1,1,263,196,0.129000," ","int(arcsinh(c*x)/(e*x+d),x)","-\frac{\arcsinh \left(c x \right)^{2}}{2 e}+\frac{\arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+1}\right) e -c d +\sqrt{c^{2} d^{2}+e^{2}}}{-c d +\sqrt{c^{2} d^{2}+e^{2}}}\right)}{e}+\frac{\arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^{2} x^{2}+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^{2} x^{2}+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*arcsinh(c*x)^2/e+1/e*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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^2*x^2+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^2*x^2+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"
2,0,0,300,0.203000," ","int(arcsinh(c*x)^2/(e*x+d),x)","\int \frac{\arcsinh \left(c x \right)^{2}}{e x +d}\, dx"," ",0,"int(arcsinh(c*x)^2/(e*x+d),x)","F"
3,0,0,402,0.183000," ","int(arcsinh(c*x)^3/(e*x+d),x)","\int \frac{\arcsinh \left(c x \right)^{3}}{e x +d}\, dx"," ",0,"int(arcsinh(c*x)^3/(e*x+d),x)","F"
4,1,259,160,0.009000," ","int((e*x+d)^3*(a+b*arcsinh(c*x)),x)","\frac{\frac{\left(c e x +c d \right)^{4} a}{4 c^{3} e}+\frac{b \left(\frac{e^{3} \arcsinh \left(c x \right) c^{4} x^{4}}{4}+e^{2} \arcsinh \left(c x \right) c^{4} x^{3} d +\frac{3 e \arcsinh \left(c x \right) c^{4} x^{2} d^{2}}{2}+\arcsinh \left(c x \right) c^{4} x \,d^{3}+\frac{\arcsinh \left(c x \right) c^{4} d^{4}}{4 e}-\frac{e^{4} \left(\frac{c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{c^{2} x^{2}+1}}{8}+\frac{3 \arcsinh \left(c x \right)}{8}\right)+4 c d \,e^{3} \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)+6 c^{2} d^{2} e^{2} \left(\frac{c x \sqrt{c^{2} x^{2}+1}}{2}-\frac{\arcsinh \left(c x \right)}{2}\right)+4 c^{3} d^{3} e \sqrt{c^{2} x^{2}+1}+c^{4} d^{4} \arcsinh \left(c x \right)}{4 e}\right)}{c^{3}}}{c}"," ",0,"1/c*(1/4*(c*e*x+c*d)^4*a/c^3/e+b/c^3*(1/4*e^3*arcsinh(c*x)*c^4*x^4+e^2*arcsinh(c*x)*c^4*x^3*d+3/2*e*arcsinh(c*x)*c^4*x^2*d^2+arcsinh(c*x)*c^4*x*d^3+1/4/e*arcsinh(c*x)*c^4*d^4-1/4/e*(e^4*(1/4*c^3*x^3*(c^2*x^2+1)^(1/2)-3/8*c*x*(c^2*x^2+1)^(1/2)+3/8*arcsinh(c*x))+4*c*d*e^3*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))+6*c^2*d^2*e^2*(1/2*c*x*(c^2*x^2+1)^(1/2)-1/2*arcsinh(c*x))+4*c^3*d^3*e*(c^2*x^2+1)^(1/2)+c^4*d^4*arcsinh(c*x))))","A"
5,1,189,109,0.006000," ","int((e*x+d)^2*(a+b*arcsinh(c*x)),x)","\frac{\frac{\left(c e x +c d \right)^{3} a}{3 c^{2} e}+\frac{b \left(\frac{e^{2} \arcsinh \left(c x \right) c^{3} x^{3}}{3}+e \arcsinh \left(c x \right) c^{3} x^{2} d +\arcsinh \left(c x \right) c^{3} x \,d^{2}+\frac{\arcsinh \left(c x \right) c^{3} d^{3}}{3 e}-\frac{e^{3} \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)+3 c d \,e^{2} \left(\frac{c x \sqrt{c^{2} x^{2}+1}}{2}-\frac{\arcsinh \left(c x \right)}{2}\right)+3 c^{2} d^{2} e \sqrt{c^{2} x^{2}+1}+c^{3} d^{3} \arcsinh \left(c x \right)}{3 e}\right)}{c^{2}}}{c}"," ",0,"1/c*(1/3*(c*e*x+c*d)^3*a/c^2/e+b/c^2*(1/3*e^2*arcsinh(c*x)*c^3*x^3+e*arcsinh(c*x)*c^3*x^2*d+arcsinh(c*x)*c^3*x*d^2+1/3/e*arcsinh(c*x)*c^3*d^3-1/3/e*(e^3*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))+3*c*d*e^2*(1/2*c*x*(c^2*x^2+1)^(1/2)-1/2*arcsinh(c*x))+3*c^2*d^2*e*(c^2*x^2+1)^(1/2)+c^3*d^3*arcsinh(c*x))))","A"
6,1,96,85,0.007000," ","int((e*x+d)*(a+b*arcsinh(c*x)),x)","\frac{\frac{a \left(\frac{1}{2} c^{2} x^{2} e +c^{2} d x \right)}{c}+\frac{b \left(\frac{\arcsinh \left(c x \right) c^{2} x^{2} e}{2}+\arcsinh \left(c x \right) c^{2} x d -\frac{e \left(\frac{c x \sqrt{c^{2} x^{2}+1}}{2}-\frac{\arcsinh \left(c x \right)}{2}\right)}{2}-c d \sqrt{c^{2} x^{2}+1}\right)}{c}}{c}"," ",0,"1/c*(a/c*(1/2*c^2*x^2*e+c^2*d*x)+b/c*(1/2*arcsinh(c*x)*c^2*x^2*e+arcsinh(c*x)*c^2*x*d-1/2*e*(1/2*c*x*(c^2*x^2+1)^(1/2)-1/2*arcsinh(c*x))-c*d*(c^2*x^2+1)^(1/2)))","A"
7,1,31,28,0.006000," ","int(a+b*arcsinh(c*x),x)","a x +\frac{b \left(\arcsinh \left(c x \right) c x -\sqrt{c^{2} x^{2}+1}\right)}{c}"," ",0,"a*x+b/c*(arcsinh(c*x)*c*x-(c^2*x^2+1)^(1/2))","A"
8,1,282,213,0.044000," ","int((a+b*arcsinh(c*x))/(e*x+d),x)","\frac{a \ln \left(c e x +c d \right)}{e}-\frac{b \arcsinh \left(c x \right)^{2}}{2 e}+\frac{b \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+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 \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^{2} x^{2}+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^{2} x^{2}+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*arcsinh(c*x)^2/e+b/e*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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^2*x^2+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^2*x^2+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"
9,1,178,78,0.017000," ","int((a+b*arcsinh(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c e x +c d \right) e}-\frac{c b \arcsinh \left(c x \right)}{\left(c e x +c d \right) e}-\frac{c b \ln \left(\frac{\frac{2 c^{2} d^{2}+2 e^{2}}{e^{2}}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{c x +\frac{c d}{e}}\right)}{e^{2} \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arcsinh(c*x)-c*b/e^2/((c^2*d^2+e^2)/e^2)^(1/2)*ln((2*(c^2*d^2+e^2)/e^2-2*c*d/e*(c*x+c*d/e)+2*((c^2*d^2+e^2)/e^2)^(1/2)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2))/(c*x+c*d/e))","B"
10,1,279,117,0.062000," ","int((a+b*arcsinh(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c e x +c d \right)^{2} e}-\frac{c^{2} b \arcsinh \left(c x \right)}{2 \left(c e x +c d \right)^{2} e}-\frac{c^{2} b \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{2 e \left(c^{2} d^{2}+e^{2}\right) \left(c x +\frac{c d}{e}\right)}-\frac{c^{3} b d \ln \left(\frac{\frac{2 c^{2} d^{2}+2 e^{2}}{e^{2}}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{c x +\frac{c d}{e}}\right)}{2 e^{2} \left(c^{2} d^{2}+e^{2}\right) \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}"," ",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*arcsinh(c*x)-1/2*c^2*b/e/(c^2*d^2+e^2)/(c*x+c*d/e)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2)-1/2*c^3*b/e^2*d/(c^2*d^2+e^2)/((c^2*d^2+e^2)/e^2)^(1/2)*ln((2*(c^2*d^2+e^2)/e^2-2*c*d/e*(c*x+c*d/e)+2*((c^2*d^2+e^2)/e^2)^(1/2)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2))/(c*x+c*d/e))","B"
11,1,516,168,0.013000," ","int((a+b*arcsinh(c*x))/(e*x+d)^4,x)","-\frac{c^{3} a}{3 \left(c e x +c d \right)^{3} e}-\frac{c^{3} b \arcsinh \left(c x \right)}{3 \left(c e x +c d \right)^{3} e}-\frac{c^{3} b \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{6 e^{2} \left(c^{2} d^{2}+e^{2}\right) \left(c x +\frac{c d}{e}\right)^{2}}-\frac{c^{4} b d \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{2 e \left(c^{2} d^{2}+e^{2}\right)^{2} \left(c x +\frac{c d}{e}\right)}-\frac{c^{5} b \,d^{2} \ln \left(\frac{\frac{2 c^{2} d^{2}+2 e^{2}}{e^{2}}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{c x +\frac{c d}{e}}\right)}{2 e^{2} \left(c^{2} d^{2}+e^{2}\right)^{2} \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}+\frac{c^{3} b \ln \left(\frac{\frac{2 c^{2} d^{2}+2 e^{2}}{e^{2}}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{c x +\frac{c d}{e}}\right)}{6 e^{2} \left(c^{2} d^{2}+e^{2}\right) \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{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*arcsinh(c*x)-1/6*c^3*b/e^2/(c^2*d^2+e^2)/(c*x+c*d/e)^2*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2)-1/2*c^4*b/e*d/(c^2*d^2+e^2)^2/(c*x+c*d/e)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2)-1/2*c^5*b/e^2*d^2/(c^2*d^2+e^2)^2/((c^2*d^2+e^2)/e^2)^(1/2)*ln((2*(c^2*d^2+e^2)/e^2-2*c*d/e*(c*x+c*d/e)+2*((c^2*d^2+e^2)/e^2)^(1/2)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2))/(c*x+c*d/e))+1/6*c^3*b/e^2/(c^2*d^2+e^2)/((c^2*d^2+e^2)/e^2)^(1/2)*ln((2*(c^2*d^2+e^2)/e^2-2*c*d/e*(c*x+c*d/e)+2*((c^2*d^2+e^2)/e^2)^(1/2)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2))/(c*x+c*d/e))","B"
12,1,641,328,0.122000," ","int((e*x+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{\frac{\left(c e x +c d \right)^{4} a^{2}}{4 c^{3} e}+\frac{b^{2} \left(c^{3} d^{3} \left(\arcsinh \left(c x \right)^{2} c x -2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 c x \right)+\frac{3 c^{2} d^{2} e \left(2 \arcsinh \left(c x \right)^{2} c^{2} x^{2}-2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x +\arcsinh \left(c x \right)^{2}+c^{2} x^{2}+1\right)}{4}+\frac{c d \,e^{2} \left(9 \arcsinh \left(c x \right)^{2} c^{3} x^{3}-6 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2} x^{2}+27 \arcsinh \left(c x \right)^{2} c x +2 c^{3} x^{3}-42 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+42 c x \right)}{9}+\frac{e^{3} \left(8 \arcsinh \left(c x \right)^{2} c^{4} x^{4}-4 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3} x^{3}+16 \arcsinh \left(c x \right)^{2} c^{2} x^{2}+c^{4} x^{4}-10 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x +5 \arcsinh \left(c x \right)^{2}+5 c^{2} x^{2}+4\right)}{32}-3 c d \,e^{2} \left(\arcsinh \left(c x \right)^{2} c x -2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 c x \right)-\frac{e^{3} \left(2 \arcsinh \left(c x \right)^{2} c^{2} x^{2}-2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x +\arcsinh \left(c x \right)^{2}+c^{2} x^{2}+1\right)}{4}\right)}{c^{3}}+\frac{2 a b \left(\frac{e^{3} \arcsinh \left(c x \right) c^{4} x^{4}}{4}+e^{2} \arcsinh \left(c x \right) c^{4} x^{3} d +\frac{3 e \arcsinh \left(c x \right) c^{4} x^{2} d^{2}}{2}+\arcsinh \left(c x \right) c^{4} x \,d^{3}+\frac{\arcsinh \left(c x \right) c^{4} d^{4}}{4 e}-\frac{e^{4} \left(\frac{c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{c^{2} x^{2}+1}}{8}+\frac{3 \arcsinh \left(c x \right)}{8}\right)+4 c d \,e^{3} \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)+6 c^{2} d^{2} e^{2} \left(\frac{c x \sqrt{c^{2} x^{2}+1}}{2}-\frac{\arcsinh \left(c x \right)}{2}\right)+4 c^{3} d^{3} e \sqrt{c^{2} x^{2}+1}+c^{4} d^{4} \arcsinh \left(c x \right)}{4 e}\right)}{c^{3}}}{c}"," ",0,"1/c*(1/4*(c*e*x+c*d)^4*a^2/c^3/e+b^2/c^3*(c^3*d^3*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+3/4*c^2*d^2*e*(2*arcsinh(c*x)^2*c^2*x^2-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+arcsinh(c*x)^2+c^2*x^2+1)+1/9*c*d*e^2*(9*arcsinh(c*x)^2*c^3*x^3-6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2*x^2+27*arcsinh(c*x)^2*c*x+2*c^3*x^3-42*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+42*c*x)+1/32*e^3*(8*arcsinh(c*x)^2*c^4*x^4-4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3*x^3+16*arcsinh(c*x)^2*c^2*x^2+c^4*x^4-10*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+5*arcsinh(c*x)^2+5*c^2*x^2+4)-3*c*d*e^2*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)-1/4*e^3*(2*arcsinh(c*x)^2*c^2*x^2-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+arcsinh(c*x)^2+c^2*x^2+1))+2*a*b/c^3*(1/4*e^3*arcsinh(c*x)*c^4*x^4+e^2*arcsinh(c*x)*c^4*x^3*d+3/2*e*arcsinh(c*x)*c^4*x^2*d^2+arcsinh(c*x)*c^4*x*d^3+1/4/e*arcsinh(c*x)*c^4*d^4-1/4/e*(e^4*(1/4*c^3*x^3*(c^2*x^2+1)^(1/2)-3/8*c*x*(c^2*x^2+1)^(1/2)+3/8*arcsinh(c*x))+4*c*d*e^3*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))+6*c^2*d^2*e^2*(1/2*c*x*(c^2*x^2+1)^(1/2)-1/2*arcsinh(c*x))+4*c^3*d^3*e*(c^2*x^2+1)^(1/2)+c^4*d^4*arcsinh(c*x))))","A"
13,1,410,215,0.094000," ","int((e*x+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{\frac{\left(c e x +c d \right)^{3} a^{2}}{3 c^{2} e}+\frac{b^{2} \left(c^{2} d^{2} \left(\arcsinh \left(c x \right)^{2} c x -2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 c x \right)+\frac{c d e \left(2 \arcsinh \left(c x \right)^{2} c^{2} x^{2}-2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x +\arcsinh \left(c x \right)^{2}+c^{2} x^{2}+1\right)}{2}+\frac{e^{2} \left(9 \arcsinh \left(c x \right)^{2} c^{3} x^{3}-6 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2} x^{2}+27 \arcsinh \left(c x \right)^{2} c x +2 c^{3} x^{3}-42 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+42 c x \right)}{27}-e^{2} \left(\arcsinh \left(c x \right)^{2} c x -2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 c x \right)\right)}{c^{2}}+\frac{2 a b \left(\frac{e^{2} \arcsinh \left(c x \right) c^{3} x^{3}}{3}+e \arcsinh \left(c x \right) c^{3} x^{2} d +\arcsinh \left(c x \right) c^{3} x \,d^{2}+\frac{\arcsinh \left(c x \right) c^{3} d^{3}}{3 e}-\frac{e^{3} \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)+3 c d \,e^{2} \left(\frac{c x \sqrt{c^{2} x^{2}+1}}{2}-\frac{\arcsinh \left(c x \right)}{2}\right)+3 c^{2} d^{2} e \sqrt{c^{2} x^{2}+1}+c^{3} d^{3} \arcsinh \left(c x \right)}{3 e}\right)}{c^{2}}}{c}"," ",0,"1/c*(1/3*(c*e*x+c*d)^3*a^2/c^2/e+b^2/c^2*(c^2*d^2*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+1/2*c*d*e*(2*arcsinh(c*x)^2*c^2*x^2-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+arcsinh(c*x)^2+c^2*x^2+1)+1/27*e^2*(9*arcsinh(c*x)^2*c^3*x^3-6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2*x^2+27*arcsinh(c*x)^2*c*x+2*c^3*x^3-42*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+42*c*x)-e^2*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x))+2*a*b/c^2*(1/3*e^2*arcsinh(c*x)*c^3*x^3+e*arcsinh(c*x)*c^3*x^2*d+arcsinh(c*x)*c^3*x*d^2+1/3/e*arcsinh(c*x)*c^3*d^3-1/3/e*(e^3*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))+3*c*d*e^2*(1/2*c*x*(c^2*x^2+1)^(1/2)-1/2*arcsinh(c*x))+3*c^2*d^2*e*(c^2*x^2+1)^(1/2)+c^3*d^3*arcsinh(c*x))))","A"
14,1,193,126,0.070000," ","int((e*x+d)*(a+b*arcsinh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{2} c^{2} x^{2} e +c^{2} d x \right)}{c}+\frac{b^{2} \left(\frac{e \left(2 \arcsinh \left(c x \right)^{2} c^{2} x^{2}-2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x +\arcsinh \left(c x \right)^{2}+c^{2} x^{2}+1\right)}{4}+c d \left(\arcsinh \left(c x \right)^{2} c x -2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 c x \right)\right)}{c}+\frac{2 a b \left(\frac{\arcsinh \left(c x \right) c^{2} x^{2} e}{2}+\arcsinh \left(c x \right) c^{2} x d -\frac{e \left(\frac{c x \sqrt{c^{2} x^{2}+1}}{2}-\frac{\arcsinh \left(c x \right)}{2}\right)}{2}-c d \sqrt{c^{2} x^{2}+1}\right)}{c}}{c}"," ",0,"1/c*(a^2/c*(1/2*c^2*x^2*e+c^2*d*x)+b^2/c*(1/4*e*(2*arcsinh(c*x)^2*c^2*x^2-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+arcsinh(c*x)^2+c^2*x^2+1)+c*d*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x))+2*a*b/c*(1/2*arcsinh(c*x)*c^2*x^2*e+arcsinh(c*x)*c^2*x*d-1/2*e*(1/2*c*x*(c^2*x^2+1)^(1/2)-1/2*arcsinh(c*x))-c*d*(c^2*x^2+1)^(1/2)))","A"
15,1,72,44,0.000000," ","int((a+b*arcsinh(c*x))^2,x)","\frac{a^{2} c x +b^{2} \left(\arcsinh \left(c x \right)^{2} c x -2 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 c x \right)+2 a b \left(\arcsinh \left(c x \right) c x -\sqrt{c^{2} x^{2}+1}\right)}{c}"," ",0,"1/c*(a^2*c*x+b^2*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+2*a*b*(arcsinh(c*x)*c*x-(c^2*x^2+1)^(1/2)))","A"
16,0,0,331,0.030000," ","int((a+b*arcsinh(c*x))^2/(e*x+d),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{e x +d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(e*x+d),x)","F"
17,1,529,283,0.344000," ","int((a+b*arcsinh(c*x))^2/(e*x+d)^2,x)","-\frac{c \,a^{2}}{\left(c e x +c d \right) e}-\frac{c \,b^{2} \arcsinh \left(c x \right)^{2}}{e \left(c e x +c d \right)}+\frac{2 c \,b^{2} \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+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} \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^{2} x^{2}+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^{2} x^{2}+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 \arcsinh \left(c x \right)}{\left(c e x +c d \right) e}-\frac{2 c a b \ln \left(\frac{\frac{2 c^{2} d^{2}+2 e^{2}}{e^{2}}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{c x +\frac{c d}{e}}\right)}{e^{2} \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}"," ",0,"-c*a^2/(c*e*x+c*d)/e-c*b^2*arcsinh(c*x)^2/e/(c*e*x+c*d)+2*c*b^2/e*arcsinh(c*x)/(c^2*d^2+e^2)^(1/2)*ln((-(c*x+(c^2*x^2+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*arcsinh(c*x)/(c^2*d^2+e^2)^(1/2)*ln(((c*x+(c^2*x^2+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^2*x^2+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^2*x^2+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*arcsinh(c*x)-2*c*a*b/e^2/((c^2*d^2+e^2)/e^2)^(1/2)*ln((2*(c^2*d^2+e^2)/e^2-2*c*d/e*(c*x+c*d/e)+2*((c^2*d^2+e^2)/e^2)^(1/2)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2))/(c*x+c*d/e))","A"
18,1,1013,365,0.667000," ","int((a+b*arcsinh(c*x))^2/(e*x+d)^3,x)","-\frac{c^{2} a^{2}}{2 \left(c e x +c d \right)^{2} e}-\frac{c^{4} b^{2} \arcsinh \left(c x \right)^{2} d^{2}}{2 e \left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}-\frac{c^{3} b^{2} \arcsinh \left(c x \right) e \sqrt{c^{2} x^{2}+1}\, x}{\left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}-\frac{c^{3} b^{2} \arcsinh \left(c x \right) d \sqrt{c^{2} x^{2}+1}}{\left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}+\frac{c^{4} b^{2} \arcsinh \left(c x \right) e \,x^{2}}{\left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}+\frac{2 c^{4} b^{2} \arcsinh \left(c x \right) d x}{\left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}+\frac{c^{4} b^{2} \arcsinh \left(c x \right) d^{2}}{e \left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}-\frac{c^{2} b^{2} \arcsinh \left(c x \right)^{2} e}{2 \left(c e x +c d \right)^{2} \left(c^{2} d^{2}+e^{2}\right)}-\frac{2 c^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{e \left(c^{2} d^{2}+e^{2}\right)}+\frac{c^{2} b^{2} \ln \left(2 c d \left(c x +\sqrt{c^{2} x^{2}+1}\right)+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2} e -e \right)}{e \left(c^{2} d^{2}+e^{2}\right)}+\frac{c^{3} b^{2} d \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+1}\right) e -c d +\sqrt{c^{2} d^{2}+e^{2}}}{-c d +\sqrt{c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}+e^{2}\right)^{\frac{3}{2}}}-\frac{c^{3} b^{2} d \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e +c d +\sqrt{c^{2} d^{2}+e^{2}}}{c d +\sqrt{c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}+e^{2}\right)^{\frac{3}{2}}}+\frac{c^{3} b^{2} d \dilog \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+1}\right) e -c d +\sqrt{c^{2} d^{2}+e^{2}}}{-c d +\sqrt{c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}+e^{2}\right)^{\frac{3}{2}}}-\frac{c^{3} b^{2} d \dilog \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e +c d +\sqrt{c^{2} d^{2}+e^{2}}}{c d +\sqrt{c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}+e^{2}\right)^{\frac{3}{2}}}-\frac{c^{2} a b \arcsinh \left(c x \right)}{\left(c e x +c d \right)^{2} e}-\frac{c^{2} a b \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{e \left(c^{2} d^{2}+e^{2}\right) \left(c x +\frac{c d}{e}\right)}-\frac{c^{3} a b d \ln \left(\frac{\frac{2 c^{2} d^{2}+2 e^{2}}{e^{2}}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \sqrt{\left(c x +\frac{c d}{e}\right)^{2}-\frac{2 c d \left(c x +\frac{c d}{e}\right)}{e}+\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}{c x +\frac{c d}{e}}\right)}{e^{2} \left(c^{2} d^{2}+e^{2}\right) \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}"," ",0,"-1/2*c^2*a^2/(c*e*x+c*d)^2/e-1/2*c^4*b^2*arcsinh(c*x)^2/e/(c*e*x+c*d)^2/(c^2*d^2+e^2)*d^2-c^3*b^2*arcsinh(c*x)*e/(c*e*x+c*d)^2/(c^2*d^2+e^2)*(c^2*x^2+1)^(1/2)*x-c^3*b^2*arcsinh(c*x)/(c*e*x+c*d)^2/(c^2*d^2+e^2)*d*(c^2*x^2+1)^(1/2)+c^4*b^2*arcsinh(c*x)*e/(c*e*x+c*d)^2/(c^2*d^2+e^2)*x^2+2*c^4*b^2*arcsinh(c*x)/(c*e*x+c*d)^2/(c^2*d^2+e^2)*d*x+c^4*b^2*arcsinh(c*x)/e/(c*e*x+c*d)^2/(c^2*d^2+e^2)*d^2-1/2*c^2*b^2*arcsinh(c*x)^2*e/(c*e*x+c*d)^2/(c^2*d^2+e^2)-2*c^2*b^2/e/(c^2*d^2+e^2)*ln(c*x+(c^2*x^2+1)^(1/2))+c^2*b^2/e/(c^2*d^2+e^2)*ln(2*c*d*(c*x+(c^2*x^2+1)^(1/2))+(c*x+(c^2*x^2+1)^(1/2))^2*e-e)+c^3*b^2/e/(c^2*d^2+e^2)^(3/2)*d*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+1)^(1/2))*e-c*d+(c^2*d^2+e^2)^(1/2))/(-c*d+(c^2*d^2+e^2)^(1/2)))-c^3*b^2/e/(c^2*d^2+e^2)^(3/2)*d*arcsinh(c*x)*ln(((c*x+(c^2*x^2+1)^(1/2))*e+c*d+(c^2*d^2+e^2)^(1/2))/(c*d+(c^2*d^2+e^2)^(1/2)))+c^3*b^2/e/(c^2*d^2+e^2)^(3/2)*d*dilog((-(c*x+(c^2*x^2+1)^(1/2))*e-c*d+(c^2*d^2+e^2)^(1/2))/(-c*d+(c^2*d^2+e^2)^(1/2)))-c^3*b^2/e/(c^2*d^2+e^2)^(3/2)*d*dilog(((c*x+(c^2*x^2+1)^(1/2))*e+c*d+(c^2*d^2+e^2)^(1/2))/(c*d+(c^2*d^2+e^2)^(1/2)))-c^2*a*b/(c*e*x+c*d)^2/e*arcsinh(c*x)-c^2*a*b/e/(c^2*d^2+e^2)/(c*x+c*d/e)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2)-c^3*a*b/e^2*d/(c^2*d^2+e^2)/((c^2*d^2+e^2)/e^2)^(1/2)*ln((2*(c^2*d^2+e^2)/e^2-2*c*d/e*(c*x+c*d/e)+2*((c^2*d^2+e^2)/e^2)^(1/2)*((c*x+c*d/e)^2-2*c*d/e*(c*x+c*d/e)+(c^2*d^2+e^2)/e^2)^(1/2))/(c*x+c*d/e))","B"
19,1,394,374,0.480000," ","int((e*x+d)^3/(a+b*arcsinh(c*x)),x)","\frac{-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \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 \arcsinh \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 \arcsinh \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 \arcsinh \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 \arcsinh \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 \arcsinh \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 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{8 c^{2} b}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) d^{3}}{2 b}+\frac{3 d \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) e^{2}}{8 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) d^{3}}{2 b}+\frac{3 d \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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 \arcsinh \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*arcsinh(c*x)-4*a/b)+1/16/c^3*e^3/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+3/4/c*e/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)*d^2-1/8/c^3*e^3/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-3/4/c*e/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*d^2+1/8/c^3*e^3/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)-3/8/c^2*d*e^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-1/2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d^3+3/8/c^2*d/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*e^2-1/2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d^3+3/8/c^2*d/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*e^2-3/8/c^2*d*e^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b))","A"
20,1,254,237,0.323000," ","int((e*x+d)^2/(a+b*arcsinh(c*x)),x)","\frac{-\frac{e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \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 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{8 c^{2} b}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) d^{2}}{2 b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) e^{2}}{8 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) d^{2}}{2 b}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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 \arcsinh \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 \arcsinh \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*arcsinh(c*x)-3*a/b)-1/8/c^2*e^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d^2+1/8/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*e^2-1/2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d^2+1/8/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*e^2-1/2/c*d*e/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)+1/2/c*d*e/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b))","A"
21,1,120,112,0.225000," ","int((e*x+d)/(a+b*arcsinh(c*x)),x)","\frac{-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) d}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) d}{2 b}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{4 c b}+\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{4 c b}}{c}"," ",0,"1/c*(-1/2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d-1/2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d-1/4/c*e/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)+1/4/c*e/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b))","A"
22,1,56,54,0.000000," ","int(1/(a+b*arcsinh(c*x)),x)","\frac{-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{2 b}}{c}"," ",0,"1/c*(-1/2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b))","A"
23,0,0,20,0.205000," ","int(1/(e*x+d)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(e x +d \right) \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arcsinh(c*x)),x)","F"
24,0,0,20,0.408000," ","int(1/(e*x+d)^2/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)^2/(a+b*arcsinh(c*x)),x)","F"
25,1,616,345,0.377000," ","int((e*x+d)^2/(a+b*arcsinh(c*x))^2,x)","\frac{\frac{\left(4 c^{3} x^{3}-4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+3 c x -\sqrt{c^{2} x^{2}+1}\right) e^{2}}{8 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \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 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+\sqrt{c^{2} x^{2}+1}\right)}{8 b \,c^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{8 b^{2} c^{2}}+\frac{\left(c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{2 b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{d^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{2 b^{2}}-\frac{\left(c x -\sqrt{c^{2} x^{2}+1}\right) e^{2}}{8 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{8 c^{2} b^{2}}-\frac{d^{2} \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{2 b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{d^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{2 b^{2}}+\frac{e^{2} \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{8 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{8 c^{2} b^{2}}+\frac{\left(2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1\right) d e}{2 c \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{e d \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{c \,b^{2}}-\frac{e d \left(2 c^{2} x^{2}+1+2 c x \sqrt{c^{2} x^{2}+1}\right)}{2 b c \left(a +b \arcsinh \left(c x \right)\right)}-\frac{e d \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{b^{2} c}}{c}"," ",0,"1/c*(1/8*(4*c^3*x^3-4*c^2*x^2*(c^2*x^2+1)^(1/2)+3*c*x-(c^2*x^2+1)^(1/2))*e^2/c^2/b/(a+b*arcsinh(c*x))+3/8*e^2/c^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/8/b*e^2/c^2*(4*c^3*x^3+3*c*x+4*c^2*x^2*(c^2*x^2+1)^(1/2)+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-3/8/b^2*e^2/c^2*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)+1/2*(c*x-(c^2*x^2+1)^(1/2))*d^2/b/(a+b*arcsinh(c*x))+1/2*d^2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/8*(c*x-(c^2*x^2+1)^(1/2))*e^2/c^2/b/(a+b*arcsinh(c*x))-1/8/c^2*e^2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/2/b*d^2*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-1/2/b^2*d^2*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+1/8/c^2/b*e^2*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))+1/8/c^2/b^2*e^2*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+1/2*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)*d*e/c/(a+b*arcsinh(c*x))/b-e*d/c/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/2/b*e*d/c*(2*c^2*x^2+1+2*c*x*(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-1/b^2*e*d/c*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b))","A"
26,1,272,176,0.270000," ","int((e*x+d)/(a+b*arcsinh(c*x))^2,x)","\frac{\frac{\left(c x -\sqrt{c^{2} x^{2}+1}\right) d}{2 b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{d \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{2 b^{2}}-\frac{d \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{2 b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{d \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{2 b^{2}}+\frac{\left(2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1\right) e}{4 c \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{2 c \,b^{2}}-\frac{e \left(2 c^{2} x^{2}+1+2 c x \sqrt{c^{2} x^{2}+1}\right)}{4 c b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{2 c \,b^{2}}}{c}"," ",0,"1/c*(1/2*(c*x-(c^2*x^2+1)^(1/2))*d/b/(a+b*arcsinh(c*x))+1/2*d/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/2/b*d*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-1/2/b^2*d*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+1/4*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)*e/c/(a+b*arcsinh(c*x))/b-1/2/c*e/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c*e/b*(2*c^2*x^2+1+2*c*x*(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-1/2/c*e/b^2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b))","A"
27,1,118,83,0.000000," ","int(1/(a+b*arcsinh(c*x))^2,x)","\frac{\frac{c x -\sqrt{c^{2} x^{2}+1}}{2 b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{2 b^{2}}-\frac{c x +\sqrt{c^{2} x^{2}+1}}{2 b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{2 b^{2}}}{c}"," ",0,"1/c*(1/2*(c*x-(c^2*x^2+1)^(1/2))/b/(a+b*arcsinh(c*x))+1/2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/2/b*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-1/2/b^2*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b))","A"
28,0,0,20,0.228000," ","int(1/(e*x+d)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(e x +d \right) \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arcsinh(c*x))^2,x)","F"
29,0,0,20,0.414000," ","int(1/(e*x+d)^2/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(e x +d \right)^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x+d)^2/(a+b*arcsinh(c*x))^2,x)","F"
30,0,0,72,3.603000," ","int((e*x+d)^m*(a+b*arcsinh(c*x))^2,x)","\int \left(e x +d \right)^{m} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int((e*x+d)^m*(a+b*arcsinh(c*x))^2,x)","F"
31,0,0,165,3.604000," ","int((e*x+d)^m*(a+b*arcsinh(c*x)),x)","\int \left(e x +d \right)^{m} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int((e*x+d)^m*(a+b*arcsinh(c*x)),x)","F"
32,0,0,20,1.197000," ","int((e*x+d)^m/(a+b*arcsinh(c*x)),x)","\int \frac{\left(e x +d \right)^{m}}{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int((e*x+d)^m/(a+b*arcsinh(c*x)),x)","F"
33,0,0,20,1.260000," ","int((e*x+d)^m/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(a+b*arcsinh(c*x))^2,x)","F"
34,1,1119,560,0.803000," ","int((g*x+f)^3*(a+b*arcsinh(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{a \,f^{3} x \sqrt{c^{2} d \,x^{2}+d}}{2}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} c^{2} \arcsinh \left(c x \right) x^{6}}{5 c^{2} x^{2}+5}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} c^{2} \arcsinh \left(c x \right) x^{3}}{2 c^{2} x^{2}+2}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} c^{2} \arcsinh \left(c x \right) x^{5}}{4 \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} \arcsinh \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,c^{2} \arcsinh \left(c x \right) x^{4} f^{2}}{c^{2} x^{2}+1}+\frac{a \,g^{3} x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 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^{3} c \,x^{5}}{25 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} x^{3}}{45 c \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} x}{15 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2}}{128 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} c \,x^{2}}{4 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} \arcsinh \left(c x \right)^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} \arcsinh \left(c x \right)}{15 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} \arcsinh \left(c x \right) x^{4}}{15 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3}}{8 c \sqrt{c^{2} x^{2}+1}}+\frac{a \,f^{3} d \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{2 \sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} \arcsinh \left(c x \right) x}{2 c^{2} x^{2}+2}-\frac{3 a f \,g^{2} d \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{8 c^{2} \sqrt{c^{2} d}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} c \,x^{4}}{16 \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} x^{2}}{16 c \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g c \,x^{3} f^{2}}{3 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g x \,f^{2}}{c \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2} g^{2}}{16 \sqrt{c^{2} x^{2}+1}\, c^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} \arcsinh \left(c x \right) x^{2}}{15 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \left(c x \right) f^{2}}{c^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \left(c x \right) x^{2} f^{2}}{c^{2} x^{2}+1}+\frac{9 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} \arcsinh \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}+1\right)}+\frac{3 a f \,g^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}"," ",0,"-2/15*a*g^3/d/c^4*(c^2*d*x^2+d)^(3/2)+1/2*a*f^3*x*(c^2*d*x^2+d)^(1/2)+3/4*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5+3/8*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+b*(d*(c^2*x^2+1))^(1/2)*g*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4*f^2+1/5*a*g^3*x^2*(c^2*d*x^2+d)^(3/2)/c^2/d-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)+1/2*b*(d*(c^2*x^2+1))^(1/2)*f^3/(c^2*x^2+1)*arcsinh(c*x)*x+1/4*b*(d*(c^2*x^2+1))^(1/2)*f^3*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c-2/15*b*(d*(c^2*x^2+1))^(1/2)*g^3/c^4/(c^2*x^2+1)*arcsinh(c*x)+4/15*b*(d*(c^2*x^2+1))^(1/2)*g^3/(c^2*x^2+1)*arcsinh(c*x)*x^4-1/25*b*(d*(c^2*x^2+1))^(1/2)*g^3*c/(c^2*x^2+1)^(1/2)*x^5-1/45*b*(d*(c^2*x^2+1))^(1/2)*g^3/c/(c^2*x^2+1)^(1/2)*x^3+2/15*b*(d*(c^2*x^2+1))^(1/2)*g^3/c^3/(c^2*x^2+1)^(1/2)*x-3/128*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/c^3/(c^2*x^2+1)^(1/2)-1/4*b*(d*(c^2*x^2+1))^(1/2)*f^3*c/(c^2*x^2+1)^(1/2)*x^2-1/8*b*(d*(c^2*x^2+1))^(1/2)*f^3/c/(c^2*x^2+1)^(1/2)+1/2*a*f^3*d*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-3/8*a*f*g^2/c^2*d*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-3/16*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*c/(c^2*x^2+1)^(1/2)*x^4-3/16*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/c/(c^2*x^2+1)^(1/2)*x^2-1/3*b*(d*(c^2*x^2+1))^(1/2)*g*c/(c^2*x^2+1)^(1/2)*x^3*f^2-b*(d*(c^2*x^2+1))^(1/2)*g/c/(c^2*x^2+1)^(1/2)*x*f^2-3/16*b*(d*(c^2*x^2+1))^(1/2)*f*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c^3*g^2+1/5*b*(d*(c^2*x^2+1))^(1/2)*g^3*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^6-1/15*b*(d*(c^2*x^2+1))^(1/2)*g^3/c^2/(c^2*x^2+1)*arcsinh(c*x)*x^2+b*(d*(c^2*x^2+1))^(1/2)*g/c^2/(c^2*x^2+1)*arcsinh(c*x)*f^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*f^3*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3+2*b*(d*(c^2*x^2+1))^(1/2)*g/(c^2*x^2+1)*arcsinh(c*x)*x^2*f^2+9/8*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/(c^2*x^2+1)*arcsinh(c*x)*x^3+3/4*a*f*g^2*x*(c^2*d*x^2+d)^(3/2)/c^2/d","A"
