)","A"
69,1,754,377,0.398000," ","int((a+b*arccosh(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{d \left(c^{4} f^{2} x^{2}-c^{2} g^{2} x^{2}-c^{2} f^{2}+g^{2}\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \mathrm{arccosh}\left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{d \left(c^{4} f^{2} x^{2}-c^{2} g^{2} x^{2}-c^{2} f^{2}+g^{2}\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{d \left(c^{4} f^{2} x^{2}-c^{2} g^{2} x^{2}-c^{2} f^{2}+g^{2}\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c^{2} f^{2}-g^{2}}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{d \left(c^{4} f^{2} x^{2}-c^{2} g^{2} x^{2}-c^{2} f^{2}+g^{2}\right)}"," ",0,"-a/g/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*arccosh(c*x)/d/(c^4*f^2*x^2-c^2*g^2*x^2-c^2*f^2+g^2)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)*arccosh(c*x)/d/(c^4*f^2*x^2-c^2*g^2*x^2-c^2*f^2+g^2)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^4*f^2*x^2-c^2*g^2*x^2-c^2*f^2+g^2)*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*(c^2*f^2-g^2)^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/d/(c^4*f^2*x^2-c^2*g^2*x^2-c^2*f^2+g^2)*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))","A"
70,1,1978,519,0.785000," ","int((a+b*arccosh(c*x))/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x)","\frac{a \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{d \left(c^{2} f^{2}-g^{2}\right) \left(x +\frac{f}{g}\right)}-\frac{a \,c^{2} f \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\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 \,c^{2} f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{3} c^{4} f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\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}\, x c g}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2} c^{2} g}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\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}\, c f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2} f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) g}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\frac{b \,c^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, f \,\mathrm{arccosh}\left(c x \right) \sqrt{c^{2} f^{2}-g^{2}}\, \ln \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}+\frac{b \,c^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, f \,\mathrm{arccosh}\left(c x \right) \sqrt{c^{2} f^{2}-g^{2}}\, \ln \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}+\frac{2 b \,c^{3} \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}\right) f^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}-\frac{b \,c^{3} \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} g +2 c f \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)+g \right) f^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}-\frac{b \,c^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, f \sqrt{c^{2} f^{2}-g^{2}}\, \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}+\frac{b \,c^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x +1}\, \sqrt{c x -1}\, f \sqrt{c^{2} f^{2}-g^{2}}\, \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right)}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}-\frac{2 b c \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}\right) g^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}+\frac{b c \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} g +2 c f \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)+g \right) g^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d}"," ",0,"a/d/(c^2*f^2-g^2)/(x+f/g)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-a/g*c^2*f/(c^2*f^2-g^2)/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*(c*x+1)*(c*x-1)*x*c^2*f+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*x^3*c^4*f-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*x*c*g+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*x^2*c^2*g-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c*f-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*x*c^2*f-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*g-b*c^2*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*f*arccosh(c*x)*(c^2*f^2-g^2)^(1/2)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+b*c^2*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*f*arccosh(c*x)*(c^2*f^2-g^2)^(1/2)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))+2*b*c^3*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*f^2-b*c^3*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*g+2*c*f*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+g)*f^2-b*c^2*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*f*(c^2*f^2-g^2)^(1/2)*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))+b*c^2*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*f*(c^2*f^2-g^2)^(1/2)*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))-2*b*c*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g^2+b*c*(-d*(c^2*x^2-1))^(1/2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d*ln((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))^2*g+2*c*f*(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+g)*g^2","B"
71,1,1238,486,0.921000," ","int((g*x+f)^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,g^{3} x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a \,g^{3}}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a f \,g^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a f \,g^{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{3 a \,f^{2} g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a \,f^{3} x}{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) x \,f^{3}}{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) g^{3}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{c x +1}\, \sqrt{c x -1}\, x}{c^{3} 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}\, f^{3} \mathrm{arccosh}\left(c x \right)}{d^{2} c \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} f^{2} g}{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) \left(c x +1\right) \left(c x -1\right) g^{3}}{c^{4} d^{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 f \,g^{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}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) f^{3}}{c \,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) g^{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) f^{3}}{c \,d^{2} \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}\, \mathrm{arccosh}\left(c x \right)^{2} f \,g^{2}}{2 d^{2} c^{3} \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}\, f \,\mathrm{arccosh}\left(c x \right) g^{2}}{d^{2} c^{3} \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) \left(c x +1\right) \left(c x -1\right) f^{2} g}{c^{2} d^{2} \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}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) f^{2} g}{c^{2} d^{2} \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}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) f \,g^{2}}{c^{3} d^{2} \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}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) f^{2} g}{c^{2} d^{2} \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}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \mathrm{arccosh}\left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a*g^3*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*a*g^3/d/c^4/(-c^2*d*x^2+d)^(1/2)+3*a*f*g^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-3*a*f*g^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3*a*f^2*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a*f^3/d*x/(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x*f^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))/c^4/d^2/(c^2*x^2-1)*g^3-b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d^2/(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*x-1)^(1/2)*(c*x+1)^(1/2)/d^2/c/(c^2*x^2-1)*f^3*arccosh(c*x)-3*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x^2*f^2*g+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/c^4/d^2/(c^2*x^2-1)*(c*x+1)*(c*x-1)*g^3-3*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/c^2/d^2/(c^2*x^2-1)*x*f*g^2+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*f^3+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)*g^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))/c/d^2/(c^2*x^2-1)*f^3+3/2*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*f*g^2-3*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)*f*arccosh(c*x)*g^2+3*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/c^2/d^2/(c^2*x^2-1)*(c*x+1)*(c*x-1)*f^2*g+3*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)*f^2*g+3*b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*f*g^2-3*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))/c^2/d^2/(c^2*x^2-1)*f^2*g+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))/c^3/d^2/(c^2*x^2-1)*f*g^2-b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d^2/(c^2*x^2-1)*arccosh(c*x)","B"
72,1,879,404,0.867000," ","int((g*x+f)^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a \,g^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \,g^{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{2 a f g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a \,f^{2} 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}\, g^{2} \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) f^{2}}{d^{2} c \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) g^{2}}{d^{2} c^{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) \left(c x +1\right) \left(c x -1\right) f g}{d^{2} c^{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^{2} f g}{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 \,f^{2}}{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 \,g^{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}\, \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) f^{2}}{d^{2} c \left(c^{2} x^{2}-1\right)}+\frac{2 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) f g}{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(c x +\sqrt{c x -1}\, \sqrt{c x +1}-1\right) g^{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}\, \ln \left(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) f^{2}}{d^{2} c \left(c^{2} x^{2}-1\right)}-\frac{2 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) f g}{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(1+c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g^{2}}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a*g^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a*g^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+2*a*f*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a*f^2/d*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)*g^2*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/(c^2*x^2-1)*arccosh(c*x)*f^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)*g^2+2*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/c^2/(c^2*x^2-1)*(c*x+1)*(c*x-1)*f*g-2*b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x^2*f*g-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x*f^2-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/c^2/(c^2*x^2-1)*x*g^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)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*f^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/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*f*g+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)-1)*g^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)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*f^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/(c^2*x^2-1)*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*f*g+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(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g^2","B"
73,1,498,128,0.664000," ","int((g*x+f)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a f 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}\, f \,\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) \left(c x -1\right) \left(c x +1\right) g}{c^{2} 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^{2} g}{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 f}{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) f}{c \,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) g}{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) f}{c \,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) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a*f/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)*f*arccosh(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/c^2/d^2/(c^2*x^2-1)*(c*x-1)*(c*x+1)*g-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x^2*g-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)*x*f+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))/c/d^2/(c^2*x^2-1)*f-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))/c^2/d^2/(c^2*x^2-1)*g+b*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*f+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)*g","B"
74,1,1926,738,0.626000," ","int((a+b*arccosh(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a g}{d \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a f \,c^{2} x}{\left(c^{2} f^{2}-g^{2}\right) d \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a g \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-\left(x +\frac{f}{g}\right)^{2} c^{2} d +\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{d \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\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) g}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x^{2} c^{2} g}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}+\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}\, c f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \mathrm{arccosh}\left(c x \right) x \,c^{2} f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}+\frac{b \sqrt{c^{2} f^{2}-g^{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(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right) g^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}-\frac{b \sqrt{c^{2} f^{2}-g^{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(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right) g^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}-\frac{2 b \left(c^{2} f^{2}-g^{2}\right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, c f \ln \left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right)}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}+\frac{b \left(c^{2} f^{2}-g^{2}\right) \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 f}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}+\frac{b \left(c^{2} f^{2}-g^{2}\right) \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 f}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}-\frac{b \left(c^{2} f^{2}-g^{2}\right) \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) g}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}+\frac{b \left(c^{2} f^{2}-g^{2}\right) \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) g}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}-\frac{b \sqrt{c^{2} f^{2}-g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(\frac{\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g +c f +\sqrt{c^{2} f^{2}-g^{2}}}{c f +\sqrt{c^{2} f^{2}-g^{2}}}\right) g^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}+\frac{b \sqrt{c^{2} f^{2}-g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{c x -1}\, \sqrt{c x +1}\, \dilog \left(\frac{-\left(c x +\sqrt{c x -1}\, \sqrt{c x +1}\right) g -c f +\sqrt{c^{2} f^{2}-g^{2}}}{-c f +\sqrt{c^{2} f^{2}-g^{2}}}\right) g^{2}}{\left(c^{6} f^{4} x^{2}-2 c^{4} f^{2} g^{2} x^{2}-c^{4} f^{4}+c^{2} g^{4} x^{2}+2 c^{2} f^{2} g^{2}-g^{4}\right) d^{2}}"," ",0,"-a*g/d/(c^2*f^2-g^2)/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)+a*f/(c^2*f^2-g^2)/d/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^2*x+a*g/d/(c^2*f^2-g^2)/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*(c*x+1)*(c*x-1)*g+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*x^2*c^2*g+b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*(c*x+1)^(1/2)*(c*x-1)^(1/2)*c*f-b*(-d*(c^2*x^2-1))^(1/2)*arccosh(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*x*c^2*f+b*(c^2*f^2-g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*arccosh(c*x)*ln((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))*g^2-b*(c^2*f^2-g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*arccosh(c*x)*ln(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))*g^2-2*b*(c^2*f^2-g^2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*c*f*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))+b*(c^2*f^2-g^2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*c*f+b*(c^2*f^2-g^2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*c*f-b*(c^2*f^2-g^2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*ln(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2)-1)*g+b*(c^2*f^2-g^2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*ln(1+c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-b*(c^2*f^2-g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*dilog(((c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g+c*f+(c^2*f^2-g^2)^(1/2))/(c*f+(c^2*f^2-g^2)^(1/2)))*g^2+b*(c^2*f^2-g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^6*f^4*x^2-2*c^4*f^2*g^2*x^2-c^4*f^4+c^2*g^4*x^2+2*c^2*f^2*g^2-g^4)/d^2*dilog((-(c*x+(c*x-1)^(1/2)*(c*x+1)^(1/2))*g-c*f+(c^2*f^2-g^2)^(1/2))/(-c*f+(c^2*f^2-g^2)^(1/2)))*g^2","B"
75,0,0,220,0.736000," ","int((g*x+f)*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(g x +f \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((g*x+f)*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x)","F"
76,0,0,187,0.861000," ","int((g*x+f)*(a+b*arccosh(c*x))^n/(-c*x+1)^(1/2)/(c*x+1)^(1/2),x)","\int \frac{\left(g x +f \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{-c x +1}\, \sqrt{c x +1}}\, dx"," ",0,"int((g*x+f)*(a+b*arccosh(c*x))^n/(-c*x+1)^(1/2)/(c*x+1)^(1/2),x)","F"
77,0,0,235,1.170000," ","int((g*x+f)*(a+b*arccosh(c*x))^n/(c*d1*x+d1)^(1/2)/(-c*d2*x+d2)^(1/2),x)","\int \frac{\left(g x +f \right) \left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n}}{\sqrt{c \mathit{d1} x +\mathit{d1}}\, \sqrt{-c \mathit{d2} x +\mathit{d2}}}\, dx"," ",0,"int((g*x+f)*(a+b*arccosh(c*x))^n/(c*d1*x+d1)^(1/2)/(-c*d2*x+d2)^(1/2),x)","F"
78,0,0,64,4.481000," ","int((a+b*arccosh(c*x))^n*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{n} \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arccosh(c*x))^n*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
79,0,0,794,4.522000," ","int((a+b*arccosh(c*x))^2*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right)^{2} \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arccosh(c*x))^2*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
80,0,0,610,4.146000," ","int((a+b*arccosh(c*x))*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right) \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arccosh(c*x))*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
81,0,0,252,0.216000," ","int(ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
82,0,0,64,2.562000," ","int(ln(h*(g*x+f)^m)/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{\ln \left(h \left(g x +f \right)^{m}\right)}{\left(a +b \,\mathrm{arccosh}\left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(ln(h*(g*x+f)^m)/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
83,1,308,130,0.031000," ","int(x^3*arccosh(b*x+a),x)","\frac{x^{4} \mathrm{arccosh}\left(b x +a \right)}{4}-\frac{x^{3} \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{16 b}+\frac{7 a \,x^{2} \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{48 b^{2}}-\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{4} \ln \left(b x +a +\sqrt{\left(b x +a \right)^{2}-1}\right)}{4 b^{4} \sqrt{\left(b x +a \right)^{2}-1}}-\frac{13 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, x \,a^{2}}{48 b^{3}}+\frac{25 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{3}}{48 b^{4}}-\frac{3 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{2} \ln \left(b x +a +\sqrt{\left(b x +a \right)^{2}-1}\right)}{4 b^{4} \sqrt{\left(b x +a \right)^{2}-1}}-\frac{3 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, x}{32 b^{3}}+\frac{55 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a}{96 b^{4}}-\frac{3 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \ln \left(b x +a +\sqrt{\left(b x +a \right)^{2}-1}\right)}{32 b^{4} \sqrt{\left(b x +a \right)^{2}-1}}"," ",0,"1/4*x^4*arccosh(b*x+a)-1/16*x^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/b+7/48*a*x^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/b^2-1/4/b^4*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/((b*x+a)^2-1)^(1/2)*a^4*ln(b*x+a+((b*x+a)^2-1)^(1/2))-13/48/b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*x*a^2+25/48/b^4*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*a^3-3/4/b^4*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/((b*x+a)^2-1)^(1/2)*a^2*ln(b*x+a+((b*x+a)^2-1)^(1/2))-3/32/b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*x+55/96/b^4*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*a-3/32/b^4*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/((b*x+a)^2-1)^(1/2)*ln(b*x+a+((b*x+a)^2-1)^(1/2))","B"
84,1,207,88,0.013000," ","int(x^2*arccosh(b*x+a),x)","\frac{x^{3} \mathrm{arccosh}\left(b x +a \right)}{3}-\frac{x^{2} \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{9 b}+\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{3} \ln \left(b x +a +\sqrt{\left(b x +a \right)^{2}-1}\right)}{3 b^{3} \sqrt{\left(b x +a \right)^{2}-1}}+\frac{5 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, x a}{18 b^{2}}-\frac{11 \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{2}}{18 b^{3}}+\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a \ln \left(b x +a +\sqrt{\left(b x +a \right)^{2}-1}\right)}{2 b^{3} \sqrt{\left(b x +a \right)^{2}-1}}-\frac{2 \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{9 b^{3}}"," ",0,"1/3*x^3*arccosh(b*x+a)-1/9*x^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/b+1/3/b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/((b*x+a)^2-1)^(1/2)*a^3*ln(b*x+a+((b*x+a)^2-1)^(1/2))+5/18/b^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*x*a-11/18/b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*a^2+1/2/b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/((b*x+a)^2-1)^(1/2)*a*ln(b*x+a+((b*x+a)^2-1)^(1/2))-2/9/b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)","B"
85,1,120,74,0.011000," ","int(x*arccosh(b*x+a),x)","\frac{x^{2} \mathrm{arccosh}\left(b x +a \right)}{2}-\frac{\mathrm{arccosh}\left(b x +a \right) a^{2}}{2 b^{2}}-\frac{x \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{4 b}+\frac{3 a \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{4 b^{2}}-\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \ln \left(b x +a +\sqrt{\left(b x +a \right)^{2}-1}\right)}{4 b^{2} \sqrt{\left(b x +a \right)^{2}-1}}"," ",0,"1/2*x^2*arccosh(b*x+a)-1/2/b^2*arccosh(b*x+a)*a^2-1/4*x*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/b+3/4*a*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/b^2-1/4/b^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/((b*x+a)^2-1)^(1/2)*ln(b*x+a+((b*x+a)^2-1)^(1/2))","A"
86,1,36,37,0.002000," ","int(arccosh(b*x+a),x)","\frac{\left(b x +a \right) \mathrm{arccosh}\left(b x +a \right)-\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{b}"," ",0,"1/b*((b*x+a)*arccosh(b*x+a)-(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))","A"
87,1,436,177,0.232000," ","int(arccosh(b*x+a)/x,x)","-\frac{\mathrm{arccosh}\left(b x +a \right)^{2}}{2}+\frac{a \,\mathrm{arccosh}\left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}-1}-b x -\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{a +\sqrt{a^{2}-1}}\right)}{\sqrt{a^{2}-1}}-\frac{a \,\mathrm{arccosh}\left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}-1}+b x +\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{-a +\sqrt{a^{2}-1}}\right)}{\sqrt{a^{2}-1}}-\frac{\left(a^{2}-1+a \sqrt{a^{2}-1}\right) \mathrm{arccosh}\left(b x +a \right) \left(2 \ln \left(\frac{\sqrt{a^{2}-1}-b x -\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{a +\sqrt{a^{2}-1}}\right) a^{2}-\ln \left(\frac{\sqrt{a^{2}-1}-b x -\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{a +\sqrt{a^{2}-1}}\right)-\ln \left(\frac{\sqrt{a^{2}-1}+b x +\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{-a +\sqrt{a^{2}-1}}\right)-2 a \sqrt{a^{2}-1}\, \ln \left(\frac{\sqrt{a^{2}-1}-b x -\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{a +\sqrt{a^{2}-1}}\right)\right)}{a^{2}-1}+\dilog \left(\frac{\sqrt{a^{2}-1}+b x +\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{-a +\sqrt{a^{2}-1}}\right)+\dilog \left(\frac{\sqrt{a^{2}-1}-b x -\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{a +\sqrt{a^{2}-1}}\right)"," ",0,"-1/2*arccosh(b*x+a)^2+a*arccosh(b*x+a)/(a^2-1)^(1/2)*ln(((a^2-1)^(1/2)-b*x-(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(a+(a^2-1)^(1/2)))-a*arccosh(b*x+a)/(a^2-1)^(1/2)*ln(((a^2-1)^(1/2)+b*x+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(-a+(a^2-1)^(1/2)))-(a^2-1+a*(a^2-1)^(1/2))*arccosh(b*x+a)*(2*ln(((a^2-1)^(1/2)-b*x-(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(a+(a^2-1)^(1/2)))*a^2-ln(((a^2-1)^(1/2)-b*x-(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(a+(a^2-1)^(1/2)))-ln(((a^2-1)^(1/2)+b*x+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(-a+(a^2-1)^(1/2)))-2*a*(a^2-1)^(1/2)*ln(((a^2-1)^(1/2)-b*x-(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(a+(a^2-1)^(1/2))))/(a^2-1)+dilog(((a^2-1)^(1/2)+b*x+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(-a+(a^2-1)^(1/2)))+dilog(((a^2-1)^(1/2)-b*x-(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/(a+(a^2-1)^(1/2)))","B"
88,1,97,54,0.018000," ","int(arccosh(b*x+a)/x^2,x)","-\frac{\mathrm{arccosh}\left(b x +a \right)}{x}-\frac{b \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \sqrt{a^{2}-1}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{\left(b x +a \right)^{2}-1}+2 a \left(b x +a \right)-2}{b x}\right)}{\sqrt{\left(b x +a \right)^{2}-1}\, \left(a -1\right) \left(1+a \right)}"," ",0,"-arccosh(b*x+a)/x-b*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(a^2-1)^(1/2)*ln(2*((a^2-1)^(1/2)*((b*x+a)^2-1)^(1/2)+a*(b*x+a)-1)/b/x)/((b*x+a)^2-1)^(1/2)/(a-1)/(1+a)","A"
89,1,181,88,0.019000," ","int(arccosh(b*x+a)/x^3,x)","-\frac{\mathrm{arccosh}\left(b x +a \right)}{2 x^{2}}+\frac{b^{2} \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{\left(b x +a \right)^{2}-1}+2 a \left(b x +a \right)-2}{b x}\right) a}{2 \sqrt{a^{2}-1}\, \left(1+a \right) \left(a -1\right) \sqrt{\left(b x +a \right)^{2}-1}}-\frac{b \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{2}}{2 x \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right)}+\frac{b \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{2 x \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right)}"," ",0,"-1/2*arccosh(b*x+a)/x^2+1/2*b^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/(a^2-1)^(1/2)/(1+a)/(a-1)/((b*x+a)^2-1)^(1/2)*ln(2*((a^2-1)^(1/2)*((b*x+a)^2-1)^(1/2)+a*(b*x+a)-1)/b/x)*a-1/2*b*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x/(a^2-1)/(1+a)/(a-1)*a^2+1/2*b*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x/(a^2-1)/(1+a)/(a-1)","B"
90,1,397,128,0.021000," ","int(arccosh(b*x+a)/x^4,x)","-\frac{\mathrm{arccosh}\left(b x +a \right)}{3 x^{3}}-\frac{b^{3} \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{\left(b x +a \right)^{2}-1}+2 a \left(b x +a \right)-2}{b x}\right) a^{2}}{3 \left(a^{2}-1\right)^{\frac{3}{2}} \left(1+a \right) \left(a -1\right) \sqrt{\left(b x +a \right)^{2}-1}}-\frac{b^{3} \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{\left(b x +a \right)^{2}-1}+2 a \left(b x +a \right)-2}{b x}\right)}{6 \left(a^{2}-1\right)^{\frac{3}{2}} \left(1+a \right) \left(a -1\right) \sqrt{\left(b x +a \right)^{2}-1}}+\frac{b^{2} \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{3}}{2 x \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}-\frac{b \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{4}}{6 x^{2} \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}-\frac{b^{2} \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a}{2 x \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}+\frac{b \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, a^{2}}{3 x^{2} \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}-\frac{b \sqrt{b x +a -1}\, \sqrt{b x +a +1}}{6 x^{2} \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}"," ",0,"-1/3*arccosh(b*x+a)/x^3-1/3*b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/(a^2-1)^(3/2)/(1+a)/(a-1)/((b*x+a)^2-1)^(1/2)*ln(2*((a^2-1)^(1/2)*((b*x+a)^2-1)^(1/2)+a*(b*x+a)-1)/b/x)*a^2-1/6*b^3*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/(a^2-1)^(3/2)/(1+a)/(a-1)/((b*x+a)^2-1)^(1/2)*ln(2*((a^2-1)^(1/2)*((b*x+a)^2-1)^(1/2)+a*(b*x+a)-1)/b/x)+1/2*b^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x/(a^2-1)^2/(1+a)/(a-1)*a^3-1/6*b*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x^2/(a^2-1)^2/(1+a)/(a-1)*a^4-1/2*b^2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x/(a^2-1)^2/(1+a)/(a-1)*a+1/3*b*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x^2/(a^2-1)^2/(1+a)/(a-1)*a^2-1/6*b*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/x^2/(a^2-1)^2/(1+a)/(a-1)","B"
91,0,0,71,0.158000," ","int(1/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{1}{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x+c))^(1/2),x)","F"
92,0,0,73,0.151000," ","int(1/(a-b*arccosh(d*x+c))^(1/2),x)","\int \frac{1}{\sqrt{a -b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int(1/(a-b*arccosh(d*x+c))^(1/2),x)","F"
93,1,78,115,0.025000," ","int((d*e*x+c*e)^4*(a+b*arccosh(d*x+c)),x)","\frac{\frac{\left(d x +c \right)^{5} e^{4} a}{5}+e^{4} b \left(\frac{\left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)}{5}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right)}{75}\right)}{d}"," ",0,"1/d*(1/5*(d*x+c)^5*e^4*a+e^4*b*(1/5*(d*x+c)^5*arccosh(d*x+c)-1/75*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(3*(d*x+c)^4+4*(d*x+c)^2+8)))","A"
94,1,359,103,0.013000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c)),x)","\frac{d^{3} x^{4} a \,e^{3}}{4}+d^{2} x^{3} a c \,e^{3}+\frac{3 d \,x^{2} a \,c^{2} e^{3}}{2}+x a \,c^{3} e^{3}+\frac{a \,c^{4} e^{3}}{4 d}+\frac{d^{3} \mathrm{arccosh}\left(d x +c \right) x^{4} b \,e^{3}}{4}+d^{2} \mathrm{arccosh}\left(d x +c \right) x^{3} b c \,e^{3}+\frac{3 d \,\mathrm{arccosh}\left(d x +c \right) x^{2} b \,c^{2} e^{3}}{2}+\mathrm{arccosh}\left(d x +c \right) x b \,c^{3} e^{3}+\frac{\mathrm{arccosh}\left(d x +c \right) b \,c^{4} e^{3}}{4 d}-\frac{d^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3} b \,e^{3}}{16}-\frac{3 d \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} b c \,e^{3}}{16}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x b \,c^{2} e^{3}}{16}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, b \,c^{3} e^{3}}{16 d}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x b \,e^{3}}{32}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, b c \,e^{3}}{32 d}-\frac{3 e^{3} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{32 d \sqrt{\left(d x +c \right)^{2}-1}}"," ",0,"1/4*d^3*x^4*a*e^3+d^2*x^3*a*c*e^3+3/2*d*x^2*a*c^2*e^3+x*a*c^3*e^3+1/4/d*a*c^4*e^3+1/4*d^3*arccosh(d*x+c)*x^4*b*e^3+d^2*arccosh(d*x+c)*x^3*b*c*e^3+3/2*d*arccosh(d*x+c)*x^2*b*c^2*e^3+arccosh(d*x+c)*x*b*c^3*e^3+1/4/d*arccosh(d*x+c)*b*c^4*e^3-1/16*d^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3*b*e^3-3/16*d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*b*c*e^3-3/16*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*b*c^2*e^3-1/16/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*b*c^3*e^3-3/32*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*b*e^3-3/32/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*b*c*e^3-3/32/d*e^3*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))","B"
95,1,67,83,0.007000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c)),x)","\frac{\frac{\left(d x +c \right)^{3} e^{2} a}{3}+e^{2} b \left(\frac{\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{3}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(\left(d x +c \right)^{2}+2\right)}{9}\right)}{d}"," ",0,"1/d*(1/3*(d*x+c)^3*e^2*a+e^2*b*(1/3*arccosh(d*x+c)*(d*x+c)^3-1/9*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*((d*x+c)^2+2)))","A"
96,1,162,65,0.006000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c)),x)","\frac{a d e \,x^{2}}{2}+x a c e +\frac{a \,c^{2} e}{2 d}+\frac{d \,\mathrm{arccosh}\left(d x +c \right) x^{2} b e}{2}+\mathrm{arccosh}\left(d x +c \right) x b c e +\frac{\mathrm{arccosh}\left(d x +c \right) b \,c^{2} e}{2 d}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x b e}{4}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, b c e}{4 d}-\frac{e b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{4 d \sqrt{\left(d x +c \right)^{2}-1}}"," ",0,"1/2*a*d*e*x^2+x*a*c*e+1/2/d*a*c^2*e+1/2*d*arccosh(d*x+c)*x^2*b*e+arccosh(d*x+c)*x*b*c*e+1/2/d*arccosh(d*x+c)*b*c^2*e-1/4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*b*e-1/4/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*b*c*e-1/4/d*e*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))","B"
97,1,41,42,0.002000," ","int(a+b*arccosh(d*x+c),x)","a x +\frac{b \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{d}"," ",0,"a*x+b/d*((d*x+c)*arccosh(d*x+c)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))","A"
98,1,111,105,0.090000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e),x)","\frac{a \ln \left(d x +c \right)}{d e}-\frac{b \mathrm{arccosh}\left(d x +c \right)^{2}}{2 d e}+\frac{b \,\mathrm{arccosh}\left(d x +c \right) \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{b \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}"," ",0,"1/d*a/e*ln(d*x+c)-1/2/d*b/e*arccosh(d*x+c)^2+1/d*b/e*arccosh(d*x+c)*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+1/2/d*b/e*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)","A"
99,1,88,54,0.007000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^2,x)","-\frac{a}{d \,e^{2} \left(d x +c \right)}-\frac{b \,\mathrm{arccosh}\left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \arctan \left(\frac{1}{\sqrt{\left(d x +c \right)^{2}-1}}\right)}{d \,e^{2} \sqrt{\left(d x +c \right)^{2}-1}}"," ",0,"-1/d*a/e^2/(d*x+c)-1/d*b/e^2/(d*x+c)*arccosh(d*x+c)-1/d*b/e^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*arctan(1/((d*x+c)^2-1)^(1/2))","A"
100,1,65,61,0.006000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^3,x)","\frac{-\frac{a}{2 e^{3} \left(d x +c \right)^{2}}+\frac{b \left(-\frac{\mathrm{arccosh}\left(d x +c \right)}{2 \left(d x +c \right)^{2}}+\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{2 d x +2 c}\right)}{e^{3}}}{d}"," ",0,"1/d*(-1/2*a/e^3/(d*x+c)^2+b/e^3*(-1/2/(d*x+c)^2*arccosh(d*x+c)+1/2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/(d*x+c)))","A"
101,1,120,88,0.009000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^4,x)","-\frac{a}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b \,\mathrm{arccosh}\left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \arctan \left(\frac{1}{\sqrt{\left(d x +c \right)^{2}-1}}\right)}{6 d \,e^{4} \sqrt{\left(d x +c \right)^{2}-1}}+\frac{b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{6 d \,e^{4} \left(d x +c \right)^{2}}"," ",0,"-1/3/d*a/e^4/(d*x+c)^3-1/3/d*b/e^4/(d*x+c)^3*arccosh(d*x+c)-1/6/d*b/e^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*arctan(1/((d*x+c)^2-1)^(1/2))+1/6*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/d/e^4/(d*x+c)^2","A"
102,1,76,93,0.009000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^5,x)","\frac{-\frac{a}{4 e^{5} \left(d x +c \right)^{4}}+\frac{b \left(-\frac{\mathrm{arccosh}\left(d x +c \right)}{4 \left(d x +c \right)^{4}}+\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(2 \left(d x +c \right)^{2}+1\right)}{12 \left(d x +c \right)^{3}}\right)}{e^{5}}}{d}"," ",0,"1/d*(-1/4*a/e^5/(d*x+c)^4+b/e^5*(-1/4/(d*x+c)^4*arccosh(d*x+c)+1/12*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(2*(d*x+c)^2+1)/(d*x+c)^3))","A"
103,1,152,120,0.006000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^6,x)","-\frac{a}{5 d \,e^{6} \left(d x +c \right)^{5}}-\frac{b \,\mathrm{arccosh}\left(d x +c \right)}{5 d \,e^{6} \left(d x +c \right)^{5}}-\frac{3 b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \arctan \left(\frac{1}{\sqrt{\left(d x +c \right)^{2}-1}}\right)}{40 d \,e^{6} \sqrt{\left(d x +c \right)^{2}-1}}+\frac{3 b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{40 d \,e^{6} \left(d x +c \right)^{2}}+\frac{b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{20 d \,e^{6} \left(d x +c \right)^{4}}"," ",0,"-1/5/d*a/e^6/(d*x+c)^5-1/5/d*b/e^6/(d*x+c)^5*arccosh(d*x+c)-3/40/d*b/e^6*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*arctan(1/((d*x+c)^2-1)^(1/2))+3/40*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/d/e^6/(d*x+c)^2+1/20*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/d/e^6/(d*x+c)^4","A"
104,1,218,192,0.044000," ","int((d*e*x+c*e)^4*(a+b*arccosh(d*x+c))^2,x)","\frac{\frac{\left(d x +c \right)^{5} e^{4} a^{2}}{5}+e^{4} b^{2} \left(\frac{\left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)^{2}}{5}-\frac{16 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{75}-\frac{2 \left(d x +c \right)^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{25}-\frac{8 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(d x +c \right)^{2}}{75}+\frac{16 d x}{75}+\frac{16 c}{75}+\frac{2 \left(d x +c \right)^{5}}{125}+\frac{8 \left(d x +c \right)^{3}}{225}\right)+2 e^{4} a b \left(\frac{\left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)}{5}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right)}{75}\right)}{d}"," ",0,"1/d*(1/5*(d*x+c)^5*e^4*a^2+e^4*b^2*(1/5*(d*x+c)^5*arccosh(d*x+c)^2-16/75*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-2/25*(d*x+c)^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-8/75*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(d*x+c)^2+16/75*d*x+16/75*c+2/125*(d*x+c)^5+8/225*(d*x+c)^3)+2*e^4*a*b*(1/5*(d*x+c)^5*arccosh(d*x+c)-1/75*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(3*(d*x+c)^4+4*(d*x+c)^2+8)))","A"
105,1,822,166,0.042000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^2,x)","\frac{d^{3} x^{4} a^{2} e^{3}}{4}-\frac{e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{8 d}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x a b \,c^{2} e^{3}}{8}-\frac{3 e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{8}+2 d^{2} \mathrm{arccosh}\left(d x +c \right) x^{3} a b c \,e^{3}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a b \,c^{3} e^{3}}{8 d}+3 d \,\mathrm{arccosh}\left(d x +c \right) x^{2} a b \,c^{2} e^{3}-\frac{d^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3} a b \,e^{3}}{8}-\frac{d^{2} e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{8}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a b c \,e^{3}}{16 d}-\frac{3 e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{16 d}+\frac{e^{3} b^{2} c^{4}}{32 d}+\frac{3 e^{3} b^{2} c^{2}}{32 d}+\frac{a^{2} c^{4} e^{3}}{4 d}+\frac{d^{3} e^{3} b^{2} x^{4}}{32}-\frac{3 d \,e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{8}-\frac{3 d \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} a b c \,e^{3}}{8}-\frac{3 e^{3} a b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{16 d \sqrt{\left(d x +c \right)^{2}-1}}+\frac{3 d \,e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2} c^{2}}{2}+d^{2} e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{3} c +\frac{3 e^{3} b^{2} x c}{16}+\frac{e^{3} b^{2} x \,c^{3}}{8}+x \,a^{2} c^{3} e^{3}+\frac{3 d \,e^{3} b^{2} x^{2}}{32}+\frac{d^{3} e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{4}}{4}+e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x \,c^{3}+\frac{d^{2} e^{3} b^{2} x^{3} c}{8}+\frac{3 d \,e^{3} b^{2} x^{2} c^{2}}{16}+\frac{3 d \,x^{2} a^{2} c^{2} e^{3}}{2}+\frac{e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} c^{4}}{4 d}-\frac{3 e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{32 d}+d^{2} x^{3} a^{2} c \,e^{3}+\frac{d^{3} \mathrm{arccosh}\left(d x +c \right) x^{4} a b \,e^{3}}{2}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x a b \,e^{3}}{16}-\frac{3 e^{3} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{16}+2 \,\mathrm{arccosh}\left(d x +c \right) x a b \,c^{3} e^{3}+\frac{\mathrm{arccosh}\left(d x +c \right) a b \,c^{4} e^{3}}{2 d}"," ",0,"1/4*d^3*x^4*a^2*e^3-1/8/d*e^3*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-3/8*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a*b*c^2*e^3-3/8*e^3*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2+2*d^2*arccosh(d*x+c)*x^3*a*b*c*e^3-1/8/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a*b*c^3*e^3+3*d*arccosh(d*x+c)*x^2*a*b*c^2*e^3-1/8*d^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3*a*b*e^3-1/8*d^2*e^3*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-3/16/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a*b*c*e^3-3/16/d*e^3*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c+1/32/d*e^3*b^2*c^4+3/32/d*e^3*b^2*c^2+1/4/d*a^2*c^4*e^3+1/32*d^3*e^3*b^2*x^4-3/8*d*e^3*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c-3/8*d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*a*b*c*e^3-3/16/d*e^3*a*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))+3/2*d*e^3*b^2*arccosh(d*x+c)^2*x^2*c^2+d^2*e^3*b^2*arccosh(d*x+c)^2*x^3*c+3/16*e^3*b^2*x*c+1/8*e^3*b^2*x*c^3+x*a^2*c^3*e^3+3/32*d*e^3*b^2*x^2+1/4*d^3*e^3*b^2*arccosh(d*x+c)^2*x^4+e^3*b^2*arccosh(d*x+c)^2*x*c^3+1/8*d^2*e^3*b^2*x^3*c+3/16*d*e^3*b^2*x^2*c^2+3/2*d*x^2*a^2*c^2*e^3+1/4/d*e^3*b^2*arccosh(d*x+c)^2*c^4-3/32/d*e^3*b^2*arccosh(d*x+c)^2+d^2*x^3*a^2*c*e^3+1/2*d^3*arccosh(d*x+c)*x^4*a*b*e^3-3/16*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a*b*e^3-3/16*e^3*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+2*arccosh(d*x+c)*x*a*b*c^3*e^3+1/2/d*arccosh(d*x+c)*a*b*c^4*e^3","B"
106,1,167,132,0.040000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^2,x)","\frac{\frac{\left(d x +c \right)^{3} e^{2} a^{2}}{3}+e^{2} b^{2} \left(\frac{\left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{2}}{3}-\frac{4 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{9}-\frac{2 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(d x +c \right)^{2}}{9}+\frac{4 d x}{9}+\frac{4 c}{9}+\frac{2 \left(d x +c \right)^{3}}{27}\right)+2 e^{2} a b \left(\frac{\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{3}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(\left(d x +c \right)^{2}+2\right)}{9}\right)}{d}"," ",0,"1/d*(1/3*(d*x+c)^3*e^2*a^2+e^2*b^2*(1/3*(d*x+c)^3*arccosh(d*x+c)^2-4/9*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-2/9*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(d*x+c)^2+4/9*d*x+4/9*c+2/27*(d*x+c)^3)+2*e^2*a*b*(1/3*arccosh(d*x+c)*(d*x+c)^3-1/9*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*((d*x+c)^2+2)))","A"
107,1,334,98,0.036000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^2,x)","\frac{a^{2} e \,x^{2} d}{2}+x \,a^{2} c e +\frac{a^{2} c^{2} e}{2 d}+\frac{d e \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2}}{2}+e \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x c +\frac{e \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} c^{2}}{2 d}-\frac{e \,b^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \mathrm{arccosh}\left(d x +c \right) x}{2}-\frac{e \,b^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \mathrm{arccosh}\left(d x +c \right) c}{2 d}-\frac{e \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{4 d}+\frac{b^{2} d e \,x^{2}}{4}+\frac{e \,b^{2} x c}{2}+\frac{e \,b^{2} c^{2}}{4 d}+d \,\mathrm{arccosh}\left(d x +c \right) x^{2} a b e +2 \,\mathrm{arccosh}\left(d x +c \right) x a b c e +\frac{\mathrm{arccosh}\left(d x +c \right) a b \,c^{2} e}{d}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x a b e}{2}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a b c e}{2 d}-\frac{e a b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{2 d \sqrt{\left(d x +c \right)^{2}-1}}"," ",0,"1/2*a^2*e*x^2*d+x*a^2*c*e+1/2/d*a^2*c^2*e+1/2*d*e*b^2*arccosh(d*x+c)^2*x^2+e*b^2*arccosh(d*x+c)^2*x*c+1/2/d*e*b^2*arccosh(d*x+c)^2*c^2-1/2*e*b^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*arccosh(d*x+c)*x-1/2/d*e*b^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*arccosh(d*x+c)*c-1/4/d*e*b^2*arccosh(d*x+c)^2+1/4*b^2*d*e*x^2+1/2*e*b^2*x*c+1/4/d*e*b^2*c^2+d*arccosh(d*x+c)*x^2*a*b*e+2*arccosh(d*x+c)*x*a*b*c*e+1/d*arccosh(d*x+c)*a*b*c^2*e-1/2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a*b*e-1/2/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a*b*c*e-1/2/d*e*a*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))","B"