35,1,791,373,0.618000," ","int((g*x+f)^2*(a+b*arcsinh(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 \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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 \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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^{2} c^{2} \arcsinh \left(c x \right) x^{5}}{4 c^{2} x^{2}+4}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} c \,x^{4}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} \arcsinh \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} x^{2}}{16 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} \arcsinh \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \arcsinh \left(c x \right)}{3 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{2} c^{2} \arcsinh \left(c x \right) x^{3}}{2 c^{2} x^{2}+2}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{2} c \,x^{2}}{4 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{2} \arcsinh \left(c x \right) x}{2 c^{2} x^{2}+2}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,c^{2} \arcsinh \left(c x \right) x^{4}}{3 \left(c^{2} x^{2}+1\right)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g c \,x^{3}}{9 \sqrt{c^{2} x^{2}+1}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \arcsinh \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}+1\right)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g x}{3 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} f^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} g^{2}}{16 \sqrt{c^{2} x^{2}+1}\, c^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2}}{128 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{2}}{8 c \sqrt{c^{2} x^{2}+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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/4*b*(d*(c^2*x^2+1))^(1/2)*g^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/16*b*(d*(c^2*x^2+1))^(1/2)*g^2*c/(c^2*x^2+1)^(1/2)*x^4+3/8*b*(d*(c^2*x^2+1))^(1/2)*g^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/16*b*(d*(c^2*x^2+1))^(1/2)*g^2/c/(c^2*x^2+1)^(1/2)*x^2+1/8*b*(d*(c^2*x^2+1))^(1/2)*g^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+2/3*b*(d*(c^2*x^2+1))^(1/2)*f*g/c^2/(c^2*x^2+1)*arcsinh(c*x)+1/2*b*(d*(c^2*x^2+1))^(1/2)*f^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)*f^2*c/(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*f^2/(c^2*x^2+1)*arcsinh(c*x)*x+2/3*b*(d*(c^2*x^2+1))^(1/2)*f*g*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-2/9*b*(d*(c^2*x^2+1))^(1/2)*f*g*c/(c^2*x^2+1)^(1/2)*x^3+4/3*b*(d*(c^2*x^2+1))^(1/2)*f*g/(c^2*x^2+1)*arcsinh(c*x)*x^2-2/3*b*(d*(c^2*x^2+1))^(1/2)*f*g/c/(c^2*x^2+1)^(1/2)*x+1/4*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c*f^2-1/16*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c^3*g^2-1/128*b*(d*(c^2*x^2+1))^(1/2)*g^2/c^3/(c^2*x^2+1)^(1/2)-1/8*b*(d*(c^2*x^2+1))^(1/2)*f^2/c/(c^2*x^2+1)^(1/2)","B"
36,1,423,195,0.423000," ","int((g*x+f)*(a+b*arcsinh(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 \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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 \arcsinh \left(c x \right)}{3 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f}{8 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,c^{2} \arcsinh \left(c x \right) x^{4}}{3 c^{2} x^{2}+3}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g c \,x^{3}}{9 \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g x}{3 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,c^{2} \arcsinh \left(c x \right) x^{3}}{2 c^{2} x^{2}+2}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f c \,x^{2}}{4 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right) x}{2 c^{2} x^{2}+2}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2}}{4 \sqrt{c^{2} x^{2}+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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/3*b*(d*(c^2*x^2+1))^(1/2)*g/c^2/(c^2*x^2+1)*arcsinh(c*x)-1/8*b*(d*(c^2*x^2+1))^(1/2)*f/c/(c^2*x^2+1)^(1/2)+1/3*b*(d*(c^2*x^2+1))^(1/2)*g*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-1/9*b*(d*(c^2*x^2+1))^(1/2)*g*c/(c^2*x^2+1)^(1/2)*x^3+2/3*b*(d*(c^2*x^2+1))^(1/2)*g/(c^2*x^2+1)*arcsinh(c*x)*x^2-1/3*b*(d*(c^2*x^2+1))^(1/2)*g/c/(c^2*x^2+1)^(1/2)*x+1/2*b*(d*(c^2*x^2+1))^(1/2)*f*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)*f*c/(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*f/(c^2*x^2+1)*arcsinh(c*x)*x+1/4*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*f*arcsinh(c*x)^2","B"
37,1,992,632,0.350000," ","int((a+b*arcsinh(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 \ln \left(\frac{-\frac{c^{2} d f}{g}+c^{2} d \left(x +\frac{f}{g}\right)}{\sqrt{c^{2} 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}}}\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 \arcsinh \left(c x \right)^{2} c}{2 \sqrt{c^{2} x^{2}+1}\, g^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2} c^{2}}{\left(c^{2} x^{2}+1\right) g}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c x}{\sqrt{c^{2} x^{2}+1}\, g}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(c^{2} x^{2}+1\right) g}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} f^{2}+g^{2}}\, \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+1}\right) g -c f +\sqrt{c^{2} f^{2}+g^{2}}}{-c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+1}\, g^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} f^{2}+g^{2}}\, \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) g +c f +\sqrt{c^{2} f^{2}+g^{2}}}{c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right) g -c f +\sqrt{c^{2} f^{2}+g^{2}}}{-c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right) g +c f +\sqrt{c^{2} f^{2}+g^{2}}}{c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(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^2*x^2+1)^(1/2)*f*arcsinh(c*x)^2*c/g^2+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)/g*arcsinh(c*x)*x^2*c^2-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/g*c*x+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)/g*arcsinh(c*x)+b*(d*(c^2*x^2+1))^(1/2)*(c^2*f^2+g^2)^(1/2)/(c^2*x^2+1)^(1/2)/g^2*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^2*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^2*dilog((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^2*dilog(((c*x+(c^2*x^2+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"
38,1,1814,745,0.714000," ","int((a+b*arcsinh(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 \ln \left(\frac{-\frac{c^{2} d f}{g}+c^{2} d \left(x +\frac{f}{g}\right)}{\sqrt{c^{2} 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}}}\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 \ln \left(\frac{-\frac{c^{2} d f}{g}+c^{2} d \left(x +\frac{f}{g}\right)}{\sqrt{c^{2} 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}}}\right)}{\left(c^{2} f^{2}+g^{2}\right) \sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c}{2 \sqrt{c^{2} x^{2}+1}\, g^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3} c^{4} f}{\left(c^{2} x^{2}+1\right) g^{2} \left(g x +f \right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \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)}\, \arcsinh \left(c x \right) x^{2} c^{2}}{\left(c^{2} x^{2}+1\right) g \left(g x +f \right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x c}{\sqrt{c^{2} x^{2}+1}\, g \left(g x +f \right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2} f}{\left(c^{2} x^{2}+1\right) g^{2} \left(g x +f \right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c f}{\sqrt{c^{2} x^{2}+1}\, g^{2} \left(g x +f \right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(c^{2} x^{2}+1\right) g \left(g x +f \right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} f \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+1}\right) g -c f +\sqrt{c^{2} f^{2}+g^{2}}}{-c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+1}\, g^{2} \sqrt{c^{2} f^{2}+g^{2}}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} f \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) g +c f +\sqrt{c^{2} f^{2}+g^{2}}}{c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right) f^{2}}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right)^{2} g +2 c f \left(c x +\sqrt{c^{2} x^{2}+1}\right)-g \right) f^{2}}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right) g -c f +\sqrt{c^{2} f^{2}+g^{2}}}{-c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right) g +c f +\sqrt{c^{2} f^{2}+g^{2}}}{c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right)^{2} g +2 c f \left(c x +\sqrt{c^{2} x^{2}+1}\right)-g \right)}{\sqrt{c^{2} x^{2}+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*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(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*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(1/2)+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c/g^2+b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/g^2/(g*x+f)*x^3*c^4*f-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/g^2/(g*x+f)*x*c^2*f-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/g/(g*x+f)*x^2*c^2+b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)^(1/2)/g/(g*x+f)*x*c+b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/g^2/(g*x+f)*x*c^2*f+b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)^(1/2)/g^2/(g*x+f)*c*f-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/g/(g*x+f)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/g^2/(c^2*f^2+g^2)^(1/2)*c^2*f*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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*x^2+1)^(1/2)/g^2/(c^2*f^2+g^2)^(1/2)*c^2*f*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^2/(c^2*f^2+g^2)*c^3*ln(c*x+(c^2*x^2+1)^(1/2))*f^2+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/g^2/(c^2*f^2+g^2)*c^3*ln((c*x+(c^2*x^2+1)^(1/2))^2*g+2*c*f*(c*x+(c^2*x^2+1)^(1/2))-g)*f^2-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/g^2/(c^2*f^2+g^2)^(1/2)*c^2*f*dilog((-(c*x+(c^2*x^2+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*x^2+1)^(1/2)/g^2/(c^2*f^2+g^2)^(1/2)*c^2*f*dilog(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/(c^2*f^2+g^2)*c*ln(c*x+(c^2*x^2+1)^(1/2))+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/(c^2*f^2+g^2)*c*ln((c*x+(c^2*x^2+1)^(1/2))^2*g+2*c*f*(c*x+(c^2*x^2+1)^(1/2))-g)","B"
39,1,1510,802,0.964000," ","int((g*x+f)^3*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d \,c^{3} x^{6}}{12 \sqrt{c^{2} x^{2}+1}}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d c \,x^{4}}{32 \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d \,x^{2}}{32 c \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \,c^{3} x^{5} f^{2}}{25 \sqrt{c^{2} x^{2}+1}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d c \,x^{3} f^{2}}{5 \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d x \,f^{2}}{5 c \sqrt{c^{2} x^{2}+1}}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d \arcsinh \left(c x \right) x^{3}}{16 \left(c^{2} x^{2}+1\right)}+\frac{9 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \arcsinh \left(c x \right) x^{2} f^{2}}{5 \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \arcsinh \left(c x \right) f^{2}}{5 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d \,c^{2} \arcsinh \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}+1\right)}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2} d \,g^{2}}{32 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{13 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \,c^{2} \arcsinh \left(c x \right) x^{6}}{35 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \arcsinh \left(c x \right) x^{2}}{35 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 a \,g^{3} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}+\frac{a \,f^{3} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{3 a \,f^{3} d x \sqrt{c^{2} d \,x^{2}+d}}{8}+\frac{3 a \,f^{3} d^{2} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{8 \sqrt{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{3 a \,f^{2} g \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}-\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d}{128 c \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d x}{35 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d}{768 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d \,c^{3} x^{4}}{16 \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d c \,x^{2}}{16 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \,c^{3} x^{7}}{49 \sqrt{c^{2} x^{2}+1}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d c \,x^{5}}{175 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \,x^{3}}{105 c \sqrt{c^{2} x^{2}+1}}+\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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{16 c^{2} \sqrt{c^{2} d}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} \arcsinh \left(c x \right)^{2} d}{16 \sqrt{c^{2} x^{2}+1}\, c}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \arcsinh \left(c x \right)}{35 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d \arcsinh \left(c x \right) x}{8 \left(c^{2} x^{2}+1\right)}+\frac{9 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \arcsinh \left(c x \right) x^{4}}{35 \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d \,c^{4} \arcsinh \left(c x \right) x^{5}}{4 c^{2} x^{2}+4}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d \,c^{4} \arcsinh \left(c x \right) x^{8}}{7 c^{2} x^{2}+7}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d \,c^{2} \arcsinh \left(c x \right) x^{5}}{8 \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d \arcsinh \left(c x \right) x}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \,c^{4} \arcsinh \left(c x \right) x^{6} f^{2}}{5 \left(c^{2} x^{2}+1\right)}+\frac{9 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \,c^{2} \arcsinh \left(c x \right) x^{4} f^{2}}{5 \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d \,c^{4} \arcsinh \left(c x \right) x^{7}}{2 c^{2} x^{2}+2}"," ",0,"17/16*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d/(c^2*x^2+1)*arcsinh(c*x)*x^3+9/5*b*(d*(c^2*x^2+1))^(1/2)*g*d/(c^2*x^2+1)*arcsinh(c*x)*x^2*f^2+3/5*b*(d*(c^2*x^2+1))^(1/2)*g*d/c^2/(c^2*x^2+1)*arcsinh(c*x)*f^2+1/4*b*(d*(c^2*x^2+1))^(1/2)*f^3*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5+7/8*b*(d*(c^2*x^2+1))^(1/2)*f^3*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-3/32*b*(d*(c^2*x^2+1))^(1/2)*f*arcsinh(c*x)^2*d/(c^2*x^2+1)^(1/2)/c^3*g^2+1/7*b*(d*(c^2*x^2+1))^(1/2)*g^3*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^8+13/35*b*(d*(c^2*x^2+1))^(1/2)*g^3*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^6-1/35*b*(d*(c^2*x^2+1))^(1/2)*g^3*d/c^2/(c^2*x^2+1)*arcsinh(c*x)*x^2-1/12*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d*c^3/(c^2*x^2+1)^(1/2)*x^6-7/32*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d*c/(c^2*x^2+1)^(1/2)*x^4-3/32*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d/c/(c^2*x^2+1)^(1/2)*x^2-3/25*b*(d*(c^2*x^2+1))^(1/2)*g*d*c^3/(c^2*x^2+1)^(1/2)*x^5*f^2-2/5*b*(d*(c^2*x^2+1))^(1/2)*g*d*c/(c^2*x^2+1)^(1/2)*x^3*f^2-3/5*b*(d*(c^2*x^2+1))^(1/2)*g*d/c/(c^2*x^2+1)^(1/2)*x*f^2-2/35*a*g^3/d/c^4*(c^2*d*x^2+d)^(5/2)+1/4*a*f^3*x*(c^2*d*x^2+d)^(3/2)+3/8*a*f^3*d*x*(c^2*d*x^2+d)^(1/2)+3/8*a*f^3*d^2*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+11/8*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5+3/16*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+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)+3/5*a*f^2*g/c^2/d*(c^2*d*x^2+d)^(5/2)-17/128*b*(d*(c^2*x^2+1))^(1/2)*f^3*d/c/(c^2*x^2+1)^(1/2)+2/35*b*(d*(c^2*x^2+1))^(1/2)*g^3*d/c^3/(c^2*x^2+1)^(1/2)*x+7/768*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d/c^3/(c^2*x^2+1)^(1/2)-1/16*b*(d*(c^2*x^2+1))^(1/2)*f^3*d*c^3/(c^2*x^2+1)^(1/2)*x^4-5/16*b*(d*(c^2*x^2+1))^(1/2)*f^3*d*c/(c^2*x^2+1)^(1/2)*x^2-1/49*b*(d*(c^2*x^2+1))^(1/2)*g^3*d*c^3/(c^2*x^2+1)^(1/2)*x^7-8/175*b*(d*(c^2*x^2+1))^(1/2)*g^3*d*c/(c^2*x^2+1)^(1/2)*x^5-1/105*b*(d*(c^2*x^2+1))^(1/2)*g^3*d/c/(c^2*x^2+1)^(1/2)*x^3+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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+3/16*b*(d*(c^2*x^2+1))^(1/2)*f^3*arcsinh(c*x)^2*d/(c^2*x^2+1)^(1/2)/c-2/35*b*(d*(c^2*x^2+1))^(1/2)*g^3*d/c^4/(c^2*x^2+1)*arcsinh(c*x)+5/8*b*(d*(c^2*x^2+1))^(1/2)*f^3*d/(c^2*x^2+1)*arcsinh(c*x)*x+9/35*b*(d*(c^2*x^2+1))^(1/2)*g^3*d/(c^2*x^2+1)*arcsinh(c*x)*x^4+3/5*b*(d*(c^2*x^2+1))^(1/2)*g*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^6*f^2+9/5*b*(d*(c^2*x^2+1))^(1/2)*g*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4*f^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7","A"
40,1,1087,567,0.845000," ","int((g*x+f)^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","-\frac{a \,g^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d \,c^{4} \arcsinh \left(c x \right) x^{7}}{6 c^{2} x^{2}+6}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right) x^{5} f^{2}}{4 c^{2} x^{2}+4}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d x}{5 c \sqrt{c^{2} x^{2}+1}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d \,c^{3} x^{5}}{25 \sqrt{c^{2} x^{2}+1}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d c \,x^{3}}{15 \sqrt{c^{2} x^{2}+1}}+\frac{6 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d \arcsinh \left(c x \right) x^{2}}{5 \left(c^{2} x^{2}+1\right)}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d \,c^{2} \arcsinh \left(c x \right) x^{5}}{24 \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d \arcsinh \left(c x \right) x}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d \arcsinh \left(c x \right)}{5 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right) x^{3} f^{2}}{8 \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d \,c^{4} \arcsinh \left(c x \right) x^{6}}{5 \left(c^{2} x^{2}+1\right)}+\frac{6 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g d \,c^{2} \arcsinh \left(c x \right) x^{4}}{5 \left(c^{2} x^{2}+1\right)}+\frac{2 a f g \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+\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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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)}\, d \,f^{2}}{128 c \sqrt{c^{2} x^{2}+1}}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d}{2304 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{3 a \,f^{2} d x \sqrt{c^{2} d \,x^{2}+d}}{8}+\frac{3 a \,f^{2} d^{2} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{8 \sqrt{c^{2} d}}+\frac{a \,f^{2} 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^{2} d \,c^{3} x^{6}}{36 \sqrt{c^{2} x^{2}+1}}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d c \,x^{4}}{96 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d \,x^{2}}{32 c \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{4} f^{2}}{16 \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \,x^{2} f^{2}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d \,f^{2}}{16 \sqrt{c^{2} x^{2}+1}\, c}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d \,g^{2}}{32 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d \arcsinh \left(c x \right) x^{3}}{48 \left(c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x \,f^{2}}{8 \left(c^{2} x^{2}+1\right)}"," ",0,"-1/24*a*g^2/c^2*x*(c^2*d*x^2+d)^(3/2)+6/5*b*(d*(c^2*x^2+1))^(1/2)*f*g*d/(c^2*x^2+1)*arcsinh(c*x)*x^2+1/6*b*(d*(c^2*x^2+1))^(1/2)*g^2*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7+11/24*b*(d*(c^2*x^2+1))^(1/2)*g^2*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5+1/16*b*(d*(c^2*x^2+1))^(1/2)*g^2*d/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+2/5*b*(d*(c^2*x^2+1))^(1/2)*f*g*d/c^2/(c^2*x^2+1)*arcsinh(c*x)+1/4*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5*f^2+7/8*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3*f^2-2/5*b*(d*(c^2*x^2+1))^(1/2)*f*g*d/c/(c^2*x^2+1)^(1/2)*x-2/25*b*(d*(c^2*x^2+1))^(1/2)*f*g*d*c^3/(c^2*x^2+1)^(1/2)*x^5-4/15*b*(d*(c^2*x^2+1))^(1/2)*f*g*d*c/(c^2*x^2+1)^(1/2)*x^3+2/5*b*(d*(c^2*x^2+1))^(1/2)*f*g*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^6+6/5*b*(d*(c^2*x^2+1))^(1/2)*f*g*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4+2/5*a*f*g/c^2/d*(c^2*d*x^2+d)^(5/2)+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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-17/128*b*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)*f^2+7/2304*b*(d*(c^2*x^2+1))^(1/2)*g^2*d/c^3/(c^2*x^2+1)^(1/2)+3/8*a*f^2*d*x*(c^2*d*x^2+d)^(1/2)+3/8*a*f^2*d^2*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/4*a*f^2*x*(c^2*d*x^2+d)^(3/2)-1/36*b*(d*(c^2*x^2+1))^(1/2)*g^2*d*c^3/(c^2*x^2+1)^(1/2)*x^6-7/96*b*(d*(c^2*x^2+1))^(1/2)*g^2*d*c/(c^2*x^2+1)^(1/2)*x^4-1/32*b*(d*(c^2*x^2+1))^(1/2)*g^2*d/c/(c^2*x^2+1)^(1/2)*x^2-1/16*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^4*f^2-5/16*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*x^2*f^2+3/16*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*d/(c^2*x^2+1)^(1/2)/c*f^2-1/32*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*d/(c^2*x^2+1)^(1/2)/c^3*g^2+17/48*b*(d*(c^2*x^2+1))^(1/2)*g^2*d/(c^2*x^2+1)*arcsinh(c*x)*x^3+5/8*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x*f^2","A"
41,1,601,305,0.499000," ","int((g*x+f)*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{8 \sqrt{c^{2} d}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2} d}{16 \sqrt{c^{2} x^{2}+1}\, c}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \,c^{4} \arcsinh \left(c x \right) x^{6}}{5 c^{2} x^{2}+5}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \,c^{3} x^{5}}{25 \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \,c^{2} \arcsinh \left(c x \right) x^{4}}{5 \left(c^{2} x^{2}+1\right)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d c \,x^{3}}{15 \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \arcsinh \left(c x \right) x^{2}}{5 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d x}{5 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f d \,c^{4} \arcsinh \left(c x \right) x^{5}}{4 c^{2} x^{2}+4}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f d \,c^{3} x^{4}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f d \,c^{2} \arcsinh \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}+1\right)}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f d c \,x^{2}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f d \arcsinh \left(c x \right) x}{8 \left(c^{2} x^{2}+1\right)}-\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f d}{128 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g d \arcsinh \left(c x \right)}{5 c^{2} \left(c^{2} x^{2}+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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+3/16*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*f*arcsinh(c*x)^2*d+1/5*b*(d*(c^2*x^2+1))^(1/2)*g*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^6-1/25*b*(d*(c^2*x^2+1))^(1/2)*g*d*c^3/(c^2*x^2+1)^(1/2)*x^5+3/5*b*(d*(c^2*x^2+1))^(1/2)*g*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-2/15*b*(d*(c^2*x^2+1))^(1/2)*g*d*c/(c^2*x^2+1)^(1/2)*x^3+3/5*b*(d*(c^2*x^2+1))^(1/2)*g*d/(c^2*x^2+1)*arcsinh(c*x)*x^2-1/5*b*(d*(c^2*x^2+1))^(1/2)*g*d/c/(c^2*x^2+1)^(1/2)*x+1/4*b*(d*(c^2*x^2+1))^(1/2)*f*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/16*b*(d*(c^2*x^2+1))^(1/2)*f*d*c^3/(c^2*x^2+1)^(1/2)*x^4+7/8*b*(d*(c^2*x^2+1))^(1/2)*f*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-5/16*b*(d*(c^2*x^2+1))^(1/2)*f*d*c/(c^2*x^2+1)^(1/2)*x^2+5/8*b*(d*(c^2*x^2+1))^(1/2)*f*d/(c^2*x^2+1)*arcsinh(c*x)*x-17/128*b*(d*(c^2*x^2+1))^(1/2)*f*d/c/(c^2*x^2+1)^(1/2)+1/5*b*(d*(c^2*x^2+1))^(1/2)*g*d/c^2/(c^2*x^2+1)*arcsinh(c*x)","A"
42,1,1838,920,0.368000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/(g*x+f),x)","-\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{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{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{3 a \,c^{2} d^{2} f \ln \left(\frac{-\frac{c^{2} d f}{g}+c^{2} d \left(x +\frac{f}{g}\right)}{\sqrt{c^{2} 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}}}\right)}{2 g^{2} \sqrt{c^{2} d}}-\frac{a \,d^{2} c^{4} f^{3} \ln \left(\frac{-\frac{c^{2} d f}{g}+c^{2} d \left(x +\frac{f}{g}\right)}{\sqrt{c^{2} 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}}}\right)}{g^{4} \sqrt{c^{2} d}}-\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{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c x}{3 \sqrt{c^{2} x^{2}+1}\, g}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f c d}{8 \sqrt{c^{2} x^{2}+1}\, g^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{3}}{9 \sqrt{c^{2} x^{2}+1}\, 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}}}\, c^{2} f^{2}}{g^{3}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{3 \left(c^{2} x^{2}+1\right) 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{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,c^{4} d \arcsinh \left(c x \right) x^{3}}{2 \left(c^{2} x^{2}+1\right) g^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,c^{2} d \arcsinh \left(c x \right) x}{2 \left(c^{2} x^{2}+1\right) g^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{2} c^{4} f^{2}}{\left(c^{2} x^{2}+1\right) g^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,c^{3} d \,x^{2}}{4 \sqrt{c^{2} x^{2}+1}\, g^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d x \,c^{3} f^{2}}{\sqrt{c^{2} x^{2}+1}\, g^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) c^{2} f^{2}}{\left(c^{2} x^{2}+1\right) 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)}\, \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+1}\right) g -c f +\sqrt{c^{2} f^{2}+g^{2}}}{-c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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)}\, \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) g +c f +\sqrt{c^{2} f^{2}+g^{2}}}{c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+1}\, g^{4}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} \arcsinh \left(c x \right)^{2} c^{3} d}{2 \sqrt{c^{2} x^{2}+1}\, g^{4}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2} c d}{4 \sqrt{c^{2} x^{2}+1}\, g^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{4} c^{4}}{3 \left(c^{2} x^{2}+1\right) g}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{2} c^{2}}{3 \left(c^{2} x^{2}+1\right) g}+\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{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^{2} x^{2}+1}\right) g +c f +\sqrt{c^{2} f^{2}+g^{2}}}{c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\right) g -c f +\sqrt{c^{2} f^{2}+g^{2}}}{-c f +\sqrt{c^{2} f^{2}+g^{2}}}\right)}{\sqrt{c^{2} x^{2}+1}\, g^{4}}"," ",0,"-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))-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^4-2*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^2-3/2*a/g^2*c^2*d^2*f*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(1/2)-a/g^4*d^2*c^4*f^3*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(1/2)-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-4/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)/g*c*x+1/8*b*(d*(c^2*x^2+1))^(1/2)*f*c*d/(c^2*x^2+1)^(1/2)/g^2-1/9*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)/g*c^3*x^3-b*(c^2*f^2+g^2)^(3/2)*d*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/g^4*dilog(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^4*dilog((-(c*x+(c^2*x^2+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+4/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)/g*arcsinh(c*x)+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)-1/2*b*(d*(c^2*x^2+1))^(1/2)*f*c^4*d/(c^2*x^2+1)/g^2*arcsinh(c*x)*x^3-1/2*b*(d*(c^2*x^2+1))^(1/2)*f*c^2*d/(c^2*x^2+1)/g^2*arcsinh(c*x)*x+b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)/g^3*arcsinh(c*x)*x^2*c^4*f^2+b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)/g^3*arcsinh(c*x)*c^2*f^2+b*(c^2*f^2+g^2)^(3/2)*d*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/g^4*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^4*arcsinh(c*x)*ln(((c*x+(c^2*x^2+1)^(1/2))*g+c*f+(c^2*f^2+g^2)^(1/2))/(c*f+(c^2*f^2+g^2)^(1/2)))-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*f^3*arcsinh(c*x)^2*c^3*d/g^4-3/4*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*f*arcsinh(c*x)^2*c*d/g^2+1/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)/g*arcsinh(c*x)*x^4*c^4+5/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)/g*arcsinh(c*x)*x^2*c^2+1/4*b*(d*(c^2*x^2+1))^(1/2)*f*c^3*d/(c^2*x^2+1)^(1/2)/g^2*x^2-b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)/g^3*x*c^3*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"
43,1,1954,1080,1.010000," ","int((g*x+f)^3*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","-\frac{2 a \,g^{3} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}+\frac{a \,f^{3} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}-\frac{59 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} c \,x^{4}}{256 \sqrt{c^{2} x^{2}+1}}-\frac{15 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} x^{2}}{256 c \sqrt{c^{2} x^{2}+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^{2} x^{2}+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^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c \,x^{3} f^{2}}{7 \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} x \,f^{2}}{7 c \sqrt{c^{2} x^{2}+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^{2} x^{2}+1}}-\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} c^{3} x^{6}}{96 \sqrt{c^{2} x^{2}+1}}+\frac{34 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} c^{2} \arcsinh \left(c x \right) x^{6}}{63 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} \arcsinh \left(c x \right) x^{2}}{63 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{12 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} \arcsinh \left(c x \right) x^{2} f^{2}}{7 \left(c^{2} x^{2}+1\right)}+\frac{133 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} \arcsinh \left(c x \right) x^{3}}{128 \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} \arcsinh \left(c x \right) f^{2}}{7 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} c^{4} \arcsinh \left(c x \right) x^{5}}{24 \left(c^{2} x^{2}+1\right)}+\frac{59 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} c^{2} \arcsinh \left(c x \right) x^{3}}{48 \left(c^{2} x^{2}+1\right)}-\frac{15 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2} d^{2} g^{2}}{256 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{26 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} c^{4} \arcsinh \left(c x \right) x^{8}}{63 \left(c^{2} x^{2}+1\right)}+\frac{15 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} \arcsinh \left(c x \right) x}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{6} \arcsinh \left(c x \right) x^{8} f^{2}}{7 \left(c^{2} x^{2}+1\right)}+\frac{12 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{4} \arcsinh \left(c x \right) x^{6} f^{2}}{7 \left(c^{2} x^{2}+1\right)}+\frac{18 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{2} \arcsinh \left(c x \right) x^{4} f^{2}}{7 \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} c^{6} \arcsinh \left(c x \right) x^{9}}{8 \left(c^{2} x^{2}+1\right)}+\frac{23 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} c^{4} \arcsinh \left(c x \right) x^{7}}{16 \left(c^{2} x^{2}+1\right)}+\frac{127 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2} c^{2} \arcsinh \left(c x \right) x^{5}}{64 \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} c^{6} \arcsinh \left(c x \right) x^{7}}{6 c^{2} x^{2}+6}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} c \,x^{5}}{21 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} x^{3}}{189 c \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} x}{63 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{359 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} d^{2}}{24576 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} c^{5} x^{6}}{36 \sqrt{c^{2} x^{2}+1}}-\frac{13 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} c^{3} x^{4}}{96 \sqrt{c^{2} x^{2}+1}}-\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} c \,x^{2}}{32 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} c^{5} x^{9}}{81 \sqrt{c^{2} x^{2}+1}}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2} \arcsinh \left(c x \right) x}{16 \left(c^{2} x^{2}+1\right)}+\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} \arcsinh \left(c x \right) x^{4}}{63 \left(c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} \arcsinh \left(c x \right)^{2} d^{2}}{32 \sqrt{c^{2} x^{2}+1}\, c}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} \arcsinh \left(c x \right)}{63 c^{4} \left(c^{2} x^{2}+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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{128 c^{2} \sqrt{c^{2} d}}-\frac{19 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} c^{3} x^{7}}{441 \sqrt{c^{2} x^{2}+1}}+\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{299 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} d^{2}}{2304 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} d^{2} c^{6} \arcsinh \left(c x \right) x^{10}}{9 c^{2} x^{2}+9}+\frac{5 a \,f^{3} d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a \,f^{3} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,f^{3} d^{3} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{16 \sqrt{c^{2} d}}"," ",0,"-2/63*a*g^3/d/c^4*(c^2*d*x^2+d)^(7/2)+1/6*a*f^3*x*(c^2*d*x^2+d)^(5/2)+34/63*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^6-1/63*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x^2+12/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2*f^2+133/128*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^3+3/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*f^2+1/6*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^7+17/24*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5+59/48*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-15/256*b*(d*(c^2*x^2+1))^(1/2)*f*arcsinh(c*x)^2*d^2/(c^2*x^2+1)^(1/2)/c^3*g^2+1/9*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^10+26/63*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^8-59/256*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2*c/(c^2*x^2+1)^(1/2)*x^4-15/256*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2/c/(c^2*x^2+1)^(1/2)*x^2-3/49*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^5/(c^2*x^2+1)^(1/2)*x^7*f^2-9/35*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^3/(c^2*x^2+1)^(1/2)*x^5*f^2-3/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c/(c^2*x^2+1)^(1/2)*x^3*f^2-3/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2/c/(c^2*x^2+1)^(1/2)*x*f^2-3/64*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2*c^5/(c^2*x^2+1)^(1/2)*x^8-17/96*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2*c^3/(c^2*x^2+1)^(1/2)*x^6+15/128*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+3/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^8*f^2+12/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^6*f^2+18/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4*f^2+3/8*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^9+23/16*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7+127/64*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/21*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2*c/(c^2*x^2+1)^(1/2)*x^5-1/189*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2/c/(c^2*x^2+1)^(1/2)*x^3+2/63*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2/c^3/(c^2*x^2+1)^(1/2)*x+359/24576*b*(d*(c^2*x^2+1))^(1/2)*f*g^2*d^2/c^3/(c^2*x^2+1)^(1/2)-1/36*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^5/(c^2*x^2+1)^(1/2)*x^6-13/96*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^3/(c^2*x^2+1)^(1/2)*x^4-11/32*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c/(c^2*x^2+1)^(1/2)*x^2-1/81*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2*c^5/(c^2*x^2+1)^(1/2)*x^9+11/16*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2/(c^2*x^2+1)*arcsinh(c*x)*x+16/63*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^4+5/32*b*(d*(c^2*x^2+1))^(1/2)*f^3*arcsinh(c*x)^2*d^2/(c^2*x^2+1)^(1/2)/c-2/63*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2/c^4/(c^2*x^2+1)*arcsinh(c*x)+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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-19/441*b*(d*(c^2*x^2+1))^(1/2)*g^3*d^2*c^3/(c^2*x^2+1)^(1/2)*x^7+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)-299/2304*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2/c/(c^2*x^2+1)^(1/2)+5/24*a*f^3*d*x*(c^2*d*x^2+d)^(3/2)+5/16*a*f^3*d^2*x*(c^2*d*x^2+d)^(1/2)+5/16*a*f^3*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)","A"