108,1,100,60,0.053000," ","int((a+b*arccosh(d*x+c))^2,x)","\frac{a^{2} \left(d x +c \right)+b^{2} \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{2}-2 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}+2 d x +2 c \right)+2 a b \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{d}"," ",0,"1/d*(a^2*(d*x+c)+b^2*((d*x+c)*arccosh(d*x+c)^2-2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+2*d*x+2*c)+2*a*b*((d*x+c)*arccosh(d*x+c)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))","A"
109,1,263,156,0.054000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e),x)","\frac{a^{2} \ln \left(d x +c \right)}{d e}-\frac{b^{2} \mathrm{arccosh}\left(d x +c \right)^{3}}{3 d e}+\frac{b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{b^{2} \mathrm{arccosh}\left(d x +c \right) \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{b^{2} \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}-\frac{a b \mathrm{arccosh}\left(d x +c \right)^{2}}{d e}+\frac{2 a b \,\mathrm{arccosh}\left(d x +c \right) \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{a b \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}"," ",0,"1/d*a^2/e*ln(d*x+c)-1/3/d*b^2/e*arccosh(d*x+c)^3+1/d*b^2/e*arccosh(d*x+c)^2*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+1/d*b^2/e*arccosh(d*x+c)*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-1/2/d*b^2/e*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-1/d*a*b/e*arccosh(d*x+c)^2+2/d*a*b/e*arccosh(d*x+c)*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+1/d*a*b/e*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)","A"
110,1,290,148,0.170000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^2,x)","-\frac{a^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{2 i b^{2} \mathrm{arccosh}\left(d x +c \right) \ln \left(1+i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{d \,e^{2}}+\frac{2 i b^{2} \mathrm{arccosh}\left(d x +c \right) \ln \left(1-i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{d \,e^{2}}-\frac{2 i b^{2} \dilog \left(1+i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{d \,e^{2}}+\frac{2 i b^{2} \dilog \left(1-i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{d \,e^{2}}-\frac{2 a b \,\mathrm{arccosh}\left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{2 a b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \arctan \left(\frac{1}{\sqrt{\left(d x +c \right)^{2}-1}}\right)}{d \,e^{2} \sqrt{\left(d x +c \right)^{2}-1}}"," ",0,"-1/d*a^2/e^2/(d*x+c)-1/d*b^2/e^2*arccosh(d*x+c)^2/(d*x+c)-2*I/d*b^2/e^2*arccosh(d*x+c)*ln(1+I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))+2*I/d*b^2/e^2*arccosh(d*x+c)*ln(1-I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))-2*I/d*b^2/e^2*dilog(1+I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))+2*I/d*b^2/e^2*dilog(1-I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))-2/d*a*b/e^2/(d*x+c)*arccosh(d*x+c)-2/d*a*b/e^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*arctan(1/((d*x+c)^2-1)^(1/2))","A"
111,1,194,86,0.273000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^3,x)","-\frac{a^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{b^{2} \mathrm{arccosh}\left(d x +c \right)}{d \,e^{3}}+\frac{b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{d \,e^{3} \left(d x +c \right)}-\frac{b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}-\frac{a b \,\mathrm{arccosh}\left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}+\frac{a b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{d \,e^{3} \left(d x +c \right)}"," ",0,"-1/2/d*a^2/e^3/(d*x+c)^2+1/d*b^2/e^3*arccosh(d*x+c)+1/d*b^2/e^3*arccosh(d*x+c)/(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)-1/2/d*b^2/e^3*arccosh(d*x+c)^2/(d*x+c)^2-1/d*b^2/e^3*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-1/d*a*b/e^3/(d*x+c)^2*arccosh(d*x+c)+1/d*a*b/e^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/(d*x+c)","B"
112,1,381,208,0.312000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^4,x)","-\frac{a^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}+\frac{b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}+\frac{b^{2}}{3 d \,e^{4} \left(d x +c \right)}-\frac{i b^{2} \mathrm{arccosh}\left(d x +c \right) \ln \left(1+i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{3 d \,e^{4}}+\frac{i b^{2} \mathrm{arccosh}\left(d x +c \right) \ln \left(1-i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{3 d \,e^{4}}-\frac{i b^{2} \dilog \left(1+i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{3 d \,e^{4}}+\frac{i b^{2} \dilog \left(1-i \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)\right)}{3 d \,e^{4}}-\frac{2 a b \,\mathrm{arccosh}\left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{a b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \arctan \left(\frac{1}{\sqrt{\left(d x +c \right)^{2}-1}}\right)}{3 d \,e^{4} \sqrt{\left(d x +c \right)^{2}-1}}+\frac{a b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{3 d \,e^{4} \left(d x +c \right)^{2}}"," ",0,"-1/3/d*a^2/e^4/(d*x+c)^3+1/3/d*b^2/e^4/(d*x+c)^2*arccosh(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)-1/3/d*b^2/e^4/(d*x+c)^3*arccosh(d*x+c)^2+1/3*b^2/d/e^4/(d*x+c)-1/3*I/d*b^2/e^4*arccosh(d*x+c)*ln(1+I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))+1/3*I/d*b^2/e^4*arccosh(d*x+c)*ln(1-I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))-1/3*I/d*b^2/e^4*dilog(1+I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))+1/3*I/d*b^2/e^4*dilog(1-I*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))-2/3/d*a*b/e^4/(d*x+c)^3*arccosh(d*x+c)-1/3/d*a*b/e^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*arctan(1/((d*x+c)^2-1)^(1/2))+1/3/d*a*b/e^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/(d*x+c)^2","A"
113,1,450,336,0.051000," ","int((d*e*x+c*e)^4*(a+b*arccosh(d*x+c))^3,x)","\frac{\frac{\left(d x +c \right)^{5} e^{4} a^{3}}{5}+e^{4} b^{3} \left(\frac{\left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)^{3}}{5}-\frac{8 \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{25}-\frac{3 \left(d x +c \right)^{4} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{25}-\frac{4 \left(d x +c \right)^{2} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{25}+\frac{16 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)}{25}-\frac{4144 \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{5625}+\frac{6 \left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)}{125}-\frac{6 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{625}-\frac{272 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{5625}+\frac{8 \,\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{75}\right)+3 e^{4} a \,b^{2} \left(\frac{\left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)^{2}}{5}-\frac{16 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{75}-\frac{2 \left(d x +c \right)^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{25}-\frac{8 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(d x +c \right)^{2}}{75}+\frac{16 d x}{75}+\frac{16 c}{75}+\frac{2 \left(d x +c \right)^{5}}{125}+\frac{8 \left(d x +c \right)^{3}}{225}\right)+3 e^{4} a^{2} b \left(\frac{\left(d x +c \right)^{5} \mathrm{arccosh}\left(d x +c \right)}{5}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right)}{75}\right)}{d}"," ",0,"1/d*(1/5*(d*x+c)^5*e^4*a^3+e^4*b^3*(1/5*(d*x+c)^5*arccosh(d*x+c)^3-8/25*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-3/25*(d*x+c)^4*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4/25*(d*x+c)^2*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+16/25*(d*x+c)*arccosh(d*x+c)-4144/5625*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+6/125*(d*x+c)^5*arccosh(d*x+c)-6/625*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-272/5625*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+8/75*arccosh(d*x+c)*(d*x+c)^3)+3*e^4*a*b^2*(1/5*(d*x+c)^5*arccosh(d*x+c)^2-16/75*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-2/25*(d*x+c)^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-8/75*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(d*x+c)^2+16/75*d*x+16/75*c+2/125*(d*x+c)^5+8/225*(d*x+c)^3)+3*e^4*a^2*b*(1/5*(d*x+c)^5*arccosh(d*x+c)-1/75*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(3*(d*x+c)^4+4*(d*x+c)^2+8)))","A"
114,1,1554,273,0.051000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^3,x)","-\frac{3 d^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3} a^{2} b \,e^{3}}{16}+3 d^{2} \mathrm{arccosh}\left(d x +c \right) x^{3} a^{2} b c \,e^{3}+3 d^{2} e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{3} c +\frac{9 d \,e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2} c^{2}}{2}-\frac{3 d^{2} e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{16}-\frac{9 d \,e^{3} b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{128}+\frac{9 d \,\mathrm{arccosh}\left(d x +c \right) x^{2} a^{2} b \,c^{2} e^{3}}{2}-\frac{9 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{32 d}-\frac{3 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{16 d}-\frac{9 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{16}-\frac{9 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,a^{2} b \,c^{2} e^{3}}{16}-\frac{9 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{16}-\frac{9 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a^{2} b c \,e^{3}}{32 d}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a^{2} b \,c^{3} e^{3}}{16 d}-\frac{9 d \,e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{8}+\frac{a^{3} c^{4} e^{3}}{4 d}-\frac{3 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{32 d}+\frac{d^{3} x^{4} a^{3} e^{3}}{4}+x \,a^{3} c^{3} e^{3}-\frac{9 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{8}-\frac{9 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{16 d}-\frac{9 d \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} a^{2} b c \,e^{3}}{16}-\frac{3 d^{2} e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{8}-\frac{9 e^{3} a^{2} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{32 d \sqrt{\left(d x +c \right)^{2}-1}}-\frac{3 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{8 d}-\frac{9 d \,e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{16}-\frac{9 e^{3} b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{128}+3 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x \,c^{3}-\frac{45 b^{3} e^{3} \mathrm{arccosh}\left(d x +c \right)}{256 d}+\frac{3 e^{3} a \,b^{2} c^{4}}{32 d}+\frac{9 e^{3} a \,b^{2} c^{2}}{32 d}+\frac{3 d^{3} e^{3} a \,b^{2} x^{4}}{32}+\frac{3 d \,x^{2} a^{3} c^{2} e^{3}}{2}-\frac{9 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{32 d}+\frac{e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} c^{4}}{4 d}+\frac{3 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) c^{4}}{32 d}+\frac{9 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) c^{2}}{32 d}+\frac{3 d^{3} e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) x^{4}}{32}+\frac{9 d \,e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) x^{2}}{32}+\frac{d^{3} e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{4}}{4}-\frac{45 e^{3} b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{256}+\frac{9 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) x c}{16}+e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x \,c^{3}+\frac{3 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) x \,c^{3}}{8}+\frac{3 e^{3} a \,b^{2} x \,c^{3}}{8}+\frac{9 e^{3} a \,b^{2} x c}{16}+\frac{9 d \,e^{3} a \,b^{2} x^{2}}{32}+d^{2} x^{3} a^{3} c \,e^{3}-\frac{45 e^{3} b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{256 d}+\frac{3 \,\mathrm{arccosh}\left(d x +c \right) a^{2} b \,c^{4} e^{3}}{4 d}-\frac{3 e^{3} b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{128 d}+3 \,\mathrm{arccosh}\left(d x +c \right) x \,a^{2} b \,c^{3} e^{3}-\frac{9 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,a^{2} b \,e^{3}}{32}+\frac{3 d \,e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{2} c^{2}}{2}+\frac{3 d^{3} e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{4}}{4}+\frac{3 e^{3} a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} c^{4}}{4 d}-\frac{9 e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{32}+\frac{3 d^{2} e^{3} a \,b^{2} x^{3} c}{8}+\frac{9 d \,e^{3} a \,b^{2} x^{2} c^{2}}{16}+\frac{3 d^{3} \mathrm{arccosh}\left(d x +c \right) x^{4} a^{2} b \,e^{3}}{4}+\frac{3 d^{2} e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) x^{3} c}{8}+\frac{9 d \,e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right) x^{2} c^{2}}{16}-\frac{3 d^{2} e^{3} b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{128}+d^{2} e^{3} b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{3} c"," ",0,"-3/16*d^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3*a^2*b*e^3+3*d^2*arccosh(d*x+c)*x^3*a^2*b*c*e^3+3*d^2*e^3*a*b^2*arccosh(d*x+c)^2*x^3*c+9/2*d*e^3*a*b^2*arccosh(d*x+c)^2*x^2*c^2-3/16*d^2*e^3*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-9/128*d*e^3*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c+9/2*d*arccosh(d*x+c)*x^2*a^2*b*c^2*e^3-9/32/d*e^3*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3/16/d*e^3*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-9/16*e^3*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-9/16*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a^2*b*c^2*e^3-9/16*e^3*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2-9/32/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a^2*b*c*e^3-3/16/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a^2*b*c^3*e^3-9/8*d*e^3*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c+1/4/d*a^3*c^4*e^3-3/32/d*e^3*b^3*arccosh(d*x+c)^3+1/4*d^3*x^4*a^3*e^3+x*a^3*c^3*e^3-9/8*e^3*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2-9/16/d*e^3*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-9/16*d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*a^2*b*c*e^3-3/8*d^2*e^3*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-9/32/d*e^3*a^2*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))-3/8/d*e^3*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-9/16*d*e^3*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c-9/128*e^3*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2+3*e^3*a*b^2*arccosh(d*x+c)^2*x*c^3-45/256*b^3*e^3*arccosh(d*x+c)/d+3/32/d*e^3*a*b^2*c^4+9/32/d*e^3*a*b^2*c^2+3/32*d^3*e^3*a*b^2*x^4+3/2*d*x^2*a^3*c^2*e^3-9/32/d*e^3*a*b^2*arccosh(d*x+c)^2+1/4/d*e^3*b^3*arccosh(d*x+c)^3*c^4+3/32/d*e^3*b^3*arccosh(d*x+c)*c^4+9/32/d*e^3*b^3*arccosh(d*x+c)*c^2+3/32*d^3*e^3*b^3*arccosh(d*x+c)*x^4+9/32*d*e^3*b^3*arccosh(d*x+c)*x^2+1/4*d^3*e^3*b^3*arccosh(d*x+c)^3*x^4-45/256*e^3*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+9/16*e^3*b^3*arccosh(d*x+c)*x*c+e^3*b^3*arccosh(d*x+c)^3*x*c^3+3/8*e^3*b^3*arccosh(d*x+c)*x*c^3+3/8*e^3*a*b^2*x*c^3+9/16*e^3*a*b^2*x*c+9/32*d*e^3*a*b^2*x^2+d^2*x^3*a^3*c*e^3-45/256/d*e^3*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c+3/4/d*arccosh(d*x+c)*a^2*b*c^4*e^3-3/128/d*e^3*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3+3*arccosh(d*x+c)*x*a^2*b*c^3*e^3-9/32*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a^2*b*e^3+3/2*d*e^3*b^3*arccosh(d*x+c)^3*x^2*c^2+3/4*d^3*e^3*a*b^2*arccosh(d*x+c)^2*x^4+3/4/d*e^3*a*b^2*arccosh(d*x+c)^2*c^4-9/32*e^3*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+3/8*d^2*e^3*a*b^2*x^3*c+9/16*d*e^3*a*b^2*x^2*c^2+3/4*d^3*arccosh(d*x+c)*x^4*a^2*b*e^3+3/8*d^2*e^3*b^3*arccosh(d*x+c)*x^3*c+9/16*d*e^3*b^3*arccosh(d*x+c)*x^2*c^2-3/128*d^2*e^3*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3+d^2*e^3*b^3*arccosh(d*x+c)^3*x^3*c","B"
115,1,326,230,0.046000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^3,x)","\frac{\frac{\left(d x +c \right)^{3} e^{2} a^{3}}{3}+e^{2} b^{3} \left(\frac{\left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{3}-\frac{2 \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{3}-\frac{\left(d x +c \right)^{2} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{3}+\frac{4 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)}{3}-\frac{40 \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{27}+\frac{2 \,\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{9}-\frac{2 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{27}\right)+3 e^{2} a \,b^{2} \left(\frac{\left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{2}}{3}-\frac{4 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{9}-\frac{2 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(d x +c \right)^{2}}{9}+\frac{4 d x}{9}+\frac{4 c}{9}+\frac{2 \left(d x +c \right)^{3}}{27}\right)+3 e^{2} a^{2} b \left(\frac{\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{3}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(\left(d x +c \right)^{2}+2\right)}{9}\right)}{d}"," ",0,"1/d*(1/3*(d*x+c)^3*e^2*a^3+e^2*b^3*(1/3*(d*x+c)^3*arccosh(d*x+c)^3-2/3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-1/3*(d*x+c)^2*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4/3*(d*x+c)*arccosh(d*x+c)-40/27*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+2/9*arccosh(d*x+c)*(d*x+c)^3-2/27*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))+3*e^2*a*b^2*(1/3*(d*x+c)^3*arccosh(d*x+c)^2-4/9*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-2/9*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(d*x+c)^2+4/9*d*x+4/9*c+2/27*(d*x+c)^3)+3*e^2*a^2*b*(1/3*arccosh(d*x+c)*(d*x+c)^3-1/9*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*((d*x+c)^2+2)))","A"
116,1,605,155,0.044000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^3,x)","\frac{3 \,\mathrm{arccosh}\left(d x +c \right) a^{2} b \,c^{2} e}{2 d}+\frac{3 e a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} c^{2}}{2 d}-\frac{3 e \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{8 d}+\frac{3 d \,\mathrm{arccosh}\left(d x +c \right) x^{2} a^{2} b e}{2}+3 e a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x c +3 \,\mathrm{arccosh}\left(d x +c \right) x \,a^{2} b c e -\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,a^{2} b e}{4}+\frac{3 d e a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2}}{2}-\frac{3 e \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{4}-\frac{3 e a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{2}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a^{2} b c e}{4 d}-\frac{3 e \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{4 d}+\frac{a^{3} c^{2} e}{2 d}+\frac{d \,x^{2} a^{3} e}{2}-\frac{e \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{4 d}+x \,a^{3} c e -\frac{3 e a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{2 d}-\frac{3 e \,a^{2} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{4 d \sqrt{\left(d x +c \right)^{2}-1}}-\frac{3 b^{3} e \,\mathrm{arccosh}\left(d x +c \right)}{8 d}+\frac{e \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} c^{2}}{2 d}+\frac{3 e \,b^{3} \mathrm{arccosh}\left(d x +c \right) c^{2}}{4 d}+\frac{3 d e a \,b^{2} x^{2}}{4}+\frac{3 e \,b^{3} \mathrm{arccosh}\left(d x +c \right) x c}{2}+\frac{3 e a \,b^{2} c^{2}}{4 d}-\frac{3 e \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{8}+e \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x c +\frac{d e \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{2}}{2}+\frac{3 d e \,b^{3} \mathrm{arccosh}\left(d x +c \right) x^{2}}{4}-\frac{3 e a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{4 d}+\frac{3 e a \,b^{2} x c}{2}"," ",0,"3/2/d*arccosh(d*x+c)*a^2*b*c^2*e+3/2/d*e*a*b^2*arccosh(d*x+c)^2*c^2-3/8/d*e*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c+3/2*d*arccosh(d*x+c)*x^2*a^2*b*e+3*e*a*b^2*arccosh(d*x+c)^2*x*c+3*arccosh(d*x+c)*x*a^2*b*c*e-3/4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a^2*b*e+3/2*d*e*a*b^2*arccosh(d*x+c)^2*x^2-3/4*e*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-3/2*e*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-3/4/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a^2*b*c*e-3/4/d*e*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c+1/2/d*a^3*c^2*e+1/2*d*x^2*a^3*e-1/4/d*e*b^3*arccosh(d*x+c)^3+x*a^3*c*e-3/2/d*e*a*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3/4/d*e*a^2*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))-3/8*b^3*e*arccosh(d*x+c)/d+1/2/d*e*b^3*arccosh(d*x+c)^3*c^2+3/4/d*e*b^3*arccosh(d*x+c)*c^2+3/4*d*e*a*b^2*x^2+3/2*e*b^3*arccosh(d*x+c)*x*c+3/4/d*e*a*b^2*c^2-3/8*e*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+e*b^3*arccosh(d*x+c)^3*x*c+1/2*d*e*b^3*arccosh(d*x+c)^3*x^2+3/4*d*e*b^3*arccosh(d*x+c)*x^2-3/4/d*e*a*b^2*arccosh(d*x+c)^2+3/2*e*a*b^2*x*c","B"
117,1,180,106,0.056000," ","int((a+b*arccosh(d*x+c))^3,x)","\frac{\left(d x +c \right) a^{3}+b^{3} \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{3}-3 \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+6 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)-6 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)+3 a \,b^{2} \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{2}-2 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}+2 d x +2 c \right)+3 a^{2} b \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{d}"," ",0,"1/d*((d*x+c)*a^3+b^3*((d*x+c)*arccosh(d*x+c)^3-3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+6*(d*x+c)*arccosh(d*x+c)-6*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))+3*a*b^2*((d*x+c)*arccosh(d*x+c)^2-2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+2*d*x+2*c)+3*a^2*b*((d*x+c)*arccosh(d*x+c)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))","A"