44,1,1424,791,0.887000," ","int((g*x+f)^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","-\frac{a \,g^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{48 c^{2}}+\frac{a \,f^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}-\frac{6 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} c^{3} x^{5}}{35 \sqrt{c^{2} x^{2}+1}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} \arcsinh \left(c x \right) x^{2}}{7 \left(c^{2} x^{2}+1\right)}+\frac{23 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} c^{4} \arcsinh \left(c x \right) x^{7}}{48 \left(c^{2} x^{2}+1\right)}+\frac{127 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} c^{2} \arcsinh \left(c x \right) x^{5}}{192 \left(c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} \arcsinh \left(c x \right) x}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} \arcsinh \left(c x \right)}{7 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{5} f^{2}}{24 \left(c^{2} x^{2}+1\right)}+\frac{59 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right) x^{3} f^{2}}{48 \left(c^{2} x^{2}+1\right)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} c \,x^{3}}{7 \sqrt{c^{2} x^{2}+1}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} x}{7 c \sqrt{c^{2} x^{2}+1}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} c^{5} x^{7}}{49 \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} c^{6} \arcsinh \left(c x \right) x^{8}}{7 \left(c^{2} x^{2}+1\right)}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} c^{4} \arcsinh \left(c x \right) x^{6}}{7 \left(c^{2} x^{2}+1\right)}+\frac{12 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \,d^{2} c^{2} \arcsinh \left(c x \right) x^{4}}{7 \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} c^{6} \arcsinh \left(c x \right) x^{9}}{8 c^{2} x^{2}+8}-\frac{5 a \,g^{2} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{128 c^{2}}-\frac{5 a \,g^{2} d^{3} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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{299 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} f^{2}}{2304 c \sqrt{c^{2} x^{2}+1}}+\frac{359 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2}}{73728 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right) x^{7} f^{2}}{6 c^{2} x^{2}+6}+\frac{5 a \,f^{2} d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a \,f^{2} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,f^{2} d^{3} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{16 \sqrt{c^{2} d}}-\frac{13 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{4} f^{2}}{96 \sqrt{c^{2} x^{2}+1}}-\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \,x^{2} f^{2}}{32 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} c^{5} x^{8}}{64 \sqrt{c^{2} x^{2}+1}}-\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} c^{3} x^{6}}{288 \sqrt{c^{2} x^{2}+1}}-\frac{59 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} c \,x^{4}}{768 \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} x^{2}}{256 c \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{6} f^{2}}{36 \sqrt{c^{2} x^{2}+1}}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x \,f^{2}}{16 \left(c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2} f^{2}}{32 \sqrt{c^{2} x^{2}+1}\, c}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2} g^{2}}{256 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{133 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} d^{2} \arcsinh \left(c x \right) x^{3}}{384 \left(c^{2} x^{2}+1\right)}"," ",0,"-1/48*a*g^2/c^2*x*(c^2*d*x^2+d)^(5/2)+1/6*a*f^2*x*(c^2*d*x^2+d)^(5/2)+8/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2+1/8*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^9+23/48*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7+127/192*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5+5/128*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+2/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)+1/6*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^7*f^2-6/35*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2*c^3/(c^2*x^2+1)^(1/2)*x^5-2/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2*c/(c^2*x^2+1)^(1/2)*x^3-2/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2/c/(c^2*x^2+1)^(1/2)*x-2/49*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2*c^5/(c^2*x^2+1)^(1/2)*x^7+17/24*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5*f^2+59/48*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3*f^2+2/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^8+8/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^6+12/7*b*(d*(c^2*x^2+1))^(1/2)*f*g*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-5/128*a*g^2/c^2*d^2*x*(c^2*d*x^2+d)^(1/2)-5/128*a*g^2/c^2*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^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)-299/2304*b*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)*f^2+359/73728*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2/c^3/(c^2*x^2+1)^(1/2)+5/24*a*f^2*d*x*(c^2*d*x^2+d)^(3/2)+5/16*a*f^2*d^2*x*(c^2*d*x^2+d)^(1/2)+5/16*a*f^2*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-13/96*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^4*f^2-11/32*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*x^2*f^2-1/64*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2*c^5/(c^2*x^2+1)^(1/2)*x^8-17/288*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2*c^3/(c^2*x^2+1)^(1/2)*x^6-59/768*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2*c/(c^2*x^2+1)^(1/2)*x^4-5/256*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2/c/(c^2*x^2+1)^(1/2)*x^2-1/36*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^6*f^2+11/16*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x*f^2+5/32*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*d^2/(c^2*x^2+1)^(1/2)/c*f^2-5/256*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*d^2/(c^2*x^2+1)^(1/2)/c^3*g^2+133/384*b*(d*(c^2*x^2+1))^(1/2)*g^2*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^3","A"
45,1,805,430,0.571000," ","int((g*x+f)*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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 \arcsinh \left(c x \right)^{2} d^{2}}{32 \sqrt{c^{2} x^{2}+1}\, c}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{6} \arcsinh \left(c x \right) x^{8}}{7 c^{2} x^{2}+7}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{5} x^{7}}{49 \sqrt{c^{2} x^{2}+1}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{4} \arcsinh \left(c x \right) x^{6}}{7 \left(c^{2} x^{2}+1\right)}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{3} x^{5}}{35 \sqrt{c^{2} x^{2}+1}}+\frac{6 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c^{2} \arcsinh \left(c x \right) x^{4}}{7 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} c \,x^{3}}{7 \sqrt{c^{2} x^{2}+1}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} \arcsinh \left(c x \right) x^{2}}{7 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} x}{7 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} c^{6} \arcsinh \left(c x \right) x^{7}}{6 c^{2} x^{2}+6}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} c^{5} x^{6}}{36 \sqrt{c^{2} x^{2}+1}}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} c^{4} \arcsinh \left(c x \right) x^{5}}{24 \left(c^{2} x^{2}+1\right)}-\frac{13 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} c^{3} x^{4}}{96 \sqrt{c^{2} x^{2}+1}}+\frac{59 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} c^{2} \arcsinh \left(c x \right) x^{3}}{48 \left(c^{2} x^{2}+1\right)}-\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} c \,x^{2}}{32 \sqrt{c^{2} x^{2}+1}}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2} \arcsinh \left(c x \right) x}{16 \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \,d^{2} \arcsinh \left(c x \right)}{7 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{299 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,d^{2}}{2304 c \sqrt{c^{2} x^{2}+1}}"," ",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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+5/32*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*f*arcsinh(c*x)^2*d^2+1/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^8-1/49*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^5/(c^2*x^2+1)^(1/2)*x^7+4/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^6-3/35*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^3/(c^2*x^2+1)^(1/2)*x^5+6/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-1/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2*c/(c^2*x^2+1)^(1/2)*x^3+4/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2-1/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2/c/(c^2*x^2+1)^(1/2)*x+1/6*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^7-1/36*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^5/(c^2*x^2+1)^(1/2)*x^6+17/24*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5-13/96*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^3/(c^2*x^2+1)^(1/2)*x^4+59/48*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-11/32*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c/(c^2*x^2+1)^(1/2)*x^2+11/16*b*(d*(c^2*x^2+1))^(1/2)*f*d^2/(c^2*x^2+1)*arcsinh(c*x)*x+1/7*b*(d*(c^2*x^2+1))^(1/2)*g*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)-299/2304*b*(d*(c^2*x^2+1))^(1/2)*f*d^2/c/(c^2*x^2+1)^(1/2)","A"
46,1,3928,1420,0.470000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/(g*x+f),x)","\text{output too large to display}"," ",0,"b*d^2*(d*(c^2*x^2+1))^(1/2)*(c^2*f^2+g^2)^(1/2)/(c^2*x^2+1)^(1/2)/g^6*dilog((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^6*dilog(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^4*dilog((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^4*dilog(((c*x+(c^2*x^2+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*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g^5*arcsinh(c*x)*x^2*c^6*f^4+1/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g^3*arcsinh(c*x)*x^4*c^6*f^2+8/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g^3*arcsinh(c*x)*x^2*c^4*f^2-1/4*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^6/(c^2*x^2+1)/g^2*arcsinh(c*x)*x^5-11/8*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^4/(c^2*x^2+1)/g^2*arcsinh(c*x)*x^3-9/8*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^2/(c^2*x^2+1)/g^2*arcsinh(c*x)*x-1/2*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^6/(c^2*x^2+1)/g^4*arcsinh(c*x)*x^3-1/2*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^4/(c^2*x^2+1)/g^4*arcsinh(c*x)*x-2*b*d^2*(d*(c^2*x^2+1))^(1/2)*(c^2*f^2+g^2)^(1/2)/(c^2*x^2+1)^(1/2)/g^4*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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*d^2*(d*(c^2*x^2+1))^(1/2)*(c^2*f^2+g^2)^(1/2)/(c^2*x^2+1)^(1/2)/g^6*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^6*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^4*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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)+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+23/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g*arcsinh(c*x)+b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g^5*arcsinh(c*x)*c^4*f^4-7/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)/g^3*x*c^3*f^2-1/9*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)/g^3*x^3*c^5*f^2+1/16*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^5/(c^2*x^2+1)^(1/2)/g^2*x^4+9/16*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c^3/(c^2*x^2+1)^(1/2)/g^2*x^2+1/4*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^5/(c^2*x^2+1)^(1/2)/g^4*x^2+34/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g*arcsinh(c*x)*x^2*c^2-5/4*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*f^3*arcsinh(c*x)^2*d^2*c^3/g^4-15/16*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*f*arcsinh(c*x)^2*d^2*c/g^2+1/5*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g*arcsinh(c*x)*x^6*c^6+14/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g*arcsinh(c*x)*x^4*c^4+b*d^2*(d*(c^2*x^2+1))^(1/2)*(c^2*f^2+g^2)^(1/2)/(c^2*x^2+1)^(1/2)/g^2*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^2*arcsinh(c*x)*ln(((c*x+(c^2*x^2+1)^(1/2))*g+c*f+(c^2*f^2+g^2)^(1/2))/(c*f+(c^2*f^2+g^2)^(1/2)))-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*f^5*arcsinh(c*x)^2*d^2*c^5/g^6-b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)/g^5*x*c^5*f^4+7/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)/g^3*arcsinh(c*x)*c^2*f^2+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+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)-1/4*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*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(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-5/2*a/g^4*d^3*c^4*f^3*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(1/2)-a/g^6*d^3*c^6*f^5*ln((-c^2*d*f/g+c^2*d*(x+f/g))/(c^2*d)^(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))/(c^2*d)^(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^4-3*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^2-23/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)/g*c*x+33/128*b*(d*(c^2*x^2+1))^(1/2)*f*d^2*c/(c^2*x^2+1)^(1/2)/g^2+1/8*b*(d*(c^2*x^2+1))^(1/2)*f^3*d^2*c^3/(c^2*x^2+1)^(1/2)/g^4-1/25*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)/g*x^5*c^5-11/45*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)/g*c^3*x^3+b*d^2*(d*(c^2*x^2+1))^(1/2)*(c^2*f^2+g^2)^(1/2)/(c^2*x^2+1)^(1/2)/g^2*dilog((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/g^2*dilog(((c*x+(c^2*x^2+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))","B"
47,1,751,382,0.810000," ","int((g*x+f)^3*(a+b*arcsinh(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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{\sqrt{c^{2} d}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2} g^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c^{3} d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} \arcsinh \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} x^{3}}{9 c d \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} \arcsinh \left(c x \right) x^{2}}{3 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} x}{3 c^{3} d \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2}}{8 c^{3} d \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \left(c x \right) f^{2}}{c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} \arcsinh \left(c x \right) x}{2 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \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)}\, g x \,f^{2}}{c d \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \,g^{2} \arcsinh \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} x^{2}}{4 c d \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f^{3} \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c d}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{3} \arcsinh \left(c x \right)}{3 c^{4} 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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+3*a*f^2*g/c^2/d*(c^2*d*x^2+d)^(1/2)+a*f^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-3/4*b*(d*(c^2*x^2+1))^(1/2)*f*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c^3/d*g^2+1/3*b*(d*(c^2*x^2+1))^(1/2)*g^3/d/(c^2*x^2+1)*arcsinh(c*x)*x^4-1/9*b*(d*(c^2*x^2+1))^(1/2)*g^3/c/d/(c^2*x^2+1)^(1/2)*x^3-1/3*b*(d*(c^2*x^2+1))^(1/2)*g^3/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x^2+2/3*b*(d*(c^2*x^2+1))^(1/2)*g^3/c^3/d/(c^2*x^2+1)^(1/2)*x-3/8*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/c^3/d/(c^2*x^2+1)^(1/2)+3*b*(d*(c^2*x^2+1))^(1/2)*g/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*f^2+3/2*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x+3*b*(d*(c^2*x^2+1))^(1/2)*g/d/(c^2*x^2+1)*arcsinh(c*x)*x^2*f^2-3*b*(d*(c^2*x^2+1))^(1/2)*g/c/d/(c^2*x^2+1)^(1/2)*x*f^2+3/2*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/d/(c^2*x^2+1)*arcsinh(c*x)*x^3-3/4*b*(d*(c^2*x^2+1))^(1/2)*f*g^2/c/d/(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*f^3*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c/d-2/3*b*(d*(c^2*x^2+1))^(1/2)*g^3/c^4/d/(c^2*x^2+1)*arcsinh(c*x)","A"
48,1,486,230,0.614000," ","int((g*x+f)^2*(a+b*arcsinh(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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\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} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{\sqrt{c^{2} d}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \arcsinh \left(c x \right) x^{2}}{d \left(c^{2} x^{2}+1\right)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g x}{c d \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} f^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} g^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c^{3} d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2}}{8 c^{3} d \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} \arcsinh \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} x^{2}}{4 c d \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g^{2} \arcsinh \left(c x \right) x}{2 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f g \arcsinh \left(c x \right)}{c^{2} d \left(c^{2} x^{2}+1\right)}"," ",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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+2*a*f*g/c^2/d*(c^2*d*x^2+d)^(1/2)+a*f^2*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+2*b*(d*(c^2*x^2+1))^(1/2)*f*g/d/(c^2*x^2+1)*arcsinh(c*x)*x^2-2*b*(d*(c^2*x^2+1))^(1/2)*f*g/c/d/(c^2*x^2+1)^(1/2)*x+1/2*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c/d*f^2-1/4*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/c^3/d*g^2-1/8*b*(d*(c^2*x^2+1))^(1/2)*g^2/c^3/d/(c^2*x^2+1)^(1/2)+1/2*b*(d*(c^2*x^2+1))^(1/2)*g^2/d/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)*g^2/c/d/(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*g^2/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x+2*b*(d*(c^2*x^2+1))^(1/2)*f*g/c^2/d/(c^2*x^2+1)*arcsinh(c*x)","B"
49,1,209,108,0.406000," ","int((g*x+f)*(a+b*arcsinh(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 \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{\sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, f \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \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 x}{c d \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, g \arcsinh \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*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d*f*arcsinh(c*x)^2+b*(d*(c^2*x^2+1))^(1/2)*g/d/(c^2*x^2+1)*arcsinh(c*x)*x^2-b*(d*(c^2*x^2+1))^(1/2)*g/c/d/(c^2*x^2+1)^(1/2)*x+b*(d*(c^2*x^2+1))^(1/2)*g/c^2/d/(c^2*x^2+1)*arcsinh(c*x)","A"
50,1,77,41,0.006000," ","int((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","\frac{a \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{\sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c d}"," ",0,"a*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d*arcsinh(c*x)^2","A"
51,1,678,329,0.272000," ","int((a+b*arcsinh(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^{2} x^{2}+1}\, \arcsinh \left(c x \right) \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\, \arcsinh \left(c x \right) \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\, \dilog \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+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^{2} x^{2}+1}\, \dilog \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^2*x^2+1)^(1/2)/d/(c^4*f^2*x^2+c^2*g^2*x^2+c^2*f^2+g^2)*arcsinh(c*x)*ln((-(c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/d/(c^4*f^2*x^2+c^2*g^2*x^2+c^2*f^2+g^2)*arcsinh(c*x)*ln(((c*x+(c^2*x^2+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^2*x^2+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^2*x^2+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^2*x^2+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^2*x^2+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"
52,1,1770,442,0.686000," ","int((a+b*arcsinh(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)}\, \arcsinh \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)}\, \arcsinh \left(c x \right) x \,c^{2} f}{d \left(c^{2} f^{2}+g^{2}\right) \left(g x +f \right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \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)}\, \arcsinh \left(c x \right) x c g}{d \sqrt{c^{2} x^{2}+1}\, \left(c^{2} f^{2}+g^{2}\right) \left(g x +f \right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \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)}\, \arcsinh \left(c x \right) c f}{d \sqrt{c^{2} x^{2}+1}\, \left(c^{2} f^{2}+g^{2}\right) \left(g x +f \right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \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 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c^{2} f \arcsinh \left(c x \right) \sqrt{c^{2} f^{2}+g^{2}}\, \ln \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+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^{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)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c^{2} f \arcsinh \left(c x \right) \sqrt{c^{2} f^{2}+g^{2}}\, \ln \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^{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)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c^{3} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right) f^{2}}{d \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)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c^{3} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2} g +2 c f \left(c x +\sqrt{c^{2} x^{2}+1}\right)-g \right) f^{2}}{d \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)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c^{2} f \sqrt{c^{2} f^{2}+g^{2}}\, \dilog \left(\frac{-\left(c x +\sqrt{c^{2} x^{2}+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^{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)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c^{2} f \sqrt{c^{2} f^{2}+g^{2}}\, \dilog \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+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^{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)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right) g^{2}}{d \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)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, c \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2} g +2 c f \left(c x +\sqrt{c^{2} x^{2}+1}\right)-g \right) g^{2}}{d \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)}"," ",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)*arcsinh(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)*arcsinh(c*x)/d/(c^2*f^2+g^2)/(g*x+f)*x*c^2*f-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(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)*arcsinh(c*x)/d/(c^2*x^2+1)^(1/2)/(c^2*f^2+g^2)/(g*x+f)*x*c*g+b*(d*(c^2*x^2+1))^(1/2)*arcsinh(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)*arcsinh(c*x)/d/(c^2*x^2+1)^(1/2)/(c^2*f^2+g^2)/(g*x+f)*c*f-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/d/(c^2*x^2+1)/(c^2*f^2+g^2)/(g*x+f)*g+b*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+1)^(1/2)/d/(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)*c^2*f*arcsinh(c*x)*(c^2*f^2+g^2)^(1/2)*ln((-(c*x+(c^2*x^2+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*x^2+1)^(1/2)/d/(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)*c^2*f*arcsinh(c*x)*(c^2*f^2+g^2)^(1/2)*ln(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/d/(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)*c^3*ln(c*x+(c^2*x^2+1)^(1/2))*f^2+b*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+1)^(1/2)/d/(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)*c^3*ln((c*x+(c^2*x^2+1)^(1/2))^2*g+2*c*f*(c*x+(c^2*x^2+1)^(1/2))-g)*f^2+b*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+1)^(1/2)/d/(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)*c^2*f*(c^2*f^2+g^2)^(1/2)*dilog((-(c*x+(c^2*x^2+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*x^2+1)^(1/2)/d/(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)*c^2*f*(c^2*f^2+g^2)^(1/2)*dilog(((c*x+(c^2*x^2+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^2*x^2+1)^(1/2)/d/(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)*c*ln(c*x+(c^2*x^2+1)^(1/2))*g^2+b*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+1)^(1/2)/d/(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)*c*ln((c*x+(c^2*x^2+1)^(1/2))^2*g+2*c*f*(c*x+(c^2*x^2+1)^(1/2))-g)*g^2","B"
53,0,0,34,2.384000," ","int((a+b*arcsinh(c*x))^n*ln(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsinh \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*arcsinh(c*x))^n*ln(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x)","F"
54,0,0,486,2.638000," ","int((a+b*arcsinh(c*x))^2*ln(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsinh \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*arcsinh(c*x))^2*ln(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x)","F"
55,0,0,366,2.128000," ","int((a+b*arcsinh(c*x))*ln(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsinh \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*arcsinh(c*x))*ln(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x)","F"
56,0,0,223,0.176000," ","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"
57,0,0,34,1.279000," ","int(ln(h*(g*x+f)^m)/(a+b*arcsinh(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 \arcsinh \left(c x \right)\right) \sqrt{c^{2} x^{2}+1}}\, dx"," ",0,"int(ln(h*(g*x+f)^m)/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","F"
58,1,200,115,0.016000," ","int(x^3*arcsinh(b*x+a),x)","\frac{\frac{\arcsinh \left(b x +a \right) \left(b x +a \right)^{4}}{4}-\arcsinh \left(b x +a \right) \left(b x +a \right)^{3} a +\frac{3 \arcsinh \left(b x +a \right) \left(b x +a \right)^{2} a^{2}}{2}-\arcsinh \left(b x +a \right) \left(b x +a \right) a^{3}-\frac{\left(b x +a \right)^{3} \sqrt{1+\left(b x +a \right)^{2}}}{16}+\frac{3 \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{32}-\frac{3 \arcsinh \left(b x +a \right)}{32}+a \left(\frac{\left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}}{3}-\frac{2 \sqrt{1+\left(b x +a \right)^{2}}}{3}\right)-\frac{3 a^{2} \left(\frac{\left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{2}-\frac{\arcsinh \left(b x +a \right)}{2}\right)}{2}+a^{3} \sqrt{1+\left(b x +a \right)^{2}}}{b^{4}}"," ",0,"1/b^4*(1/4*arcsinh(b*x+a)*(b*x+a)^4-arcsinh(b*x+a)*(b*x+a)^3*a+3/2*arcsinh(b*x+a)*(b*x+a)^2*a^2-arcsinh(b*x+a)*(b*x+a)*a^3-1/16*(b*x+a)^3*(1+(b*x+a)^2)^(1/2)+3/32*(b*x+a)*(1+(b*x+a)^2)^(1/2)-3/32*arcsinh(b*x+a)+a*(1/3*(b*x+a)^2*(1+(b*x+a)^2)^(1/2)-2/3*(1+(b*x+a)^2)^(1/2))-3/2*a^2*(1/2*(b*x+a)*(1+(b*x+a)^2)^(1/2)-1/2*arcsinh(b*x+a))+a^3*(1+(b*x+a)^2)^(1/2))","A"
59,1,130,78,0.004000," ","int(x^2*arcsinh(b*x+a),x)","\frac{\frac{\arcsinh \left(b x +a \right) \left(b x +a \right)^{3}}{3}-\arcsinh \left(b x +a \right) \left(b x +a \right)^{2} a +\arcsinh \left(b x +a \right) \left(b x +a \right) a^{2}-\frac{\left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}}{9}+\frac{2 \sqrt{1+\left(b x +a \right)^{2}}}{9}+a \left(\frac{\left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{2}-\frac{\arcsinh \left(b x +a \right)}{2}\right)-a^{2} \sqrt{1+\left(b x +a \right)^{2}}}{b^{3}}"," ",0,"1/b^3*(1/3*arcsinh(b*x+a)*(b*x+a)^3-arcsinh(b*x+a)*(b*x+a)^2*a+arcsinh(b*x+a)*(b*x+a)*a^2-1/9*(b*x+a)^2*(1+(b*x+a)^2)^(1/2)+2/9*(1+(b*x+a)^2)^(1/2)+a*(1/2*(b*x+a)*(1+(b*x+a)^2)^(1/2)-1/2*arcsinh(b*x+a))-a^2*(1+(b*x+a)^2)^(1/2))","A"
60,1,74,64,0.004000," ","int(x*arcsinh(b*x+a),x)","\frac{\frac{\arcsinh \left(b x +a \right) \left(b x +a \right)^{2}}{2}-\arcsinh \left(b x +a \right) a \left(b x +a \right)-\frac{\left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{4}+\frac{\arcsinh \left(b x +a \right)}{4}+a \sqrt{1+\left(b x +a \right)^{2}}}{b^{2}}"," ",0,"1/b^2*(1/2*arcsinh(b*x+a)*(b*x+a)^2-arcsinh(b*x+a)*a*(b*x+a)-1/4*(b*x+a)*(1+(b*x+a)^2)^(1/2)+1/4*arcsinh(b*x+a)+a*(1+(b*x+a)^2)^(1/2))","A"
61,1,31,32,0.002000," ","int(arcsinh(b*x+a),x)","\frac{\left(b x +a \right) \arcsinh \left(b x +a \right)-\sqrt{1+\left(b x +a \right)^{2}}}{b}"," ",0,"1/b*((b*x+a)*arcsinh(b*x+a)-(1+(b*x+a)^2)^(1/2))","A"
62,1,388,153,0.171000," ","int(arcsinh(b*x+a)/x,x)","-\frac{\arcsinh \left(b x +a \right)^{2}}{2}+\frac{\left(a^{2}+1+\sqrt{a^{2}+1}\, a \right) \arcsinh \left(b x +a \right) \left(2 \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right) a^{2}+\ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)-2 \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right) \sqrt{a^{2}+1}\, a +\ln \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)\right)}{a^{2}+1}+\dilog \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)+\dilog \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)+\frac{a \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{\sqrt{a^{2}+1}}-\frac{a \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{\sqrt{a^{2}+1}}"," ",0,"-1/2*arcsinh(b*x+a)^2+(a^2+1+(a^2+1)^(1/2)*a)/(a^2+1)*arcsinh(b*x+a)*(2*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))*a^2+ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))-2*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))*(a^2+1)^(1/2)*a+ln(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2))))+dilog(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))+dilog(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))+a*arcsinh(b*x+a)/(a^2+1)^(1/2)*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))-a*arcsinh(b*x+a)/(a^2+1)^(1/2)*ln(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))","B"
63,1,71,51,0.006000," ","int(arcsinh(b*x+a)/x^2,x)","-\frac{\arcsinh \left(b x +a \right)}{x}-\frac{b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b x}\right)}{\sqrt{a^{2}+1}}"," ",0,"-arcsinh(b*x+a)/x-b/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/b/x)","A"
64,1,106,78,0.008000," ","int(arcsinh(b*x+a)/x^3,x)","-\frac{\arcsinh \left(b x +a \right)}{2 x^{2}}-\frac{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right) x}+\frac{b^{2} a \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b x}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-1/2*arcsinh(b*x+a)/x^2-1/2*b/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*b^2*a/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/b/x)","A"
65,1,203,111,0.008000," ","int(arcsinh(b*x+a)/x^4,x)","-\frac{\arcsinh \left(b x +a \right)}{3 x^{3}}-\frac{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{6 \left(a^{2}+1\right) x^{2}}+\frac{b^{2} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right)^{2} x}-\frac{b^{3} a^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b x}\right)}{6 \left(a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-1/3*arcsinh(b*x+a)/x^3-1/6*b/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*b^2*a/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*b^3*a^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/b/x)+1/6*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/b/x)","A"
66,1,275,145,0.009000," ","int(arcsinh(b*x+a)/x^5,x)","-\frac{\arcsinh \left(b x +a \right)}{4 x^{4}}-\frac{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{12 \left(a^{2}+1\right) x^{3}}+\frac{5 b^{2} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{24 \left(a^{2}+1\right)^{2} x^{2}}-\frac{5 b^{3} a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 \left(a^{2}+1\right)^{3} x}+\frac{5 b^{4} a^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b x}\right)}{8 \left(a^{2}+1\right)^{\frac{7}{2}}}-\frac{3 b^{4} a \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b x}\right)}{8 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{6 \left(a^{2}+1\right)^{2} x}"," ",0,"-1/4*arcsinh(b*x+a)/x^4-1/12*b/(a^2+1)/x^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5/24*b^2*a/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/8*b^3*a^2/(a^2+1)^3/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5/8*b^4*a^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/b/x)-3/8*b^4*a/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/b/x)+1/6*b^3/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","A"
67,1,377,291,0.109000," ","int(x^3*arcsinh(b*x+a)^2,x)","\frac{-a^{3} \left(\arcsinh \left(b x +a \right)^{2} \left(b x +a \right)-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+2 b x +2 a \right)+\frac{3 a^{2} \left(2 \arcsinh \left(b x +a \right)^{2} \left(b x +a \right)^{2}-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)+\arcsinh \left(b x +a \right)^{2}+\left(b x +a \right)^{2}+1\right)}{4}-\frac{a \left(9 \arcsinh \left(b x +a \right)^{2} \left(b x +a \right)^{3}-6 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)^{2}+27 \arcsinh \left(b x +a \right)^{2} \left(b x +a \right)+2 \left(b x +a \right)^{3}-42 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+42 b x +42 a \right)}{9}+\frac{\arcsinh \left(b x +a \right)^{2} \left(1+\left(b x +a \right)^{2}\right)^{2}}{4}-\frac{\arcsinh \left(b x +a \right) \left(b x +a \right) \left(1+\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{8}+\frac{5 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)}{16}+\frac{5 \arcsinh \left(b x +a \right)^{2}}{32}+\frac{\left(1+\left(b x +a \right)^{2}\right)^{2}}{32}-\frac{5 \left(b x +a \right)^{2}}{32}-\frac{5}{32}+3 a \left(\arcsinh \left(b x +a \right)^{2} \left(b x +a \right)-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+2 b x +2 a \right)-\frac{\arcsinh \left(b x +a \right)^{2} \left(1+\left(b x +a \right)^{2}\right)}{2}}{b^{4}}"," ",0,"1/b^4*(-a^3*(arcsinh(b*x+a)^2*(b*x+a)-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+2*b*x+2*a)+3/4*a^2*(2*arcsinh(b*x+a)^2*(b*x+a)^2-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)*(b*x+a)+arcsinh(b*x+a)^2+(b*x+a)^2+1)-1/9*a*(9*arcsinh(b*x+a)^2*(b*x+a)^3-6*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)*(b*x+a)^2+27*arcsinh(b*x+a)^2*(b*x+a)+2*(b*x+a)^3-42*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+42*b*x+42*a)+1/4*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^2-1/8*arcsinh(b*x+a)*(b*x+a)*(1+(b*x+a)^2)^(3/2)+5/16*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)*(b*x+a)+5/32*arcsinh(b*x+a)^2+1/32*(1+(b*x+a)^2)^2-5/32*(b*x+a)^2-5/32+3*a*(arcsinh(b*x+a)^2*(b*x+a)-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+2*b*x+2*a)-1/2*arcsinh(b*x+a)^2*(1+(b*x+a)^2))","A"
68,1,212,187,0.086000," ","int(x^2*arcsinh(b*x+a)^2,x)","\frac{-\frac{a \left(2 \arcsinh \left(b x +a \right)^{2} \left(b x +a \right)^{2}-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)+\arcsinh \left(b x +a \right)^{2}+\left(b x +a \right)^{2}+1\right)}{2}-\frac{\arcsinh \left(b x +a \right)^{2} \left(b x +a \right)}{3}+\frac{\arcsinh \left(b x +a \right)^{2} \left(b x +a \right) \left(1+\left(b x +a \right)^{2}\right)}{3}+\frac{2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{3}-\frac{14 b x}{27}-\frac{14 a}{27}-\frac{2 \arcsinh \left(b x +a \right) \left(1+\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{9}+\frac{2 \left(1+\left(b x +a \right)^{2}\right) \left(b x +a \right)}{27}+a^{2} \left(\arcsinh \left(b x +a \right)^{2} \left(b x +a \right)-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+2 b x +2 a \right)}{b^{3}}"," ",0,"1/b^3*(-1/2*a*(2*arcsinh(b*x+a)^2*(b*x+a)^2-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)*(b*x+a)+arcsinh(b*x+a)^2+(b*x+a)^2+1)-1/3*arcsinh(b*x+a)^2*(b*x+a)+1/3*arcsinh(b*x+a)^2*(b*x+a)*(1+(b*x+a)^2)+2/3*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)-14/27*b*x-14/27*a-2/9*arcsinh(b*x+a)*(1+(b*x+a)^2)^(3/2)+2/27*(1+(b*x+a)^2)*(b*x+a)+a^2*(arcsinh(b*x+a)^2*(b*x+a)-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+2*b*x+2*a))","A"
69,1,113,112,0.077000," ","int(x*arcsinh(b*x+a)^2,x)","\frac{\frac{\arcsinh \left(b x +a \right)^{2} \left(1+\left(b x +a \right)^{2}\right)}{2}-\frac{\arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)}{2}-\frac{\arcsinh \left(b x +a \right)^{2}}{4}+\frac{\left(b x +a \right)^{2}}{4}+\frac{1}{4}-a \left(\arcsinh \left(b x +a \right)^{2} \left(b x +a \right)-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+2 b x +2 a \right)}{b^{2}}"," ",0,"1/b^2*(1/2*arcsinh(b*x+a)^2*(1+(b*x+a)^2)-1/2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)*(b*x+a)-1/4*arcsinh(b*x+a)^2+1/4*(b*x+a)^2+1/4-a*(arcsinh(b*x+a)^2*(b*x+a)-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+2*b*x+2*a))","A"
70,1,46,43,0.053000," ","int(arcsinh(b*x+a)^2,x)","\frac{\arcsinh \left(b x +a \right)^{2} \left(b x +a \right)-2 \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+2 b x +2 a}{b}"," ",0,"1/b*(arcsinh(b*x+a)^2*(b*x+a)-2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+2*b*x+2*a)","A"
71,0,0,239,0.217000," ","int(arcsinh(b*x+a)^2/x,x)","\int \frac{\arcsinh \left(b x +a \right)^{2}}{x}\, dx"," ",0,"int(arcsinh(b*x+a)^2/x,x)","F"
72,1,217,194,0.394000," ","int(arcsinh(b*x+a)^2/x^2,x)","-\frac{\arcsinh \left(b x +a \right)^{2}}{x}+\frac{2 b \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{\sqrt{a^{2}+1}}-\frac{2 b \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{\sqrt{a^{2}+1}}+\frac{2 b \dilog \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{\sqrt{a^{2}+1}}-\frac{2 b \dilog \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{\sqrt{a^{2}+1}}"," ",0,"-arcsinh(b*x+a)^2/x+2*b*arcsinh(b*x+a)/(a^2+1)^(1/2)*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))-2*b*arcsinh(b*x+a)/(a^2+1)^(1/2)*ln(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))+2*b/(a^2+1)^(1/2)*dilog(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))-2*b/(a^2+1)^(1/2)*dilog(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))","A"
73,1,384,247,0.662000," ","int(arcsinh(b*x+a)^2/x^3,x)","\frac{b^{2} \arcsinh \left(b x +a \right)}{a^{2}+1}-\frac{\arcsinh \left(b x +a \right)^{2} a^{2}}{2 x^{2} \left(a^{2}+1\right)}-\frac{b \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{\left(a^{2}+1\right) x}-\frac{\arcsinh \left(b x +a \right)^{2}}{2 x^{2} \left(a^{2}+1\right)}-\frac{b^{2} a \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{b^{2} a \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{b^{2} \dilog \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right) a}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{b^{2} \dilog \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right) a}{\left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{2 b^{2} \ln \left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)}{a^{2}+1}+\frac{b^{2} \ln \left(\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}-2 a \left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)-1\right)}{a^{2}+1}"," ",0,"b^2*arcsinh(b*x+a)/(a^2+1)-1/2*arcsinh(b*x+a)^2/x^2/(a^2+1)*a^2-b*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)/(a^2+1)/x-1/2*arcsinh(b*x+a)^2/x^2/(a^2+1)-b^2/(a^2+1)^(3/2)*a*arcsinh(b*x+a)*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))+b^2/(a^2+1)^(3/2)*a*arcsinh(b*x+a)*ln(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))-b^2/(a^2+1)^(3/2)*dilog(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))*a+b^2/(a^2+1)^(3/2)*dilog(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))*a-2*b^2/(a^2+1)*ln(b*x+a+(1+(b*x+a)^2)^(1/2))+b^2/(a^2+1)*ln((b*x+a+(1+(b*x+a)^2)^(1/2))^2-2*a*(b*x+a+(1+(b*x+a)^2)^(1/2))-1)","A"
74,1,730,492,0.887000," ","int(arcsinh(b*x+a)^2/x^4,x)","-\frac{b^{3} \arcsinh \left(b x +a \right) a}{\left(a^{2}+1\right)^{2}}+\frac{a \,b^{2} \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{\left(a^{2}+1\right)^{2} x}-\frac{\arcsinh \left(b x +a \right)^{2} a^{4}}{3 \left(a^{2}+1\right)^{2} x^{3}}-\frac{b \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}\, a^{2}}{3 \left(a^{2}+1\right)^{2} x^{2}}-\frac{b^{2} a^{2}}{3 \left(a^{2}+1\right)^{2} x}-\frac{2 \arcsinh \left(b x +a \right)^{2} a^{2}}{3 \left(a^{2}+1\right)^{2} x^{3}}-\frac{b \arcsinh \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{3 \left(a^{2}+1\right)^{2} x^{2}}-\frac{b^{2}}{3 \left(a^{2}+1\right)^{2} x}-\frac{\arcsinh \left(b x +a \right)^{2}}{3 \left(a^{2}+1\right)^{2} x^{3}}+\frac{2 b^{3} a \ln \left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)}{\left(a^{2}+1\right)^{2}}-\frac{b^{3} a \ln \left(\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}-2 a \left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)-1\right)}{\left(a^{2}+1\right)^{2}}-\frac{b^{3} \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{3} \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{b^{3} \dilog \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{3} \dilog \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{2 b^{3} a^{2} \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{2 b^{3} a^{2} \arcsinh \left(b x +a \right) \ln \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{2 b^{3} a^{2} \dilog \left(\frac{\sqrt{a^{2}+1}-b x -\sqrt{1+\left(b x +a \right)^{2}}}{a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{2 b^{3} a^{2} \dilog \left(\frac{\sqrt{a^{2}+1}+b x +\sqrt{1+\left(b x +a \right)^{2}}}{-a +\sqrt{a^{2}+1}}\right)}{3 \left(a^{2}+1\right)^{\frac{5}{2}}}"," ",0,"-b^3/(a^2+1)^2*arcsinh(b*x+a)*a+a*b^2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)/(a^2+1)^2/x-1/3/(a^2+1)^2/x^3*arcsinh(b*x+a)^2*a^4-1/3*b/(a^2+1)^2/x^2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)*a^2-1/3*b^2/(a^2+1)^2/x*a^2-2/3/(a^2+1)^2/x^3*arcsinh(b*x+a)^2*a^2-1/3*b/(a^2+1)^2/x^2*arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)-1/3*b^2/(a^2+1)^2/x-1/3/(a^2+1)^2/x^3*arcsinh(b*x+a)^2+2*b^3/(a^2+1)^2*a*ln(b*x+a+(1+(b*x+a)^2)^(1/2))-b^3/(a^2+1)^2*a*ln((b*x+a+(1+(b*x+a)^2)^(1/2))^2-2*a*(b*x+a+(1+(b*x+a)^2)^(1/2))-1)-1/3*b^3/(a^2+1)^(5/2)*arcsinh(b*x+a)*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))+1/3*b^3/(a^2+1)^(5/2)*arcsinh(b*x+a)*ln(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))-1/3*b^3/(a^2+1)^(5/2)*dilog(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))+1/3*b^3/(a^2+1)^(5/2)*dilog(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))+2/3*b^3/(a^2+1)^(5/2)*a^2*arcsinh(b*x+a)*ln(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))-2/3*b^3/(a^2+1)^(5/2)*a^2*arcsinh(b*x+a)*ln(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))+2/3*b^3/(a^2+1)^(5/2)*a^2*dilog(((a^2+1)^(1/2)-b*x-(1+(b*x+a)^2)^(1/2))/(a+(a^2+1)^(1/2)))-2/3*b^3/(a^2+1)^(5/2)*a^2*dilog(((a^2+1)^(1/2)+b*x+(1+(b*x+a)^2)^(1/2))/(-a+(a^2+1)^(1/2)))","A"
75,1,311,313,0.099000," ","int(x^2*arcsinh(b*x+a)^3,x)","\frac{-\frac{a \left(4 \arcsinh \left(b x +a \right)^{3} \left(b x +a \right)^{2}-6 \arcsinh \left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)+2 \arcsinh \left(b x +a \right)^{3}+6 \arcsinh \left(b x +a \right) \left(b x +a \right)^{2}-3 \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+3 \arcsinh \left(b x +a \right)\right)}{4}-\frac{\arcsinh \left(b x +a \right)^{3} \left(b x +a \right)}{3}+\frac{\arcsinh \left(b x +a \right)^{3} \left(b x +a \right) \left(1+\left(b x +a \right)^{2}\right)}{3}+\arcsinh \left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}-\frac{14 \left(b x +a \right) \arcsinh \left(b x +a \right)}{9}+\frac{14 \sqrt{1+\left(b x +a \right)^{2}}}{9}-\frac{\arcsinh \left(b x +a \right)^{2} \left(1+\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{3}+\frac{2 \left(b x +a \right) \left(1+\left(b x +a \right)^{2}\right) \arcsinh \left(b x +a \right)}{9}-\frac{2 \left(1+\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{27}+a^{2} \left(\arcsinh \left(b x +a \right)^{3} \left(b x +a \right)-3 \arcsinh \left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}+6 \left(b x +a \right) \arcsinh \left(b x +a \right)-6 \sqrt{1+\left(b x +a \right)^{2}}\right)}{b^{3}}"," ",0,"1/b^3*(-1/4*a*(4*arcsinh(b*x+a)^3*(b*x+a)^2-6*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)*(b*x+a)+2*arcsinh(b*x+a)^3+6*arcsinh(b*x+a)*(b*x+a)^2-3*(b*x+a)*(1+(b*x+a)^2)^(1/2)+3*arcsinh(b*x+a))-1/3*arcsinh(b*x+a)^3*(b*x+a)+1/3*arcsinh(b*x+a)^3*(b*x+a)*(1+(b*x+a)^2)+arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)-14/9*(b*x+a)*arcsinh(b*x+a)+14/9*(1+(b*x+a)^2)^(1/2)-1/3*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(3/2)+2/9*(b*x+a)*(1+(b*x+a)^2)*arcsinh(b*x+a)-2/27*(1+(b*x+a)^2)^(3/2)+a^2*(arcsinh(b*x+a)^3*(b*x+a)-3*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)+6*(b*x+a)*arcsinh(b*x+a)-6*(1+(b*x+a)^2)^(1/2)))","A"
76,1,169,181,0.076000," ","int(x*arcsinh(b*x+a)^3,x)","\frac{\frac{\arcsinh \left(b x +a \right)^{3} \left(1+\left(b x +a \right)^{2}\right)}{2}-\frac{3 \arcsinh \left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}\, \left(b x +a \right)}{4}-\frac{\arcsinh \left(b x +a \right)^{3}}{4}+\frac{3 \arcsinh \left(b x +a \right) \left(1+\left(b x +a \right)^{2}\right)}{4}-\frac{3 \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}}{8}-\frac{3 \arcsinh \left(b x +a \right)}{8}-a \left(\arcsinh \left(b x +a \right)^{3} \left(b x +a \right)-3 \arcsinh \left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}+6 \left(b x +a \right) \arcsinh \left(b x +a \right)-6 \sqrt{1+\left(b x +a \right)^{2}}\right)}{b^{2}}"," ",0,"1/b^2*(1/2*arcsinh(b*x+a)^3*(1+(b*x+a)^2)-3/4*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)*(b*x+a)-1/4*arcsinh(b*x+a)^3+3/4*arcsinh(b*x+a)*(1+(b*x+a)^2)-3/8*(b*x+a)*(1+(b*x+a)^2)^(1/2)-3/8*arcsinh(b*x+a)-a*(arcsinh(b*x+a)^3*(b*x+a)-3*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)+6*(b*x+a)*arcsinh(b*x+a)-6*(1+(b*x+a)^2)^(1/2)))","A"
77,1,67,74,0.052000," ","int(arcsinh(b*x+a)^3,x)","\frac{\arcsinh \left(b x +a \right)^{3} \left(b x +a \right)-3 \arcsinh \left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}+6 \left(b x +a \right) \arcsinh \left(b x +a \right)-6 \sqrt{1+\left(b x +a \right)^{2}}}{b}"," ",0,"1/b*(arcsinh(b*x+a)^3*(b*x+a)-3*arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)+6*(b*x+a)*arcsinh(b*x+a)-6*(1+(b*x+a)^2)^(1/2))","A"
78,0,0,321,0.191000," ","int(arcsinh(b*x+a)^3/x,x)","\int \frac{\arcsinh \left(b x +a \right)^{3}}{x}\, dx"," ",0,"int(arcsinh(b*x+a)^3/x,x)","F"
79,0,0,292,0.446000," ","int(arcsinh(b*x+a)^3/x^2,x)","\int \frac{\arcsinh \left(b x +a \right)^{3}}{x^{2}}\, dx"," ",0,"int(arcsinh(b*x+a)^3/x^2,x)","F"
80,0,0,550,0.765000," ","int(arcsinh(b*x+a)^3/x^3,x)","\int \frac{\arcsinh \left(b x +a \right)^{3}}{x^{3}}\, dx"," ",0,"int(arcsinh(b*x+a)^3/x^3,x)","F"
81,1,49,56,0.122000," ","int(x^2/arcsinh(b*x+a),x)","\frac{-a \Shi \left(2 \arcsinh \left(b x +a \right)\right)-\frac{\Chi \left(\arcsinh \left(b x +a \right)\right)}{4}+\frac{\Chi \left(3 \arcsinh \left(b x +a \right)\right)}{4}+a^{2} \Chi \left(\arcsinh \left(b x +a \right)\right)}{b^{3}}"," ",0,"1/b^3*(-a*Shi(2*arcsinh(b*x+a))-1/4*Chi(arcsinh(b*x+a))+1/4*Chi(3*arcsinh(b*x+a))+a^2*Chi(arcsinh(b*x+a)))","A"
82,1,27,28,0.058000," ","int(x/arcsinh(b*x+a),x)","\frac{\frac{\Shi \left(2 \arcsinh \left(b x +a \right)\right)}{2}-a \Chi \left(\arcsinh \left(b x +a \right)\right)}{b^{2}}"," ",0,"1/b^2*(1/2*Shi(2*arcsinh(b*x+a))-a*Chi(arcsinh(b*x+a)))","A"
83,1,12,11,0.049000," ","int(1/arcsinh(b*x+a),x)","\frac{\Chi \left(\arcsinh \left(b x +a \right)\right)}{b}"," ",0,"Chi(arcsinh(b*x+a))/b","A"
84,0,0,14,0.171000," ","int(1/x/arcsinh(b*x+a),x)","\int \frac{1}{x \arcsinh \left(b x +a \right)}\, dx"," ",0,"int(1/x/arcsinh(b*x+a),x)","F"
85,1,146,144,0.131000," ","int(x^2/arcsinh(b*x+a)^2,x)","\frac{-\frac{a \left(2 \Chi \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\sinh \left(2 \arcsinh \left(b x +a \right)\right)\right)}{\arcsinh \left(b x +a \right)}+\frac{\sqrt{1+\left(b x +a \right)^{2}}}{4 \arcsinh \left(b x +a \right)}-\frac{\Shi \left(\arcsinh \left(b x +a \right)\right)}{4}-\frac{\cosh \left(3 \arcsinh \left(b x +a \right)\right)}{4 \arcsinh \left(b x +a \right)}+\frac{3 \Shi \left(3 \arcsinh \left(b x +a \right)\right)}{4}+\frac{a^{2} \left(\Shi \left(\arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\sqrt{1+\left(b x +a \right)^{2}}\right)}{\arcsinh \left(b x +a \right)}}{b^{3}}"," ",0,"1/b^3*(-a*(2*Chi(2*arcsinh(b*x+a))*arcsinh(b*x+a)-sinh(2*arcsinh(b*x+a)))/arcsinh(b*x+a)+1/4/arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)-1/4*Shi(arcsinh(b*x+a))-1/4/arcsinh(b*x+a)*cosh(3*arcsinh(b*x+a))+3/4*Shi(3*arcsinh(b*x+a))+a^2*(Shi(arcsinh(b*x+a))*arcsinh(b*x+a)-(1+(b*x+a)^2)^(1/2))/arcsinh(b*x+a))","A"
86,1,73,80,0.081000," ","int(x/arcsinh(b*x+a)^2,x)","\frac{-\frac{\sinh \left(2 \arcsinh \left(b x +a \right)\right)}{2 \arcsinh \left(b x +a \right)}+\Chi \left(2 \arcsinh \left(b x +a \right)\right)-\frac{a \left(\Shi \left(\arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\sqrt{1+\left(b x +a \right)^{2}}\right)}{\arcsinh \left(b x +a \right)}}{b^{2}}"," ",0,"1/b^2*(-1/2*sinh(2*arcsinh(b*x+a))/arcsinh(b*x+a)+Chi(2*arcsinh(b*x+a))-a*(Shi(arcsinh(b*x+a))*arcsinh(b*x+a)-(1+(b*x+a)^2)^(1/2))/arcsinh(b*x+a))","A"
87,1,34,36,0.053000," ","int(1/arcsinh(b*x+a)^2,x)","\frac{-\frac{\sqrt{1+\left(b x +a \right)^{2}}}{\arcsinh \left(b x +a \right)}+\Shi \left(\arcsinh \left(b x +a \right)\right)}{b}"," ",0,"1/b*(-1/arcsinh(b*x+a)*(1+(b*x+a)^2)^(1/2)+Shi(arcsinh(b*x+a)))","A"
88,0,0,14,0.181000," ","int(1/x/arcsinh(b*x+a)^2,x)","\int \frac{1}{x \arcsinh \left(b x +a \right)^{2}}\, dx"," ",0,"int(1/x/arcsinh(b*x+a)^2,x)","F"
89,1,215,239,0.158000," ","int(x^2/arcsinh(b*x+a)^3,x)","\frac{-\frac{a \left(4 \Shi \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)^{2}-2 \cosh \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\sinh \left(2 \arcsinh \left(b x +a \right)\right)\right)}{2 \arcsinh \left(b x +a \right)^{2}}+\frac{\sqrt{1+\left(b x +a \right)^{2}}}{8 \arcsinh \left(b x +a \right)^{2}}+\frac{b x +a}{8 \arcsinh \left(b x +a \right)}-\frac{\Chi \left(\arcsinh \left(b x +a \right)\right)}{8}-\frac{\cosh \left(3 \arcsinh \left(b x +a \right)\right)}{8 \arcsinh \left(b x +a \right)^{2}}-\frac{3 \sinh \left(3 \arcsinh \left(b x +a \right)\right)}{8 \arcsinh \left(b x +a \right)}+\frac{9 \Chi \left(3 \arcsinh \left(b x +a \right)\right)}{8}+\frac{a^{2} \left(\Chi \left(\arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)^{2}-\left(b x +a \right) \arcsinh \left(b x +a \right)-\sqrt{1+\left(b x +a \right)^{2}}\right)}{2 \arcsinh \left(b x +a \right)^{2}}}{b^{3}}"," ",0,"1/b^3*(-1/2*a*(4*Shi(2*arcsinh(b*x+a))*arcsinh(b*x+a)^2-2*cosh(2*arcsinh(b*x+a))*arcsinh(b*x+a)-sinh(2*arcsinh(b*x+a)))/arcsinh(b*x+a)^2+1/8/arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)+1/8/arcsinh(b*x+a)*(b*x+a)-1/8*Chi(arcsinh(b*x+a))-1/8/arcsinh(b*x+a)^2*cosh(3*arcsinh(b*x+a))-3/8/arcsinh(b*x+a)*sinh(3*arcsinh(b*x+a))+9/8*Chi(3*arcsinh(b*x+a))+1/2*a^2*(Chi(arcsinh(b*x+a))*arcsinh(b*x+a)^2-(b*x+a)*arcsinh(b*x+a)-(1+(b*x+a)^2)^(1/2))/arcsinh(b*x+a)^2)","A"
90,1,107,133,0.083000," ","int(x/arcsinh(b*x+a)^3,x)","\frac{-\frac{\sinh \left(2 \arcsinh \left(b x +a \right)\right)}{4 \arcsinh \left(b x +a \right)^{2}}-\frac{\cosh \left(2 \arcsinh \left(b x +a \right)\right)}{2 \arcsinh \left(b x +a \right)}+\Shi \left(2 \arcsinh \left(b x +a \right)\right)-\frac{a \left(\Chi \left(\arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)^{2}-\left(b x +a \right) \arcsinh \left(b x +a \right)-\sqrt{1+\left(b x +a \right)^{2}}\right)}{2 \arcsinh \left(b x +a \right)^{2}}}{b^{2}}"," ",0,"1/b^2*(-1/4*sinh(2*arcsinh(b*x+a))/arcsinh(b*x+a)^2-1/2/arcsinh(b*x+a)*cosh(2*arcsinh(b*x+a))+Shi(2*arcsinh(b*x+a))-1/2*a*(Chi(arcsinh(b*x+a))*arcsinh(b*x+a)^2-(b*x+a)*arcsinh(b*x+a)-(1+(b*x+a)^2)^(1/2))/arcsinh(b*x+a)^2)","A"
91,1,51,58,0.028000," ","int(1/arcsinh(b*x+a)^3,x)","\frac{-\frac{\sqrt{1+\left(b x +a \right)^{2}}}{2 \arcsinh \left(b x +a \right)^{2}}-\frac{b x +a}{2 \arcsinh \left(b x +a \right)}+\frac{\Chi \left(\arcsinh \left(b x +a \right)\right)}{2}}{b}"," ",0,"1/b*(-1/2/arcsinh(b*x+a)^2*(1+(b*x+a)^2)^(1/2)-1/2/arcsinh(b*x+a)*(b*x+a)+1/2*Chi(arcsinh(b*x+a)))","A"
92,0,0,14,0.181000," ","int(1/x/arcsinh(b*x+a)^3,x)","\int \frac{1}{x \arcsinh \left(b x +a \right)^{3}}\, dx"," ",0,"int(1/x/arcsinh(b*x+a)^3,x)","F"
93,0,0,18,0.188000," ","int(x^m*(a+b*arcsinh(d*x+c))^n,x)","\int x^{m} \left(a +b \arcsinh \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(x^m*(a+b*arcsinh(d*x+c))^n,x)","F"
94,-2,0,543,180.000000," ","int(x^2*(a+b*arcsinh(d*x+c))^n,x)","\int x^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(x^2*(a+b*arcsinh(d*x+c))^n,x)","F"
95,0,0,268,0.317000," ","int(x*(a+b*arcsinh(d*x+c))^n,x)","\int x \left(a +b \arcsinh \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(x*(a+b*arcsinh(d*x+c))^n,x)","F"
96,0,0,127,0.104000," ","int((a+b*arcsinh(d*x+c))^n,x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^n,x)","F"
97,0,0,18,0.185000," ","int((a+b*arcsinh(d*x+c))^n/x,x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{n}}{x}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^n/x,x)","F"
98,-2,0,392,180.000000," ","int(x^2*(a+b*arcsinh(d*x+c))^(1/2),x)","\int x^{2} \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int(x^2*(a+b*arcsinh(d*x+c))^(1/2),x)","F"
99,0,0,206,0.520000," ","int(x*(a+b*arcsinh(d*x+c))^(1/2),x)","\int x \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int(x*(a+b*arcsinh(d*x+c))^(1/2),x)","F"
100,0,0,92,0.070000," ","int((a+b*arcsinh(d*x+c))^(1/2),x)","\int \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(1/2),x)","F"
101,0,0,263,0.504000," ","int(x*(a+b*arcsinh(d*x+c))^(3/2),x)","\int x \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a+b*arcsinh(d*x+c))^(3/2),x)","F"
102,0,0,121,0.120000," ","int((a+b*arcsinh(d*x+c))^(3/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(3/2),x)","F"
103,0,0,318,0.507000," ","int(x*(a+b*arcsinh(d*x+c))^(5/2),x)","\int x \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(x*(a+b*arcsinh(d*x+c))^(5/2),x)","F"
104,0,0,146,0.128000," ","int((a+b*arcsinh(d*x+c))^(5/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(5/2),x)","F"
105,-2,0,317,180.000000," ","int(x^2/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{x^{2}}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int(x^2/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
106,0,0,157,0.486000," ","int(x/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{x}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int(x/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
107,0,0,71,0.067000," ","int(1/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
108,0,0,224,0.472000," ","int(x/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{x}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
109,0,0,101,0.124000," ","int(1/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
110,0,0,298,0.483000," ","int(x/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{x}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(x/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
111,0,0,127,0.125000," ","int(1/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
112,0,0,366,0.476000," ","int(x/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{x}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(x/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
113,0,0,158,0.126000," ","int(1/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
114,0,0,87,2.146000," ","int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c)),x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsinh \left(d x +c \right)\right)\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c)),x)","F"
115,1,93,86,0.014000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(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} \arcsinh \left(d x +c \right)}{5}-\frac{\left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{75}-\frac{8 \sqrt{1+\left(d x +c \right)^{2}}}{75}\right)}{d}"," ",0,"1/d*(1/5*(d*x+c)^5*e^4*a+e^4*b*(1/5*(d*x+c)^5*arcsinh(d*x+c)-1/25*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+4/75*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-8/75*(1+(d*x+c)^2)^(1/2)))","A"
116,1,86,93,0.006000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c)),x)","\frac{\frac{\left(d x +c \right)^{4} e^{3} a}{4}+e^{3} b \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)}{4}-\frac{\left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsinh \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*(d*x+c)^4*e^3*a+e^3*b*(1/4*(d*x+c)^4*arcsinh(d*x+c)-1/16*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/32*arcsinh(d*x+c)))","A"
117,1,73,66,0.006000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c)),x)","\frac{\frac{\left(d x +c \right)^{3} e^{2} a}{3}+e^{2} b \left(\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{3}-\frac{\left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1+\left(d x +c \right)^{2}}}{9}\right)}{d}"," ",0,"1/d*(1/3*(d*x+c)^3*e^2*a+e^2*b*(1/3*(d*x+c)^3*arcsinh(d*x+c)-1/9*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+2/9*(1+(d*x+c)^2)^(1/2)))","A"
118,1,62,60,0.006000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c)),x)","\frac{\frac{\left(d x +c \right)^{2} e a}{2}+e b \left(\frac{\left(d x +c \right)^{2} \arcsinh \left(d x +c \right)}{2}-\frac{\left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{4}+\frac{\arcsinh \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*(d*x+c)^2*e*a+e*b*(1/2*(d*x+c)^2*arcsinh(d*x+c)-1/4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1/4*arcsinh(d*x+c)))","A"
119,1,36,37,0.003000," ","int(a+b*arcsinh(d*x+c),x)","a x +\frac{b \left(\left(d x +c \right) \arcsinh \left(d x +c \right)-\sqrt{1+\left(d x +c \right)^{2}}\right)}{d}"," ",0,"a*x+b/d*((d*x+c)*arcsinh(d*x+c)-(1+(d*x+c)^2)^(1/2))","A"
120,1,159,93,0.100000," ","int((a+b*arcsinh(d*x+c))/(d*e*x+c*e),x)","\frac{a \ln \left(d x +c \right)}{d e}-\frac{b \arcsinh \left(d x +c \right)^{2}}{2 d e}+\frac{b \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"1/d*a/e*ln(d*x+c)-1/2/d*b/e*arcsinh(d*x+c)^2+1/d*b/e*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+1/d*b/e*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+1/d*b/e*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+1/d*b/e*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))","A"
121,1,54,49,0.005000," ","int((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^2,x)","\frac{-\frac{a}{e^{2} \left(d x +c \right)}+\frac{b \left(-\frac{\arcsinh \left(d x +c \right)}{d x +c}-\arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)\right)}{e^{2}}}{d}"," ",0,"1/d*(-a/e^2/(d*x+c)+b/e^2*(-1/(d*x+c)*arcsinh(d*x+c)-arctanh(1/(1+(d*x+c)^2)^(1/2))))","A"
122,1,60,56,0.006000," ","int((a+b*arcsinh(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{\arcsinh \left(d x +c \right)}{2 \left(d x +c \right)^{2}}-\frac{\sqrt{1+\left(d x +c \right)^{2}}}{2 \left(d x +c \right)}\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*arcsinh(d*x+c)-1/2/(d*x+c)*(1+(d*x+c)^2)^(1/2)))","A"
123,1,74,77,0.006000," ","int((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^4,x)","\frac{-\frac{a}{3 e^{4} \left(d x +c \right)^{3}}+\frac{b \left(-\frac{\arcsinh \left(d x +c \right)}{3 \left(d x +c \right)^{3}}-\frac{\sqrt{1+\left(d x +c \right)^{2}}}{6 \left(d x +c \right)^{2}}+\frac{\arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{6}\right)}{e^{4}}}{d}"," ",0,"1/d*(-1/3*a/e^4/(d*x+c)^3+b/e^4*(-1/3/(d*x+c)^3*arcsinh(d*x+c)-1/6/(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+1/6*arctanh(1/(1+(d*x+c)^2)^(1/2))))","A"
124,1,80,83,0.006000," ","int((a+b*arcsinh(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{\arcsinh \left(d x +c \right)}{4 \left(d x +c \right)^{4}}-\frac{\sqrt{1+\left(d x +c \right)^{2}}}{12 \left(d x +c \right)^{3}}+\frac{\sqrt{1+\left(d x +c \right)^{2}}}{6 d x +6 c}\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*arcsinh(d*x+c)-1/12/(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+1/6/(d*x+c)*(1+(d*x+c)^2)^(1/2)))","A"
125,1,94,104,0.008000," ","int((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^6,x)","\frac{-\frac{a}{5 e^{6} \left(d x +c \right)^{5}}+\frac{b \left(-\frac{\arcsinh \left(d x +c \right)}{5 \left(d x +c \right)^{5}}-\frac{\sqrt{1+\left(d x +c \right)^{2}}}{20 \left(d x +c \right)^{4}}+\frac{3 \sqrt{1+\left(d x +c \right)^{2}}}{40 \left(d x +c \right)^{2}}-\frac{3 \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{40}\right)}{e^{6}}}{d}"," ",0,"1/d*(-1/5*a/e^6/(d*x+c)^5+b/e^6*(-1/5/(d*x+c)^5*arcsinh(d*x+c)-1/20/(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+3/40/(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-3/40*arctanh(1/(1+(d*x+c)^2)^(1/2))))","A"
126,0,0,169,1.951000," ","int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^2,x)","F"
127,1,218,177,0.052000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{2}}{5}-\frac{16 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{75}-\frac{2 \left(d x +c \right)^{4} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{8 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \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} \arcsinh \left(d x +c \right)}{5}-\frac{\left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{75}-\frac{8 \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^2-16/75*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/25*(d*x+c)^4*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+8/75*arcsinh(d*x+c)*(1+(d*x+c)^2)^(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*arcsinh(d*x+c)-1/25*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+4/75*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-8/75*(1+(d*x+c)^2)^(1/2)))","A"
128,1,194,156,0.038000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{\left(d x +c \right)^{4} e^{3} a^{2}}{4}+e^{3} b^{2} \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{2}}{4}-\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{8}+\frac{3 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{16}-\frac{3 \arcsinh \left(d x +c \right)^{2}}{32}+\frac{\left(d x +c \right)^{4}}{32}-\frac{3 \left(d x +c \right)^{2}}{32}-\frac{3}{32}\right)+2 e^{3} a b \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)}{4}-\frac{\left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsinh \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*(d*x+c)^4*e^3*a^2+e^3*b^2*(1/4*(d*x+c)^4*arcsinh(d*x+c)^2-1/8*(d*x+c)^3*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+3/16*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-3/32*arcsinh(d*x+c)^2+1/32*(d*x+c)^4-3/32*(d*x+c)^2-3/32)+2*e^3*a*b*(1/4*(d*x+c)^4*arcsinh(d*x+c)-1/16*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/32*arcsinh(d*x+c)))","A"
129,1,163,122,0.041000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{2}}{3}+\frac{4 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{9}-\frac{2 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \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{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{3}-\frac{\left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^2+4/9*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/9*arcsinh(d*x+c)*(1+(d*x+c)^2)^(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*(d*x+c)^3*arcsinh(d*x+c)-1/9*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+2/9*(1+(d*x+c)^2)^(1/2)))","A"
130,1,135,93,0.033000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{\left(d x +c \right)^{2} e \,a^{2}}{2}+e \,b^{2} \left(\frac{\arcsinh \left(d x +c \right)^{2} \left(1+\left(d x +c \right)^{2}\right)}{2}-\frac{\arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{2}-\frac{\arcsinh \left(d x +c \right)^{2}}{4}+\frac{\left(d x +c \right)^{2}}{4}+\frac{1}{4}\right)+2 e a b \left(\frac{\left(d x +c \right)^{2} \arcsinh \left(d x +c \right)}{2}-\frac{\left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{4}+\frac{\arcsinh \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*(d*x+c)^2*e*a^2+e*b^2*(1/2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)-1/2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-1/4*arcsinh(d*x+c)^2+1/4*(d*x+c)^2+1/4)+2*e*a*b*(1/2*(d*x+c)^2*arcsinh(d*x+c)-1/4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1/4*arcsinh(d*x+c)))","A"
131,1,90,55,0.052000," ","int((a+b*arcsinh(d*x+c))^2,x)","\frac{a^{2} \left(d x +c \right)+b^{2} \left(\left(d x +c \right) \arcsinh \left(d x +c \right)^{2}-2 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+2 d x +2 c \right)+2 a b \left(\left(d x +c \right) \arcsinh \left(d x +c \right)-\sqrt{1+\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*(a^2*(d*x+c)+b^2*((d*x+c)*arcsinh(d*x+c)^2-2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+2*d*x+2*c)+2*a*b*((d*x+c)*arcsinh(d*x+c)-(1+(d*x+c)^2)^(1/2)))","A"
132,1,404,136,0.082000," ","int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e),x)","\frac{a^{2} \ln \left(d x +c \right)}{d e}-\frac{b^{2} \arcsinh \left(d x +c \right)^{3}}{3 d e}+\frac{b^{2} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 b^{2} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 b^{2} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{2} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 b^{2} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 b^{2} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{a b \arcsinh \left(d x +c \right)^{2}}{d e}+\frac{2 a b \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 a b \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 a b \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 a b \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"1/d*a^2/e*ln(d*x+c)-1/3/d*b^2/e*arcsinh(d*x+c)^3+1/d*b^2/e*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+2/d*b^2/e*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-2/d*b^2/e*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+1/d*b^2/e*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+2/d*b^2/e*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-2/d*b^2/e*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-1/d*a*b/e*arcsinh(d*x+c)^2+2/d*a*b/e*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+2/d*a*b/e*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+2/d*a*b/e*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+2/d*a*b/e*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))","B"
133,1,229,127,0.138000," ","int((a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{2 b^{2} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{2 b^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{2 b^{2} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{2 b^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{2 a b \arcsinh \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{2 a b \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}"," ",0,"-1/d*a^2/e^2/(d*x+c)-1/d*b^2/e^2*arcsinh(d*x+c)^2/(d*x+c)-2/d*b^2/e^2*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-2*b^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^2+2/d*b^2/e^2*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+2*b^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^2-2/d*a*b/e^2/(d*x+c)*arcsinh(d*x+c)-2/d*a*b/e^2*arctanh(1/(1+(d*x+c)^2)^(1/2))","A"
134,1,180,81,0.205000," ","int((a+b*arcsinh(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} \arcsinh \left(d x +c \right)}{d \,e^{3}}-\frac{b^{2} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{b^{2} \arcsinh \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{b^{2} \ln \left(\left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)^{2}-1\right)}{d \,e^{3}}-\frac{a b \arcsinh \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{a b \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)-1/d*b^2/e^3*arcsinh(d*x+c)/(d*x+c)*(1+(d*x+c)^2)^(1/2)-1/2/d*b^2/e^3*arcsinh(d*x+c)^2/(d*x+c)^2+1/d*b^2/e^3*ln((d*x+c+(1+(d*x+c)^2)^(1/2))^2-1)-1/d*a*b/e^3/(d*x+c)^2*arcsinh(d*x+c)-1/d*a*b/e^3/(d*x+c)*(1+(d*x+c)^2)^(1/2)","B"
135,1,310,182,0.278000," ","int((a+b*arcsinh(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} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{b^{2} \arcsinh \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{b^{2} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}+\frac{b^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{b^{2} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{b^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{2 a b \arcsinh \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{a b \sqrt{1+\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}+\frac{a b \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{3 d \,e^{4}}"," ",0,"-1/3/d*a^2/e^4/(d*x+c)^3-1/3/d*b^2/e^4/(d*x+c)^2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-1/3/d*b^2/e^4/(d*x+c)^3*arcsinh(d*x+c)^2-1/3*b^2/d/e^4/(d*x+c)+1/3/d*b^2/e^4*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+1/3*b^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^4-1/3/d*b^2/e^4*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-1/3*b^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^4-2/3/d*a*b/e^4/(d*x+c)^3*arcsinh(d*x+c)-1/3/d*a*b/e^4/(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+1/3/d*a*b/e^4*arctanh(1/(1+(d*x+c)^2)^(1/2))","A"
136,0,0,84,1.957000," ","int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^3,x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsinh \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^3,x)","F"