118,1,471,207,0.073000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e),x)","\frac{a^{3} \ln \left(d x +c \right)}{d e}-\frac{b^{3} \mathrm{arccosh}\left(d x +c \right)^{4}}{4 d e}+\frac{b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{3 b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}-\frac{3 b^{3} \mathrm{arccosh}\left(d x +c \right) \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}+\frac{3 b^{3} \polylog \left(4, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{4 d e}-\frac{a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{3}}{d e}+\frac{3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{3 a \,b^{2} \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}-\frac{3 a^{2} b \mathrm{arccosh}\left(d x +c \right)^{2}}{2 d e}+\frac{3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right) \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{3 a^{2} b \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}"," ",0,"1/d*a^3/e*ln(d*x+c)-1/4/d*b^3/e*arccosh(d*x+c)^4+1/d*b^3/e*arccosh(d*x+c)^3*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/2/d*b^3/e*arccosh(d*x+c)^2*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/2/d*b^3/e*arccosh(d*x+c)*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/4/d*b^3/e*polylog(4,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-1/d*a*b^2/e*arccosh(d*x+c)^3+3/d*a*b^2/e*arccosh(d*x+c)^2*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/d*a*b^2/e*arccosh(d*x+c)*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/2/d*a*b^2/e*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/2/d*a^2*b/e*arccosh(d*x+c)^2+3/d*a^2*b/e*arccosh(d*x+c)*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/2/d*a^2*b/e*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)","B"
119,0,0,248,0.225000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^2,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{2}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^2,x)","F"
120,1,375,180,0.291000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^3,x)","-\frac{a^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{3 b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{2 d \,e^{3} \left(d x +c \right)}+\frac{3 b^{3} \mathrm{arccosh}\left(d x +c \right)^{2}}{2 d \,e^{3}}-\frac{b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 b^{3} \mathrm{arccosh}\left(d x +c \right) \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}-\frac{3 b^{3} \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d \,e^{3}}+\frac{3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)}{d \,e^{3}}+\frac{3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{d \,e^{3} \left(d x +c \right)}-\frac{3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}-\frac{3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{3 a^{2} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{2 d \,e^{3} \left(d x +c \right)}"," ",0,"-1/2/d*a^3/e^3/(d*x+c)^2+3/2/d*b^3/e^3*arccosh(d*x+c)^2/(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)+3/2/d*b^3/e^3*arccosh(d*x+c)^2-1/2/d*b^3/e^3*arccosh(d*x+c)^3/(d*x+c)^2-3/d*b^3/e^3*arccosh(d*x+c)*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/2/d*b^3/e^3*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/d*a*b^2/e^3*arccosh(d*x+c)+3/d*a*b^2/e^3*arccosh(d*x+c)/(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)-3/2/d*a*b^2/e^3*arccosh(d*x+c)^2/(d*x+c)^2-3/d*a*b^2/e^3*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/2/d*a^2*b/e^3/(d*x+c)^2*arccosh(d*x+c)+3/2/d*a^2*b/e^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/(d*x+c)","B"
121,0,0,347,0.507000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^4,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{4}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^4,x)","F"
122,1,2465,339,0.053000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^4,x)","-\frac{9 d \,e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{4}-\frac{9 d \,e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{4}+\frac{3 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} c^{4}}{2 d}+\frac{9 d \,e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x^{2}}{8}+d^{3} e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{4}+\frac{3 d^{3} e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x^{4}}{8}+\frac{3 d^{2} e^{3} a^{2} b^{2} x^{3} c}{4}+\frac{9 d \,e^{3} a^{2} b^{2} x^{2} c^{2}}{8}+\frac{\mathrm{arccosh}\left(d x +c \right) a^{3} b \,c^{4} e^{3}}{d}+\frac{e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} c^{4}}{d}+\frac{3 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) c^{4}}{8 d}+\frac{3 d^{3} e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{4}}{2}+d^{3} \mathrm{arccosh}\left(d x +c \right) x^{4} a^{3} b \,e^{3}-\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{8}+\frac{9 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) c^{2}}{8 d}-\frac{45 e^{3} a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{64}+\frac{9 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x c}{4}+4 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x \,c^{3}+6 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x \,c^{3}+\frac{3 d \,e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} x^{2} c^{2}}{2}+\frac{3 d^{2} e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x^{3} c}{4}+\frac{9 d \,e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2} c^{2}}{8}+d^{2} e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} x^{3} c -\frac{45 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{64}+4 \,\mathrm{arccosh}\left(d x +c \right) x \,a^{3} b \,c^{3} e^{3}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,a^{3} b \,e^{3}}{8}+\frac{3 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x \,c^{3}}{2}+\frac{a^{4} c^{4} e^{3}}{4 d}-\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{4}}{32 d}-\frac{45 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2}}{128 d}+\frac{45 d \,e^{3} b^{4} x^{2}}{128}+\frac{3 d^{3} e^{3} b^{4} x^{4}}{128}+\frac{d^{3} x^{4} a^{4} e^{3}}{4}+x \,a^{4} c^{3} e^{3}+\frac{45 e^{3} b^{4} x c}{64}+\frac{3 e^{3} b^{4} x \,c^{3}}{32}+\frac{45 e^{3} b^{4} c^{2}}{128 d}+\frac{3 e^{3} b^{4} c^{4}}{128 d}+\frac{9 e^{3} a^{2} b^{2} x c}{8}-\frac{9 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{4}+\frac{3 e^{3} a^{2} b^{2} c^{4}}{16 d}+\frac{9 e^{3} a^{2} b^{2} c^{2}}{16 d}-\frac{3 e^{3} a^{3} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{8 d \sqrt{\left(d x +c \right)^{2}-1}}-\frac{3 d^{2} e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{4}-\frac{9 d \,e^{3} a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{32}-\frac{9 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{4}-\frac{3 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{4 d}-\frac{3 d^{2} e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{4}-\frac{9 d \,e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{32}-\frac{3 d \,e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} c}{4}-\frac{3 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{4 d}-\frac{3 d \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{2} a^{3} b c \,e^{3}}{4}-\frac{9 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{8 d}-\frac{9 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{8 d}+\frac{3 e^{3} a^{2} b^{2} x \,c^{3}}{4}+d^{2} x^{3} a^{4} c \,e^{3}+\frac{3 d \,x^{2} a^{4} c^{2} e^{3}}{2}+\frac{3 d^{3} e^{3} a^{2} b^{2} x^{4}}{16}+\frac{9 d \,e^{3} a^{2} b^{2} x^{2}}{16}+\frac{9 d \,e^{3} b^{4} x^{2} c^{2}}{64}+\frac{3 d^{2} e^{3} b^{4} x^{3} c}{32}+e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} x \,c^{3}+\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x \,c^{3}}{4}+\frac{9 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x c}{8}-\frac{45 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)}{64 d}-\frac{3 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{8 d}+\frac{e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} c^{4}}{4 d}+\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} c^{4}}{16 d}+\frac{9 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} c^{2}}{16 d}+\frac{9 d \,e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2}}{16}+\frac{d^{3} e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} x^{4}}{4}+\frac{3 d^{3} e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x^{4}}{16}-\frac{9 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{16 d}-\frac{9 e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{8}-\frac{9 e^{3} a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{32}-\frac{9 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{32}-\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{8 d}-\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{32 d}-\frac{45 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{64 d}+4 d^{2} \mathrm{arccosh}\left(d x +c \right) x^{3} a^{3} b c \,e^{3}+6 d \,\mathrm{arccosh}\left(d x +c \right) x^{2} a^{3} b \,c^{2} e^{3}-\frac{d^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3} a^{3} b \,e^{3}}{4}+\frac{9 d \,e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x^{2} c^{2}}{4}-\frac{3 e^{3} a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{32 d}-\frac{e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c^{3}}{4 d}-\frac{9 e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{8}-\frac{3 e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,c^{2}}{4}-\frac{d^{2} e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{4}-\frac{3 d^{2} e^{3} b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{32}-\frac{45 e^{3} a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{64 d}-\frac{3 d^{2} e^{3} a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x^{3}}{32}+4 d^{2} e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{3} c +6 d \,e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{2} c^{2}+6 d^{2} e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{3} c +9 d \,e^{3} a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2} c^{2}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a^{3} b c \,e^{3}}{8 d}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a^{3} b \,c^{3} e^{3}}{4 d}+\frac{3 d^{2} e^{3} a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x^{3} c}{2}-\frac{3 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,a^{3} b \,c^{2} e^{3}}{4}"," ",0,"-9/4*d*e^3*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c-9/4*d*e^3*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c+3/2/d*e^3*a^2*b^2*arccosh(d*x+c)^2*c^4+9/8*d*e^3*a*b^3*arccosh(d*x+c)*x^2+d^3*e^3*a*b^3*arccosh(d*x+c)^3*x^4+3/8*d^3*e^3*a*b^3*arccosh(d*x+c)*x^4+3/4*d^2*e^3*a^2*b^2*x^3*c+9/8*d*e^3*a^2*b^2*x^2*c^2+1/d*arccosh(d*x+c)*a^3*b*c^4*e^3+1/d*e^3*a*b^3*arccosh(d*x+c)^3*c^4+3/8/d*e^3*a*b^3*arccosh(d*x+c)*c^4+3/2*d^3*e^3*a^2*b^2*arccosh(d*x+c)^2*x^4+d^3*arccosh(d*x+c)*x^4*a^3*b*e^3-3/8*e^3*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+9/8/d*e^3*a*b^3*arccosh(d*x+c)*c^2-45/64*e^3*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+9/4*e^3*a*b^3*arccosh(d*x+c)*x*c+4*e^3*a*b^3*arccosh(d*x+c)^3*x*c^3+6*e^3*a^2*b^2*arccosh(d*x+c)^2*x*c^3+3/2*d*e^3*b^4*arccosh(d*x+c)^4*x^2*c^2+3/4*d^2*e^3*b^4*arccosh(d*x+c)^2*x^3*c+9/8*d*e^3*b^4*arccosh(d*x+c)^2*x^2*c^2+d^2*e^3*b^4*arccosh(d*x+c)^4*x^3*c-45/64*e^3*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+4*arccosh(d*x+c)*x*a^3*b*c^3*e^3-3/8*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a^3*b*e^3+3/2*e^3*a*b^3*arccosh(d*x+c)*x*c^3+1/4/d*a^4*c^4*e^3-3/32/d*e^3*b^4*arccosh(d*x+c)^4-45/128/d*e^3*b^4*arccosh(d*x+c)^2+45/128*d*e^3*b^4*x^2+3/128*d^3*e^3*b^4*x^4+1/4*d^3*x^4*a^4*e^3+x*a^4*c^3*e^3+45/64*e^3*b^4*x*c+3/32*e^3*b^4*x*c^3+45/128/d*e^3*b^4*c^2+3/128/d*e^3*b^4*c^4+9/8*e^3*a^2*b^2*x*c-9/4*e^3*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2+3/16/d*e^3*a^2*b^2*c^4+9/16/d*e^3*a^2*b^2*c^2-3/8/d*e^3*a^3*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))-3/4*d^2*e^3*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-9/32*d*e^3*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c-9/4*e^3*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2-3/4/d*e^3*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-3/4*d^2*e^3*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-9/32*d*e^3*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c-3/4*d*e^3*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*c-3/4/d*e^3*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-3/4*d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^2*a^3*b*c*e^3-9/8/d*e^3*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-9/8/d*e^3*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c+3/4*e^3*a^2*b^2*x*c^3+d^2*x^3*a^4*c*e^3+3/2*d*x^2*a^4*c^2*e^3+3/16*d^3*e^3*a^2*b^2*x^4+9/16*d*e^3*a^2*b^2*x^2+9/64*d*e^3*b^4*x^2*c^2+3/32*d^2*e^3*b^4*x^3*c+e^3*b^4*arccosh(d*x+c)^4*x*c^3+3/4*e^3*b^4*arccosh(d*x+c)^2*x*c^3+9/8*e^3*b^4*arccosh(d*x+c)^2*x*c-45/64/d*e^3*a*b^3*arccosh(d*x+c)-3/8/d*e^3*a*b^3*arccosh(d*x+c)^3+1/4/d*e^3*b^4*arccosh(d*x+c)^4*c^4+3/16/d*e^3*b^4*arccosh(d*x+c)^2*c^4+9/16/d*e^3*b^4*arccosh(d*x+c)^2*c^2+9/16*d*e^3*b^4*arccosh(d*x+c)^2*x^2+1/4*d^3*e^3*b^4*arccosh(d*x+c)^4*x^4+3/16*d^3*e^3*b^4*arccosh(d*x+c)^2*x^4-9/16/d*e^3*a^2*b^2*arccosh(d*x+c)^2-9/8*e^3*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-9/32*e^3*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2-9/32*e^3*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2-3/8/d*e^3*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3/32/d*e^3*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-45/64/d*e^3*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c+4*d^2*arccosh(d*x+c)*x^3*a^3*b*c*e^3+6*d*arccosh(d*x+c)*x^2*a^3*b*c^2*e^3-1/4*d^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3*a^3*b*e^3+9/4*d*e^3*a*b^3*arccosh(d*x+c)*x^2*c^2-3/32/d*e^3*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-1/4/d*e^3*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c^3-9/8*e^3*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-3/4*e^3*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*c^2-1/4*d^2*e^3*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-3/32*d^2*e^3*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3-45/64/d*e^3*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3/32*d^2*e^3*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x^3+4*d^2*e^3*a*b^3*arccosh(d*x+c)^3*x^3*c+6*d*e^3*a*b^3*arccosh(d*x+c)^3*x^2*c^2+6*d^2*e^3*a^2*b^2*arccosh(d*x+c)^2*x^3*c+9*d*e^3*a^2*b^2*arccosh(d*x+c)^2*x^2*c^2-3/8/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a^3*b*c*e^3-1/4/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a^3*b*c^3*e^3+3/2*d^2*e^3*a*b^3*arccosh(d*x+c)*x^3*c-3/4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a^3*b*c^2*e^3","B"
123,1,517,275,0.069000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^4,x)","\frac{\frac{\left(d x +c \right)^{3} e^{2} a^{4}}{3}+e^{2} b^{4} \left(\frac{\left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{4}}{3}-\frac{8 \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{9}-\frac{4 \left(d x +c \right)^{2} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{9}+\frac{8 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{2}}{3}-\frac{160 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{27}+\frac{160 d x}{27}+\frac{160 c}{27}+\frac{4 \left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{2}}{9}-\frac{8 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(d x +c \right)^{2}}{27}+\frac{8 \left(d x +c \right)^{3}}{81}\right)+4 e^{2} a \,b^{3} \left(\frac{\left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{3}-\frac{2 \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{3}-\frac{\left(d x +c \right)^{2} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{3}+\frac{4 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)}{3}-\frac{40 \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{27}+\frac{2 \,\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{9}-\frac{2 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{27}\right)+6 e^{2} a^{2} b^{2} \left(\frac{\left(d x +c \right)^{3} \mathrm{arccosh}\left(d x +c \right)^{2}}{3}-\frac{4 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{9}-\frac{2 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(d x +c \right)^{2}}{9}+\frac{4 d x}{9}+\frac{4 c}{9}+\frac{2 \left(d x +c \right)^{3}}{27}\right)+4 e^{2} a^{3} b \left(\frac{\mathrm{arccosh}\left(d x +c \right) \left(d x +c \right)^{3}}{3}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \left(\left(d x +c \right)^{2}+2\right)}{9}\right)}{d}"," ",0,"1/d*(1/3*(d*x+c)^3*e^2*a^4+e^2*b^4*(1/3*(d*x+c)^3*arccosh(d*x+c)^4-8/9*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4/9*(d*x+c)^2*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+8/3*(d*x+c)*arccosh(d*x+c)^2-160/27*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+160/27*d*x+160/27*c+4/9*(d*x+c)^3*arccosh(d*x+c)^2-8/27*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(d*x+c)^2+8/81*(d*x+c)^3)+4*e^2*a*b^3*(1/3*(d*x+c)^3*arccosh(d*x+c)^3-2/3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-1/3*(d*x+c)^2*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4/3*(d*x+c)*arccosh(d*x+c)-40/27*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+2/9*arccosh(d*x+c)*(d*x+c)^3-2/27*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))+6*e^2*a^2*b^2*(1/3*(d*x+c)^3*arccosh(d*x+c)^2-4/9*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-2/9*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*(d*x+c)^2+4/9*d*x+4/9*c+2/27*(d*x+c)^3)+4*e^2*a^3*b*(1/3*arccosh(d*x+c)*(d*x+c)^3-1/9*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*((d*x+c)^2+2)))","A"
124,1,933,189,0.041000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^4,x)","-\frac{3 e a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{2}+4 \,\mathrm{arccosh}\left(d x +c \right) x \,a^{3} b c e +3 d e a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x^{2}+6 e \,a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x c +2 d e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x^{2}+4 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} x c +6 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right) x c -e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x -\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x \,a^{3} b e +\frac{2 \,\mathrm{arccosh}\left(d x +c \right) a^{3} b \,c^{2} e}{d}+\frac{3 e \,a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} c^{2}}{d}+\frac{a^{4} c^{2} e}{2 d}-\frac{e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{4}}{4 d}-\frac{3 e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{2}}{4 d}+\frac{3 d e \,b^{4} x^{2}}{4}+\frac{d \,x^{2} a^{4} e}{2}+\frac{3 e \,b^{4} x c}{2}+x \,a^{4} c e +\frac{3 e \,b^{4} c^{2}}{4 d}+2 d \,\mathrm{arccosh}\left(d x +c \right) x^{2} a^{3} b e +3 d e \,a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2}+\frac{2 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} c^{2}}{d}+\frac{3 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right) c^{2}}{d}-\frac{3 e \,b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x}{2}-\frac{e \,a^{3} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, \ln \left(d x +c +\sqrt{\left(d x +c \right)^{2}-1}\right)}{d \sqrt{\left(d x +c \right)^{2}-1}}-\frac{3 e \,a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{d}-\frac{3 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{d}-3 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x -\frac{3 e \,b^{4} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{2 d}-\frac{\sqrt{d x +c -1}\, \sqrt{d x +c +1}\, a^{3} b c e}{d}-\frac{3 e a \,b^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{2 d}-\frac{e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, c}{d}-3 e \,a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}\, x +\frac{3 d e \,a^{2} b^{2} x^{2}}{2}+3 e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x c +e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} x c +\frac{d e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} x^{2}}{2}+\frac{3 d e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} x^{2}}{2}-\frac{3 e \,a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{2 d}-\frac{e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{d}-\frac{3 e a \,b^{3} \mathrm{arccosh}\left(d x +c \right)}{2 d}+\frac{e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} c^{2}}{2 d}+\frac{3 e \,b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} c^{2}}{2 d}+3 e \,a^{2} b^{2} x c +\frac{3 e \,a^{2} b^{2} c^{2}}{2 d}"," ",0,"-3/2*e*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+4*arccosh(d*x+c)*x*a^3*b*c*e+3*d*e*a*b^3*arccosh(d*x+c)*x^2+6*e*a^2*b^2*arccosh(d*x+c)^2*x*c+2*d*e*a*b^3*arccosh(d*x+c)^3*x^2+4*e*a*b^3*arccosh(d*x+c)^3*x*c+6*e*a*b^3*arccosh(d*x+c)*x*c-e*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x*a^3*b*e+2/d*arccosh(d*x+c)*a^3*b*c^2*e+3/d*e*a^2*b^2*arccosh(d*x+c)^2*c^2+1/2/d*a^4*c^2*e-1/4/d*e*b^4*arccosh(d*x+c)^4-3/4/d*e*b^4*arccosh(d*x+c)^2+3/4*d*e*b^4*x^2+1/2*d*x^2*a^4*e+3/2*e*b^4*x*c+x*a^4*c*e+3/4/d*e*b^4*c^2+2*d*arccosh(d*x+c)*x^2*a^3*b*e+3*d*e*a^2*b^2*arccosh(d*x+c)^2*x^2+2/d*e*a*b^3*arccosh(d*x+c)^3*c^2+3/d*e*a*b^3*arccosh(d*x+c)*c^2-3/2*e*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-1/d*e*a^3*b*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/((d*x+c)^2-1)^(1/2)*ln(d*x+c+((d*x+c)^2-1)^(1/2))-3/d*e*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3/d*e*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3*e*a*b^3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x-3/2/d*e*b^4*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-1/d*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*a^3*b*c*e-3/2/d*e*a*b^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-1/d*e*b^4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*c-3*e*a^2*b^2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)*x+3/2*d*e*a^2*b^2*x^2+3*e*b^4*arccosh(d*x+c)^2*x*c+e*b^4*arccosh(d*x+c)^4*x*c+1/2*d*e*b^4*arccosh(d*x+c)^4*x^2+3/2*d*e*b^4*arccosh(d*x+c)^2*x^2-3/2/d*e*a^2*b^2*arccosh(d*x+c)^2-1/d*e*a*b^3*arccosh(d*x+c)^3-3/2/d*e*a*b^3*arccosh(d*x+c)+1/2/d*e*b^4*arccosh(d*x+c)^4*c^2+3/2/d*e*b^4*arccosh(d*x+c)^2*c^2+3*e*a^2*b^2*x*c+3/2/d*e*a^2*b^2*c^2","B"