137,1,420,292,0.052000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{3}}{5}-\frac{8 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{25}-\frac{3 \left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{16 \left(d x +c \right) \arcsinh \left(d x +c \right)}{25}-\frac{4144 \sqrt{1+\left(d x +c \right)^{2}}}{5625}+\frac{6 \left(d x +c \right)^{5} \arcsinh \left(d x +c \right)}{125}-\frac{6 \left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}}{625}+\frac{272 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{5625}-\frac{8 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{75}\right)+3 e^{4} a \,b^{2} \left(\frac{\left(d x +c \right)^{5} \arcsinh \left(d x +c \right)^{2}}{5}-\frac{16 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{75}-\frac{2 \left(d x +c \right)^{4} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{8 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \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} \arcsinh \left(d x +c \right)}{5}-\frac{\left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{75}-\frac{8 \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^3-8/25*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-3/25*(d*x+c)^4*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4/25*(d*x+c)^2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+16/25*(d*x+c)*arcsinh(d*x+c)-4144/5625*(1+(d*x+c)^2)^(1/2)+6/125*(d*x+c)^5*arcsinh(d*x+c)-6/625*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+272/5625*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-8/75*(d*x+c)^3*arcsinh(d*x+c))+3*e^4*a*b^2*(1/5*(d*x+c)^5*arcsinh(d*x+c)^2-16/75*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/25*(d*x+c)^4*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+8/75*arcsinh(d*x+c)*(1+(d*x+c)^2)^(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*arcsinh(d*x+c)-1/25*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+4/75*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-8/75*(1+(d*x+c)^2)^(1/2)))","A"
138,1,365,253,0.065000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^3,x)","\frac{\frac{\left(d x +c \right)^{4} e^{3} a^{3}}{4}+e^{3} b^{3} \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{3}}{4}-\frac{3 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{16}+\frac{9 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{32}-\frac{3 \arcsinh \left(d x +c \right)^{3}}{32}+\frac{3 \left(d x +c \right)^{4} \arcsinh \left(d x +c \right)}{32}-\frac{3 \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{128}+\frac{45 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{256}+\frac{27 \arcsinh \left(d x +c \right)}{256}-\frac{9 \arcsinh \left(d x +c \right) \left(1+\left(d x +c \right)^{2}\right)}{32}\right)+3 e^{3} a \,b^{2} \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{2}}{4}-\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{8}+\frac{3 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{16}-\frac{3 \arcsinh \left(d x +c \right)^{2}}{32}+\frac{\left(d x +c \right)^{4}}{32}-\frac{3 \left(d x +c \right)^{2}}{32}-\frac{3}{32}\right)+3 e^{3} a^{2} b \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)}{4}-\frac{\left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsinh \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*(d*x+c)^4*e^3*a^3+e^3*b^3*(1/4*(d*x+c)^4*arcsinh(d*x+c)^3-3/16*(d*x+c)^3*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+9/32*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)*(d*x+c)-3/32*arcsinh(d*x+c)^3+3/32*(d*x+c)^4*arcsinh(d*x+c)-3/128*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+45/256*(d*x+c)*(1+(d*x+c)^2)^(1/2)+27/256*arcsinh(d*x+c)-9/32*arcsinh(d*x+c)*(1+(d*x+c)^2))+3*e^3*a*b^2*(1/4*(d*x+c)^4*arcsinh(d*x+c)^2-1/8*(d*x+c)^3*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+3/16*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-3/32*arcsinh(d*x+c)^2+1/32*(d*x+c)^4-3/32*(d*x+c)^2-3/32)+3*e^3*a^2*b*(1/4*(d*x+c)^4*arcsinh(d*x+c)-1/16*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/32*arcsinh(d*x+c)))","A"
139,1,302,203,0.041000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{3}}{3}+\frac{2 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{3}-\frac{\left(d x +c \right)^{2} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{3}-\frac{4 \left(d x +c \right) \arcsinh \left(d x +c \right)}{3}+\frac{40 \sqrt{1+\left(d x +c \right)^{2}}}{27}+\frac{2 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{9}-\frac{2 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{27}\right)+3 e^{2} a \,b^{2} \left(\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)^{2}}{3}+\frac{4 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{9}-\frac{2 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \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{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{3}-\frac{\left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^3+2/3*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-1/3*(d*x+c)^2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-4/3*(d*x+c)*arcsinh(d*x+c)+40/27*(1+(d*x+c)^2)^(1/2)+2/9*(d*x+c)^3*arcsinh(d*x+c)-2/27*(d*x+c)^2*(1+(d*x+c)^2)^(1/2))+3*e^2*a*b^2*(1/3*(d*x+c)^3*arcsinh(d*x+c)^2+4/9*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/9*arcsinh(d*x+c)*(1+(d*x+c)^2)^(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*(d*x+c)^3*arcsinh(d*x+c)-1/9*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+2/9*(1+(d*x+c)^2)^(1/2)))","A"
140,1,243,145,0.056000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^3,x)","\frac{\frac{\left(d x +c \right)^{2} e \,a^{3}}{2}+e \,b^{3} \left(\frac{\arcsinh \left(d x +c \right)^{3} \left(1+\left(d x +c \right)^{2}\right)}{2}-\frac{3 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{4}-\frac{\arcsinh \left(d x +c \right)^{3}}{4}+\frac{3 \arcsinh \left(d x +c \right) \left(1+\left(d x +c \right)^{2}\right)}{4}-\frac{3 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{8}-\frac{3 \arcsinh \left(d x +c \right)}{8}\right)+3 e a \,b^{2} \left(\frac{\arcsinh \left(d x +c \right)^{2} \left(1+\left(d x +c \right)^{2}\right)}{2}-\frac{\arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{2}-\frac{\arcsinh \left(d x +c \right)^{2}}{4}+\frac{\left(d x +c \right)^{2}}{4}+\frac{1}{4}\right)+3 e \,a^{2} b \left(\frac{\left(d x +c \right)^{2} \arcsinh \left(d x +c \right)}{2}-\frac{\left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{4}+\frac{\arcsinh \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*(d*x+c)^2*e*a^3+e*b^3*(1/2*arcsinh(d*x+c)^3*(1+(d*x+c)^2)-3/4*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)*(d*x+c)-1/4*arcsinh(d*x+c)^3+3/4*arcsinh(d*x+c)*(1+(d*x+c)^2)-3/8*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/8*arcsinh(d*x+c))+3*e*a*b^2*(1/2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)-1/2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-1/4*arcsinh(d*x+c)^2+1/4*(d*x+c)^2+1/4)+3*e*a^2*b*(1/2*(d*x+c)^2*arcsinh(d*x+c)-1/4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1/4*arcsinh(d*x+c)))","A"
141,1,160,96,0.071000," ","int((a+b*arcsinh(d*x+c))^3,x)","\frac{a^{3} \left(d x +c \right)+b^{3} \left(\left(d x +c \right) \arcsinh \left(d x +c \right)^{3}-3 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+6 \left(d x +c \right) \arcsinh \left(d x +c \right)-6 \sqrt{1+\left(d x +c \right)^{2}}\right)+3 a \,b^{2} \left(\left(d x +c \right) \arcsinh \left(d x +c \right)^{2}-2 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+2 d x +2 c \right)+3 a^{2} b \left(\left(d x +c \right) \arcsinh \left(d x +c \right)-\sqrt{1+\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*(a^3*(d*x+c)+b^3*((d*x+c)*arcsinh(d*x+c)^3-3*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+6*(d*x+c)*arcsinh(d*x+c)-6*(1+(d*x+c)^2)^(1/2))+3*a*b^2*((d*x+c)*arcsinh(d*x+c)^2-2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+2*d*x+2*c)+3*a^2*b*((d*x+c)*arcsinh(d*x+c)-(1+(d*x+c)^2)^(1/2)))","A"
142,1,736,179,0.089000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e),x)","\frac{a^{3} \ln \left(d x +c \right)}{d e}-\frac{b^{3} \arcsinh \left(d x +c \right)^{4}}{4 d e}+\frac{b^{3} \arcsinh \left(d x +c \right)^{3} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 b^{3} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{6 b^{3} \arcsinh \left(d x +c \right) \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 b^{3} \polylog \left(4, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{3} \arcsinh \left(d x +c \right)^{3} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 b^{3} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{6 b^{3} \arcsinh \left(d x +c \right) \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 b^{3} \polylog \left(4, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{a \,b^{2} \arcsinh \left(d x +c \right)^{3}}{d e}+\frac{3 a \,b^{2} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a \,b^{2} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{6 a \,b^{2} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a \,b^{2} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a \,b^{2} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{6 a \,b^{2} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{3 a^{2} b \arcsinh \left(d x +c \right)^{2}}{2 d e}+\frac{3 a^{2} b \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a^{2} b \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a^{2} b \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a^{2} b \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"1/d*a^3/e*ln(d*x+c)-1/4/d*b^3/e*arcsinh(d*x+c)^4+1/d*b^3/e*arcsinh(d*x+c)^3*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+3/d*b^3/e*arcsinh(d*x+c)^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-6/d*b^3/e*arcsinh(d*x+c)*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*b^3/e*polylog(4,-d*x-c-(1+(d*x+c)^2)^(1/2))+1/d*b^3/e*arcsinh(d*x+c)^3*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+3/d*b^3/e*arcsinh(d*x+c)^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*b^3/e*arcsinh(d*x+c)*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))+6/d*b^3/e*polylog(4,d*x+c+(1+(d*x+c)^2)^(1/2))-1/d*a*b^2/e*arcsinh(d*x+c)^3+3/d*a*b^2/e*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+6/d*a*b^2/e*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-6/d*a*b^2/e*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+3/d*a*b^2/e*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*a*b^2/e*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*a*b^2/e*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-3/2/d*a^2*b/e*arcsinh(d*x+c)^2+3/d*a^2*b/e*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+3/d*a^2*b/e*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+3/d*a^2*b/e*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+3/d*a^2*b/e*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))","B"
143,1,481,212,0.149000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^2,x)","-\frac{a^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{3} \arcsinh \left(d x +c \right)^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{3 b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 b^{3} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{3 b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 b^{3} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{6 a \,b^{2} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 a \,b^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 a \,b^{2} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 a \,b^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{3 a^{2} b \arcsinh \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{3 a^{2} b \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}"," ",0,"-1/d*a^3/e^2/(d*x+c)-1/d*b^3/e^2*arcsinh(d*x+c)^3/(d*x+c)-3/d*b^3/e^2*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*b^3/e^2*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+6*b^3*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^2+3/d*b^3/e^2*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*b^3/e^2*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-6*b^3*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^2-3/d*a*b^2/e^2/(d*x+c)*arcsinh(d*x+c)^2-6/d*a*b^2/e^2*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*a*b^2/e^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*a*b^2/e^2*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*a*b^2/e^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-3/d*a^2*b/e^2/(d*x+c)*arcsinh(d*x+c)-3/d*a^2*b/e^2*arctanh(1/(1+(d*x+c)^2)^(1/2))","B"
144,1,409,163,0.217000," ","int((a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{2 d \,e^{3} \left(d x +c \right)}-\frac{3 b^{3} \arcsinh \left(d x +c \right)^{2}}{2 d \,e^{3}}-\frac{b^{3} \arcsinh \left(d x +c \right)^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{3 b^{3} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{3 b^{3} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{3 b^{3} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{3 b^{3} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{3 a \,b^{2} \arcsinh \left(d x +c \right)}{d \,e^{3}}-\frac{3 a \,b^{2} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \ln \left(\left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)^{2}-1\right)}{d \,e^{3}}-\frac{3 a^{2} b \arcsinh \left(d x +c \right)}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 a^{2} b \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^2/(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/2/d*b^3/e^3*arcsinh(d*x+c)^2-1/2/d*b^3/e^3*arcsinh(d*x+c)^3/(d*x+c)^2+3/d*b^3/e^3*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+3/d*b^3/e^3*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+3/d*b^3/e^3*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+3/d*b^3/e^3*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-3/d*a*b^2/e^3*arcsinh(d*x+c)-3/d*a*b^2/e^3*arcsinh(d*x+c)/(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/2/d*a*b^2/e^3*arcsinh(d*x+c)^2/(d*x+c)^2+3/d*a*b^2/e^3*ln((d*x+c+(1+(d*x+c)^2)^(1/2))^2-1)-3/2/d*a^2*b/e^3/(d*x+c)^2*arcsinh(d*x+c)-3/2/d*a^2*b/e^3/(d*x+c)*(1+(d*x+c)^2)^(1/2)","B"
145,1,651,299,0.311000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^4,x)","-\frac{a^{3}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{3} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{2 d \,e^{4} \left(d x +c \right)^{2}}-\frac{b^{3} \arcsinh \left(d x +c \right)^{3}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{3} \arcsinh \left(d x +c \right)}{d \,e^{4} \left(d x +c \right)}+\frac{b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{2 d \,e^{4}}+\frac{b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{b^{3} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{2 d \,e^{4}}-\frac{b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{b^{3} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 b^{3} \arctanh \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a \,b^{2} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{4} \left(d x +c \right)^{2}}-\frac{a \,b^{2} \arcsinh \left(d x +c \right)^{2}}{d \,e^{4} \left(d x +c \right)^{3}}-\frac{a \,b^{2}}{d \,e^{4} \left(d x +c \right)}+\frac{a \,b^{2} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{a \,b^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a \,b^{2} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a \,b^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a^{2} b \arcsinh \left(d x +c \right)}{d \,e^{4} \left(d x +c \right)^{3}}-\frac{a^{2} b \sqrt{1+\left(d x +c \right)^{2}}}{2 d \,e^{4} \left(d x +c \right)^{2}}+\frac{a^{2} b \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{2 d \,e^{4}}"," ",0,"-1/3/d*a^3/e^4/(d*x+c)^3-1/2/d*b^3/e^4/(d*x+c)^2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-1/3/d*b^3/e^4/(d*x+c)^3*arcsinh(d*x+c)^3-1/d*b^3/e^4/(d*x+c)*arcsinh(d*x+c)+1/2/d*b^3/e^4*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+1/d*b^3/e^4*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-b^3*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^4-1/2/d*b^3/e^4*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-1/d*b^3/e^4*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))+b^3*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^4-2/d*b^3/e^4*arctanh(d*x+c+(1+(d*x+c)^2)^(1/2))-1/d*a*b^2/e^4/(d*x+c)^2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-1/d*a*b^2/e^4/(d*x+c)^3*arcsinh(d*x+c)^2-1/d*a*b^2/e^4/(d*x+c)+1/d*a*b^2/e^4*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+1/d*a*b^2/e^4*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-1/d*a*b^2/e^4*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-1/d*a*b^2/e^4*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-1/d*a^2*b/e^4/(d*x+c)^3*arcsinh(d*x+c)-1/2/d*a^2*b/e^4/(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+1/2/d*a^2*b/e^4*arctanh(1/(1+(d*x+c)^2)^(1/2))","B"
146,0,0,84,2.039000," ","int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^4,x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsinh \left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^4,x)","F"
147,1,573,319,0.048000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(d x +c \right)^{4} e^{3} a^{4}}{4}+e^{3} b^{4} \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{4}}{4}-\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{4}+\frac{3 \arcsinh \left(d x +c \right)^{3} \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{8}-\frac{3 \arcsinh \left(d x +c \right)^{4}}{32}+\frac{3 \left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{2}}{16}-\frac{3 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{32}+\frac{45 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{64}+\frac{27 \arcsinh \left(d x +c \right)^{2}}{128}+\frac{3 \left(d x +c \right)^{4}}{128}-\frac{45 \left(d x +c \right)^{2}}{128}-\frac{45}{128}-\frac{9 \arcsinh \left(d x +c \right)^{2} \left(1+\left(d x +c \right)^{2}\right)}{16}\right)+4 e^{3} a \,b^{3} \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{3}}{4}-\frac{3 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{16}+\frac{9 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{32}-\frac{3 \arcsinh \left(d x +c \right)^{3}}{32}+\frac{3 \left(d x +c \right)^{4} \arcsinh \left(d x +c \right)}{32}-\frac{3 \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{128}+\frac{45 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{256}+\frac{27 \arcsinh \left(d x +c \right)}{256}-\frac{9 \arcsinh \left(d x +c \right) \left(1+\left(d x +c \right)^{2}\right)}{32}\right)+6 e^{3} a^{2} b^{2} \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)^{2}}{4}-\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{8}+\frac{3 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{16}-\frac{3 \arcsinh \left(d x +c \right)^{2}}{32}+\frac{\left(d x +c \right)^{4}}{32}-\frac{3 \left(d x +c \right)^{2}}{32}-\frac{3}{32}\right)+4 e^{3} a^{3} b \left(\frac{\left(d x +c \right)^{4} \arcsinh \left(d x +c \right)}{4}-\frac{\left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsinh \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*(d*x+c)^4*e^3*a^4+e^3*b^4*(1/4*(d*x+c)^4*arcsinh(d*x+c)^4-1/4*(d*x+c)^3*arcsinh(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+3/8*arcsinh(d*x+c)^3*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/32*arcsinh(d*x+c)^4+3/16*(d*x+c)^4*arcsinh(d*x+c)^2-3/32*(d*x+c)^3*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+45/64*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)+27/128*arcsinh(d*x+c)^2+3/128*(d*x+c)^4-45/128*(d*x+c)^2-45/128-9/16*arcsinh(d*x+c)^2*(1+(d*x+c)^2))+4*e^3*a*b^3*(1/4*(d*x+c)^4*arcsinh(d*x+c)^3-3/16*(d*x+c)^3*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+9/32*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)*(d*x+c)-3/32*arcsinh(d*x+c)^3+3/32*(d*x+c)^4*arcsinh(d*x+c)-3/128*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+45/256*(d*x+c)*(1+(d*x+c)^2)^(1/2)+27/256*arcsinh(d*x+c)-9/32*arcsinh(d*x+c)*(1+(d*x+c)^2))+6*e^3*a^2*b^2*(1/4*(d*x+c)^4*arcsinh(d*x+c)^2-1/8*(d*x+c)^3*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+3/16*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-3/32*arcsinh(d*x+c)^2+1/32*(d*x+c)^4-3/32*(d*x+c)^2-3/32)+4*e^3*a^3*b*(1/4*(d*x+c)^4*arcsinh(d*x+c)-1/16*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/32*arcsinh(d*x+c)))","A"
148,1,473,255,0.046000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{4}}{3}+\frac{8 \arcsinh \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{9}-\frac{4 \left(d x +c \right)^{2} \arcsinh \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{9}-\frac{8 \left(d x +c \right) \arcsinh \left(d x +c \right)^{2}}{3}+\frac{160 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{27}-\frac{160 d x}{27}-\frac{160 c}{27}+\frac{4 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right)^{2}}{9}-\frac{8 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \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} \arcsinh \left(d x +c \right)^{3}}{3}+\frac{2 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{3}-\frac{\left(d x +c \right)^{2} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{3}-\frac{4 \left(d x +c \right) \arcsinh \left(d x +c \right)}{3}+\frac{40 \sqrt{1+\left(d x +c \right)^{2}}}{27}+\frac{2 \left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{9}-\frac{2 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{27}\right)+6 e^{2} a^{2} b^{2} \left(\frac{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)^{2}}{3}+\frac{4 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{9}-\frac{2 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \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{\left(d x +c \right)^{3} \arcsinh \left(d x +c \right)}{3}-\frac{\left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^4+8/9*arcsinh(d*x+c)^3*(1+(d*x+c)^2)^(1/2)-4/9*(d*x+c)^2*arcsinh(d*x+c)^3*(1+(d*x+c)^2)^(1/2)-8/3*(d*x+c)*arcsinh(d*x+c)^2+160/27*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-160/27*d*x-160/27*c+4/9*(d*x+c)^3*arcsinh(d*x+c)^2-8/27*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)^2+8/81*(d*x+c)^3)+4*e^2*a*b^3*(1/3*(d*x+c)^3*arcsinh(d*x+c)^3+2/3*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-1/3*(d*x+c)^2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-4/3*(d*x+c)*arcsinh(d*x+c)+40/27*(1+(d*x+c)^2)^(1/2)+2/9*(d*x+c)^3*arcsinh(d*x+c)-2/27*(d*x+c)^2*(1+(d*x+c)^2)^(1/2))+6*e^2*a^2*b^2*(1/3*(d*x+c)^3*arcsinh(d*x+c)^2+4/9*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/9*arcsinh(d*x+c)*(1+(d*x+c)^2)^(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*(d*x+c)^3*arcsinh(d*x+c)-1/9*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+2/9*(1+(d*x+c)^2)^(1/2)))","A"
149,1,371,179,0.038000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(d x +c \right)^{2} e \,a^{4}}{2}+e \,b^{4} \left(\frac{\left(1+\left(d x +c \right)^{2}\right) \arcsinh \left(d x +c \right)^{4}}{2}-\arcsinh \left(d x +c \right)^{3} \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}-\frac{\arcsinh \left(d x +c \right)^{4}}{4}+\frac{3 \arcsinh \left(d x +c \right)^{2} \left(1+\left(d x +c \right)^{2}\right)}{2}-\frac{3 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{2}-\frac{3 \arcsinh \left(d x +c \right)^{2}}{4}+\frac{3 \left(d x +c \right)^{2}}{4}+\frac{3}{4}\right)+4 e a \,b^{3} \left(\frac{\arcsinh \left(d x +c \right)^{3} \left(1+\left(d x +c \right)^{2}\right)}{2}-\frac{3 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{4}-\frac{\arcsinh \left(d x +c \right)^{3}}{4}+\frac{3 \arcsinh \left(d x +c \right) \left(1+\left(d x +c \right)^{2}\right)}{4}-\frac{3 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{8}-\frac{3 \arcsinh \left(d x +c \right)}{8}\right)+6 e \,a^{2} b^{2} \left(\frac{\arcsinh \left(d x +c \right)^{2} \left(1+\left(d x +c \right)^{2}\right)}{2}-\frac{\arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\, \left(d x +c \right)}{2}-\frac{\arcsinh \left(d x +c \right)^{2}}{4}+\frac{\left(d x +c \right)^{2}}{4}+\frac{1}{4}\right)+4 e \,a^{3} b \left(\frac{\left(d x +c \right)^{2} \arcsinh \left(d x +c \right)}{2}-\frac{\left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{4}+\frac{\arcsinh \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*(d*x+c)^2*e*a^4+e*b^4*(1/2*(1+(d*x+c)^2)*arcsinh(d*x+c)^4-arcsinh(d*x+c)^3*(d*x+c)*(1+(d*x+c)^2)^(1/2)-1/4*arcsinh(d*x+c)^4+3/2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)-3/2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-3/4*arcsinh(d*x+c)^2+3/4*(d*x+c)^2+3/4)+4*e*a*b^3*(1/2*arcsinh(d*x+c)^3*(1+(d*x+c)^2)-3/4*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)*(d*x+c)-1/4*arcsinh(d*x+c)^3+3/4*arcsinh(d*x+c)*(1+(d*x+c)^2)-3/8*(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/8*arcsinh(d*x+c))+6*e*a^2*b^2*(1/2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)-1/2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)*(d*x+c)-1/4*arcsinh(d*x+c)^2+1/4*(d*x+c)^2+1/4)+4*e*a^3*b*(1/2*(d*x+c)^2*arcsinh(d*x+c)-1/4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1/4*arcsinh(d*x+c)))","B"
150,1,245,111,0.060000," ","int((a+b*arcsinh(d*x+c))^4,x)","\frac{\left(d x +c \right) a^{4}+b^{4} \left(\left(d x +c \right) \arcsinh \left(d x +c \right)^{4}-4 \arcsinh \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}+12 \left(d x +c \right) \arcsinh \left(d x +c \right)^{2}-24 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+24 d x +24 c \right)+4 a \,b^{3} \left(\left(d x +c \right) \arcsinh \left(d x +c \right)^{3}-3 \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+6 \left(d x +c \right) \arcsinh \left(d x +c \right)-6 \sqrt{1+\left(d x +c \right)^{2}}\right)+6 a^{2} b^{2} \left(\left(d x +c \right) \arcsinh \left(d x +c \right)^{2}-2 \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+2 d x +2 c \right)+4 a^{3} b \left(\left(d x +c \right) \arcsinh \left(d x +c \right)-\sqrt{1+\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*((d*x+c)*a^4+b^4*((d*x+c)*arcsinh(d*x+c)^4-4*arcsinh(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+12*(d*x+c)*arcsinh(d*x+c)^2-24*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+24*d*x+24*c)+4*a*b^3*((d*x+c)*arcsinh(d*x+c)^3-3*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+6*(d*x+c)*arcsinh(d*x+c)-6*(1+(d*x+c)^2)^(1/2))+6*a^2*b^2*((d*x+c)*arcsinh(d*x+c)^2-2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)+2*d*x+2*c)+4*a^3*b*((d*x+c)*arcsinh(d*x+c)-(1+(d*x+c)^2)^(1/2)))","B"
151,1,1153,222,0.116000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e),x)","\frac{12 a^{2} b^{2} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a^{3} b \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a^{3} b \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a \,b^{3} \arcsinh \left(d x +c \right)^{3} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{24 a \,b^{3} \arcsinh \left(d x +c \right) \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a \,b^{3} \arcsinh \left(d x +c \right)^{3} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{12 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{24 a \,b^{3} \arcsinh \left(d x +c \right) \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{12 a^{2} b^{2} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a^{2} b^{2} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a^{2} b^{2} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{a^{4} \ln \left(d x +c \right)}{d e}-\frac{24 b^{4} \polylog \left(5, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{24 b^{4} \polylog \left(5, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{b^{4} \arcsinh \left(d x +c \right)^{5}}{5 d e}-\frac{12 b^{4} \arcsinh \left(d x +c \right)^{2} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 b^{4} \arcsinh \left(d x +c \right) \polylog \left(4, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 a \,b^{3} \polylog \left(4, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 a \,b^{3} \polylog \left(4, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 b^{4} \arcsinh \left(d x +c \right)^{3} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 a^{2} b^{2} \arcsinh \left(d x +c \right)^{3}}{d e}-\frac{12 a^{2} b^{2} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{12 a^{2} b^{2} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 a^{3} b \arcsinh \left(d x +c \right)^{2}}{d e}+\frac{4 a^{3} b \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a^{3} b \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{4} \arcsinh \left(d x +c \right)^{4} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 b^{4} \arcsinh \left(d x +c \right)^{3} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{4} \arcsinh \left(d x +c \right)^{4} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{12 b^{4} \arcsinh \left(d x +c \right)^{2} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 b^{4} \arcsinh \left(d x +c \right) \polylog \left(4, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}-\frac{a \,b^{3} \arcsinh \left(d x +c \right)^{4}}{d e}+\frac{12 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"12/d*a^2*b^2/e*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*a^3*b/e*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*a^3*b/e*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+4/d*a*b^3/e*arcsinh(d*x+c)^3*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+12/d*a*b^3/e*arcsinh(d*x+c)^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-24/d*a*b^3/e*arcsinh(d*x+c)*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+4/d*a*b^3/e*arcsinh(d*x+c)^3*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*a*b^3/e*arcsinh(d*x+c)^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-24/d*a*b^3/e*arcsinh(d*x+c)*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))+12/d*a^2*b^2/e*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*a^2*b^2/e*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+6/d*a^2*b^2/e*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-24/d*b^4/e*polylog(5,d*x+c+(1+(d*x+c)^2)^(1/2))-24/d*b^4/e*polylog(5,-d*x-c-(1+(d*x+c)^2)^(1/2))+1/d*a^4/e*ln(d*x+c)-1/5/d*b^4/e*arcsinh(d*x+c)^5-12/d*b^4/e*arcsinh(d*x+c)^2*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+24/d*b^4/e*arcsinh(d*x+c)*polylog(4,-d*x-c-(1+(d*x+c)^2)^(1/2))+24/d*a*b^3/e*polylog(4,-d*x-c-(1+(d*x+c)^2)^(1/2))+24/d*a*b^3/e*polylog(4,d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*b^4/e*arcsinh(d*x+c)^3*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e*arcsinh(d*x+c)^3-12/d*a^2*b^2/e*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))-12/d*a^2*b^2/e*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-2/d*a^3*b/e*arcsinh(d*x+c)^2+4/d*a^3*b/e*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+4/d*a^3*b/e*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))+1/d*b^4/e*arcsinh(d*x+c)^4*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*b^4/e*arcsinh(d*x+c)^3*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+1/d*b^4/e*arcsinh(d*x+c)^4*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-12/d*b^4/e*arcsinh(d*x+c)^2*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))+24/d*b^4/e*arcsinh(d*x+c)*polylog(4,d*x+c+(1+(d*x+c)^2)^(1/2))-1/d*a*b^3/e*arcsinh(d*x+c)^4","B"
152,1,820,299,0.199000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^2,x)","-\frac{a^{4}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{4} \arcsinh \left(d x +c \right)^{4}}{d \,e^{2} \left(d x +c \right)}-\frac{4 b^{4} \arcsinh \left(d x +c \right)^{3} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{12 b^{4} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 b^{4} \arcsinh \left(d x +c \right) \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 b^{4} \polylog \left(4, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{4 b^{4} \arcsinh \left(d x +c \right)^{3} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 b^{4} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 b^{4} \arcsinh \left(d x +c \right) \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 b^{4} \polylog \left(4, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{4 a \,b^{3} \arcsinh \left(d x +c \right)^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{12 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 a \,b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 a \,b^{3} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 a \,b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 a \,b^{3} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 a^{2} b^{2} \arcsinh \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{12 a^{2} b^{2} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{12 a^{2} b^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 a^{2} b^{2} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 a^{2} b^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{4 a^{3} b \arcsinh \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{4 a^{3} b \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}"," ",0,"-1/d*a^4/e^2/(d*x+c)-1/d*b^4/e^2*arcsinh(d*x+c)^4/(d*x+c)-4/d*b^4/e^2*arcsinh(d*x+c)^3*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-12/d*b^4/e^2*arcsinh(d*x+c)^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+24/d*b^4/e^2*arcsinh(d*x+c)*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))-24*b^4*polylog(4,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^2+4/d*b^4/e^2*arcsinh(d*x+c)^3*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*b^4/e^2*arcsinh(d*x+c)^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-24/d*b^4/e^2*arcsinh(d*x+c)*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))+24*b^4*polylog(4,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^2-4/d*a*b^3/e^2*arcsinh(d*x+c)^3/(d*x+c)-12/d*a*b^3/e^2*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-24/d*a*b^3/e^2*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+24/d*a*b^3/e^2*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*a*b^3/e^2*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+24/d*a*b^3/e^2*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-24/d*a*b^3/e^2*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*a^2*b^2/e^2*arcsinh(d*x+c)^2/(d*x+c)-12/d*a^2*b^2/e^2*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-12/d*a^2*b^2/e^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*a^2*b^2/e^2*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*a^2*b^2/e^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-4/d*a^3*b/e^2/(d*x+c)*arcsinh(d*x+c)-4/d*a^3*b/e^2*arctanh(1/(1+(d*x+c)^2)^(1/2))","B"
153,1,723,206,0.223000," ","int((a+b*arcsinh(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} \arcsinh \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{2 b^{4} \arcsinh \left(d x +c \right)^{3}}{d \,e^{3}}-\frac{b^{4} \arcsinh \left(d x +c \right)^{4}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{6 b^{4} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 b^{4} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{12 b^{4} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{6 b^{4} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 b^{4} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{12 b^{4} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{6 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{6 a \,b^{3} \arcsinh \left(d x +c \right)^{2}}{d \,e^{3}}-\frac{2 a \,b^{3} \arcsinh \left(d x +c \right)^{3}}{d \,e^{3} \left(d x +c \right)^{2}}+\frac{12 a \,b^{3} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 a \,b^{3} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 a \,b^{3} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 a \,b^{3} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{6 a^{2} b^{2} \arcsinh \left(d x +c \right)}{d \,e^{3}}-\frac{6 a^{2} b^{2} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{3 a^{2} b^{2} \arcsinh \left(d x +c \right)^{2}}{d \,e^{3} \left(d x +c \right)^{2}}+\frac{6 a^{2} b^{2} \ln \left(\left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)^{2}-1\right)}{d \,e^{3}}-\frac{2 a^{3} b \arcsinh \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{2 a^{3} b \sqrt{1+\left(d x +c \right)^{2}}}{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*arcsinh(d*x+c)^3/(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/d*b^4/e^3*arcsinh(d*x+c)^3-1/2/d*b^4/e^3*arcsinh(d*x+c)^4/(d*x+c)^2+6/d*b^4/e^3*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+12/d*b^4/e^3*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-12/d*b^4/e^3*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))+6/d*b^4/e^3*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*b^4/e^3*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-12/d*b^4/e^3*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*a*b^3/e^3*arcsinh(d*x+c)^2/(d*x+c)*(1+(d*x+c)^2)^(1/2)-6/d*a*b^3/e^3*arcsinh(d*x+c)^2-2/d*a*b^3/e^3*arcsinh(d*x+c)^3/(d*x+c)^2+12/d*a*b^3/e^3*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+12/d*a*b^3/e^3*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*a*b^3/e^3*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))+12/d*a*b^3/e^3*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-6/d*a^2*b^2/e^3*arcsinh(d*x+c)-6/d*a^2*b^2/e^3*arcsinh(d*x+c)/(d*x+c)*(1+(d*x+c)^2)^(1/2)-3/d*a^2*b^2/e^3*arcsinh(d*x+c)^2/(d*x+c)^2+6/d*a^2*b^2/e^3*ln((d*x+c+(1+(d*x+c)^2)^(1/2))^2-1)-2/d*a^3*b/e^3/(d*x+c)^2*arcsinh(d*x+c)-2/d*a^3*b/e^3/(d*x+c)*(1+(d*x+c)^2)^(1/2)","B"
154,1,1202,469,0.312000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^4,x)","-\frac{2 a^{2} b^{2} \arcsinh \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}}{d \,e^{4} \left(d x +c \right)^{2}}-\frac{4 a \,b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a^{2} b^{2} \arcsinh \left(d x +c \right)^{2}}{d \,e^{4} \left(d x +c \right)^{3}}+\frac{2 a^{2} b^{2} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 a \,b^{3} \arcsinh \left(d x +c \right)^{3}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{4 a \,b^{3} \arcsinh \left(d x +c \right)}{d \,e^{4} \left(d x +c \right)}+\frac{2 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 a \,b^{3} \arcsinh \left(d x +c \right) \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a \,b^{3} \arcsinh \left(d x +c \right)^{2} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a^{2} b^{2} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 a^{3} b \arcsinh \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{2 b^{4} \arcsinh \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 a^{3} b \sqrt{1+\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 a^{2} b^{2}}{d \,e^{4} \left(d x +c \right)}+\frac{4 a \,b^{3} \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{8 a \,b^{3} \arctanh \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 b^{4} \arcsinh \left(d x +c \right) \polylog \left(3, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 b^{4} \arcsinh \left(d x +c \right) \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 b^{4} \arcsinh \left(d x +c \right) \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{b^{4} \arcsinh \left(d x +c \right)^{4}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{2 b^{4} \arcsinh \left(d x +c \right)^{2}}{d \,e^{4} \left(d x +c \right)}+\frac{2 b^{4} \arcsinh \left(d x +c \right)^{3} \ln \left(1+d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}+\frac{2 b^{4} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 b^{4} \arcsinh \left(d x +c \right) \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 b^{4} \arcsinh \left(d x +c \right)^{3} \ln \left(1-d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{2 b^{4} \arcsinh \left(d x +c \right)^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{2 a^{2} b^{2} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a^{2} b^{2} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{2 a^{3} b \arctanh \left(\frac{1}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{3 d \,e^{4}}-\frac{4 a \,b^{3} \polylog \left(3, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 b^{4} \polylog \left(2, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 b^{4} \polylog \left(2, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 b^{4} \polylog \left(4, -d x -c -\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 b^{4} \polylog \left(4, d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a^{4}}{3 d \,e^{4} \left(d x +c \right)^{3}}"," ",0,"-2/d*a^2*b^2/e^4/(d*x+c)^2*arcsinh(d*x+c)*(1+(d*x+c)^2)^(1/2)-2/d*a*b^3/e^4/(d*x+c)^2*arcsinh(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-4/d*a*b^3/e^4*arcsinh(d*x+c)*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4/(d*x+c)^3*arcsinh(d*x+c)^2+2/d*a^2*b^2/e^4*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))-4/3/d*a*b^3/e^4/(d*x+c)^3*arcsinh(d*x+c)^3-4/d*a*b^3/e^4/(d*x+c)*arcsinh(d*x+c)+2/d*a*b^3/e^4*arcsinh(d*x+c)^2*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*a*b^3/e^4*arcsinh(d*x+c)*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-2/d*a*b^3/e^4*arcsinh(d*x+c)^2*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-4/3/d*a^3*b/e^4/(d*x+c)^3*arcsinh(d*x+c)-2/3/d*a^3*b/e^4/(d*x+c)^2*(1+(d*x+c)^2)^(1/2)-2/3/d*b^4/e^4/(d*x+c)^2*arcsinh(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+4/d*a*b^3/e^4*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-8/d*a*b^3/e^4*arctanh(d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*b^4/e^4*arcsinh(d*x+c)*polylog(3,d*x+c+(1+(d*x+c)^2)^(1/2))-4/d*b^4/e^4*arcsinh(d*x+c)*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+4/d*b^4/e^4*arcsinh(d*x+c)*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-1/3/d*b^4/e^4/(d*x+c)^3*arcsinh(d*x+c)^4-2/d*b^4/e^4/(d*x+c)*arcsinh(d*x+c)^2+2/3/d*b^4/e^4*arcsinh(d*x+c)^3*ln(1+d*x+c+(1+(d*x+c)^2)^(1/2))+2/d*b^4/e^4*arcsinh(d*x+c)^2*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-4/d*b^4/e^4*arcsinh(d*x+c)*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))-2/3/d*b^4/e^4*arcsinh(d*x+c)^3*ln(1-d*x-c-(1+(d*x+c)^2)^(1/2))-2/d*b^4/e^4*arcsinh(d*x+c)^2*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))+2/d*a^2*b^2/e^4*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))+2/3/d*a^3*b/e^4*arctanh(1/(1+(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4/(d*x+c)-4*b^4*polylog(2,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^4+4*b^4*polylog(2,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^4+4*b^4*polylog(4,-d*x-c-(1+(d*x+c)^2)^(1/2))/d/e^4-4*b^4*polylog(4,d*x+c+(1+(d*x+c)^2)^(1/2))/d/e^4-4/d*a*b^3/e^4*polylog(3,-d*x-c-(1+(d*x+c)^2)^(1/2))-1/3/d*a^4/e^4/(d*x+c)^3","B"
155,0,0,24,0.787000," ","int((d*e*x+c*e)^m/(a+b*arcsinh(d*x+c)),x)","\int \frac{\left(d e x +c e \right)^{m}}{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^m/(a+b*arcsinh(d*x+c)),x)","F"
156,1,194,201,0.318000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c)),x)","\frac{-\frac{e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \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 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{32 b}-\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{16 b}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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 \arcsinh \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 \arcsinh \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*arcsinh(d*x+c)+5*a/b)+3/32*e^4/b*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)-1/16*e^4/b*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/16*e^4/b*exp(-a/b)*Ei(1,-arcsinh(d*x+c)-a/b)+3/32*e^4/b*exp(-3*a/b)*Ei(1,-3*arcsinh(d*x+c)-3*a/b)-1/32*e^4/b*exp(-5*a/b)*Ei(1,-5*arcsinh(d*x+c)-5*a/b))","A"
157,1,134,137,0.248000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c)),x)","\frac{\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \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 \arcsinh \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 \arcsinh \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 \arcsinh \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*arcsinh(d*x+c)+4*a/b)-1/8*e^3/b*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)+1/8*e^3/b*exp(-2*a/b)*Ei(1,-2*arcsinh(d*x+c)-2*a/b)-1/16*e^3/b*exp(-4*a/b)*Ei(1,-4*arcsinh(d*x+c)-4*a/b))","A"
158,1,130,133,0.155000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c)),x)","\frac{-\frac{e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{8 b}+\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{8 b}+\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(d x +c \right)-\frac{a}{b}\right)}{8 b}-\frac{e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \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*arcsinh(d*x+c)+3*a/b)+1/8*e^2/b*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)+1/8*e^2/b*exp(-a/b)*Ei(1,-arcsinh(d*x+c)-a/b)-1/8*e^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(d*x+c)-3*a/b))","A"
159,1,66,65,0.039000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c)),x)","\frac{\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(d x +c \right)+\frac{2 a}{b}\right)}{4 b}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \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*arcsinh(d*x+c)+2*a/b)-1/4*e/b*exp(-2*a/b)*Ei(1,-2*arcsinh(d*x+c)-2*a/b))","A"
160,1,60,58,0.031000," ","int(1/(a+b*arcsinh(d*x+c)),x)","\frac{-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{2 b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(d x +c \right)-\frac{a}{b}\right)}{2 b}}{d}"," ",0,"1/d*(-1/2/b*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/2/b*exp(-a/b)*Ei(1,-arcsinh(d*x+c)-a/b))","A"
161,0,0,26,0.169000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c)),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c)),x)","F"
162,1,602,242,0.377000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{\left(16 \left(d x +c \right)^{5}-16 \left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}+20 \left(d x +c \right)^{3}-12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+5 d x +5 c -\sqrt{1+\left(d x +c \right)^{2}}\right) e^{4}}{32 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{5 e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(d x +c \right)+\frac{5 a}{b}\right)}{32 b^{2}}-\frac{3 \left(-4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right)^{3}-\sqrt{1+\left(d x +c \right)^{2}}+3 d x +3 c \right) e^{4}}{32 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{9 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{32 b^{2}}+\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) e^{4}}{16 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{16 b^{2}}-\frac{e^{4} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{32 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{9 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \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{1+\left(d x +c \right)^{2}}+5 d x +5 c +12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{32 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{5 e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(d x +c \right)-\frac{5 a}{b}\right)}{32 b^{2}}}{d}"," ",0,"1/d*(1/32*(16*(d*x+c)^5-16*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+20*(d*x+c)^3-12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c-(1+(d*x+c)^2)^(1/2))*e^4/b/(a+b*arcsinh(d*x+c))+5/32*e^4/b^2*exp(5*a/b)*Ei(1,5*arcsinh(d*x+c)+5*a/b)-3/32*(-4*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)^3-(1+(d*x+c)^2)^(1/2)+3*d*x+3*c)*e^4/b/(a+b*arcsinh(d*x+c))-9/32*e^4/b^2*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)+1/16*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*e^4/b/(a+b*arcsinh(d*x+c))+1/16*e^4/b^2*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/16/b*e^4*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/16/b^2*e^4*exp(-a/b)*Ei(1,-arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+9/32/b^2*e^4*exp(-3*a/b)*Ei(1,-3*arcsinh(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*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c+12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-5/32/b^2*e^4*exp(-5*a/b)*Ei(1,-5*arcsinh(d*x+c)-5*a/b))","B"
163,1,388,178,0.302000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{\left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}+8 \left(d x +c \right)^{2}-4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e^{3}}{16 \left(a +b \arcsinh \left(d x +c \right)\right) b}-\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(d x +c \right)+\frac{4 a}{b}\right)}{4 b^{2}}-\frac{\left(2 \left(d x +c \right)^{2}-2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e^{3}}{8 \left(a +b \arcsinh \left(d x +c \right)\right) b}+\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \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 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{8 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \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{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right)}{16 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(d x +c \right)-\frac{4 a}{b}\right)}{4 b^{2}}}{d}"," ",0,"1/d*(1/16*(8*(d*x+c)^4-8*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+8*(d*x+c)^2-4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e^3/(a+b*arcsinh(d*x+c))/b-1/4*e^3/b^2*exp(4*a/b)*Ei(1,4*arcsinh(d*x+c)+4*a/b)-1/8*(2*(d*x+c)^2-2*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e^3/(a+b*arcsinh(d*x+c))/b+1/4*e^3/b^2*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)+1/8/b*e^3*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+1/4/b^2*e^3*exp(-2*a/b)*Ei(1,-2*arcsinh(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*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)/(a+b*arcsinh(d*x+c))-1/4/b^2*e^3*exp(-4*a/b)*Ei(1,-4*arcsinh(d*x+c)-4*a/b))","B"
164,1,342,174,0.235000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right)^{3}-\sqrt{1+\left(d x +c \right)^{2}}+3 d x +3 c \right) e^{2}}{8 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{3 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{8 b^{2}}-\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) e^{2}}{8 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{8 b^{2}}+\frac{e^{2} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{8 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{8 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{3 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(d x +c \right)-\frac{3 a}{b}\right)}{8 b^{2}}}{d}"," ",0,"1/d*(1/8*(-4*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)^3-(1+(d*x+c)^2)^(1/2)+3*d*x+3*c)*e^2/b/(a+b*arcsinh(d*x+c))+3/8*e^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)-1/8*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*e^2/b/(a+b*arcsinh(d*x+c))-1/8*e^2/b^2*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)+1/8/b*e^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+1/8/b^2*e^2*exp(-a/b)*Ei(1,-arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-3/8/b^2*e^2*exp(-3*a/b)*Ei(1,-3*arcsinh(d*x+c)-3*a/b))","A"
165,1,160,101,0.056000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{\left(2 \left(d x +c \right)^{2}-2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e}{4 \left(a +b \arcsinh \left(d x +c \right)\right) b}-\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \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 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{4 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(d x +c \right)-\frac{2 a}{b}\right)}{2 b^{2}}}{d}"," ",0,"1/d*(1/4*(2*(d*x+c)^2-2*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e/(a+b*arcsinh(d*x+c))/b-1/2*e/b^2*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)-1/4/b*e*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/2/b^2*e*exp(-2*a/b)*Ei(1,-2*arcsinh(d*x+c)-2*a/b))","A"
166,1,128,89,0.050000," ","int(1/(a+b*arcsinh(d*x+c))^2,x)","\frac{\frac{-\sqrt{1+\left(d x +c \right)^{2}}+d x +c}{2 b \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{2 b^{2}}-\frac{d x +c +\sqrt{1+\left(d x +c \right)^{2}}}{2 b \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(d x +c \right)-\frac{a}{b}\right)}{2 b^{2}}}{d}"," ",0,"1/d*(1/2*(-(1+(d*x+c)^2)^(1/2)+d*x+c)/b/(a+b*arcsinh(d*x+c))+1/2/b^2*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/2/b*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/2/b^2*exp(-a/b)*Ei(1,-arcsinh(d*x+c)-a/b))","A"
167,0,0,26,0.167000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^2,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^2,x)","F"
168,1,896,302,0.388000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^3,x)","\frac{-\frac{\left(16 \left(d x +c \right)^{5}-16 \left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}+20 \left(d x +c \right)^{3}-12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+5 d x +5 c -\sqrt{1+\left(d x +c \right)^{2}}\right) e^{4} \left(5 b \arcsinh \left(d x +c \right)+5 a -b \right)}{64 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}-\frac{25 e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(d x +c \right)+\frac{5 a}{b}\right)}{64 b^{3}}+\frac{3 \left(-4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right)^{3}-\sqrt{1+\left(d x +c \right)^{2}}+3 d x +3 c \right) e^{4} \left(3 b \arcsinh \left(d x +c \right)+3 a -b \right)}{64 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}+\frac{27 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{64 b^{3}}-\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) e^{4} \left(b \arcsinh \left(d x +c \right)+a -b \right)}{32 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}-\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{32 b^{3}}-\frac{e^{4} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{32 b \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}-\frac{e^{4} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{32 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{64 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{64 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{27 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \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{1+\left(d x +c \right)^{2}}+5 d x +5 c +12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{64 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+5 d x +5 c +12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{64 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{25 e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(d x +c \right)-\frac{5 a}{b}\right)}{64 b^{3}}}{d}"," ",0,"1/d*(-1/64*(16*(d*x+c)^5-16*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+20*(d*x+c)^3-12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c-(1+(d*x+c)^2)^(1/2))*e^4*(5*b*arcsinh(d*x+c)+5*a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)-25/64*e^4/b^3*exp(5*a/b)*Ei(1,5*arcsinh(d*x+c)+5*a/b)+3/64*(-4*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)^3-(1+(d*x+c)^2)^(1/2)+3*d*x+3*c)*e^4*(3*b*arcsinh(d*x+c)+3*a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)+27/64*e^4/b^3*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)-1/32*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*e^4*(b*arcsinh(d*x+c)+a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)-1/32*e^4/b^3*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/32/b*e^4*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2-1/32/b^2*e^4*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/32/b^3*e^4*exp(-a/b)*Ei(1,-arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+27/64/b^3*e^4*exp(-3*a/b)*Ei(1,-3*arcsinh(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*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c+12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c+12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-25/64/b^3*e^4*exp(-5*a/b)*Ei(1,-5*arcsinh(d*x+c)-5*a/b))","B"
169,1,579,237,0.310000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^3,x)","\frac{-\frac{\left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}+8 \left(d x +c \right)^{2}-4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e^{3} \left(4 b \arcsinh \left(d x +c \right)+4 a -b \right)}{32 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}+\frac{e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(d x +c \right)+\frac{4 a}{b}\right)}{2 b^{3}}+\frac{\left(2 \left(d x +c \right)^{2}-2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e^{3} \left(2 b \arcsinh \left(d x +c \right)+2 a -b \right)}{16 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}-\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \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 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}+\frac{e^{3} \left(2 \left(d x +c \right)^{2}+1+2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{8 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \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{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right)}{32 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right)}{8 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(d x +c \right)-\frac{4 a}{b}\right)}{2 b^{3}}}{d}"," ",0,"1/d*(-1/32*(8*(d*x+c)^4-8*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+8*(d*x+c)^2-4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e^3*(4*b*arcsinh(d*x+c)+4*a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)+1/2*e^3/b^3*exp(4*a/b)*Ei(1,4*arcsinh(d*x+c)+4*a/b)+1/16*(2*(d*x+c)^2-2*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e^3*(2*b*arcsinh(d*x+c)+2*a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)-1/4*e^3/b^3*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)+1/16/b*e^3*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2+1/8/b^2*e^3*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+1/4/b^3*e^3*exp(-2*a/b)*Ei(1,-2*arcsinh(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*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)/(a+b*arcsinh(d*x+c))-1/2/b^3*e^3*exp(-4*a/b)*Ei(1,-4*arcsinh(d*x+c)-4*a/b))","B"
170,1,507,232,0.241000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^3,x)","\frac{-\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right)^{3}-\sqrt{1+\left(d x +c \right)^{2}}+3 d x +3 c \right) e^{2} \left(3 b \arcsinh \left(d x +c \right)+3 a -b \right)}{16 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}-\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{16 b^{3}}+\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) e^{2} \left(b \arcsinh \left(d x +c \right)+a -b \right)}{16 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}+\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{16 b^{3}}+\frac{e^{2} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}+\frac{e^{2} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(d x +c \right)-\frac{3 a}{b}\right)}{16 b^{3}}}{d}"," ",0,"1/d*(-1/16*(-4*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)^3-(1+(d*x+c)^2)^(1/2)+3*d*x+3*c)*e^2*(3*b*arcsinh(d*x+c)+3*a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)-9/16*e^2/b^3*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)+1/16*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*e^2*(b*arcsinh(d*x+c)+a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)+1/16*e^2/b^3*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)+1/16/b*e^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2+1/16/b^2*e^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+1/16/b^3*e^2*exp(-a/b)*Ei(1,-arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-9/16/b^3*e^2*exp(-3*a/b)*Ei(1,-3*arcsinh(d*x+c)-3*a/b))","B"
171,1,239,150,0.066000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^3,x)","\frac{-\frac{\left(2 \left(d x +c \right)^{2}-2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e \left(2 b \arcsinh \left(d x +c \right)+2 a -b \right)}{8 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}+\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \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 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{8 b \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}-\frac{e \left(2 \left(d x +c \right)^{2}+1+2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{4 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(d x +c \right)-\frac{2 a}{b}\right)}{2 b^{3}}}{d}"," ",0,"1/d*(-1/8*(2*(d*x+c)^2-2*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e*(2*b*arcsinh(d*x+c)+2*a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)+1/2*e/b^3*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)-1/8/b*e*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2-1/4/b^2*e*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/2/b^3*e*exp(-2*a/b)*Ei(1,-2*arcsinh(d*x+c)-2*a/b))","A"
172,1,190,118,0.059000," ","int(1/(a+b*arcsinh(d*x+c))^3,x)","\frac{-\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) \left(b \arcsinh \left(d x +c \right)+a -b \right)}{4 b^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)+a^{2}\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{4 b^{3}}-\frac{d x +c +\sqrt{1+\left(d x +c \right)^{2}}}{4 b \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}-\frac{d x +c +\sqrt{1+\left(d x +c \right)^{2}}}{4 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(d x +c \right)-\frac{a}{b}\right)}{4 b^{3}}}{d}"," ",0,"1/d*(-1/4*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*(b*arcsinh(d*x+c)+a-b)/b^2/(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)+a^2)-1/4/b^3*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/4/b*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2-1/4/b^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/4/b^3*exp(-a/b)*Ei(1,-arcsinh(d*x+c)-a/b))","A"
173,0,0,26,0.192000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^3,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^3,x)","F"
174,1,1244,384,0.431000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(16 \left(d x +c \right)^{5}-16 \left(d x +c \right)^{4} \sqrt{1+\left(d x +c \right)^{2}}+20 \left(d x +c \right)^{3}-12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+5 d x +5 c -\sqrt{1+\left(d x +c \right)^{2}}\right) e^{4} \left(25 b^{2} \arcsinh \left(d x +c \right)^{2}+50 a b \arcsinh \left(d x +c \right)-5 \arcsinh \left(d x +c \right) b^{2}+25 a^{2}-5 a b +2 b^{2}\right)}{192 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}+\frac{125 e^{4} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(d x +c \right)+\frac{5 a}{b}\right)}{192 b^{4}}-\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right)^{3}-\sqrt{1+\left(d x +c \right)^{2}}+3 d x +3 c \right) e^{4} \left(9 b^{2} \arcsinh \left(d x +c \right)^{2}+18 a b \arcsinh \left(d x +c \right)-3 \arcsinh \left(d x +c \right) b^{2}+9 a^{2}-3 a b +2 b^{2}\right)}{64 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}-\frac{27 e^{4} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{64 b^{4}}+\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) e^{4} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)-\arcsinh \left(d x +c \right) b^{2}+a^{2}-a b +2 b^{2}\right)}{96 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}+\frac{e^{4} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{96 b^{4}}-\frac{e^{4} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{48 b \left(a +b \arcsinh \left(d x +c \right)\right)^{3}}-\frac{e^{4} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{96 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}-\frac{e^{4} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{96 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e^{4} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{32 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{64 b^{2} \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{64 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{27 e^{4} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \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{1+\left(d x +c \right)^{2}}+5 d x +5 c +12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{96 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+5 d x +5 c +12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{192 b^{2} \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+5 d x +5 c +12 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{192 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{125 e^{4} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(d x +c \right)-\frac{5 a}{b}\right)}{192 b^{4}}}{d}"," ",0,"1/d*(1/192*(16*(d*x+c)^5-16*(d*x+c)^4*(1+(d*x+c)^2)^(1/2)+20*(d*x+c)^3-12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c-(1+(d*x+c)^2)^(1/2))*e^4*(25*b^2*arcsinh(d*x+c)^2+50*a*b*arcsinh(d*x+c)-5*arcsinh(d*x+c)*b^2+25*a^2-5*a*b+2*b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)+125/192*e^4/b^4*exp(5*a/b)*Ei(1,5*arcsinh(d*x+c)+5*a/b)-1/64*(-4*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)^3-(1+(d*x+c)^2)^(1/2)+3*d*x+3*c)*e^4*(9*b^2*arcsinh(d*x+c)^2+18*a*b*arcsinh(d*x+c)-3*arcsinh(d*x+c)*b^2+9*a^2-3*a*b+2*b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)-27/64*e^4/b^4*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)+1/96*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*e^4*(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)-arcsinh(d*x+c)*b^2+a^2-a*b+2*b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)+1/96*e^4/b^4*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/48/b*e^4*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^3-1/96/b^2*e^4*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2-1/96/b^3*e^4*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/96/b^4*e^4*exp(-a/b)*Ei(1,-arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+27/64/b^4*e^4*exp(-3*a/b)*Ei(1,-3*arcsinh(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*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c+12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c+12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+5*d*x+5*c+12*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-125/192/b^4*e^4*exp(-5*a/b)*Ei(1,-5*arcsinh(d*x+c)-5*a/b))","B"
175,1,800,318,0.352000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(8 \left(d x +c \right)^{4}-8 \left(d x +c \right)^{3} \sqrt{1+\left(d x +c \right)^{2}}+8 \left(d x +c \right)^{2}-4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e^{3} \left(8 b^{2} \arcsinh \left(d x +c \right)^{2}+16 a b \arcsinh \left(d x +c \right)-2 \arcsinh \left(d x +c \right) b^{2}+8 a^{2}-2 a b +b^{2}\right)}{48 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}-\frac{2 e^{3} {\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(d x +c \right)+\frac{4 a}{b}\right)}{3 b^{4}}-\frac{\left(2 \left(d x +c \right)^{2}-2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e^{3} \left(2 b^{2} \arcsinh \left(d x +c \right)^{2}+4 a b \arcsinh \left(d x +c \right)-\arcsinh \left(d x +c \right) b^{2}+2 a^{2}-a b +b^{2}\right)}{24 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}+\frac{e^{3} {\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \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 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{24 b \left(a +b \arcsinh \left(d x +c \right)\right)^{3}}+\frac{e^{3} \left(2 \left(d x +c \right)^{2}+1+2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{24 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}+\frac{e^{3} \left(2 \left(d x +c \right)^{2}+1+2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{12 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{3} {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \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{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right)}{48 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right)}{24 b^{2} \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right)}{6 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{2 e^{3} {\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(d x +c \right)-\frac{4 a}{b}\right)}{3 b^{4}}}{d}"," ",0,"1/d*(1/48*(8*(d*x+c)^4-8*(d*x+c)^3*(1+(d*x+c)^2)^(1/2)+8*(d*x+c)^2-4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e^3*(8*b^2*arcsinh(d*x+c)^2+16*a*b*arcsinh(d*x+c)-2*arcsinh(d*x+c)*b^2+8*a^2-2*a*b+b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)-2/3*e^3/b^4*exp(4*a/b)*Ei(1,4*arcsinh(d*x+c)+4*a/b)-1/24*(2*(d*x+c)^2-2*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e^3*(2*b^2*arcsinh(d*x+c)^2+4*a*b*arcsinh(d*x+c)-arcsinh(d*x+c)*b^2+2*a^2-a*b+b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)+1/6*e^3/b^4*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)+1/24/b*e^3*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^3+1/24/b^2*e^3*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2+1/12/b^3*e^3*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+1/6/b^4*e^3*exp(-2*a/b)*Ei(1,-2*arcsinh(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*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)/(a+b*arcsinh(d*x+c))-2/3/b^4*e^3*exp(-4*a/b)*Ei(1,-4*arcsinh(d*x+c)-4*a/b))","B"
176,1,709,307,0.281000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(-4 \left(d x +c \right)^{2} \sqrt{1+\left(d x +c \right)^{2}}+4 \left(d x +c \right)^{3}-\sqrt{1+\left(d x +c \right)^{2}}+3 d x +3 c \right) e^{2} \left(9 b^{2} \arcsinh \left(d x +c \right)^{2}+18 a b \arcsinh \left(d x +c \right)-3 \arcsinh \left(d x +c \right) b^{2}+9 a^{2}-3 a b +2 b^{2}\right)}{48 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}+\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(d x +c \right)+\frac{3 a}{b}\right)}{16 b^{4}}-\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) e^{2} \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)-\arcsinh \left(d x +c \right) b^{2}+a^{2}-a b +2 b^{2}\right)}{48 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}-\frac{e^{2} {\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{48 b^{4}}+\frac{e^{2} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{24 b \left(a +b \arcsinh \left(d x +c \right)\right)^{3}}+\frac{e^{2} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{48 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}+\frac{e^{2} \left(d x +c +\sqrt{1+\left(d x +c \right)^{2}}\right)}{48 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}+\frac{e^{2} {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{24 b \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b^{2} \left(a +b \arcsinh \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{1+\left(d x +c \right)^{2}}+\sqrt{1+\left(d x +c \right)^{2}}\right)}{16 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(d x +c \right)-\frac{3 a}{b}\right)}{16 b^{4}}}{d}"," ",0,"1/d*(1/48*(-4*(d*x+c)^2*(1+(d*x+c)^2)^(1/2)+4*(d*x+c)^3-(1+(d*x+c)^2)^(1/2)+3*d*x+3*c)*e^2*(9*b^2*arcsinh(d*x+c)^2+18*a*b*arcsinh(d*x+c)-3*arcsinh(d*x+c)*b^2+9*a^2-3*a*b+2*b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)+9/16*e^2/b^4*exp(3*a/b)*Ei(1,3*arcsinh(d*x+c)+3*a/b)-1/48*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*e^2*(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)-arcsinh(d*x+c)*b^2+a^2-a*b+2*b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)-1/48*e^2/b^4*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)+1/24/b*e^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^3+1/48/b^2*e^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2+1/48/b^3*e^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))+1/48/b^4*e^2*exp(-a/b)*Ei(1,-arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(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*(1+(d*x+c)^2)^(1/2)+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-9/16/b^4*e^2*exp(-3*a/b)*Ei(1,-3*arcsinh(d*x+c)-3*a/b))","B"