125,1,275,121,0.058000," ","int((a+b*arccosh(d*x+c))^4,x)","\frac{\left(d x +c \right) a^{4}+b^{4} \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{4}-4 \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+12 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{2}-24 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}+24 d x +24 c \right)+4 a \,b^{3} \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{3}-3 \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+6 \left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)-6 \sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)+6 a^{2} b^{2} \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)^{2}-2 \,\mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c -1}\, \sqrt{d x +c +1}+2 d x +2 c \right)+4 a^{3} b \left(\left(d x +c \right) \mathrm{arccosh}\left(d x +c \right)-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{d}"," ",0,"1/d*((d*x+c)*a^4+b^4*((d*x+c)*arccosh(d*x+c)^4-4*arccosh(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+12*(d*x+c)*arccosh(d*x+c)^2-24*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+24*d*x+24*c)+4*a*b^3*((d*x+c)*arccosh(d*x+c)^3-3*arccosh(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+6*(d*x+c)*arccosh(d*x+c)-6*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))+6*a^2*b^2*((d*x+c)*arccosh(d*x+c)^2-2*arccosh(d*x+c)*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+2*d*x+2*c)+4*a^3*b*((d*x+c)*arccosh(d*x+c)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)))","B"
126,1,727,258,0.074000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e),x)","\frac{a^{4} \ln \left(d x +c \right)}{d e}-\frac{b^{4} \mathrm{arccosh}\left(d x +c \right)^{5}}{5 d e}+\frac{b^{4} \mathrm{arccosh}\left(d x +c \right)^{4} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{2 b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{3 b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{3 b^{4} \mathrm{arccosh}\left(d x +c \right) \polylog \left(4, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{3 b^{4} \polylog \left(5, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{2 d e}-\frac{a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{4}}{d e}+\frac{4 a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{6 a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{6 a \,b^{3} \mathrm{arccosh}\left(d x +c \right) \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{3 a \,b^{3} \polylog \left(4, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{2 a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{3}}{d e}+\frac{6 a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{6 a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{3 a^{2} b^{2} \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}-\frac{2 a^{3} b \mathrm{arccosh}\left(d x +c \right)^{2}}{d e}+\frac{4 a^{3} b \,\mathrm{arccosh}\left(d x +c \right) \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}+\frac{2 a^{3} b \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d e}"," ",0,"1/d*a^4/e*ln(d*x+c)-1/5/d*b^4/e*arccosh(d*x+c)^5+1/d*b^4/e*arccosh(d*x+c)^4*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+2/d*b^4/e*arccosh(d*x+c)^3*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/d*b^4/e*arccosh(d*x+c)^2*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/d*b^4/e*arccosh(d*x+c)*polylog(4,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/2/d*b^4/e*polylog(5,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-1/d*a*b^3/e*arccosh(d*x+c)^4+4/d*a*b^3/e*arccosh(d*x+c)^3*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+6/d*a*b^3/e*arccosh(d*x+c)^2*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-6/d*a*b^3/e*arccosh(d*x+c)*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/d*a*b^3/e*polylog(4,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-2/d*a^2*b^2/e*arccosh(d*x+c)^3+6/d*a^2*b^2/e*arccosh(d*x+c)^2*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+6/d*a^2*b^2/e*arccosh(d*x+c)*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-3/d*a^2*b^2/e*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-2/d*a^3*b/e*arccosh(d*x+c)^2+4/d*a^3*b/e*arccosh(d*x+c)*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+2/d*a^3*b/e*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)","B"
127,0,0,350,0.221000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^2,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{2}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^2,x)","F"
128,1,605,231,0.294000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^3,x)","-\frac{a^{4}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{2 b^{4} \mathrm{arccosh}\left(d x +c \right)^{3} \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{d \,e^{3} \left(d x +c \right)}+\frac{2 b^{4} \mathrm{arccosh}\left(d x +c \right)^{3}}{d \,e^{3}}-\frac{b^{4} \mathrm{arccosh}\left(d x +c \right)^{4}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{6 b^{4} \mathrm{arccosh}\left(d x +c \right)^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}-\frac{6 b^{4} \mathrm{arccosh}\left(d x +c \right) \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}+\frac{3 b^{4} \polylog \left(3, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}+\frac{6 a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2} \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{d \,e^{3} \left(d x +c \right)}+\frac{6 a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{2}}{d \,e^{3}}-\frac{2 a \,b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{12 a \,b^{3} \mathrm{arccosh}\left(d x +c \right) \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}-\frac{6 a \,b^{3} \polylog \left(2, -\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}+\frac{6 a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)}{d \,e^{3}}+\frac{6 a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right) \sqrt{d x +c +1}\, \sqrt{d x +c -1}}{d \,e^{3} \left(d x +c \right)}-\frac{3 a^{2} b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{6 a^{2} b^{2} \ln \left(1+\left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)^{2}\right)}{d \,e^{3}}-\frac{2 a^{3} b \,\mathrm{arccosh}\left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}+\frac{2 a^{3} b \sqrt{d x +c -1}\, \sqrt{d x +c +1}}{d \,e^{3} \left(d x +c \right)}"," ",0,"-1/2/d*a^4/e^3/(d*x+c)^2+2/d*b^4/e^3*arccosh(d*x+c)^3/(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)+2/d*b^4/e^3*arccosh(d*x+c)^3-1/2/d*b^4/e^3*arccosh(d*x+c)^4/(d*x+c)^2-6/d*b^4/e^3*arccosh(d*x+c)^2*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-6/d*b^4/e^3*arccosh(d*x+c)*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+3/d*b^4/e^3*polylog(3,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+6/d*a*b^3/e^3*arccosh(d*x+c)^2/(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)+6/d*a*b^3/e^3*arccosh(d*x+c)^2-2/d*a*b^3/e^3*arccosh(d*x+c)^3/(d*x+c)^2-12/d*a*b^3/e^3*arccosh(d*x+c)*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-6/d*a*b^3/e^3*polylog(2,-(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)+6/d*a^2*b^2/e^3*arccosh(d*x+c)+6/d*a^2*b^2/e^3*arccosh(d*x+c)/(d*x+c)*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)-3/d*a^2*b^2/e^3*arccosh(d*x+c)^2/(d*x+c)^2-6/d*a^2*b^2/e^3*ln(1+(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))^2)-2/d*a^3*b/e^3/(d*x+c)^2*arccosh(d*x+c)+2/d*a^3*b/e^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)/(d*x+c)","B"
129,0,0,546,0.478000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^4,x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{4}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^4,x)","F"
130,1,194,201,0.401000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c)),x)","\frac{\frac{e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \,\mathrm{arccosh}\left(d x +c \right)+\frac{5 a}{b}\right)}{32 b}+\frac{3 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{32 b}+\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{16 b}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{16 b}-\frac{3 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{32 b}-\frac{e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(d x +c \right)-\frac{5 a}{b}\right)}{32 b}}{d}"," ",0,"1/d*(1/32*e^4/b*exp(5*a/b)*Ei(1,5*arccosh(d*x+c)+5*a/b)+3/32*e^4/b*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)+1/16*e^4/b*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/16*e^4/b*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-3/32*e^4/b*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b)-1/32*e^4/b*exp(-5*a/b)*Ei(1,-5*arccosh(d*x+c)-5*a/b))","A"
131,1,134,137,0.339000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c)),x)","\frac{\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \,\mathrm{arccosh}\left(d x +c \right)+\frac{4 a}{b}\right)}{16 b}+\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{8 b}-\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{8 b}-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \,\mathrm{arccosh}\left(d x +c \right)-\frac{4 a}{b}\right)}{16 b}}{d}"," ",0,"1/d*(1/16*e^3/b*exp(4*a/b)*Ei(1,4*arccosh(d*x+c)+4*a/b)+1/8*e^3/b*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/8*e^3/b*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b)-1/16*e^3/b*exp(-4*a/b)*Ei(1,-4*arccosh(d*x+c)-4*a/b))","A"
132,1,130,133,0.192000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c)),x)","\frac{\frac{e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{8 b}+\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{8 b}-\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{8 b}-\frac{e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{8 b}}{d}"," ",0,"1/d*(1/8*e^2/b*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)+1/8*e^2/b*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/8*e^2/b*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-1/8*e^2/b*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b))","A"
133,1,66,65,0.034000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c)),x)","\frac{\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{4 b}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{4 b}}{d}"," ",0,"1/d*(1/4*e/b*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/4*e/b*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b))","A"
134,1,60,58,0.030000," ","int(1/(a+b*arccosh(d*x+c)),x)","\frac{\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{2 b}}{d}"," ",0,"1/d*(1/2/b*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/2/b*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b))","A"
135,0,0,26,0.259000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c)),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c)),x)","F"
136,1,665,247,0.408000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^2,x)","\frac{\frac{\left(-16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+5 d x +5 c \right) e^{4}}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{5 e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \,\mathrm{arccosh}\left(d x +c \right)+\frac{5 a}{b}\right)}{32 b^{2}}+\frac{3 \left(-4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \left(d x +c \right)^{3}-3 d x -3 c \right) e^{4}}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{9 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{32 b^{2}}+\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) e^{4}}{16 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{16 b^{2}}-\frac{e^{4} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{16 b^{2}}-\frac{3 e^{4} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{9 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{32 b^{2}}-\frac{e^{4} \left(16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+5 d x +5 c -12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{5 e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(d x +c \right)-\frac{5 a}{b}\right)}{32 b^{2}}}{d}"," ",0,"1/d*(1/32*(-16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+16*(d*x+c)^5-20*(d*x+c)^3+5*d*x+5*c)*e^4/b/(a+b*arccosh(d*x+c))-5/32*e^4/b^2*exp(5*a/b)*Ei(1,5*arccosh(d*x+c)+5*a/b)+3/32*(-4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c)^3-3*d*x-3*c)*e^4/b/(a+b*arccosh(d*x+c))-9/32*e^4/b^2*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)+1/16*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*e^4/b/(a+b*arccosh(d*x+c))-1/16*e^4/b^2*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/16/b*e^4*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/16/b^2*e^4*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-3/32/b*e^4*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-9/32/b^2*e^4*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b)-1/32/b*e^4*(16*(d*x+c)^5-20*(d*x+c)^3+16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+5*d*x+5*c-12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-5/32/b^2*e^4*exp(-5*a/b)*Ei(1,-5*arccosh(d*x+c)-5*a/b))","B"
137,1,418,183,0.372000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^2,x)","\frac{\frac{\left(-8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+1\right) e^{3}}{16 \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right) b}-\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \,\mathrm{arccosh}\left(d x +c \right)+\frac{4 a}{b}\right)}{4 b^{2}}+\frac{\left(-2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+2 \left(d x +c \right)^{2}-1\right) e^{3}}{8 \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right) b}-\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{4 b^{2}}-\frac{e^{3} \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{8 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{4 b^{2}}-\frac{e^{3} \left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+1\right)}{16 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \,\mathrm{arccosh}\left(d x +c \right)-\frac{4 a}{b}\right)}{4 b^{2}}}{d}"," ",0,"1/d*(1/16*(-8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+8*(d*x+c)^4-8*(d*x+c)^2+1)*e^3/(a+b*arccosh(d*x+c))/b-1/4*e^3/b^2*exp(4*a/b)*Ei(1,4*arccosh(d*x+c)+4*a/b)+1/8*(-2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+2*(d*x+c)^2-1)*e^3/(a+b*arccosh(d*x+c))/b-1/4*e^3/b^2*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/8/b*e^3*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))-1/4/b^2*e^3*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b)-1/16/b*e^3*(8*(d*x+c)^4-8*(d*x+c)^2+8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+1)/(a+b*arccosh(d*x+c))-1/4/b^2*e^3*exp(-4*a/b)*Ei(1,-4*arccosh(d*x+c)-4*a/b))","B"
138,1,374,179,0.217000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^2,x)","\frac{\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \left(d x +c \right)^{3}-3 d x -3 c \right) e^{2}}{8 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{3 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{8 b^{2}}+\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) e^{2}}{8 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{8 b^{2}}-\frac{e^{2} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{8 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{8 b^{2}}-\frac{e^{2} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{8 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{3 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{8 b^{2}}}{d}"," ",0,"1/d*(1/8*(-4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c)^3-3*d*x-3*c)*e^2/b/(a+b*arccosh(d*x+c))-3/8*e^2/b^2*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)+1/8*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*e^2/b/(a+b*arccosh(d*x+c))-1/8*e^2/b^2*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/8/b*e^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/8/b^2*e^2*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-1/8/b*e^2*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-3/8/b^2*e^2*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b))","B"
139,1,170,106,0.050000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^2,x)","\frac{\frac{\left(-2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+2 \left(d x +c \right)^{2}-1\right) e}{4 \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right) b}-\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{2 b^{2}}-\frac{e \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{4 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{2 b^{2}}}{d}"," ",0,"1/d*(1/4*(-2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+2*(d*x+c)^2-1)*e/(a+b*arccosh(d*x+c))/b-1/2*e/b^2*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/4/b*e*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))-1/2/b^2*e*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b))","A"
140,1,139,94,0.042000," ","int(1/(a+b*arccosh(d*x+c))^2,x)","\frac{-\frac{d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{2 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{2 b^{2}}+\frac{-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c}{2 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{2 b^{2}}}{d}"," ",0,"1/d*(-1/2/b*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/2/b^2*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)+1/2*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)/b/(a+b*arccosh(d*x+c))-1/2/b^2*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b))","A"
141,0,0,26,0.232000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^2,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^2,x)","F"
142,1,993,307,0.450000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^3,x)","\frac{-\frac{\left(-16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+5 d x +5 c \right) e^{4} \left(5 b \,\mathrm{arccosh}\left(d x +c \right)+5 a -b \right)}{64 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{25 e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \,\mathrm{arccosh}\left(d x +c \right)+\frac{5 a}{b}\right)}{64 b^{3}}-\frac{3 \left(-4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \left(d x +c \right)^{3}-3 d x -3 c \right) e^{4} \left(3 b \,\mathrm{arccosh}\left(d x +c \right)+3 a -b \right)}{64 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{27 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{64 b^{3}}-\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) e^{4} \left(b \,\mathrm{arccosh}\left(d x +c \right)+a -b \right)}{32 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{32 b^{3}}-\frac{e^{4} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{4} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{32 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{32 b^{3}}-\frac{3 e^{4} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{64 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{9 e^{4} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{64 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{27 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{64 b^{3}}-\frac{e^{4} \left(16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+5 d x +5 c -12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{64 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{5 e^{4} \left(16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+5 d x +5 c -12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{64 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{25 e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(d x +c \right)-\frac{5 a}{b}\right)}{64 b^{3}}}{d}"," ",0,"1/d*(-1/64*(-16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+16*(d*x+c)^5-20*(d*x+c)^3+5*d*x+5*c)*e^4*(5*b*arccosh(d*x+c)+5*a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+25/64*e^4/b^3*exp(5*a/b)*Ei(1,5*arccosh(d*x+c)+5*a/b)-3/64*(-4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c)^3-3*d*x-3*c)*e^4*(3*b*arccosh(d*x+c)+3*a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+27/64*e^4/b^3*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)-1/32*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*e^4*(b*arccosh(d*x+c)+a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+1/32*e^4/b^3*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/32/b*e^4*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-1/32/b^2*e^4*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/32/b^3*e^4*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-3/64/b*e^4*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-9/64/b^2*e^4*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-27/64/b^3*e^4*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b)-1/64/b*e^4*(16*(d*x+c)^5-20*(d*x+c)^3+16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+5*d*x+5*c-12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-5/64/b^2*e^4*(16*(d*x+c)^5-20*(d*x+c)^3+16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+5*d*x+5*c-12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-25/64/b^3*e^4*exp(-5*a/b)*Ei(1,-5*arccosh(d*x+c)-5*a/b))","B"
143,1,624,242,0.399000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^3,x)","\frac{-\frac{\left(-8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+1\right) e^{3} \left(4 b \,\mathrm{arccosh}\left(d x +c \right)+4 a -b \right)}{32 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \,\mathrm{arccosh}\left(d x +c \right)+\frac{4 a}{b}\right)}{2 b^{3}}-\frac{\left(-2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+2 \left(d x +c \right)^{2}-1\right) e^{3} \left(2 b \,\mathrm{arccosh}\left(d x +c \right)+2 a -b \right)}{16 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{4 b^{3}}-\frac{e^{3} \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{16 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{3} \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{8 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{4 b^{3}}-\frac{e^{3} \left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+1\right)}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{3} \left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+1\right)}{8 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \,\mathrm{arccosh}\left(d x +c \right)-\frac{4 a}{b}\right)}{2 b^{3}}}{d}"," ",0,"1/d*(-1/32*(-8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+8*(d*x+c)^4-8*(d*x+c)^2+1)*e^3*(4*b*arccosh(d*x+c)+4*a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+1/2*e^3/b^3*exp(4*a/b)*Ei(1,4*arccosh(d*x+c)+4*a/b)-1/16*(-2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+2*(d*x+c)^2-1)*e^3*(2*b*arccosh(d*x+c)+2*a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+1/4*e^3/b^3*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/16/b*e^3*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))^2-1/8/b^2*e^3*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))-1/4/b^3*e^3*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b)-1/32/b*e^3*(8*(d*x+c)^4-8*(d*x+c)^2+8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+1)/(a+b*arccosh(d*x+c))^2-1/8/b^2*e^3*(8*(d*x+c)^4-8*(d*x+c)^2+8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+1)/(a+b*arccosh(d*x+c))-1/2/b^3*e^3*exp(-4*a/b)*Ei(1,-4*arccosh(d*x+c)-4*a/b))","B"