177,1,333,188,0.076000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(2 \left(d x +c \right)^{2}-2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}+1\right) e \left(2 b^{2} \arcsinh \left(d x +c \right)^{2}+4 a b \arcsinh \left(d x +c \right)-\arcsinh \left(d x +c \right) b^{2}+2 a^{2}-a b +b^{2}\right)}{12 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}-\frac{e \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \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 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{12 b \left(a +b \arcsinh \left(d x +c \right)\right)^{3}}-\frac{e \left(2 \left(d x +c \right)^{2}+1+2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{12 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}-\frac{e \left(2 \left(d x +c \right)^{2}+1+2 \left(d x +c \right) \sqrt{1+\left(d x +c \right)^{2}}\right)}{6 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{e \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(d x +c \right)-\frac{2 a}{b}\right)}{3 b^{4}}}{d}"," ",0,"1/d*(1/12*(2*(d*x+c)^2-2*(d*x+c)*(1+(d*x+c)^2)^(1/2)+1)*e*(2*b^2*arcsinh(d*x+c)^2+4*a*b*arcsinh(d*x+c)-arcsinh(d*x+c)*b^2+2*a^2-a*b+b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)-1/3*e/b^4*exp(2*a/b)*Ei(1,2*arcsinh(d*x+c)+2*a/b)-1/12/b*e*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^3-1/12/b^2*e*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2-1/6/b^3*e*(2*(d*x+c)^2+1+2*(d*x+c)*(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/3/b^4*e*exp(-2*a/b)*Ei(1,-2*arcsinh(d*x+c)-2*a/b))","A"
178,1,272,149,0.068000," ","int(1/(a+b*arcsinh(d*x+c))^4,x)","\frac{\frac{\left(-\sqrt{1+\left(d x +c \right)^{2}}+d x +c \right) \left(b^{2} \arcsinh \left(d x +c \right)^{2}+2 a b \arcsinh \left(d x +c \right)-\arcsinh \left(d x +c \right) b^{2}+a^{2}-a b +2 b^{2}\right)}{12 b^{3} \left(b^{3} \arcsinh \left(d x +c \right)^{3}+3 a \,b^{2} \arcsinh \left(d x +c \right)^{2}+3 a^{2} b \arcsinh \left(d x +c \right)+a^{3}\right)}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(d x +c \right)+\frac{a}{b}\right)}{12 b^{4}}-\frac{d x +c +\sqrt{1+\left(d x +c \right)^{2}}}{6 b \left(a +b \arcsinh \left(d x +c \right)\right)^{3}}-\frac{d x +c +\sqrt{1+\left(d x +c \right)^{2}}}{12 b^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}}-\frac{d x +c +\sqrt{1+\left(d x +c \right)^{2}}}{12 b^{3} \left(a +b \arcsinh \left(d x +c \right)\right)}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(d x +c \right)-\frac{a}{b}\right)}{12 b^{4}}}{d}"," ",0,"1/d*(1/12*(-(1+(d*x+c)^2)^(1/2)+d*x+c)*(b^2*arcsinh(d*x+c)^2+2*a*b*arcsinh(d*x+c)-arcsinh(d*x+c)*b^2+a^2-a*b+2*b^2)/b^3/(b^3*arcsinh(d*x+c)^3+3*a*b^2*arcsinh(d*x+c)^2+3*a^2*b*arcsinh(d*x+c)+a^3)+1/12/b^4*exp(a/b)*Ei(1,arcsinh(d*x+c)+a/b)-1/6/b*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^3-1/12/b^2*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))^2-1/12/b^3*(d*x+c+(1+(d*x+c)^2)^(1/2))/(a+b*arcsinh(d*x+c))-1/12/b^4*exp(-a/b)*Ei(1,-arcsinh(d*x+c)-a/b))","A"
179,0,0,26,0.208000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^4,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^4,x)","F"
180,-2,0,284,180.000000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right)^{4} \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(1/2),x)","F"
181,-2,0,218,180.000000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right)^{3} \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(1/2),x)","F"
182,-2,0,194,180.000000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right)^{2} \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(1/2),x)","F"
183,0,0,130,0.111000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(1/2),x)","\int \left(d e x +c e \right) \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(1/2),x)","F"
184,0,0,92,0.000000," ","int((a+b*arcsinh(d*x+c))^(1/2),x)","\int \sqrt{a +b \arcsinh \left(d x +c \right)}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(1/2),x)","F"
185,0,0,26,0.218000," ","int((a+b*arcsinh(d*x+c))^(1/2)/(d*e*x+c*e),x)","\int \frac{\sqrt{a +b \arcsinh \left(d x +c \right)}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(1/2)/(d*e*x+c*e),x)","F"
186,-2,0,394,180.000000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right)^{4} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(3/2),x)","F"
187,-2,0,294,180.000000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right)^{3} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(3/2),x)","F"
188,-2,0,265,180.000000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right)^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(3/2),x)","F"
189,0,0,165,0.115000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(3/2),x)","\int \left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(3/2),x)","F"
190,0,0,121,0.009000," ","int((a+b*arcsinh(d*x+c))^(3/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(3/2),x)","F"
191,0,0,26,0.247000," ","int((a+b*arcsinh(d*x+c))^(3/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(3/2)/(d*e*x+c*e),x)","F"
192,-2,0,482,180.000000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right)^{4} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(5/2),x)","F"
193,-2,0,377,180.000000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right)^{3} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(5/2),x)","F"
194,-2,0,323,180.000000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right)^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(5/2),x)","F"
195,0,0,214,0.109000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(5/2),x)","\int \left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(5/2),x)","F"
196,0,0,146,0.003000," ","int((a+b*arcsinh(d*x+c))^(5/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(5/2),x)","F"
197,0,0,26,0.243000," ","int((a+b*arcsinh(d*x+c))^(5/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(5/2)/(d*e*x+c*e),x)","F"
198,-2,0,598,180.000000," ","int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(7/2),x)","\int \left(d e x +c e \right)^{4} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(7/2),x)","F"
199,-2,0,457,180.000000," ","int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(7/2),x)","\int \left(d e x +c e \right)^{3} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(7/2),x)","F"
200,-2,0,398,180.000000," ","int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(7/2),x)","\int \left(d e x +c e \right)^{2} \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(7/2),x)","F"
201,0,0,251,0.108000," ","int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(7/2),x)","\int \left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(7/2),x)","F"
202,0,0,177,0.075000," ","int((a+b*arcsinh(d*x+c))^(7/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(7/2),x)","F"
203,0,0,26,0.253000," ","int((a+b*arcsinh(d*x+c))^(7/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^(7/2)/(d*e*x+c*e),x)","F"
204,-2,0,257,180.000000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
205,-2,0,171,180.000000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
206,-2,0,167,180.000000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
207,0,0,87,0.118000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{d e x +c e}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
208,0,0,71,0.000000," ","int(1/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
209,0,0,26,0.204000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(1/2),x)","\int \frac{1}{\left(d e x +c e \right) \sqrt{a +b \arcsinh \left(d x +c \right)}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(1/2),x)","F"
210,-2,0,298,180.000000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
211,-2,0,212,180.000000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
212,-2,0,208,180.000000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
213,0,0,124,0.095000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{d e x +c e}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
214,0,0,101,0.000000," ","int(1/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
215,0,0,26,0.219000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(3/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(3/2),x)","F"
216,-2,0,358,180.000000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
217,-2,0,272,180.000000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
218,-2,0,266,180.000000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
219,0,0,173,0.099000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{d e x +c e}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
220,0,0,127,0.000000," ","int(1/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
221,0,0,26,0.225000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(5/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(5/2),x)","F"
222,-2,0,440,180.000000," ","int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{\left(d e x +c e \right)^{4}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
223,-2,0,352,180.000000," ","int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{\left(d e x +c e \right)^{3}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
224,-2,0,341,180.000000," ","int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{\left(d e x +c e \right)^{2}}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
225,0,0,210,0.095000," ","int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{d e x +c e}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
226,0,0,158,0.000000," ","int(1/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
227,0,0,26,0.221000," ","int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(7/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsinh \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(7/2),x)","F"
228,1,238,338,0.026000," ","int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(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}} \arcsinh \left(\frac{d e x +c e}{e}\right)}{9}-\frac{2 \left(\frac{e^{2} \left(d e x +c e \right)^{\frac{7}{2}} \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{9}-\frac{7 e^{4} \left(d e x +c e \right)^{\frac{3}{2}} \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{45}+\frac{7 i e^{5} \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)\right)}{15 \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{9 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)*arcsinh((d*e*x+c*e)/e)-2/9/e*(1/9*e^2*(d*e*x+c*e)^(7/2)*((d*e*x+c*e)^2/e^2+1)^(1/2)-7/45*e^4*(d*e*x+c*e)^(3/2)*((d*e*x+c*e)^2/e^2+1)^(1/2)+7/15*I*e^5/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)))))","C"
229,1,212,192,0.012000," ","int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(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}} \arcsinh \left(\frac{d e x +c e}{e}\right)}{7}-\frac{2 \left(\frac{e^{2} \left(d e x +c e \right)^{\frac{5}{2}} \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{7}-\frac{5 e^{4} \sqrt{d e x +c e}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{21}+\frac{5 e^{4} \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)}{21 \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{7 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)*arcsinh((d*e*x+c*e)/e)-2/7/e*(1/7*e^2*(d*e*x+c*e)^(5/2)*((d*e*x+c*e)^2/e^2+1)^(1/2)-5/21*e^4*(d*e*x+c*e)^(1/2)*((d*e*x+c*e)^2/e^2+1)^(1/2)+5/21*e^4/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I))))","C"
230,1,205,307,0.010000," ","int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(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}} \arcsinh \left(\frac{d e x +c e}{e}\right)}{5}-\frac{2 \left(\frac{e^{2} \left(d e x +c e \right)^{\frac{3}{2}} \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{5}-\frac{3 i e^{3} \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)\right)}{5 \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{5 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)*arcsinh((d*e*x+c*e)/e)-2/5/e*(1/5*e^2*(d*e*x+c*e)^(3/2)*((d*e*x+c*e)^2/e^2+1)^(1/2)-3/5*I*e^3/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)))))","C"
231,1,179,163,0.011000," ","int((a+b*arcsinh(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}} \arcsinh \left(\frac{d e x +c e}{e}\right)}{3}-\frac{2 \left(\frac{e^{2} \sqrt{d e x +c e}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{3}-\frac{e^{2} \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)}{3 \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{3 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)*arcsinh((d*e*x+c*e)/e)-2/3/e*(1/3*e^2*(d*e*x+c*e)^(1/2)*((d*e*x+c*e)^2/e^2+1)^(1/2)-1/3*e^2/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I))))","C"
232,1,161,283,0.014000," ","int((a+b*arcsinh(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}\, \arcsinh \left(\frac{d e x +c e}{e}\right)-\frac{2 i \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)\right)}{\sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{d e}"," ",0,"2/d/e*(a*(d*e*x+c*e)^(1/2)+b*((d*e*x+c*e)^(1/2)*arcsinh((d*e*x+c*e)/e)-2*I/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I))))","C"
233,1,140,137,0.013000," ","int((a+b*arcsinh(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{\arcsinh \left(\frac{d e x +c e}{e}\right)}{\sqrt{d e x +c e}}+\frac{2 \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)}{e \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{d e}"," ",0,"2/d/e*(-a/(d*e*x+c*e)^(1/2)+b*(-1/(d*e*x+c*e)^(1/2)*arcsinh((d*e*x+c*e)/e)+2/e/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)))","C"
234,1,202,312,0.013000," ","int((a+b*arcsinh(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{\arcsinh \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{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{3 \sqrt{d e x +c e}}+\frac{2 i \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)\right)}{3 e \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}}{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)*arcsinh((d*e*x+c*e)/e)+2/3/e*(-((d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(1/2)+I/e/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I)))))","C"
235,1,176,166,0.016000," ","int((a+b*arcsinh(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{\arcsinh \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{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{15 \left(d e x +c e \right)^{\frac{3}{2}}}-\frac{2 \sqrt{1-\frac{i \left(d e x +c e \right)}{e}}\, \sqrt{1+\frac{i \left(d e x +c e \right)}{e}}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{i}{e}}, i\right)}{15 e^{2} \sqrt{\frac{i}{e}}\, \sqrt{\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}}{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)*arcsinh((d*e*x+c*e)/e)+2/5/e*(-1/3*((d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(3/2)-1/3/e^2/(I/e)^(1/2)*(1-I/e*(d*e*x+c*e))^(1/2)*(1+I/e*(d*e*x+c*e))^(1/2)/((d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(I/e)^(1/2),I))))","C"
236,-2,0,110,180.000000," ","int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{7}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^2,x)","F"
237,-2,0,110,180.000000," ","int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^2,x)","F"
238,-2,0,110,180.000000," ","int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^2,x)","F"
239,-2,0,110,180.000000," ","int((a+b*arcsinh(d*x+c))^2*(d*e*x+c*e)^(1/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{2} \sqrt{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^2*(d*e*x+c*e)^(1/2),x)","F"
240,-2,0,110,180.000000," ","int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{2}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(1/2),x)","F"
241,-2,0,110,180.000000," ","int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(3/2),x)","F"
242,-2,0,110,180.000000," ","int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(5/2),x)","F"
243,-2,0,110,180.000000," ","int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(7/2),x)","F"
244,-2,0,71,180.000000," ","int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^3,x)","\int \left(d e x +c e \right)^{\frac{7}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^3,x)","F"
245,-2,0,71,180.000000," ","int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^3,x)","\int \left(d e x +c e \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^3,x)","F"
246,-2,0,71,180.000000," ","int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^3,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^3,x)","F"
247,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^3*(d*e*x+c*e)^(1/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{3} \sqrt{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^3*(d*e*x+c*e)^(1/2),x)","F"
248,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{3}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(1/2),x)","F"
249,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(3/2),x)","F"
250,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(5/2),x)","F"
251,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(7/2),x)","F"
252,-2,0,71,180.000000," ","int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^4,x)","\int \left(d e x +c e \right)^{\frac{7}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^4,x)","F"
253,-2,0,71,180.000000," ","int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^4,x)","\int \left(d e x +c e \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^4,x)","F"
254,-2,0,71,180.000000," ","int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^4,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^4,x)","F"
255,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^4*(d*e*x+c*e)^(1/2),x)","\int \left(a +b \arcsinh \left(d x +c \right)\right)^{4} \sqrt{d e x +c e}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^4*(d*e*x+c*e)^(1/2),x)","F"
256,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{4}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(1/2),x)","F"
257,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(3/2),x)","F"
258,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(5/2),x)","F"
259,-2,0,71,180.000000," ","int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \arcsinh \left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(7/2),x)","F"
260,1,204,115,0.133000," ","int(arcsinh(b*x+a)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} x b -6 \arcsinh \left(b x +a \right)^{2} x^{2} b^{2}+4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} a -12 \arcsinh \left(b x +a \right)^{2} x a b +6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x b +\arcsinh \left(b x +a \right)^{4}-6 \arcsinh \left(b x +a \right)^{2} a^{2}-3 b^{2} x^{2}+6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) a -6 a b x -3 \arcsinh \left(b x +a \right)^{2}-3 a^{2}-3}{8 b}"," ",0,"1/8*(4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*x*b-6*arcsinh(b*x+a)^2*x^2*b^2+4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*a-12*arcsinh(b*x+a)^2*x*a*b+6*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x*b+arcsinh(b*x+a)^4-6*arcsinh(b*x+a)^2*a^2-3*b^2*x^2+6*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*a-6*a*b*x-3*arcsinh(b*x+a)^2-3*a^2-3)/b","A"
261,1,167,93,0.112000," ","int(arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{6 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b -6 \arcsinh \left(b x +a \right) x^{2} b^{2}+6 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a -12 \arcsinh \left(b x +a \right) x a b +2 \arcsinh \left(b x +a \right)^{3}-6 \arcsinh \left(b x +a \right) a^{2}+3 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b +3 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a -3 \arcsinh \left(b x +a \right)}{12 b}"," ",0,"1/12*(6*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b-6*arcsinh(b*x+a)*x^2*b^2+6*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-12*arcsinh(b*x+a)*x*a*b+2*arcsinh(b*x+a)^3-6*arcsinh(b*x+a)*a^2+3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b+3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-3*arcsinh(b*x+a))/b","A"
262,1,91,53,0.098000," ","int(arcsinh(b*x+a)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x b -b^{2} x^{2}+2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) a -2 a b x +\arcsinh \left(b x +a \right)^{2}-a^{2}-1}{4 b}"," ",0,"1/4*(2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x*b-b^2*x^2+2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*a-2*a*b*x+arcsinh(b*x+a)^2-a^2-1)/b","A"
263,1,28,27,0.126000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(1/2)/arcsinh(b*x+a),x)","\frac{\Chi \left(2 \arcsinh \left(b x +a \right)\right)}{2 b}+\frac{\ln \left(\arcsinh \left(b x +a \right)\right)}{2 b}"," ",0,"1/2*Chi(2*arcsinh(b*x+a))/b+1/2*ln(arcsinh(b*x+a))/b","A"
264,1,44,37,0.122000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(1/2)/arcsinh(b*x+a)^2,x)","\frac{2 \Shi \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\cosh \left(2 \arcsinh \left(b x +a \right)\right)-1}{2 b \arcsinh \left(b x +a \right)}"," ",0,"1/2/b*(2*Shi(2*arcsinh(b*x+a))*arcsinh(b*x+a)-cosh(2*arcsinh(b*x+a))-1)/arcsinh(b*x+a)","A"
265,1,63,67,0.126000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(1/2)/arcsinh(b*x+a)^3,x)","\frac{4 \Chi \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)^{2}-2 \sinh \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\cosh \left(2 \arcsinh \left(b x +a \right)\right)-1}{4 b \arcsinh \left(b x +a \right)^{2}}"," ",0,"1/4/b*(4*Chi(2*arcsinh(b*x+a))*arcsinh(b*x+a)^2-2*sinh(2*arcsinh(b*x+a))*arcsinh(b*x+a)-cosh(2*arcsinh(b*x+a))-1)/arcsinh(b*x+a)^2","A"
266,1,592,207,0.139000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(3/2)*arcsinh(b*x+a)^3,x)","\frac{-48-102 a b x +80 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} x b -240 \arcsinh \left(b x +a \right)^{2} x a b +102 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x b -51 b^{2} x^{2}-51 a^{2}-24 \arcsinh \left(b x +a \right)^{2} a^{4}-3 x^{4} b^{4}-120 \arcsinh \left(b x +a \right)^{2} a^{2}-96 \arcsinh \left(b x +a \right)^{2} x^{3} a \,b^{3}+32 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} x^{3} b^{3}+12 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x^{3} b^{3}-144 \arcsinh \left(b x +a \right)^{2} x^{2} a^{2} b^{2}-96 \arcsinh \left(b x +a \right)^{2} x \,a^{3} b -3 a^{4}-51 \arcsinh \left(b x +a \right)^{2}+32 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} a^{3}+12 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) a^{3}-24 \arcsinh \left(b x +a \right)^{2} x^{4} b^{4}-12 x^{3} a \,b^{3}-18 x^{2} a^{2} b^{2}-12 x \,a^{3} b +12 \arcsinh \left(b x +a \right)^{4}-120 \arcsinh \left(b x +a \right)^{2} x^{2} b^{2}+80 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} a +102 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) a +36 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x \,a^{2} b +96 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} x^{2} a \,b^{2}+96 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right)^{3} x \,a^{2} b +36 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x^{2} a \,b^{2}}{128 b}"," ",0,"1/128*(-48-102*a*b*x+80*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*x*b-240*arcsinh(b*x+a)^2*x*a*b+102*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x*b-51*arcsinh(b*x+a)^2+36*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x*a^2*b-51*b^2*x^2-51*a^2-120*arcsinh(b*x+a)^2*x^2*b^2-24*arcsinh(b*x+a)^2*a^4-3*x^4*b^4+32*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*x^3*b^3+12*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x^3*b^3-144*arcsinh(b*x+a)^2*x^2*a^2*b^2-96*arcsinh(b*x+a)^2*x*a^3*b-96*arcsinh(b*x+a)^2*x^3*a*b^3-3*a^4+12*arcsinh(b*x+a)^4-120*arcsinh(b*x+a)^2*a^2-12*x^3*a*b^3-18*x^2*a^2*b^2-12*x*a^3*b+32*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*a^3+12*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*a^3-24*arcsinh(b*x+a)^2*x^4*b^4+80*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*a+102*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*a+96*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*x^2*a*b^2+96*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)^3*x*a^2*b+36*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x^2*a*b^2)/b","B"
267,1,479,165,0.126000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(3/2)*arcsinh(b*x+a)^2,x)","\frac{16 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x^{3} b^{3}-8 \arcsinh \left(b x +a \right) x^{4} b^{4}+48 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x^{2} a \,b^{2}-32 \arcsinh \left(b x +a \right) x^{3} a \,b^{3}+48 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x \,a^{2} b +2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x^{3} b^{3}-48 \arcsinh \left(b x +a \right) x^{2} a^{2} b^{2}+16 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a^{3}+6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x^{2} a \,b^{2}-32 \arcsinh \left(b x +a \right) x \,a^{3} b +40 \arcsinh \left(b x +a \right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b +6 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x \,a^{2} b -40 \arcsinh \left(b x +a \right) x^{2} b^{2}-8 \arcsinh \left(b x +a \right) a^{4}+40 \arcsinh \left(b x +a \right)^{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}\, a^{3}-80 \arcsinh \left(b x +a \right) x a b +17 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b +8 \arcsinh \left(b x +a \right)^{3}-40 \arcsinh \left(b x +a \right) a^{2}+17 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a -17 \arcsinh \left(b x +a \right)}{64 b}"," ",0,"1/64*(16*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x^3*b^3-8*arcsinh(b*x+a)*x^4*b^4+48*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x^2*a*b^2-32*arcsinh(b*x+a)*x^3*a*b^3+48*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*a^2*b+2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x^3*b^3-48*arcsinh(b*x+a)*x^2*a^2*b^2+16*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3+6*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x^2*a*b^2-32*arcsinh(b*x+a)*x*a^3*b+40*arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b+6*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*a^2*b-40*arcsinh(b*x+a)*x^2*b^2-8*arcsinh(b*x+a)*a^4+40*arcsinh(b*x+a)^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)*a^3-80*arcsinh(b*x+a)*x*a*b+17*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b+8*arcsinh(b*x+a)^3-40*arcsinh(b*x+a)*a^2+17*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-17*arcsinh(b*x+a))/b","B"
268,1,262,92,0.110000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(3/2)*arcsinh(b*x+a),x)","\frac{4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x^{3} b^{3}-x^{4} b^{4}+12 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x^{2} a \,b^{2}-4 x^{3} a \,b^{3}+12 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x \,a^{2} b -6 x^{2} a^{2} b^{2}+4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) a^{3}-4 x \,a^{3} b +10 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) x b -5 b^{2} x^{2}-a^{4}+10 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, \arcsinh \left(b x +a \right) a -10 a b x +3 \arcsinh \left(b x +a \right)^{2}-5 a^{2}-4}{16 b}"," ",0,"1/16*(4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x^3*b^3-x^4*b^4+12*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x^2*a*b^2-4*x^3*a*b^3+12*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x*a^2*b-6*x^2*a^2*b^2+4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*a^3-4*x*a^3*b+10*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*x*b-5*b^2*x^2-a^4+10*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*arcsinh(b*x+a)*a-10*a*b*x+3*arcsinh(b*x+a)^2-5*a^2-4)/b","B"
269,1,42,41,0.128000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a),x)","\frac{\Chi \left(2 \arcsinh \left(b x +a \right)\right)}{2 b}+\frac{\Chi \left(4 \arcsinh \left(b x +a \right)\right)}{8 b}+\frac{3 \ln \left(\arcsinh \left(b x +a \right)\right)}{8 b}"," ",0,"1/2*Chi(2*arcsinh(b*x+a))/b+1/8*Chi(4*arcsinh(b*x+a))/b+3/8*ln(arcsinh(b*x+a))/b","A"
270,1,72,52,0.123000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^2,x)","\frac{4 \Shi \left(4 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)+8 \Shi \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-\cosh \left(4 \arcsinh \left(b x +a \right)\right)-4 \cosh \left(2 \arcsinh \left(b x +a \right)\right)-3}{8 b \arcsinh \left(b x +a \right)}"," ",0,"1/8/b*(4*Shi(4*arcsinh(b*x+a))*arcsinh(b*x+a)+8*Shi(2*arcsinh(b*x+a))*arcsinh(b*x+a)-cosh(4*arcsinh(b*x+a))-4*cosh(2*arcsinh(b*x+a))-3)/arcsinh(b*x+a)","A"
271,1,110,80,0.120000," ","int((b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^3,x)","\frac{16 \Chi \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)^{2}+16 \Chi \left(4 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)^{2}-8 \sinh \left(2 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-4 \sinh \left(4 \arcsinh \left(b x +a \right)\right) \arcsinh \left(b x +a \right)-4 \cosh \left(2 \arcsinh \left(b x +a \right)\right)-\cosh \left(4 \arcsinh \left(b x +a \right)\right)-3}{16 b \arcsinh \left(b x +a \right)^{2}}"," ",0,"1/16/b*(16*Chi(2*arcsinh(b*x+a))*arcsinh(b*x+a)^2+16*Chi(4*arcsinh(b*x+a))*arcsinh(b*x+a)^2-8*sinh(2*arcsinh(b*x+a))*arcsinh(b*x+a)-4*sinh(4*arcsinh(b*x+a))*arcsinh(b*x+a)-4*cosh(2*arcsinh(b*x+a))-cosh(4*arcsinh(b*x+a))-3)/arcsinh(b*x+a)^2","A"
272,1,14,13,0.074000," ","int(arcsinh(b*x+a)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{\arcsinh \left(b x +a \right)^{4}}{4 b}"," ",0,"1/4*arcsinh(b*x+a)^4/b","A"
273,1,14,13,0.067000," ","int(arcsinh(b*x+a)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{\arcsinh \left(b x +a \right)^{3}}{3 b}"," ",0,"1/3*arcsinh(b*x+a)^3/b","A"
274,1,14,13,0.074000," ","int(arcsinh(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{\arcsinh \left(b x +a \right)^{2}}{2 b}"," ",0,"1/2*arcsinh(b*x+a)^2/b","A"
275,1,12,11,0.077000," ","int(1/arcsinh(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{\ln \left(\arcsinh \left(b x +a \right)\right)}{b}"," ",0,"ln(arcsinh(b*x+a))/b","A"
276,1,14,13,0.077000," ","int(1/arcsinh(b*x+a)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","-\frac{1}{b \arcsinh \left(b x +a \right)}"," ",0,"-1/b/arcsinh(b*x+a)","A"
277,1,14,13,0.081000," ","int(1/arcsinh(b*x+a)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","-\frac{1}{2 b \arcsinh \left(b x +a \right)^{2}}"," ",0,"-1/2/b/arcsinh(b*x+a)^2","A"
278,1,203,135,0.259000," ","int(arcsinh(b*x+a)^3/(b^2*x^2+2*a*b*x+a^2+1)^(3/2),x)","-\frac{\left(b^{2} x^{2}-\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b +2 a b x -\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a +a^{2}+1\right) \arcsinh \left(b x +a \right)^{3}}{b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}+\frac{2 \arcsinh \left(b x +a \right)^{3}}{b}-\frac{3 \arcsinh \left(b x +a \right)^{2} \ln \left(1+\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}\right)}{b}-\frac{3 \arcsinh \left(b x +a \right) \polylog \left(2, -\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}\right)}{b}+\frac{3 \polylog \left(3, -\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}\right)}{2 b}"," ",0,"-(b^2*x^2-(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b+2*a*b*x-(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+a^2+1)/b/(b^2*x^2+2*a*b*x+a^2+1)*arcsinh(b*x+a)^3+2*arcsinh(b*x+a)^3/b-3*arcsinh(b*x+a)^2*ln(1+(b*x+a+(1+(b*x+a)^2)^(1/2))^2)/b-3*arcsinh(b*x+a)*polylog(2,-(b*x+a+(1+(b*x+a)^2)^(1/2))^2)/b+3/2*polylog(3,-(b*x+a+(1+(b*x+a)^2)^(1/2))^2)/b","A"
279,1,168,100,0.248000," ","int(arcsinh(b*x+a)^2/(b^2*x^2+2*a*b*x+a^2+1)^(3/2),x)","-\frac{\left(b^{2} x^{2}-\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b +2 a b x -\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a +a^{2}+1\right) \arcsinh \left(b x +a \right)^{2}}{b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}+\frac{2 \arcsinh \left(b x +a \right)^{2}}{b}-\frac{2 \arcsinh \left(b x +a \right) \ln \left(1+\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}\right)}{b}-\frac{\polylog \left(2, -\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}\right)}{b}"," ",0,"-(b^2*x^2-(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b+2*a*b*x-(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+a^2+1)/b/(b^2*x^2+2*a*b*x+a^2+1)*arcsinh(b*x+a)^2+2*arcsinh(b*x+a)^2/b-2*arcsinh(b*x+a)*ln(1+(b*x+a+(1+(b*x+a)^2)^(1/2))^2)/b-polylog(2,-(b*x+a+(1+(b*x+a)^2)^(1/2))^2)/b","A"
280,1,131,42,0.231000," ","int(arcsinh(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(3/2),x)","\frac{2 \arcsinh \left(b x +a \right)}{b}-\frac{\left(b^{2} x^{2}-\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x b +2 a b x -\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a +a^{2}+1\right) \arcsinh \left(b x +a \right)}{b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}-\frac{\ln \left(1+\left(b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)^{2}\right)}{b}"," ",0,"2*arcsinh(b*x+a)/b-(b^2*x^2-(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b+2*a*b*x-(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+a^2+1)/b/(b^2*x^2+2*a*b*x+a^2+1)*arcsinh(b*x+a)-1/b*ln(1+(b*x+a+(1+(b*x+a)^2)^(1/2))^2)","B"
281,0,0,22,0.294000," ","int(1/(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a),x)","\int \frac{1}{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}} \arcsinh \left(b x +a \right)}\, dx"," ",0,"int(1/(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a),x)","F"
282,0,0,54,0.250000," ","int(1/(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^2,x)","\int \frac{1}{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}} \arcsinh \left(b x +a \right)^{2}}\, dx"," ",0,"int(1/(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^2,x)","F"
283,1,67,42,0.033000," ","int(x^3*arcsinh(a*x^2),x)","\frac{x^{4} \arcsinh \left(a \,x^{2}\right)}{4}-\frac{x^{2} \sqrt{a^{2} x^{4}+1}}{8 a}+\frac{\ln \left(\frac{a^{2} x^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{4}+1}\right)}{8 a \sqrt{a^{2}}}"," ",0,"1/4*x^4*arcsinh(a*x^2)-1/8*x^2*(a^2*x^4+1)^(1/2)/a+1/8/a*ln(a^2*x^2/(a^2)^(1/2)+(a^2*x^4+1)^(1/2))/(a^2)^(1/2)","A"