144,1,557,236,0.237000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^3,x)","\frac{-\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \left(d x +c \right)^{3}-3 d x -3 c \right) e^{2} \left(3 b \,\mathrm{arccosh}\left(d x +c \right)+3 a -b \right)}{16 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{16 b^{3}}-\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) e^{2} \left(b \,\mathrm{arccosh}\left(d x +c \right)+a -b \right)}{16 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{16 b^{3}}-\frac{e^{2} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{2} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{16 b^{3}}-\frac{e^{2} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{3 e^{2} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{16 b^{3}}}{d}"," ",0,"1/d*(-1/16*(-4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c)^3-3*d*x-3*c)*e^2*(3*b*arccosh(d*x+c)+3*a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+9/16*e^2/b^3*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)-1/16*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*e^2*(b*arccosh(d*x+c)+a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+1/16*e^2/b^3*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/16/b*e^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-1/16/b^2*e^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/16/b^3*e^2*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-1/16/b*e^2*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-3/16/b^2*e^2*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-9/16/b^3*e^2*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b))","B"
145,1,254,155,0.061000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^3,x)","\frac{-\frac{\left(-2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+2 \left(d x +c \right)^{2}-1\right) e \left(2 b \,\mathrm{arccosh}\left(d x +c \right)+2 a -b \right)}{8 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{2 b^{3}}-\frac{e \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{8 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{4 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{2 b^{3}}}{d}"," ",0,"1/d*(-1/8*(-2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+2*(d*x+c)^2-1)*e*(2*b*arccosh(d*x+c)+2*a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+1/2*e/b^3*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/8/b*e*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))^2-1/4/b^2*e*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))-1/2/b^3*e*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b))","A"
146,1,207,123,0.064000," ","int(1/(a+b*arccosh(d*x+c))^3,x)","\frac{-\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) \left(b \,\mathrm{arccosh}\left(d x +c \right)+a -b \right)}{4 b^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)+a^{2}\right)}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{4 b^{3}}-\frac{d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{4 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{4 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{4 b^{3}}}{d}"," ",0,"1/d*(-1/4*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*(b*arccosh(d*x+c)+a-b)/b^2/(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)+a^2)+1/4/b^3*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/4/b*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-1/4/b^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/4/b^3*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b))","A"
147,0,0,26,0.240000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^3,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^3,x)","F"
148,1,1375,399,0.471000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^4,x)","\frac{\frac{\left(-16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+5 d x +5 c \right) e^{4} \left(25 b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+50 a b \,\mathrm{arccosh}\left(d x +c \right)-5 \,\mathrm{arccosh}\left(d x +c \right) b^{2}+25 a^{2}-5 a b +2 b^{2}\right)}{192 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{125 e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \,\mathrm{arccosh}\left(d x +c \right)+\frac{5 a}{b}\right)}{192 b^{4}}+\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \left(d x +c \right)^{3}-3 d x -3 c \right) e^{4} \left(9 b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+18 a b \,\mathrm{arccosh}\left(d x +c \right)-3 \,\mathrm{arccosh}\left(d x +c \right) b^{2}+9 a^{2}-3 a b +2 b^{2}\right)}{64 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{27 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{64 b^{4}}+\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) e^{4} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)-\mathrm{arccosh}\left(d x +c \right) b^{2}+a^{2}-a b +2 b^{2}\right)}{96 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{96 b^{4}}-\frac{e^{4} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{48 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{e^{4} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{96 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{4} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{96 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{96 b^{4}}-\frac{e^{4} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{32 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{3 e^{4} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{64 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{9 e^{4} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{64 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{27 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{64 b^{4}}-\frac{e^{4} \left(16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+5 d x +5 c -12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{96 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{5 e^{4} \left(16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+5 d x +5 c -12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{192 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{25 e^{4} \left(16 \left(d x +c \right)^{5}-20 \left(d x +c \right)^{3}+16 \left(d x +c \right)^{4} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+5 d x +5 c -12 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{192 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{125 e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \,\mathrm{arccosh}\left(d x +c \right)-\frac{5 a}{b}\right)}{192 b^{4}}}{d}"," ",0,"1/d*(1/192*(-16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+16*(d*x+c)^5-20*(d*x+c)^3+5*d*x+5*c)*e^4*(25*b^2*arccosh(d*x+c)^2+50*a*b*arccosh(d*x+c)-5*arccosh(d*x+c)*b^2+25*a^2-5*a*b+2*b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-125/192*e^4/b^4*exp(5*a/b)*Ei(1,5*arccosh(d*x+c)+5*a/b)+1/64*(-4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c)^3-3*d*x-3*c)*e^4*(9*b^2*arccosh(d*x+c)^2+18*a*b*arccosh(d*x+c)-3*arccosh(d*x+c)*b^2+9*a^2-3*a*b+2*b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-27/64*e^4/b^4*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)+1/96*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*e^4*(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)-arccosh(d*x+c)*b^2+a^2-a*b+2*b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-1/96*e^4/b^4*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/48/b*e^4*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^3-1/96/b^2*e^4*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-1/96/b^3*e^4*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/96/b^4*e^4*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-1/32/b*e^4*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^3-3/64/b^2*e^4*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-9/64/b^3*e^4*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-27/64/b^4*e^4*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b)-1/96/b*e^4*(16*(d*x+c)^5-20*(d*x+c)^3+16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+5*d*x+5*c-12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^3-5/192/b^2*e^4*(16*(d*x+c)^5-20*(d*x+c)^3+16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+5*d*x+5*c-12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-25/192/b^3*e^4*(16*(d*x+c)^5-20*(d*x+c)^3+16*(d*x+c)^4*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+5*d*x+5*c-12*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-125/192/b^4*e^4*exp(-5*a/b)*Ei(1,-5*arccosh(d*x+c)-5*a/b))","B"
149,1,860,332,0.419000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^4,x)","\frac{\frac{\left(-8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+1\right) e^{3} \left(8 b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+16 a b \,\mathrm{arccosh}\left(d x +c \right)-2 \,\mathrm{arccosh}\left(d x +c \right) b^{2}+8 a^{2}-2 a b +b^{2}\right)}{48 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{2 e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \,\mathrm{arccosh}\left(d x +c \right)+\frac{4 a}{b}\right)}{3 b^{4}}+\frac{\left(-2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+2 \left(d x +c \right)^{2}-1\right) e^{3} \left(2 b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+4 a b \,\mathrm{arccosh}\left(d x +c \right)-\mathrm{arccosh}\left(d x +c \right) b^{2}+2 a^{2}-a b +b^{2}\right)}{24 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{6 b^{4}}-\frac{e^{3} \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{24 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{e^{3} \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{24 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{3} \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{12 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{6 b^{4}}-\frac{e^{3} \left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+1\right)}{48 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{e^{3} \left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+1\right)}{24 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{3} \left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{2}+8 \left(d x +c \right)^{3} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-4 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+1\right)}{6 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{2 e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \,\mathrm{arccosh}\left(d x +c \right)-\frac{4 a}{b}\right)}{3 b^{4}}}{d}"," ",0,"1/d*(1/48*(-8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+8*(d*x+c)^4-8*(d*x+c)^2+1)*e^3*(8*b^2*arccosh(d*x+c)^2+16*a*b*arccosh(d*x+c)-2*arccosh(d*x+c)*b^2+8*a^2-2*a*b+b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-2/3*e^3/b^4*exp(4*a/b)*Ei(1,4*arccosh(d*x+c)+4*a/b)+1/24*(-2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+2*(d*x+c)^2-1)*e^3*(2*b^2*arccosh(d*x+c)^2+4*a*b*arccosh(d*x+c)-arccosh(d*x+c)*b^2+2*a^2-a*b+b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-1/6*e^3/b^4*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/24/b*e^3*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))^3-1/24/b^2*e^3*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))^2-1/12/b^3*e^3*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))-1/6/b^4*e^3*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b)-1/48/b*e^3*(8*(d*x+c)^4-8*(d*x+c)^2+8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+1)/(a+b*arccosh(d*x+c))^3-1/24/b^2*e^3*(8*(d*x+c)^4-8*(d*x+c)^2+8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+1)/(a+b*arccosh(d*x+c))^2-1/6/b^3*e^3*(8*(d*x+c)^4-8*(d*x+c)^2+8*(d*x+c)^3*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-4*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+1)/(a+b*arccosh(d*x+c))-2/3/b^4*e^3*exp(-4*a/b)*Ei(1,-4*arccosh(d*x+c)-4*a/b))","B"
150,1,777,322,0.261000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^4,x)","\frac{\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}+\sqrt{d x +c -1}\, \sqrt{d x +c +1}+4 \left(d x +c \right)^{3}-3 d x -3 c \right) e^{2} \left(9 b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+18 a b \,\mathrm{arccosh}\left(d x +c \right)-3 \,\mathrm{arccosh}\left(d x +c \right) b^{2}+9 a^{2}-3 a b +2 b^{2}\right)}{48 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \,\mathrm{arccosh}\left(d x +c \right)+\frac{3 a}{b}\right)}{16 b^{4}}+\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) e^{2} \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)-\mathrm{arccosh}\left(d x +c \right) b^{2}+a^{2}-a b +2 b^{2}\right)}{48 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{48 b^{4}}-\frac{e^{2} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{24 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{e^{2} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{48 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e^{2} \left(d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{48 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{48 b^{4}}-\frac{e^{2} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{24 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{e^{2} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{3 e^{2} \left(4 \left(d x +c \right)^{3}-3 d x -3 c +4 \left(d x +c \right)^{2} \sqrt{d x +c -1}\, \sqrt{d x +c +1}-\sqrt{d x +c -1}\, \sqrt{d x +c +1}\right)}{16 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arccosh}\left(d x +c \right)-\frac{3 a}{b}\right)}{16 b^{4}}}{d}"," ",0,"1/d*(1/48*(-4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+4*(d*x+c)^3-3*d*x-3*c)*e^2*(9*b^2*arccosh(d*x+c)^2+18*a*b*arccosh(d*x+c)-3*arccosh(d*x+c)*b^2+9*a^2-3*a*b+2*b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-9/16*e^2/b^4*exp(3*a/b)*Ei(1,3*arccosh(d*x+c)+3*a/b)+1/48*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*e^2*(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)-arccosh(d*x+c)*b^2+a^2-a*b+2*b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-1/48*e^2/b^4*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/24/b*e^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^3-1/48/b^2*e^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-1/48/b^3*e^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/48/b^4*e^2*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b)-1/24/b*e^2*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^3-1/16/b^2*e^2*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-3/16/b^3*e^2*(4*(d*x+c)^3-3*d*x-3*c+4*(d*x+c)^2*(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-9/16/b^4*e^2*exp(-3*a/b)*Ei(1,-3*arccosh(d*x+c)-3*a/b))","B"
151,1,353,198,0.070000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^4,x)","\frac{\frac{\left(-2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)+2 \left(d x +c \right)^{2}-1\right) e \left(2 b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+4 a b \,\mathrm{arccosh}\left(d x +c \right)-\mathrm{arccosh}\left(d x +c \right) b^{2}+2 a^{2}-a b +b^{2}\right)}{12 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \,\mathrm{arccosh}\left(d x +c \right)+\frac{2 a}{b}\right)}{3 b^{4}}-\frac{e \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{12 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{e \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{12 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{e \left(2 \left(d x +c \right)^{2}-1+2 \sqrt{d x +c +1}\, \sqrt{d x +c -1}\, \left(d x +c \right)\right)}{6 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arccosh}\left(d x +c \right)-\frac{2 a}{b}\right)}{3 b^{4}}}{d}"," ",0,"1/d*(1/12*(-2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c)+2*(d*x+c)^2-1)*e*(2*b^2*arccosh(d*x+c)^2+4*a*b*arccosh(d*x+c)-arccosh(d*x+c)*b^2+2*a^2-a*b+b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-1/3*e/b^4*exp(2*a/b)*Ei(1,2*arccosh(d*x+c)+2*a/b)-1/12/b*e*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))^3-1/12/b^2*e*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))^2-1/6/b^3*e*(2*(d*x+c)^2-1+2*(d*x+c+1)^(1/2)*(d*x+c-1)^(1/2)*(d*x+c))/(a+b*arccosh(d*x+c))-1/3/b^4*e*exp(-2*a/b)*Ei(1,-2*arccosh(d*x+c)-2*a/b))","A"
152,1,295,159,0.074000," ","int(1/(a+b*arccosh(d*x+c))^4,x)","\frac{\frac{\left(-\sqrt{d x +c -1}\, \sqrt{d x +c +1}+d x +c \right) \left(b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+2 a b \,\mathrm{arccosh}\left(d x +c \right)-\mathrm{arccosh}\left(d x +c \right) b^{2}+a^{2}-a b +2 b^{2}\right)}{12 b^{3} \left(b^{3} \mathrm{arccosh}\left(d x +c \right)^{3}+3 a \,b^{2} \mathrm{arccosh}\left(d x +c \right)^{2}+3 a^{2} b \,\mathrm{arccosh}\left(d x +c \right)+a^{3}\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \mathrm{arccosh}\left(d x +c \right)+\frac{a}{b}\right)}{12 b^{4}}-\frac{d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{6 b \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}-\frac{d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{12 b^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}-\frac{d x +c +\sqrt{d x +c -1}\, \sqrt{d x +c +1}}{12 b^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arccosh}\left(d x +c \right)-\frac{a}{b}\right)}{12 b^{4}}}{d}"," ",0,"1/d*(1/12*(-(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2)+d*x+c)*(b^2*arccosh(d*x+c)^2+2*a*b*arccosh(d*x+c)-arccosh(d*x+c)*b^2+a^2-a*b+2*b^2)/b^3/(b^3*arccosh(d*x+c)^3+3*a*b^2*arccosh(d*x+c)^2+3*a^2*b*arccosh(d*x+c)+a^3)-1/12/b^4*exp(a/b)*Ei(1,arccosh(d*x+c)+a/b)-1/6/b*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^3-1/12/b^2*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))^2-1/12/b^3*(d*x+c+(d*x+c-1)^(1/2)*(d*x+c+1)^(1/2))/(a+b*arccosh(d*x+c))-1/12/b^4*exp(-a/b)*Ei(1,-arccosh(d*x+c)-a/b))","A"
153,0,0,26,0.256000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^4,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^4,x)","F"
154,-2,0,284,180.000000," ","int((d*e*x+c*e)^4*(a+b*arccosh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right)^{4} \sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^4*(a+b*arccosh(d*x+c))^(1/2),x)","F"
155,-2,0,218,180.000000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right)^{3} \sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(1/2),x)","F"
156,-2,0,194,180.000000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right)^{2} \sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(1/2),x)","F"
157,0,0,130,0.158000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right) \sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(1/2),x)","F"
158,0,0,92,0.140000," ","int((a+b*arccosh(d*x+c))^(1/2),x)","\int \sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(1/2),x)","F"
159,0,0,26,0.255000," ","int((a+b*arccosh(d*x+c))^(1/2)/(d*e*x+c*e),x)","\int \frac{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(1/2)/(d*e*x+c*e),x)","F"
160,-2,0,304,180.000000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right)^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(3/2),x)","F"
161,-2,0,275,180.000000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right)^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(3/2),x)","F"
162,0,0,170,0.161000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(3/2),x)","F"
163,0,0,126,0.144000," ","int((a+b*arccosh(d*x+c))^(3/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(3/2),x)","F"
164,0,0,26,0.275000," ","int((a+b*arccosh(d*x+c))^(3/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(3/2)/(d*e*x+c*e),x)","F"
165,-2,0,387,180.000000," ","int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right)^{3} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(5/2),x)","F"
166,-2,0,333,180.000000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right)^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(5/2),x)","F"
167,0,0,219,0.164000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(5/2),x)","F"
168,0,0,151,0.145000," ","int((a+b*arccosh(d*x+c))^(5/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(5/2),x)","F"
169,0,0,26,0.291000," ","int((a+b*arccosh(d*x+c))^(5/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(5/2)/(d*e*x+c*e),x)","F"
170,-2,0,418,180.000000," ","int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(7/2),x)","\int \left(d e x +c e \right)^{2} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(7/2),x)","F"
171,0,0,261,0.203000," ","int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(7/2),x)","\int \left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(7/2),x)","F"
172,0,0,187,0.143000," ","int((a+b*arccosh(d*x+c))^(7/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(7/2),x)","F"
173,0,0,26,0.270000," ","int((a+b*arccosh(d*x+c))^(7/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^(7/2)/(d*e*x+c*e),x)","F"
174,-2,0,257,180.000000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(1/2),x)","F"
175,-2,0,171,180.000000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(1/2),x)","F"
176,-2,0,167,180.000000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(1/2),x)","F"
177,0,0,87,0.165000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{d e x +c e}{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(1/2),x)","F"
178,0,0,71,0.000000," ","int(1/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{1}{\sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x+c))^(1/2),x)","F"
179,0,0,26,0.282000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(1/2),x)","\int \frac{1}{\left(d e x +c e \right) \sqrt{a +b \,\mathrm{arccosh}\left(d x +c \right)}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(1/2),x)","F"
180,-2,0,303,180.000000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(3/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(3/2),x)","F"
181,-2,0,217,180.000000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(3/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(3/2),x)","F"
182,-2,0,213,180.000000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(3/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(3/2),x)","F"
183,0,0,129,0.146000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(3/2),x)","\int \frac{d e x +c e}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(3/2),x)","F"
184,0,0,105,0.147000," ","int(1/(a+b*arccosh(d*x+c))^(3/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x+c))^(3/2),x)","F"
185,0,0,26,0.301000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(3/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(3/2),x)","F"
186,-2,0,363,180.000000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(5/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(5/2),x)","F"
187,-2,0,277,180.000000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(5/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(5/2),x)","F"
188,-2,0,271,180.000000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(5/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(5/2),x)","F"
189,0,0,178,0.146000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(5/2),x)","\int \frac{d e x +c e}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(5/2),x)","F"
190,0,0,132,0.141000," ","int(1/(a+b*arccosh(d*x+c))^(5/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x+c))^(5/2),x)","F"
191,0,0,26,0.284000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(5/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(5/2),x)","F"
192,-2,0,455,180.000000," ","int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(7/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(7/2),x)","F"
193,-2,0,367,180.000000," ","int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(7/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(7/2),x)","F"
194,-2,0,356,180.000000," ","int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(7/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(7/2),x)","F"
195,0,0,220,0.148000," ","int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(7/2),x)","\int \frac{d e x +c e}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(7/2),x)","F"
196,0,0,168,0.143000," ","int(1/(a+b*arccosh(d*x+c))^(7/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x+c))^(7/2),x)","F"
197,0,0,26,0.286000," ","int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(7/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(7/2),x)","F"
198,1,277,157,0.053000," ","int((d*e*x+c*e)^(7/2)*(a+b*arccosh(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{9}{2}} a}{9}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{9}{2}} \mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{9}-\frac{2 \left(5 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{11}{2}}+2 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{7}{2}} e^{2}+21 e^{5} \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)-21 e^{5} \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \EllipticE \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)-7 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{3}{2}} e^{4}\right)}{405 e \sqrt{-\frac{1}{e}}\, \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(1/9*(d*e*x+c*e)^(9/2)*a+b*(1/9*(d*e*x+c*e)^(9/2)*arccosh((d*e*x+c*e)/e)-2/405/e*(5*(-1/e)^(1/2)*(d*e*x+c*e)^(11/2)+2*(-1/e)^(1/2)*(d*e*x+c*e)^(7/2)*e^2+21*e^5*((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)-21*e^5*((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*EllipticE((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)-7*(-1/e)^(1/2)*(d*e*x+c*e)^(3/2)*e^4)/(-1/e)^(1/2)/((d*e*x+c*e+e)/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","C"
199,1,218,137,0.026000," ","int((d*e*x+c*e)^(5/2)*(a+b*arccosh(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{7}{2}} a}{7}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{7}{2}} \mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{7}-\frac{2 \left(3 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{9}{2}}+2 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{5}{2}} e^{2}+5 e^{4} \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)-5 \sqrt{-\frac{1}{e}}\, \sqrt{d e x +c e}\, e^{4}\right)}{147 e \sqrt{-\frac{1}{e}}\, \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(1/7*(d*e*x+c*e)^(7/2)*a+b*(1/7*(d*e*x+c*e)^(7/2)*arccosh((d*e*x+c*e)/e)-2/147/e*(3*(-1/e)^(1/2)*(d*e*x+c*e)^(9/2)+2*(-1/e)^(1/2)*(d*e*x+c*e)^(5/2)*e^2+5*e^4*((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)-5*(-1/e)^(1/2)*(d*e*x+c*e)^(1/2)*e^4)/(-1/e)^(1/2)/((d*e*x+c*e+e)/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","A"
200,1,254,121,0.021000," ","int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{5}{2}} a}{5}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{5}{2}} \mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{5}-\frac{2 \left(\sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{7}{2}}+3 \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, e^{3} \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)-3 e^{3} \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \EllipticE \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)-\sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{3}{2}} e^{2}\right)}{25 e \sqrt{-\frac{1}{e}}\, \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(1/5*(d*e*x+c*e)^(5/2)*a+b*(1/5*(d*e*x+c*e)^(5/2)*arccosh((d*e*x+c*e)/e)-2/25/e*((-1/e)^(1/2)*(d*e*x+c*e)^(7/2)+3*((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*e^3*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)-3*e^3*((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*EllipticE((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)-(-1/e)^(1/2)*(d*e*x+c*e)^(3/2)*e^2)/(-1/e)^(1/2)/((d*e*x+c*e+e)/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","C"
201,1,194,103,0.018000," ","int((a+b*arccosh(d*x+c))*(d*e*x+c*e)^(1/2),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{3}{2}} a}{3}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{3}{2}} \mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{3}-\frac{2 \left(\sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{5}{2}}+\sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right) e^{2}-\sqrt{-\frac{1}{e}}\, \sqrt{d e x +c e}\, e^{2}\right)}{9 e \sqrt{-\frac{1}{e}}\, \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(1/3*(d*e*x+c*e)^(3/2)*a+b*(1/3*(d*e*x+c*e)^(3/2)*arccosh((d*e*x+c*e)/e)-2/9/e*((-1/e)^(1/2)*(d*e*x+c*e)^(5/2)+((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)*e^2-(-1/e)^(1/2)*(d*e*x+c*e)^(1/2)*e^2)/(-1/e)^(1/2)/((d*e*x+c*e+e)/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","A"
202,1,138,92,0.020000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(1/2),x)","\frac{2 a \sqrt{d e x +c e}+2 b \left(\sqrt{d e x +c e}\, \mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)-\frac{2 \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right)\right) \sqrt{-\frac{d e x +c e -e}{e}}}{\sqrt{-\frac{1}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(a*(d*e*x+c*e)^(1/2)+b*((d*e*x+c*e)^(1/2)*arccosh((d*e*x+c*e)/e)-2*(EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I))*(-(d*e*x+c*e-e)/e)^(1/2)/(-1/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","C"
203,1,119,72,0.018000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(3/2),x)","\frac{-\frac{2 a}{\sqrt{d e x +c e}}+2 b \left(-\frac{\mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{\sqrt{d e x +c e}}+\frac{2 \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right) \sqrt{-\frac{d e x +c e -e}{e}}}{e \sqrt{-\frac{1}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(-a/(d*e*x+c*e)^(1/2)+b*(-1/(d*e*x+c*e)^(1/2)*arccosh((d*e*x+c*e)/e)+2/e*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)*(-(d*e*x+c*e-e)/e)^(1/2)/(-1/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","A"
204,1,269,126,0.029000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(5/2),x)","\frac{-\frac{2 a}{3 \left(d e x +c e \right)^{\frac{3}{2}}}+2 b \left(-\frac{\mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{3 \left(d e x +c e \right)^{\frac{3}{2}}}+\frac{-\frac{2 \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \sqrt{d e x +c e}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right) e}{3}+\frac{2 \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \sqrt{d e x +c e}\, \EllipticE \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right) e}{3}+\frac{2 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{2}}{3}-\frac{2 \sqrt{-\frac{1}{e}}\, e^{2}}{3}}{e^{3} \sqrt{-\frac{1}{e}}\, \sqrt{d e x +c e}\, \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(-1/3*a/(d*e*x+c*e)^(3/2)+b*(-1/3/(d*e*x+c*e)^(3/2)*arccosh((d*e*x+c*e)/e)+2/3/e^3*(-((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*(d*e*x+c*e)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)*e+((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*(d*e*x+c*e)^(1/2)*EllipticE((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)*e+(-1/e)^(1/2)*(d*e*x+c*e)^2-(-1/e)^(1/2)*e^2)/(-1/e)^(1/2)/(d*e*x+c*e)^(1/2)/((d*e*x+c*e+e)/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","C"
205,1,201,106,0.029000," ","int((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(7/2),x)","\frac{-\frac{2 a}{5 \left(d e x +c e \right)^{\frac{5}{2}}}+2 b \left(-\frac{\mathrm{arccosh}\left(\frac{d e x +c e}{e}\right)}{5 \left(d e x +c e \right)^{\frac{5}{2}}}+\frac{\frac{2 \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{-\frac{d e x +c e -e}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{-\frac{1}{e}}, i\right) \left(d e x +c e \right)^{\frac{3}{2}}}{15}+\frac{2 \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{2}}{15}-\frac{2 \sqrt{-\frac{1}{e}}\, e^{2}}{15}}{e^{3} \sqrt{-\frac{1}{e}}\, \left(d e x +c e \right)^{\frac{3}{2}} \sqrt{\frac{d e x +c e +e}{e}}\, \sqrt{\frac{d e x +c e -e}{e}}}\right)}{d e}"," ",0,"2/d/e*(-1/5*a/(d*e*x+c*e)^(5/2)+b*(-1/5/(d*e*x+c*e)^(5/2)*arccosh((d*e*x+c*e)/e)+2/15/e^3*(((d*e*x+c*e+e)/e)^(1/2)*(-(d*e*x+c*e-e)/e)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(-1/e)^(1/2),I)*(d*e*x+c*e)^(3/2)+(-1/e)^(1/2)*(d*e*x+c*e)^2-(-1/e)^(1/2)*e^2)/(-1/e)^(1/2)/(d*e*x+c*e)^(3/2)/((d*e*x+c*e+e)/e)^(1/2)/((d*e*x+c*e-e)/e)^(1/2)))","A"
206,-2,0,125,180.000000," ","int((d*e*x+c*e)^(7/2)*(a+b*arccosh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{7}{2}} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(7/2)*(a+b*arccosh(d*x+c))^2,x)","F"
207,-2,0,125,180.000000," ","int((d*e*x+c*e)^(5/2)*(a+b*arccosh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{5}{2}} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(5/2)*(a+b*arccosh(d*x+c))^2,x)","F"
208,-2,0,125,180.000000," ","int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c))^2,x)","F"
209,-2,0,125,180.000000," ","int((a+b*arccosh(d*x+c))^2*(d*e*x+c*e)^(1/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2} \sqrt{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^2*(d*e*x+c*e)^(1/2),x)","F"
210,-2,0,125,180.000000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(1/2),x)","F"
211,-2,0,125,180.000000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(3/2),x)","F"
212,-2,0,125,180.000000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(5/2),x)","F"
213,-2,0,125,180.000000," ","int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^(7/2),x)","F"
214,-2,0,76,180.000000," ","int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c))^3,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c))^3,x)","F"
215,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^3*(d*e*x+c*e)^(1/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3} \sqrt{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3*(d*e*x+c*e)^(1/2),x)","F"
216,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(1/2),x)","F"
217,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(3/2),x)","F"
218,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(5/2),x)","F"
219,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(7/2),x)","F"
220,-2,0,76,180.000000," ","int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c))^4,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c))^4,x)","F"
221,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^4*(d*e*x+c*e)^(1/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4} \sqrt{d e x +c e}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4*(d*e*x+c*e)^(1/2),x)","F"
222,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(1/2),x)","F"
223,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(3/2),x)","F"
224,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(5/2),x)","F"
225,-2,0,76,180.000000," ","int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^(7/2),x)","F"
226,0,0,89,2.653000," ","int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c))^4,x)","\int \left(d e x +c e \right)^{m} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c))^4,x)","F"
227,0,0,89,2.543000," ","int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c))^3,x)","\int \left(d e x +c e \right)^{m} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c))^3,x)","F"
228,0,0,184,2.997000," ","int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{m} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c))^2,x)","F"
229,0,0,112,2.694000," ","int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c)),x)","\int \left(d e x +c e \right)^{m} \left(a +b \,\mathrm{arccosh}\left(d x +c \right)\right)\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arccosh(d*x+c)),x)","F"
230,0,0,24,1.182000," ","int((d*e*x+c*e)^m/(a+b*arccosh(d*x+c)),x)","\int \frac{\left(d e x +c e \right)^{m}}{a +b \,\mathrm{arccosh}\left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^m/(a+b*arccosh(d*x+c)),x)","F"
231,0,0,82,0.080000," ","int(arccosh(a*x^5)/x,x)","\int \frac{\mathrm{arccosh}\left(a \,x^{5}\right)}{x}\, dx"," ",0,"int(arccosh(a*x^5)/x,x)","F"
232,1,75,73,0.033000," ","int(x^2*arccosh(x^(1/2)),x)","\frac{x^{3} \mathrm{arccosh}\left(\sqrt{x}\right)}{3}-\frac{\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}\, \left(8 x^{\frac{5}{2}} \sqrt{-1+x}+10 x^{\frac{3}{2}} \sqrt{-1+x}+15 \sqrt{x}\, \sqrt{-1+x}+15 \ln \left(\sqrt{x}+\sqrt{-1+x}\right)\right)}{144 \sqrt{-1+x}}"," ",0,"1/3*x^3*arccosh(x^(1/2))-1/144*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*(8*x^(5/2)*(-1+x)^(1/2)+10*x^(3/2)*(-1+x)^(1/2)+15*x^(1/2)*(-1+x)^(1/2)+15*ln(x^(1/2)+(-1+x)^(1/2)))/(-1+x)^(1/2)","A"
233,1,65,54,0.004000," ","int(x*arccosh(x^(1/2)),x)","\frac{x^{2} \mathrm{arccosh}\left(\sqrt{x}\right)}{2}-\frac{\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}\, \left(2 x^{\frac{3}{2}} \sqrt{-1+x}+3 \sqrt{x}\, \sqrt{-1+x}+3 \ln \left(\sqrt{x}+\sqrt{-1+x}\right)\right)}{16 \sqrt{-1+x}}"," ",0,"1/2*x^2*arccosh(x^(1/2))-1/16*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*(2*x^(3/2)*(-1+x)^(1/2)+3*x^(1/2)*(-1+x)^(1/2)+3*ln(x^(1/2)+(-1+x)^(1/2)))/(-1+x)^(1/2)","A"
234,1,49,32,0.005000," ","int(arccosh(x^(1/2)),x)","x \,\mathrm{arccosh}\left(\sqrt{x}\right)-\frac{\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}\, \left(\sqrt{x}\, \sqrt{-1+x}+\ln \left(\sqrt{x}+\sqrt{-1+x}\right)\right)}{2 \sqrt{-1+x}}"," ",0,"x*arccosh(x^(1/2))-1/2*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*(x^(1/2)*(-1+x)^(1/2)+ln(x^(1/2)+(-1+x)^(1/2)))/(-1+x)^(1/2)","A"
235,1,65,64,0.090000," ","int(arccosh(x^(1/2))/x,x)","-\mathrm{arccosh}\left(\sqrt{x}\right)^{2}+2 \,\mathrm{arccosh}\left(\sqrt{x}\right) \ln \left(1+\left(\sqrt{x}+\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}\right)^{2}\right)+\polylog \left(2, -\left(\sqrt{x}+\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}\right)^{2}\right)"," ",0,"-arccosh(x^(1/2))^2+2*arccosh(x^(1/2))*ln(1+(x^(1/2)+(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2))^2)+polylog(2,-(x^(1/2)+(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2))^2)","A"
236,1,29,28,0.003000," ","int(arccosh(x^(1/2))/x^2,x)","-\frac{\mathrm{arccosh}\left(\sqrt{x}\right)}{x}+\frac{\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}}{\sqrt{x}}"," ",0,"-arccosh(x^(1/2))/x+(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(1/2)","A"
237,1,35,48,0.003000," ","int(arccosh(x^(1/2))/x^3,x)","-\frac{\mathrm{arccosh}\left(\sqrt{x}\right)}{2 x^{2}}+\frac{\sqrt{-1+\sqrt{x}}\, \sqrt{1+\sqrt{x}}\, \left(1+2 x \right)}{6 x^{\frac{3}{2}}}"," ",0,"-1/2*arccosh(x^(1/2))/x^2+1/6*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*(1+2*x)/x^(3/2)","A"
238,1,38,20,0.022000," ","int(arccosh(1/x),x)","\mathrm{arccosh}\left(\frac{1}{x}\right) x +\frac{\sqrt{\frac{1}{x}-1}\, \sqrt{\frac{1}{x}+1}\, \arctan \left(\frac{1}{\sqrt{\frac{1}{x^{2}}-1}}\right)}{\sqrt{\frac{1}{x^{2}}-1}}"," ",0,"arccosh(1/x)*x+(1/x-1)^(1/2)*(1/x+1)^(1/2)/(1/x^2-1)^(1/2)*arctan(1/(1/x^2-1)^(1/2))","A"
239,1,91,90,0.021000," ","int(arccosh(a*x^n)/x,x)","-\frac{\mathrm{arccosh}\left(a \,x^{n}\right)^{2}}{2 n}+\frac{\mathrm{arccosh}\left(a \,x^{n}\right) \ln \left(1+\left(a \,x^{n}+\sqrt{a \,x^{n}-1}\, \sqrt{a \,x^{n}+1}\right)^{2}\right)}{n}+\frac{\polylog \left(2, -\left(a \,x^{n}+\sqrt{a \,x^{n}-1}\, \sqrt{a \,x^{n}+1}\right)^{2}\right)}{2 n}"," ",0,"-1/2*arccosh(a*x^n)^2/n+arccosh(a*x^n)*ln(1+(a*x^n+(a*x^n-1)^(1/2)*(a*x^n+1)^(1/2))^2)/n+1/2*polylog(2,-(a*x^n+(a*x^n-1)^(1/2)*(a*x^n+1)^(1/2))^2)/n","A"
240,0,0,137,0.141000," ","int((a+b*arccosh(d*x^2+1))^4,x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{4}\, dx"," ",0,"int((a+b*arccosh(d*x^2+1))^4,x)","F"
241,0,0,119,0.115000," ","int((a+b*arccosh(d*x^2+1))^3,x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{3}\, dx"," ",0,"int((a+b*arccosh(d*x^2+1))^3,x)","F"
242,0,0,68,0.118000," ","int((a+b*arccosh(d*x^2+1))^2,x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{2}\, dx"," ",0,"int((a+b*arccosh(d*x^2+1))^2,x)","F"
243,1,37,47,0.008000," ","int(a+b*arccosh(d*x^2+1),x)","a x +b \left(x \,\mathrm{arccosh}\left(d \,x^{2}+1\right)-\frac{2 x \sqrt{d \,x^{2}+2}}{\sqrt{d \,x^{2}}}\right)"," ",0,"a*x+b*(x*arccosh(d*x^2+1)-2/(d*x^2)^(1/2)*x*(d*x^2+2)^(1/2))","A"
244,0,0,83,0.069000," ","int(1/(a+b*arccosh(d*x^2+1)),x)","\int \frac{1}{a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1)),x)","F"
245,0,0,124,0.087000," ","int(1/(a+b*arccosh(d*x^2+1))^2,x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1))^2,x)","F"
246,0,0,153,0.069000," ","int(1/(a+b*arccosh(d*x^2+1))^3,x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1))^3,x)","F"
247,0,0,139,0.120000," ","int((a+b*arccosh(d*x^2-1))^4,x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{4}\, dx"," ",0,"int((a+b*arccosh(d*x^2-1))^4,x)","F"
248,0,0,104,0.117000," ","int((a+b*arccosh(d*x^2-1))^3,x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{3}\, dx"," ",0,"int((a+b*arccosh(d*x^2-1))^3,x)","F"
249,0,0,69,0.117000," ","int((a+b*arccosh(d*x^2-1))^2,x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{2}\, dx"," ",0,"int((a+b*arccosh(d*x^2-1))^2,x)","F"
250,1,37,31,0.005000," ","int(a+b*arccosh(d*x^2-1),x)","a x +b \left(x \,\mathrm{arccosh}\left(d \,x^{2}-1\right)-\frac{2 x \sqrt{d \,x^{2}-2}}{\sqrt{d \,x^{2}}}\right)"," ",0,"a*x+b*(x*arccosh(d*x^2-1)-2/(d*x^2)^(1/2)*x*(d*x^2-2)^(1/2))","A"
251,0,0,83,0.074000," ","int(1/(a+b*arccosh(d*x^2-1)),x)","\int \frac{1}{a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1)),x)","F"
252,0,0,124,0.071000," ","int(1/(a+b*arccosh(d*x^2-1))^2,x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1))^2,x)","F"
253,0,0,153,0.069000," ","int(1/(a+b*arccosh(d*x^2-1))^3,x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1))^3,x)","F"
254,0,0,236,0.069000," ","int((a+b*arccosh(d*x^2+1))^(5/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x^2+1))^(5/2),x)","F"
255,0,0,198,0.069000," ","int((a+b*arccosh(d*x^2+1))^(3/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x^2+1))^(3/2),x)","F"
256,0,0,170,0.069000," ","int((a+b*arccosh(d*x^2+1))^(1/2),x)","\int \sqrt{a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)}\, dx"," ",0,"int((a+b*arccosh(d*x^2+1))^(1/2),x)","F"
257,0,0,135,0.072000," ","int(1/(a+b*arccosh(d*x^2+1))^(1/2),x)","\int \frac{1}{\sqrt{a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1))^(1/2),x)","F"
258,0,0,176,0.069000," ","int(1/(a+b*arccosh(d*x^2+1))^(3/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1))^(3/2),x)","F"
259,0,0,205,0.069000," ","int(1/(a+b*arccosh(d*x^2+1))^(5/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1))^(5/2),x)","F"
260,0,0,246,0.069000," ","int(1/(a+b*arccosh(d*x^2+1))^(7/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}+1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2+1))^(7/2),x)","F"
261,0,0,237,0.071000," ","int((a+b*arccosh(d*x^2-1))^(5/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x^2-1))^(5/2),x)","F"
262,0,0,199,0.072000," ","int((a+b*arccosh(d*x^2-1))^(3/2),x)","\int \left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arccosh(d*x^2-1))^(3/2),x)","F"
263,0,0,170,0.071000," ","int((a+b*arccosh(d*x^2-1))^(1/2),x)","\int \sqrt{a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)}\, dx"," ",0,"int((a+b*arccosh(d*x^2-1))^(1/2),x)","F"
264,0,0,135,0.072000," ","int(1/(a+b*arccosh(d*x^2-1))^(1/2),x)","\int \frac{1}{\sqrt{a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1))^(1/2),x)","F"
265,0,0,176,0.069000," ","int(1/(a+b*arccosh(d*x^2-1))^(3/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1))^(3/2),x)","F"
266,0,0,205,0.070000," ","int(1/(a+b*arccosh(d*x^2-1))^(5/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1))^(5/2),x)","F"
267,0,0,246,0.069000," ","int(1/(a+b*arccosh(d*x^2-1))^(7/2),x)","\int \frac{1}{\left(a +b \,\mathrm{arccosh}\left(d \,x^{2}-1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arccosh(d*x^2-1))^(7/2),x)","F"