284,1,89,112,0.009000," ","int(x^2*arcsinh(a*x^2),x)","\frac{x^{3} \arcsinh \left(a \,x^{2}\right)}{3}-\frac{2 a \left(\frac{x \sqrt{a^{2} x^{4}+1}}{3 a^{2}}-\frac{\sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \EllipticF \left(x \sqrt{i a}, i\right)}{3 a^{2} \sqrt{i a}\, \sqrt{a^{2} x^{4}+1}}\right)}{3}"," ",0,"1/3*x^3*arcsinh(a*x^2)-2/3*a*(1/3/a^2*x*(a^2*x^4+1)^(1/2)-1/3/a^2/(I*a)^(1/2)*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)/(a^2*x^4+1)^(1/2)*EllipticF(x*(I*a)^(1/2),I))","C"
285,1,31,28,0.002000," ","int(x*arcsinh(a*x^2),x)","\frac{x^{2} a \arcsinh \left(a \,x^{2}\right)-\sqrt{a^{2} x^{4}+1}}{2 a}"," ",0,"1/2/a*(x^2*a*arcsinh(a*x^2)-(a^2*x^4+1)^(1/2))","A"
286,1,77,198,0.007000," ","int(arcsinh(a*x^2),x)","x \arcsinh \left(a \,x^{2}\right)-\frac{2 i \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \left(\EllipticF \left(x \sqrt{i a}, i\right)-\EllipticE \left(x \sqrt{i a}, i\right)\right)}{\sqrt{i a}\, \sqrt{a^{2} x^{4}+1}}"," ",0,"x*arcsinh(a*x^2)-2*I/(I*a)^(1/2)*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)/(a^2*x^4+1)^(1/2)*(EllipticF(x*(I*a)^(1/2),I)-EllipticE(x*(I*a)^(1/2),I))","C"
287,0,0,66,0.069000," ","int(arcsinh(a*x^2)/x,x)","\int \frac{\arcsinh \left(a \,x^{2}\right)}{x}\, dx"," ",0,"int(arcsinh(a*x^2)/x,x)","F"
288,1,66,94,0.008000," ","int(arcsinh(a*x^2)/x^2,x)","-\frac{\arcsinh \left(a \,x^{2}\right)}{x}+\frac{2 a \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \EllipticF \left(x \sqrt{i a}, i\right)}{\sqrt{i a}\, \sqrt{a^{2} x^{4}+1}}"," ",0,"-arcsinh(a*x^2)/x+2*a/(I*a)^(1/2)*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)/(a^2*x^4+1)^(1/2)*EllipticF(x*(I*a)^(1/2),I)","C"
289,1,28,27,0.011000," ","int(arcsinh(a*x^2)/x^3,x)","-\frac{\arcsinh \left(a \,x^{2}\right)}{2 x^{2}}-\frac{a \arctanh \left(\frac{1}{\sqrt{a^{2} x^{4}+1}}\right)}{2}"," ",0,"-1/2*arcsinh(a*x^2)/x^2-1/2*a*arctanh(1/(a^2*x^4+1)^(1/2))","A"
290,1,101,221,0.010000," ","int(arcsinh(a*x^2)/x^4,x)","-\frac{\arcsinh \left(a \,x^{2}\right)}{3 x^{3}}+\frac{2 a \left(-\frac{\sqrt{a^{2} x^{4}+1}}{x}+\frac{i a \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \left(\EllipticF \left(x \sqrt{i a}, i\right)-\EllipticE \left(x \sqrt{i a}, i\right)\right)}{\sqrt{i a}\, \sqrt{a^{2} x^{4}+1}}\right)}{3}"," ",0,"-1/3*arcsinh(a*x^2)/x^3+2/3*a*(-(a^2*x^4+1)^(1/2)/x+I*a/(I*a)^(1/2)*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)/(a^2*x^4+1)^(1/2)*(EllipticF(x*(I*a)^(1/2),I)-EllipticE(x*(I*a)^(1/2),I)))","C"
291,0,0,66,0.054000," ","int(arcsinh(a*x^5)/x,x)","\int \frac{\arcsinh \left(a \,x^{5}\right)}{x}\, dx"," ",0,"int(arcsinh(a*x^5)/x,x)","F"
292,1,47,46,0.013000," ","int(x^2*arcsinh(x^(1/2)),x)","\frac{5 \arcsinh \left(\sqrt{x}\right)}{48}+\frac{x^{3} \arcsinh \left(\sqrt{x}\right)}{3}+\frac{5 x^{\frac{3}{2}} \sqrt{1+x}}{72}-\frac{x^{\frac{5}{2}} \sqrt{1+x}}{18}-\frac{5 \sqrt{x}\, \sqrt{1+x}}{48}"," ",0,"5/48*arcsinh(x^(1/2))+1/3*x^3*arcsinh(x^(1/2))+5/72*x^(3/2)*(1+x)^(1/2)-1/18*x^(5/2)*(1+x)^(1/2)-5/48*x^(1/2)*(1+x)^(1/2)","A"
293,1,37,36,0.003000," ","int(x*arcsinh(x^(1/2)),x)","-\frac{3 \arcsinh \left(\sqrt{x}\right)}{16}+\frac{x^{2} \arcsinh \left(\sqrt{x}\right)}{2}-\frac{x^{\frac{3}{2}} \sqrt{1+x}}{8}+\frac{3 \sqrt{x}\, \sqrt{1+x}}{16}"," ",0,"-3/16*arcsinh(x^(1/2))+1/2*x^2*arcsinh(x^(1/2))-1/8*x^(3/2)*(1+x)^(1/2)+3/16*x^(1/2)*(1+x)^(1/2)","A"
294,1,24,23,0.003000," ","int(arcsinh(x^(1/2)),x)","\frac{\arcsinh \left(\sqrt{x}\right)}{2}+x \arcsinh \left(\sqrt{x}\right)-\frac{\sqrt{x}\, \sqrt{1+x}}{2}"," ",0,"1/2*arcsinh(x^(1/2))+x*arcsinh(x^(1/2))-1/2*x^(1/2)*(1+x)^(1/2)","A"
295,1,78,44,0.068000," ","int(arcsinh(x^(1/2))/x,x)","-\arcsinh \left(\sqrt{x}\right)^{2}+2 \arcsinh \left(\sqrt{x}\right) \ln \left(1+\sqrt{x}+\sqrt{1+x}\right)+2 \polylog \left(2, -\sqrt{x}-\sqrt{1+x}\right)+2 \arcsinh \left(\sqrt{x}\right) \ln \left(1-\sqrt{x}-\sqrt{1+x}\right)+2 \polylog \left(2, \sqrt{x}+\sqrt{1+x}\right)"," ",0,"-arcsinh(x^(1/2))^2+2*arcsinh(x^(1/2))*ln(1+x^(1/2)+(1+x)^(1/2))+2*polylog(2,-x^(1/2)-(1+x)^(1/2))+2*arcsinh(x^(1/2))*ln(1-x^(1/2)-(1+x)^(1/2))+2*polylog(2,x^(1/2)+(1+x)^(1/2))","A"
296,1,21,20,0.003000," ","int(arcsinh(x^(1/2))/x^2,x)","-\frac{\arcsinh \left(\sqrt{x}\right)}{x}-\frac{\sqrt{1+x}}{\sqrt{x}}"," ",0,"-arcsinh(x^(1/2))/x-(1+x)^(1/2)/x^(1/2)","A"
297,1,31,30,0.003000," ","int(arcsinh(x^(1/2))/x^3,x)","-\frac{\arcsinh \left(\sqrt{x}\right)}{2 x^{2}}-\frac{\sqrt{1+x}}{6 x^{\frac{3}{2}}}+\frac{\sqrt{1+x}}{3 \sqrt{x}}"," ",0,"-1/2*arcsinh(x^(1/2))/x^2-1/6*(1+x)^(1/2)/x^(3/2)+1/3*(1+x)^(1/2)/x^(1/2)","A"
298,1,41,40,0.004000," ","int(arcsinh(x^(1/2))/x^4,x)","-\frac{\arcsinh \left(\sqrt{x}\right)}{3 x^{3}}-\frac{\sqrt{1+x}}{15 x^{\frac{5}{2}}}+\frac{4 \sqrt{1+x}}{45 x^{\frac{3}{2}}}-\frac{8 \sqrt{1+x}}{45 \sqrt{x}}"," ",0,"-1/3*arcsinh(x^(1/2))/x^3-1/15*(1+x)^(1/2)/x^(5/2)+4/45*(1+x)^(1/2)/x^(3/2)-8/45*(1+x)^(1/2)/x^(1/2)","A"
299,1,51,50,0.007000," ","int(arcsinh(x^(1/2))/x^5,x)","-\frac{\arcsinh \left(\sqrt{x}\right)}{4 x^{4}}-\frac{\sqrt{1+x}}{28 x^{\frac{7}{2}}}+\frac{3 \sqrt{1+x}}{70 x^{\frac{5}{2}}}-\frac{2 \sqrt{1+x}}{35 x^{\frac{3}{2}}}+\frac{4 \sqrt{1+x}}{35 \sqrt{x}}"," ",0,"-1/4*arcsinh(x^(1/2))/x^4-1/28*(1+x)^(1/2)/x^(7/2)+3/70*(1+x)^(1/2)/x^(5/2)-2/35*(1+x)^(1/2)/x^(3/2)+4/35*(1+x)^(1/2)/x^(1/2)","A"
300,1,54,46,0.027000," ","int(x^2*arcsinh(a/x),x)","-a^{3} \left(-\frac{x^{3} \arcsinh \left(\frac{a}{x}\right)}{3 a^{3}}-\frac{x^{2} \sqrt{1+\frac{a^{2}}{x^{2}}}}{6 a^{2}}+\frac{\arctanh \left(\frac{1}{\sqrt{1+\frac{a^{2}}{x^{2}}}}\right)}{6}\right)"," ",0,"-a^3*(-1/3/a^3*x^3*arcsinh(a/x)-1/6/a^2*x^2*(1+a^2/x^2)^(1/2)+1/6*arctanh(1/(1+a^2/x^2)^(1/2)))","A"
301,1,38,27,0.005000," ","int(x*arcsinh(a/x),x)","-a^{2} \left(-\frac{x^{2} \arcsinh \left(\frac{a}{x}\right)}{2 a^{2}}-\frac{x \sqrt{1+\frac{a^{2}}{x^{2}}}}{2 a}\right)"," ",0,"-a^2*(-1/2/a^2*x^2*arcsinh(a/x)-1/2/a*x*(1+a^2/x^2)^(1/2))","A"
302,1,31,23,0.006000," ","int(arcsinh(a/x),x)","-a \left(-\frac{\arcsinh \left(\frac{a}{x}\right) x}{a}-\arctanh \left(\frac{1}{\sqrt{1+\frac{a^{2}}{x^{2}}}}\right)\right)"," ",0,"-a*(-arcsinh(a/x)/a*x-arctanh(1/(1+a^2/x^2)^(1/2)))","A"
303,1,114,66,0.007000," ","int(arcsinh(a/x)/x,x)","\frac{\arcsinh \left(\frac{a}{x}\right)^{2}}{2}-\arcsinh \left(\frac{a}{x}\right) \ln \left(1+\frac{a}{x}+\sqrt{1+\frac{a^{2}}{x^{2}}}\right)-\polylog \left(2, -\frac{a}{x}-\sqrt{1+\frac{a^{2}}{x^{2}}}\right)-\arcsinh \left(\frac{a}{x}\right) \ln \left(1-\frac{a}{x}-\sqrt{1+\frac{a^{2}}{x^{2}}}\right)-\polylog \left(2, \frac{a}{x}+\sqrt{1+\frac{a^{2}}{x^{2}}}\right)"," ",0,"1/2*arcsinh(a/x)^2-arcsinh(a/x)*ln(1+a/x+(1+a^2/x^2)^(1/2))-polylog(2,-a/x-(1+a^2/x^2)^(1/2))-arcsinh(a/x)*ln(1-a/x-(1+a^2/x^2)^(1/2))-polylog(2,a/x+(1+a^2/x^2)^(1/2))","A"
304,1,31,27,0.005000," ","int(arcsinh(a/x)/x^2,x)","-\frac{\frac{a \arcsinh \left(\frac{a}{x}\right)}{x}-\sqrt{1+\frac{a^{2}}{x^{2}}}}{a}"," ",0,"-1/a*(a/x*arcsinh(a/x)-(1+a^2/x^2)^(1/2))","A"
305,1,46,42,0.005000," ","int(arcsinh(a/x)/x^3,x)","-\frac{\frac{a^{2} \arcsinh \left(\frac{a}{x}\right)}{2 x^{2}}-\frac{a \sqrt{1+\frac{a^{2}}{x^{2}}}}{4 x}+\frac{\arcsinh \left(\frac{a}{x}\right)}{4}}{a^{2}}"," ",0,"-1/a^2*(1/2*a^2/x^2*arcsinh(a/x)-1/4*a/x*(1+a^2/x^2)^(1/2)+1/4*arcsinh(a/x))","A"
306,1,53,44,0.007000," ","int(arcsinh(a/x)/x^4,x)","-\frac{\frac{a^{3} \arcsinh \left(\frac{a}{x}\right)}{3 x^{3}}-\frac{a^{2} \sqrt{1+\frac{a^{2}}{x^{2}}}}{9 x^{2}}+\frac{2 \sqrt{1+\frac{a^{2}}{x^{2}}}}{9}}{a^{3}}"," ",0,"-1/a^3*(1/3*a^3/x^3*arcsinh(a/x)-1/9*a^2/x^2*(1+a^2/x^2)^(1/2)+2/9*(1+a^2/x^2)^(1/2))","A"
307,0,0,73,0.040000," ","int(x^m*arcsinh(a*x^n),x)","\int x^{m} \arcsinh \left(a \,x^{n}\right)\, dx"," ",0,"int(x^m*arcsinh(a*x^n),x)","F"
308,0,0,56,0.023000," ","int(x^2*arcsinh(a*x^n),x)","\int x^{2} \arcsinh \left(a \,x^{n}\right)\, dx"," ",0,"int(x^2*arcsinh(a*x^n),x)","F"
309,0,0,53,0.012000," ","int(x*arcsinh(a*x^n),x)","\int x \arcsinh \left(a \,x^{n}\right)\, dx"," ",0,"int(x*arcsinh(a*x^n),x)","F"
310,0,0,52,0.012000," ","int(arcsinh(a*x^n),x)","\int \arcsinh \left(a \,x^{n}\right)\, dx"," ",0,"int(arcsinh(a*x^n),x)","F"
311,1,133,78,0.004000," ","int(arcsinh(a*x^n)/x,x)","-\frac{\arcsinh \left(a \,x^{n}\right)^{2}}{2 n}+\frac{\arcsinh \left(a \,x^{n}\right) \ln \left(1+a \,x^{n}+\sqrt{1+a^{2} x^{2 n}}\right)}{n}+\frac{\polylog \left(2, -a \,x^{n}-\sqrt{1+a^{2} x^{2 n}}\right)}{n}+\frac{\arcsinh \left(a \,x^{n}\right) \ln \left(1-a \,x^{n}-\sqrt{1+a^{2} x^{2 n}}\right)}{n}+\frac{\polylog \left(2, a \,x^{n}+\sqrt{1+a^{2} x^{2 n}}\right)}{n}"," ",0,"-1/2*arcsinh(a*x^n)^2/n+1/n*arcsinh(a*x^n)*ln(1+a*x^n+(1+a^2*(x^n)^2)^(1/2))+1/n*polylog(2,-a*x^n-(1+a^2*(x^n)^2)^(1/2))+1/n*arcsinh(a*x^n)*ln(1-a*x^n-(1+a^2*(x^n)^2)^(1/2))+1/n*polylog(2,a*x^n+(1+a^2*(x^n)^2)^(1/2))","A"
312,0,0,57,0.013000," ","int(arcsinh(a*x^n)/x^2,x)","\int \frac{\arcsinh \left(a \,x^{n}\right)}{x^{2}}\, dx"," ",0,"int(arcsinh(a*x^n)/x^2,x)","F"
313,0,0,56,0.015000," ","int(arcsinh(a*x^n)/x^3,x)","\int \frac{\arcsinh \left(a \,x^{n}\right)}{x^{3}}\, dx"," ",0,"int(arcsinh(a*x^n)/x^3,x)","F"
314,0,0,139,0.234000," ","int((a+b*arcsinh(I+d*x^2))^4,x)","\int \left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{4}\, dx"," ",0,"int((a+b*arcsinh(I+d*x^2))^4,x)","F"
315,0,0,117,0.212000," ","int((a+b*arcsinh(I+d*x^2))^3,x)","\int \left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{3}\, dx"," ",0,"int((a+b*arcsinh(I+d*x^2))^3,x)","F"
316,0,0,69,0.203000," ","int((a+b*arcsinh(I+d*x^2))^2,x)","\int \left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{2}\, dx"," ",0,"int((a+b*arcsinh(I+d*x^2))^2,x)","F"
317,1,47,45,0.023000," ","int(a+b*arcsinh(I+d*x^2),x)","a x +b \left(x \arcsinh \left(d \,x^{2}+i\right)-\frac{2 x \left(d \,x^{2}+2 i\right)}{\sqrt{d^{2} x^{4}+2 i d \,x^{2}}}\right)"," ",0,"a*x+b*(x*arcsinh(I+d*x^2)-2/(2*I*d*x^2+d^2*x^4)^(1/2)*x*(d*x^2+2*I))","A"
318,0,0,153,0.155000," ","int(1/(a+b*arcsinh(I+d*x^2)),x)","\int \frac{1}{a +b \arcsinh \left(d \,x^{2}+i\right)}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2)),x)","F"
319,0,0,197,0.108000," ","int(1/(a+b*arcsinh(I+d*x^2))^2,x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2))^2,x)","F"
320,0,0,223,0.107000," ","int(1/(a+b*arcsinh(I+d*x^2))^3,x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2))^3,x)","F"
321,0,0,139,0.191000," ","int((a+b*arcsinh(-I+d*x^2))^4,x)","\int \left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{4}\, dx"," ",0,"int((a+b*arcsinh(-I+d*x^2))^4,x)","F"
322,0,0,117,0.186000," ","int((a+b*arcsinh(-I+d*x^2))^3,x)","\int \left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{3}\, dx"," ",0,"int((a+b*arcsinh(-I+d*x^2))^3,x)","F"
323,0,0,69,0.177000," ","int((a+b*arcsinh(-I+d*x^2))^2,x)","\int \left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{2}\, dx"," ",0,"int((a+b*arcsinh(-I+d*x^2))^2,x)","F"
324,1,48,45,0.017000," ","int(a+b*arcsinh(-I+d*x^2),x)","a x +b \left(x \arcsinh \left(d \,x^{2}-i\right)+\frac{2 x \left(-d \,x^{2}+2 i\right)}{\sqrt{d^{2} x^{4}-2 i d \,x^{2}}}\right)"," ",0,"a*x+b*(x*arcsinh(-I+d*x^2)+2/(-2*I*d*x^2+d^2*x^4)^(1/2)*x*(-d*x^2+2*I))","A"
325,0,0,156,0.105000," ","int(1/(a+b*arcsinh(-I+d*x^2)),x)","\int \frac{1}{a +b \arcsinh \left(d \,x^{2}-i\right)}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2)),x)","F"
326,0,0,202,0.102000," ","int(1/(a+b*arcsinh(-I+d*x^2))^2,x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2))^2,x)","F"
327,0,0,226,0.104000," ","int(1/(a+b*arcsinh(-I+d*x^2))^3,x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2))^3,x)","F"
328,0,0,279,0.108000," ","int((a+b*arcsinh(I+d*x^2))^(5/2),x)","\int \left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arcsinh(I+d*x^2))^(5/2),x)","F"
329,0,0,247,0.103000," ","int((a+b*arcsinh(I+d*x^2))^(3/2),x)","\int \left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsinh(I+d*x^2))^(3/2),x)","F"
330,0,0,205,0.115000," ","int((a+b*arcsinh(I+d*x^2))^(1/2),x)","\int \sqrt{a +b \arcsinh \left(d \,x^{2}+i\right)}\, dx"," ",0,"int((a+b*arcsinh(I+d*x^2))^(1/2),x)","F"
331,0,0,177,0.112000," ","int(1/(a+b*arcsinh(I+d*x^2))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsinh \left(d \,x^{2}+i\right)}}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2))^(1/2),x)","F"
332,0,0,230,0.125000," ","int(1/(a+b*arcsinh(I+d*x^2))^(3/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2))^(3/2),x)","F"
333,0,0,253,0.108000," ","int(1/(a+b*arcsinh(I+d*x^2))^(5/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2))^(5/2),x)","F"
334,0,0,307,0.133000," ","int(1/(a+b*arcsinh(I+d*x^2))^(7/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}+i\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(I+d*x^2))^(7/2),x)","F"
335,0,0,283,0.109000," ","int((a+b*arcsinh(-I+d*x^2))^(5/2),x)","\int \left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arcsinh(-I+d*x^2))^(5/2),x)","F"
336,0,0,249,0.106000," ","int((a+b*arcsinh(-I+d*x^2))^(3/2),x)","\int \left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsinh(-I+d*x^2))^(3/2),x)","F"
337,0,0,208,0.105000," ","int((a+b*arcsinh(-I+d*x^2))^(1/2),x)","\int \sqrt{a +b \arcsinh \left(d \,x^{2}-i\right)}\, dx"," ",0,"int((a+b*arcsinh(-I+d*x^2))^(1/2),x)","F"
338,0,0,181,0.107000," ","int(1/(a+b*arcsinh(-I+d*x^2))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsinh \left(d \,x^{2}-i\right)}}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2))^(1/2),x)","F"
339,0,0,234,0.104000," ","int(1/(a+b*arcsinh(-I+d*x^2))^(3/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2))^(3/2),x)","F"
340,0,0,257,0.103000," ","int(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x)","F"
341,0,0,311,0.111000," ","int(1/(a+b*arcsinh(-I+d*x^2))^(7/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(d \,x^{2}-i\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(-I+d*x^2))^(7/2),x)","F"
342,0,0,38,0.470000," ","int((a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","\int \frac{\left(a +b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{n}}{-c^{2} x^{2}+1}\, dx"," ",0,"int((a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","F"
343,1,1175,285,0.706000," ","int((a+b*arcsinh((-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} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{4}}{4 c}-\frac{b^{3} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 b^{3} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{6 b^{3} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 b^{3} \polylog \left(4, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b^{3} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1-\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 b^{3} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{6 b^{3} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 b^{3} \polylog \left(4, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{a \,b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3}}{c}-\frac{3 a \,b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 a \,b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{6 a \,b^{2} \polylog \left(3, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a \,b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 a \,b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{6 a \,b^{2} \polylog \left(3, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{3 a^{2} b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{2 c}-\frac{3 a^{2} b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a^{2} b \polylog \left(2, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a^{2} b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a^{2} b \polylog \left(2, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{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*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^4-b^3/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1+(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-3*b^3/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))+6*b^3/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-6*b^3/c*polylog(4,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-b^3/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-3*b^3/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))+6*b^3/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-6*b^3/c*polylog(4,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))+a*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3-3*a*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-6*a*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))+6*a*b^2/c*polylog(3,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-3*a*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-6*a*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))+6*a*b^2/c*polylog(3,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))+3/2*a^2*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-3*a^2*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-3*a^2*b/c*polylog(2,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-3*a^2*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-3*a^2*b/c*polylog(2,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))","B"
344,1,649,214,0.009000," ","int((a+b*arcsinh((-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} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3}}{3 c}-\frac{b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{2 b^{2} \polylog \left(3, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 b^{2} \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{2 b^{2} \polylog \left(3, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}+\frac{a b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{c}-\frac{2 a b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 a b \polylog \left(2, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 a b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 a b \polylog \left(2, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\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*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3-b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-2*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))+2*b^2/c*polylog(3,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-2*b^2/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))+2*b^2/c*polylog(3,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))+a*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-2*a*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-2*a*b/c*polylog(2,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-2*a*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-2*a*b/c*polylog(2,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))","B"
345,1,263,145,0.008000," ","int((a+b*arcsinh((-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 \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{2 c}-\frac{b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b \polylog \left(2, -\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b \polylog \left(2, \frac{\sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1+\frac{-c x +1}{c x +1}}\right)}{c}"," ",0,"1/2*a/c*ln(c*x+1)-1/2*a/c*ln(c*x-1)+1/2*b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))-b/c*polylog(2,-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-b/c*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1+(-c*x+1)/(c*x+1))^(1/2))-b/c*polylog(2,(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1+(-c*x+1)/(c*x+1))^(1/2))","A"
346,0,0,38,0.283000," ","int(1/(-c^2*x^2+1)/(a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","F"
347,0,0,38,0.267000," ","int(1/(-c^2*x^2+1)/(a+b*arcsinh((-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 \arcsinh \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","F"
348,1,166,96,0.006000," ","int(arcsinh(c*exp(b*x+a)),x)","-\frac{\arcsinh \left(c \,{\mathrm e}^{b x +a}\right)^{2}}{2 b}+\frac{\arcsinh \left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1+c \,{\mathrm e}^{b x +a}+\sqrt{1+c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}+\frac{\polylog \left(2, -c \,{\mathrm e}^{b x +a}-\sqrt{1+c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}+\frac{\arcsinh \left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1-c \,{\mathrm e}^{b x +a}-\sqrt{1+c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}+\frac{\polylog \left(2, c \,{\mathrm e}^{b x +a}+\sqrt{1+c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}"," ",0,"-1/2*arcsinh(c*exp(b*x+a))^2/b+1/b*arcsinh(c*exp(b*x+a))*ln(1+c*exp(b*x+a)+(1+c^2*exp(b*x+a)^2)^(1/2))+1/b*polylog(2,-c*exp(b*x+a)-(1+c^2*exp(b*x+a)^2)^(1/2))+1/b*arcsinh(c*exp(b*x+a))*ln(1-c*exp(b*x+a)-(1+c^2*exp(b*x+a)^2)^(1/2))+1/b*polylog(2,c*exp(b*x+a)+(1+c^2*exp(b*x+a)^2)^(1/2))","A"
349,1,322,205,0.012000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))*x^3,x)","\frac{x^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{5 b^{2}}-\frac{7 a x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{20 b^{3}}+\frac{9 a^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{20 b^{4}}-\frac{a^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 b^{3}}-\frac{a^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{4}}-\frac{a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}+\frac{3 a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{8 b^{3}}+\frac{3 a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{4}}+\frac{3 a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{3} \sqrt{b^{2}}}-\frac{2 \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{15 b^{4}}+\frac{b \,x^{5}}{5}+\frac{x^{4} a}{4}"," ",0,"1/5*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/b^2-7/20*a/b^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+9/20*a^2/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/2*a^3/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/2*a^4/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*a^3/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+3/8*a/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3/8*a^2/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/8*a/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-2/15/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/5*b*x^5+1/4*x^4*a","A"
350,1,264,143,0.005000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))*x^2,x)","\frac{x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 b^{2}}-\frac{5 a \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{12 b^{3}}+\frac{a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 b^{2}}+\frac{a^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{3}}+\frac{a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{2} \sqrt{b^{2}}}-\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{8 b^{2}}-\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{8 b^{3}}-\frac{\ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{2} \sqrt{b^{2}}}+\frac{b \,x^{4}}{4}+\frac{x^{3} a}{3}"," ",0,"1/4*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/b^2-5/12*a/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/2*a^2/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/2*a^3/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*a^2/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/8/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/8/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-1/8/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/4*b*x^4+1/3*x^3*a","A"
351,1,138,83,0.004000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))*x,x)","\frac{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{3 b^{2}}-\frac{a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b}-\frac{a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{2}}-\frac{a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b \sqrt{b^{2}}}+\frac{b \,x^{3}}{3}+\frac{a \,x^{2}}{2}"," ",0,"1/3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/b^2-1/2*a/b*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*a^2/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*a/b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/3*b*x^3+1/2*a*x^2","A"
352,1,89,35,0.003000," ","int(b*x+a+(1+(b*x+a)^2)^(1/2),x)","a x +\frac{\left(2 b^{2} x +2 a b \right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 b^{2}}+\frac{\ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \sqrt{b^{2}}}+\frac{b \,x^{2}}{2}"," ",0,"a*x+1/4*(2*b^2*x+2*a*b)/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*b*x^2","B"
353,1,126,81,0.005000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))/x,x)","\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}+\frac{a b \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\sqrt{b^{2}}}-\sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)+b x +a \ln \left(x \right)"," ",0,"(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+a*b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+b*x+a*ln(x)","A"
354,1,267,91,0.010000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))/x^2,x)","-\frac{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{\left(a^{2}+1\right) x}+\frac{2 a b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{a^{2}+1}+\frac{a^{2} b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{a b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\sqrt{a^{2}+1}}+\frac{b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{a^{2}+1}+\frac{b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(a^{2}+1\right) \sqrt{b^{2}}}+b \ln \left(x \right)-\frac{a}{x}"," ",0,"-1/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+2*a*b/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+a^2*b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-a*b/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+b*ln(x)-a/x","B"
355,1,457,102,0.008000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))/x^3,x)","-\frac{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(a^{2}+1\right) x^{2}}+\frac{a b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(a^{2}+1\right)^{2} x}-\frac{a^{2} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(a^{2}+1\right)^{2}}-\frac{a^{3} b^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{a^{2} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{a \,b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(a^{2}+1\right)^{2}}-\frac{a \,b^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 a^{2}+2}+\frac{b^{3} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \sqrt{a^{2}+1}}-\frac{b}{x}-\frac{a}{2 x^{2}}"," ",0,"-1/2/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/2*a*b/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-a^2*b^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*a^3*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*a^2*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/2*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/2*a*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*b^3/(a^2+1)*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*b^2/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-b/x-1/2*a/x^2","B"
356,1,501,136,0.010000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))/x^4,x)","-\frac{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{3 \left(a^{2}+1\right) x^{3}}+\frac{a b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(a^{2}+1\right)^{2} x^{2}}-\frac{a^{2} b^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(a^{2}+1\right)^{3} x}+\frac{a^{3} b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(a^{2}+1\right)^{3}}+\frac{a^{4} b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2}}}-\frac{a^{3} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{a^{2} b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(a^{2}+1\right)^{3}}+\frac{a^{2} b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2}}}-\frac{a \,b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right)^{2}}-\frac{a^{2} b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{a \,b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{a}{3 x^{3}}-\frac{b}{2 x^{2}}"," ",0,"-1/3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/(a^2+1)/x^3+1/2*a*b/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/2*a^2*b^2/(a^2+1)^3/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+a^3*b^3/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*a^4*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*a^3*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/2*a^2*b^4/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/2*a^2*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*a^2*b^4/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*a*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/3*a/x^3-1/2*b/x^2","B"
357,1,841,183,0.010000," ","int((b*x+a+(1+(b*x+a)^2)^(1/2))/x^5,x)","-\frac{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 \left(a^{2}+1\right) x^{4}}+\frac{5 a b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{12 \left(a^{2}+1\right)^{2} x^{3}}-\frac{5 a^{2} b^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{8 \left(a^{2}+1\right)^{3} x^{2}}+\frac{5 a^{3} b^{3} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{8 \left(a^{2}+1\right)^{4} x}-\frac{5 a^{4} b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 \left(a^{2}+1\right)^{4}}-\frac{5 a^{5} b^{5} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{4} \sqrt{b^{2}}}+\frac{5 a^{4} b^{4} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{8 \left(a^{2}+1\right)^{\frac{7}{2}}}-\frac{5 a^{3} b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{8 \left(a^{2}+1\right)^{4}}-\frac{5 a^{3} b^{5} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{4} \sqrt{b^{2}}}+\frac{7 a^{2} b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 \left(a^{2}+1\right)^{3}}+\frac{3 a^{3} b^{5} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{4 \left(a^{2}+1\right)^{3} \sqrt{b^{2}}}-\frac{3 a^{2} b^{4} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{4 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{8 \left(a^{2}+1\right)^{2} x^{2}}-\frac{b^{3} a \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{8 \left(a^{2}+1\right)^{3} x}+\frac{b^{5} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{8 \left(a^{2}+1\right)^{3}}+\frac{b^{5} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{3} \sqrt{b^{2}}}-\frac{b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 \left(a^{2}+1\right)^{2}}-\frac{b^{5} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{b^{4} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{8 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{b}{3 x^{3}}-\frac{a}{4 x^{4}}"," ",0,"-1/4*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/(a^2+1)/x^4+5/12*a*b*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/(a^2+1)^2/x^3-5/8*a^2*b^2/(a^2+1)^3/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+5/8*a^3*b^3/(a^2+1)^4/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-5/4*a^4*b^4/(a^2+1)^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/8*a^5*b^5/(a^2+1)^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+5/8*a^4*b^4/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-5/8*a^3*b^5/(a^2+1)^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-5/8*a^3*b^5/(a^2+1)^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+7/8*a^2*b^4/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/4*a^3*b^5/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/4*a^2*b^4/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/8*b^2/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/8*b^3/(a^2+1)^3*a/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/8*b^5/(a^2+1)^3*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/8*b^5/(a^2+1)^3*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/8*b^4/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/8*b^5/(a^2+1)^2*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/8*b^4/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/3*b/x^3-1/4*a/x^4","B"
358,0,0,265,0.011000," ","int(exp(arcsinh(b*x+a)^2)*x^3,x)","\int {\mathrm e}^{\arcsinh \left(b x +a \right)^{2}} x^{3}\, dx"," ",0,"int(exp(arcsinh(b*x+a)^2)*x^3,x)","F"
359,0,0,175,0.010000," ","int(exp(arcsinh(b*x+a)^2)*x^2,x)","\int {\mathrm e}^{\arcsinh \left(b x +a \right)^{2}} x^{2}\, dx"," ",0,"int(exp(arcsinh(b*x+a)^2)*x^2,x)","F"
360,0,0,85,0.009000," ","int(exp(arcsinh(b*x+a)^2)*x,x)","\int {\mathrm e}^{\arcsinh \left(b x +a \right)^{2}} x\, dx"," ",0,"int(exp(arcsinh(b*x+a)^2)*x,x)","F"
361,0,0,43,0.004000," ","int(exp(arcsinh(b*x+a)^2),x)","\int {\mathrm e}^{\arcsinh \left(b x +a \right)^{2}}\, dx"," ",0,"int(exp(arcsinh(b*x+a)^2),x)","F"
362,0,0,15,0.009000," ","int(exp(arcsinh(b*x+a)^2)/x,x)","\int \frac{{\mathrm e}^{\arcsinh \left(b x +a \right)^{2}}}{x}\, dx"," ",0,"int(exp(arcsinh(b*x+a)^2)/x,x)","F"
363,0,0,15,0.009000," ","int(exp(arcsinh(b*x+a)^2)/x^2,x)","\int \frac{{\mathrm e}^{\arcsinh \left(b x +a \right)^{2}}}{x^{2}}\, dx"," ",0,"int(exp(arcsinh(b*x+a)^2)/x^2,x)","F"
364,1,125,72,0.057000," ","int(arcsinh(b*x+a)/(a*d/b+d*x),x)","-\frac{\arcsinh \left(b x +a \right)^{2}}{2 d}+\frac{\arcsinh \left(b x +a \right) \ln \left(1+b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)}{d}+\frac{\polylog \left(2, -b x -a -\sqrt{1+\left(b x +a \right)^{2}}\right)}{d}+\frac{\arcsinh \left(b x +a \right) \ln \left(1-b x -a -\sqrt{1+\left(b x +a \right)^{2}}\right)}{d}+\frac{\polylog \left(2, b x +a +\sqrt{1+\left(b x +a \right)^{2}}\right)}{d}"," ",0,"-1/2*arcsinh(b*x+a)^2/d+1/d*arcsinh(b*x+a)*ln(1+b*x+a+(1+(b*x+a)^2)^(1/2))+1/d*polylog(2,-b*x-a-(1+(b*x+a)^2)^(1/2))+1/d*arcsinh(b*x+a)*ln(1-b*x-a-(1+(b*x+a)^2)^(1/2))+1/d*polylog(2,b*x+a+(1+(b*x+a)^2)^(1/2))","A"
365,1,4,3,0.126000," ","int(x/arcsinh(x)/(x^2+1)^(1/2),x)","\Shi \left(\arcsinh \left(x \right)\right)"," ",0,"Shi(arcsinh(x))","A"
366,1,38,39,0.003000," ","int(x^3*arcsinh(b*x^4+a),x)","\frac{\left(b \,x^{4}+a \right) \arcsinh \left(b \,x^{4}+a \right)-\sqrt{1+\left(b \,x^{4}+a \right)^{2}}}{4 b}"," ",0,"1/4/b*((b*x^4+a)*arcsinh(b*x^4+a)-(1+(b*x^4+a)^2)^(1/2))","A"
367,0,0,44,0.031000," ","int(x^(-1+n)*arcsinh(a+b*x^n),x)","\int x^{-1+n} \arcsinh \left(a +b \,x^{n}\right)\, dx"," ",0,"int(x^(-1+n)*arcsinh(a+b*x^n),x)","F"
368,1,46,47,0.044000," ","int(arcsinh(c/(b*x+a)),x)","-\frac{c \left(-\frac{\arcsinh \left(\frac{c}{b x +a}\right) \left(b x +a \right)}{c}-\arctanh \left(\frac{1}{\sqrt{\frac{c^{2}}{\left(b x +a \right)^{2}}+1}}\right)\right)}{b}"," ",0,"-1/b*c*(-arcsinh(c/(b*x+a))/c*(b*x+a)-arctanh(1/(c^2/(b*x+a)^2+1)^(1/2)))","A"
369,0,0,25,0.095000," ","int(x/arcsinh(sinh(x)),x)","\int \frac{x}{\arcsinh \left(\sinh \left(x \right)\right)}\, dx"," ",0,"int(x/arcsinh(sinh(x)),x)","F"
370,0,0,33,0.252000," ","int(arcsinh((b*x^2-1)^(1/2))^n/(b*x^2-1)^(1/2),x)","\int \frac{\arcsinh \left(\sqrt{b \,x^{2}-1}\right)^{n}}{\sqrt{b \,x^{2}-1}}\, dx"," ",0,"int(arcsinh((b*x^2-1)^(1/2))^n/(b*x^2-1)^(1/2),x)","F"
371,0,0,25,0.214000," ","int(1/arcsinh((b*x^2-1)^(1/2))/(b*x^2-1)^(1/2),x)","\int \frac{1}{\arcsinh \left(\sqrt{b \,x^{2}-1}\right) \sqrt{b \,x^{2}-1}}\, dx"," ",0,"int(1/arcsinh((b*x^2-1)^(1/2))/(b*x^2-1)^(1/2),x)","F"