268,0,0,38,0.585000," ","int((a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","\int \frac{\left(a +b \,\mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{n}}{-c^{2} x^{2}+1}\, dx"," ",0,"int((a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","F"
269,1,870,381,0.903000," ","int((a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x)","\frac{a^{3} \ln \left(c x +1\right)}{2 c}-\frac{a^{3} \ln \left(c x -1\right)}{2 c}+\frac{b^{3} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{4}}{4 c}-\frac{b^{3} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1+\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}-\frac{3 b^{3} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{2 c}+\frac{3 b^{3} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{2 c}-\frac{3 b^{3} \polylog \left(4, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{4 c}+\frac{a \,b^{2} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3}}{c}-\frac{3 a \,b^{2} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}-\frac{3 a \,b^{2} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}+\frac{3 a \,b^{2} \polylog \left(3, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{2 c}+\frac{3 a^{2} b \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{2 c}-\frac{3 a^{2} b \,\mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}-\frac{3 a^{2} b \polylog \left(2, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{2 c}"," ",0,"1/2*a^3/c*ln(c*x+1)-1/2*a^3/c*ln(c*x-1)+1/4*b^3/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^4-b^3/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1+((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-3/2*b^3/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)+3/2*b^3/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-3/4*b^3/c*polylog(4,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)+a*b^2/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3-3*a*b^2/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-3*a*b^2/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)+3/2*a*b^2/c*polylog(3,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)+3/2*a^2*b/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-3*a^2*b/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-3/2*a^2*b/c*polylog(2,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)","B"
270,1,491,285,0.010000," ","int((a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x)","\frac{a^{2} \ln \left(c x +1\right)}{2 c}-\frac{a^{2} \ln \left(c x -1\right)}{2 c}+\frac{b^{2} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3}}{3 c}-\frac{b^{2} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}-\frac{b^{2} \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}+\frac{b^{2} \polylog \left(3, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{2 c}+\frac{a b \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{c}-\frac{2 a b \,\mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}-\frac{a b \polylog \left(2, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}"," ",0,"1/2*a^2/c*ln(c*x+1)-1/2*a^2/c*ln(c*x-1)+1/3*b^2/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3-b^2/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-b^2/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)+1/2*b^2/c*polylog(3,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)+a*b/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-2*a*b/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-a*b/c*polylog(2,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)","A"
271,1,207,191,0.008000," ","int((a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x)","\frac{a \ln \left(c x +1\right)}{2 c}-\frac{a \ln \left(c x -1\right)}{2 c}+\frac{b \mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{2 c}-\frac{b \,\mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{c}-\frac{b \polylog \left(2, -\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-1}\, \sqrt{\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+1}\right)^{2}\right)}{2 c}"," ",0,"1/2*a/c*ln(c*x+1)-1/2*a/c*ln(c*x-1)+1/2*b/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-b/c*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)-1/2*b/c*polylog(2,-((-c*x+1)^(1/2)/(c*x+1)^(1/2)+((-c*x+1)^(1/2)/(c*x+1)^(1/2)-1)^(1/2)*((-c*x+1)^(1/2)/(c*x+1)^(1/2)+1)^(1/2))^2)","A"
272,0,0,38,0.373000," ","int(1/(-c^2*x^2+1)/(a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \,\mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","F"
273,0,0,38,0.353000," ","int(1/(-c^2*x^2+1)/(a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \,\mathrm{arccosh}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","F"
274,1,115,114,0.007000," ","int(arccosh(c*exp(b*x+a)),x)","-\frac{\mathrm{arccosh}\left(c \,{\mathrm e}^{b x +a}\right)^{2}}{2 b}+\frac{\mathrm{arccosh}\left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1+\left(c \,{\mathrm e}^{b x +a}+\sqrt{c \,{\mathrm e}^{b x +a}-1}\, \sqrt{c \,{\mathrm e}^{b x +a}+1}\right)^{2}\right)}{b}+\frac{\polylog \left(2, -\left(c \,{\mathrm e}^{b x +a}+\sqrt{c \,{\mathrm e}^{b x +a}-1}\, \sqrt{c \,{\mathrm e}^{b x +a}+1}\right)^{2}\right)}{2 b}"," ",0,"-1/2*arccosh(c*exp(b*x+a))^2/b+arccosh(c*exp(b*x+a))*ln(1+(c*exp(b*x+a)+(c*exp(b*x+a)-1)^(1/2)*(c*exp(b*x+a)+1)^(1/2))^2)/b+1/2*polylog(2,-(c*exp(b*x+a)+(c*exp(b*x+a)-1)^(1/2)*(c*exp(b*x+a)+1)^(1/2))^2)/b","A"
275,1,376,247,0.045000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))*x^3,x)","\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(24 \,\mathrm{csgn}\left(b \right) x^{4} b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+6 \,\mathrm{csgn}\left(b \right) x^{3} a \,b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-6 \,\mathrm{csgn}\left(b \right) x^{2} a^{2} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) x \,a^{3} b -8 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) x^{2} b^{2}-6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) a^{4}+29 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) x a b -83 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) a^{2}+60 \ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) a^{3}-16 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+45 \ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) a \right) \mathrm{csgn}\left(b \right)}{120 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}}+\frac{b \,x^{5}}{5}+\frac{x^{4} a}{4}"," ",0,"1/120*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(24*csgn(b)*x^4*b^4*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+6*csgn(b)*x^3*a*b^3*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-6*csgn(b)*x^2*a^2*b^2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+6*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*x*a^3*b-8*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*x^2*b^2-6*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*a^4+29*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*x*a*b-83*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*a^2+60*ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*a^3-16*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+45*ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*a)*csgn(b)/b^4/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+1/5*b*x^5+1/4*x^4*a","C"
276,1,288,173,0.012000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))*x^2,x)","\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(6 \,\mathrm{csgn}\left(b \right) x^{3} b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 \,\mathrm{csgn}\left(b \right) x^{2} a \,b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-2 \,\mathrm{csgn}\left(b \right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x \,a^{2} b +2 \,\mathrm{csgn}\left(b \right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, a^{3}-3 \,\mathrm{csgn}\left(b \right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x b +13 \,\mathrm{csgn}\left(b \right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, a -12 \ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) a^{2}-3 \ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right)\right) \mathrm{csgn}\left(b \right)}{24 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}}+\frac{b \,x^{4}}{4}+\frac{x^{3} a}{3}"," ",0,"1/24*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(6*csgn(b)*x^3*b^3*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+2*csgn(b)*x^2*a*b^2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-2*csgn(b)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x*a^2*b+2*csgn(b)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*a^3-3*csgn(b)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x*b+13*csgn(b)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*a-12*ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*a^2-3*ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b)))*csgn(b)/b^3/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+1/4*b*x^4+1/3*x^3*a","C"
277,1,194,101,0.009000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))*x,x)","\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) x^{2} b^{2}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) x a b -\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) a^{2}-2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+3 \ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) a \right) \mathrm{csgn}\left(b \right)}{6 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}}+\frac{b \,x^{3}}{3}+\frac{a \,x^{2}}{2}"," ",0,"1/6*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*x^2*b^2+(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*x*a*b-(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*a^2-2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+3*ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*a)*csgn(b)/b^2/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+1/3*b*x^3+1/2*a*x^2","C"
278,1,147,41,0.015000," ","int(b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2),x)","\frac{b \,x^{2}}{2}+a x +\frac{\sqrt{b x +a -1}\, \left(b x +a +1\right)^{\frac{3}{2}}}{2 b}-\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}}{2 b}-\frac{\sqrt{\left(b x +a -1\right) \left(b x +a +1\right)}\, \ln \left(\frac{\frac{\left(a -1\right) b}{2}+\frac{b \left(1+a \right)}{2}+b^{2} x}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+\left(\left(a -1\right) b +b \left(1+a \right)\right) x +\left(a -1\right) \left(1+a \right)}\right)}{2 \sqrt{b x +a +1}\, \sqrt{b x +a -1}\, \sqrt{b^{2}}}"," ",0,"1/2*b*x^2+a*x+1/2/b*(b*x+a-1)^(1/2)*(b*x+a+1)^(3/2)-1/2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)/b-1/2*((b*x+a-1)*(b*x+a+1))^(1/2)/(b*x+a+1)^(1/2)/(b*x+a-1)^(1/2)*ln((1/2*(a-1)*b+1/2*b*(1+a)+b^2*x)/(b^2)^(1/2)+(b^2*x^2+((a-1)*b+b*(1+a))*x+(a-1)*(1+a))^(1/2))/(b^2)^(1/2)","B"
279,1,156,83,0.013000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x,x)","\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(-\mathrm{csgn}\left(b \right) \ln \left(\frac{2 a b x +2 \sqrt{a^{2}-1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 a^{2}-2}{x}\right) \sqrt{a^{2}-1}+\ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) a +\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}}+b x +a \ln \left(x \right)"," ",0,"(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(-csgn(b)*ln(2*(a*b*x+(a^2-1)^(1/2)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+a^2-1)/x)*(a^2-1)^(1/2)+ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*a+(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b))*csgn(b)/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+b*x+a*ln(x)","C"
280,1,237,92,0.016000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^2,x)","\frac{\left(-\mathrm{csgn}\left(b \right) \sqrt{a^{2}-1}\, \ln \left(\frac{2 a b x +2 \sqrt{a^{2}-1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 a^{2}-2}{x}\right) x a b +\ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) x \,a^{2} b -\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right) a^{2}-\ln \left(\left(\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)+b x +a \right) \mathrm{csgn}\left(b \right)\right) x b +\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \mathrm{csgn}\left(b \right)\right) \sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \mathrm{csgn}\left(b \right)}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \left(a^{2}-1\right) x}+b \ln \left(x \right)-\frac{a}{x}"," ",0,"(-csgn(b)*(a^2-1)^(1/2)*ln(2*(a*b*x+(a^2-1)^(1/2)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+a^2-1)/x)*x*a*b+ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*x*a^2*b-(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)*a^2-ln(((b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b)+b*x+a)*csgn(b))*x*b+(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*csgn(b))*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*csgn(b)/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)/(a^2-1)/x+b*ln(x)-a/x","C"
281,1,236,114,0.016000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^3,x)","\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(\sqrt{a^{2}-1}\, \ln \left(\frac{2 a b x +2 \sqrt{a^{2}-1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 a^{2}-2}{x}\right) x^{2} b^{2}-x \,a^{3} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-a^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x a b +2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, a^{2}-\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\right)}{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \left(a^{2}-1\right)^{2} x^{2}}-\frac{b}{x}-\frac{a}{2 x^{2}}"," ",0,"1/2*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*((a^2-1)^(1/2)*ln(2*(a*b*x+(a^2-1)^(1/2)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+a^2-1)/x)*x^2*b^2-x*a^3*b*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-a^4*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x*a*b+2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*a^2-(b^2*x^2+2*a*b*x+a^2-1)^(1/2))/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)/(a^2-1)^2/x^2-b/x-1/2*a/x^2","B"
282,1,374,157,0.014000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^4,x)","-\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(3 \sqrt{a^{2}-1}\, \ln \left(\frac{2 a b x +2 \sqrt{a^{2}-1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 a^{2}-2}{x}\right) x^{3} a \,b^{3}-x^{2} a^{4} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+x \,a^{5} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x^{2} a^{2} b^{2}+2 a^{6} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-2 x \,a^{3} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x^{2} b^{2}-6 a^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x a b +6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, a^{2}-2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\right)}{6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \left(a^{2}-1\right)^{3} x^{3}}-\frac{a}{3 x^{3}}-\frac{b}{2 x^{2}}"," ",0,"-1/6*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(3*(a^2-1)^(1/2)*ln(2*(a*b*x+(a^2-1)^(1/2)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+a^2-1)/x)*x^3*a*b^3-x^2*a^4*b^2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+x*a^5*b*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x^2*a^2*b^2+2*a^6*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-2*x*a^3*b*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x^2*b^2-6*a^4*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x*a*b+6*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*a^2-2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2))/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)/(a^2-1)^3/x^3-1/3*a/x^3-1/2*b/x^2","B"
283,1,603,198,0.016000," ","int((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^5,x)","\frac{\sqrt{b x +a -1}\, \sqrt{b x +a +1}\, \left(12 \sqrt{a^{2}-1}\, \ln \left(\frac{2 a b x +2 \sqrt{a^{2}-1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 a^{2}-2}{x}\right) x^{4} a^{2} b^{4}-2 x^{3} a^{5} b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 x^{2} a^{6} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+3 \sqrt{a^{2}-1}\, \ln \left(\frac{2 a b x +2 \sqrt{a^{2}-1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 a^{2}-2}{x}\right) x^{4} b^{4}-11 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x^{3} a^{3} b^{3}-2 x \,a^{7} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-x^{2} a^{4} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-6 a^{8} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+13 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x^{3} a \,b^{3}+6 x \,a^{5} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x^{2} a^{2} b^{2}+24 a^{6} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}-6 x \,a^{3} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+3 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x^{2} b^{2}-36 a^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}+2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, x a b +24 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, a^{2}-6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\right)}{24 \sqrt{b^{2} x^{2}+2 a b x +a^{2}-1}\, \left(a^{2}-1\right)^{4} x^{4}}-\frac{b}{3 x^{3}}-\frac{a}{4 x^{4}}"," ",0,"1/24*(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2)*(12*(a^2-1)^(1/2)*ln(2*(a*b*x+(a^2-1)^(1/2)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+a^2-1)/x)*x^4*a^2*b^4-2*x^3*a^5*b^3*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+2*x^2*a^6*b^2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+3*(a^2-1)^(1/2)*ln(2*(a*b*x+(a^2-1)^(1/2)*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+a^2-1)/x)*x^4*b^4-11*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x^3*a^3*b^3-2*x*a^7*b*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-x^2*a^4*b^2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-6*a^8*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+13*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x^3*a*b^3+6*x*a^5*b*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-4*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x^2*a^2*b^2+24*a^6*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)-6*x*a^3*b*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+3*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x^2*b^2-36*a^4*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)+2*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*x*a*b+24*(b^2*x^2+2*a*b*x+a^2-1)^(1/2)*a^2-6*(b^2*x^2+2*a*b*x+a^2-1)^(1/2))/(b^2*x^2+2*a*b*x+a^2-1)^(1/2)/(a^2-1)^4/x^4-1/3*b/x^3-1/4*a/x^4","B"
284,0,0,265,0.010000," ","int(exp(arccosh(b*x+a)^2)*x^3,x)","\int {\mathrm e}^{\mathrm{arccosh}\left(b x +a \right)^{2}} x^{3}\, dx"," ",0,"int(exp(arccosh(b*x+a)^2)*x^3,x)","F"
285,0,0,175,0.008000," ","int(exp(arccosh(b*x+a)^2)*x^2,x)","\int {\mathrm e}^{\mathrm{arccosh}\left(b x +a \right)^{2}} x^{2}\, dx"," ",0,"int(exp(arccosh(b*x+a)^2)*x^2,x)","F"
286,0,0,85,0.007000," ","int(exp(arccosh(b*x+a)^2)*x,x)","\int {\mathrm e}^{\mathrm{arccosh}\left(b x +a \right)^{2}} x\, dx"," ",0,"int(exp(arccosh(b*x+a)^2)*x,x)","F"
287,0,0,43,0.003000," ","int(exp(arccosh(b*x+a)^2),x)","\int {\mathrm e}^{\mathrm{arccosh}\left(b x +a \right)^{2}}\, dx"," ",0,"int(exp(arccosh(b*x+a)^2),x)","F"
288,0,0,15,0.007000," ","int(exp(arccosh(b*x+a)^2)/x,x)","\int \frac{{\mathrm e}^{\mathrm{arccosh}\left(b x +a \right)^{2}}}{x}\, dx"," ",0,"int(exp(arccosh(b*x+a)^2)/x,x)","F"
289,0,0,15,0.007000," ","int(exp(arccosh(b*x+a)^2)/x^2,x)","\int \frac{{\mathrm e}^{\mathrm{arccosh}\left(b x +a \right)^{2}}}{x^{2}}\, dx"," ",0,"int(exp(arccosh(b*x+a)^2)/x^2,x)","F"
290,1,85,84,0.065000," ","int(arccosh(b*x+a)/(a*d/b+d*x),x)","-\frac{\mathrm{arccosh}\left(b x +a \right)^{2}}{2 d}+\frac{\mathrm{arccosh}\left(b x +a \right) \ln \left(1+\left(b x +a +\sqrt{b x +a -1}\, \sqrt{b x +a +1}\right)^{2}\right)}{d}+\frac{\polylog \left(2, -\left(b x +a +\sqrt{b x +a -1}\, \sqrt{b x +a +1}\right)^{2}\right)}{2 d}"," ",0,"-1/2*arccosh(b*x+a)^2/d+arccosh(b*x+a)*ln(1+(b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))^2)/d+1/2*polylog(2,-(b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))^2)/d","A"
291,1,78,3,0.422000," ","int(x/arccosh(x)/(-1+x)^(1/2)/(1+x)^(1/2),x)","-\frac{\sqrt{-2+2 x}\, \sqrt{2+2 x}\, \sqrt{-1+x}\, \sqrt{1+x}\, \Ei \left(1, \mathrm{arccosh}\left(x \right)\right)}{4 \left(x^{2}-1\right)}-\frac{\sqrt{-2+2 x}\, \sqrt{2+2 x}\, \sqrt{-1+x}\, \sqrt{1+x}\, \Ei \left(1, -\mathrm{arccosh}\left(x \right)\right)}{4 \left(x^{2}-1\right)}"," ",0,"-1/4*(-2+2*x)^(1/2)*(2+2*x)^(1/2)*(-1+x)^(1/2)*(1+x)^(1/2)*Ei(1,arccosh(x))/(x^2-1)-1/4*(-2+2*x)^(1/2)*(2+2*x)^(1/2)*(-1+x)^(1/2)*(1+x)^(1/2)*Ei(1,-arccosh(x))/(x^2-1)","B"
292,1,45,46,0.003000," ","int(x^3*arccosh(b*x^4+a),x)","\frac{\left(b \,x^{4}+a \right) \mathrm{arccosh}\left(b \,x^{4}+a \right)-\sqrt{b \,x^{4}+a -1}\, \sqrt{b \,x^{4}+a +1}}{4 b}"," ",0,"1/4/b*((b*x^4+a)*arccosh(b*x^4+a)-(b*x^4+a-1)^(1/2)*(b*x^4+a+1)^(1/2))","A"
293,0,0,51,0.043000," ","int(x^(-1+n)*arccosh(a+b*x^n),x)","\int x^{-1+n} \mathrm{arccosh}\left(a +b \,x^{n}\right)\, dx"," ",0,"int(x^(-1+n)*arccosh(a+b*x^n),x)","F"
294,1,91,56,0.049000," ","int(arccosh(c/(b*x+a)),x)","\mathrm{arccosh}\left(\frac{c}{b x +a}\right) x +\frac{\mathrm{arccosh}\left(\frac{c}{b x +a}\right) a}{b}+\frac{c \sqrt{\frac{c}{b x +a}-1}\, \sqrt{\frac{c}{b x +a}+1}\, \arctan \left(\frac{1}{\sqrt{\frac{c^{2}}{\left(b x +a \right)^{2}}-1}}\right)}{b \sqrt{\frac{c^{2}}{\left(b x +a \right)^{2}}-1}}"," ",0,"arccosh(c/(b*x+a))*x+1/b*arccosh(c/(b*x+a))*a+1/b*c*(c/(b*x+a)-1)^(1/2)*(c/(b*x+a)+1)^(1/2)/(c^2/(b*x+a)^2-1)^(1/2)*arctan(1/(c^2/(b*x+a)^2-1)^(1/2))","A"
295,0,0,52,0.304000," ","int(arccosh((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x)","\int \frac{\mathrm{arccosh}\left(\sqrt{b \,x^{2}+1}\right)^{n}}{\sqrt{b \,x^{2}+1}}\, dx"," ",0,"int(arccosh((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x)","F"
296,0,0,44,0.278000," ","int(1/arccosh((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x)","\int \frac{1}{\mathrm{arccosh}\left(\sqrt{b \,x^{2}+1}\right) \sqrt{b \,x^{2}+1}}\, dx"," ",0,"int(1/arccosh((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x)","F"