1,1,124,104,0.037000," ","int(x^4*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","\frac{d a \left(\frac{1}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d b \left(\frac{\arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{49}-\frac{19 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1225}+\frac{76 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3675}-\frac{152 \sqrt{c^{2} x^{2}+1}}{3675}\right)}{c^{5}}"," ",0,"1/c^5*(d*a*(1/7*c^7*x^7+1/5*c^5*x^5)+d*b*(1/7*arcsinh(c*x)*c^7*x^7+1/5*arcsinh(c*x)*c^5*x^5-1/49*c^6*x^6*(c^2*x^2+1)^(1/2)-19/1225*c^4*x^4*(c^2*x^2+1)^(1/2)+76/3675*c^2*x^2*(c^2*x^2+1)^(1/2)-152/3675*(c^2*x^2+1)^(1/2)))","A"
2,1,113,102,0.012000," ","int(x^3*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","\frac{d a \left(\frac{1}{6} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d b \left(\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{6}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}-\frac{c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{36}-\frac{c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{36}+\frac{c x \sqrt{c^{2} x^{2}+1}}{24}-\frac{\arcsinh \left(c x \right)}{24}\right)}{c^{4}}"," ",0,"1/c^4*(d*a*(1/6*c^6*x^6+1/4*c^4*x^4)+d*b*(1/6*arcsinh(c*x)*c^6*x^6+1/4*arcsinh(c*x)*c^4*x^4-1/36*c^5*x^5*(c^2*x^2+1)^(1/2)-1/36*c^3*x^3*(c^2*x^2+1)^(1/2)+1/24*c*x*(c^2*x^2+1)^(1/2)-1/24*arcsinh(c*x)))","A"
3,1,105,86,0.010000," ","int(x^2*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","\frac{d a \left(\frac{1}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d b \left(\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}-\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{25}-\frac{13 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{225}+\frac{26 \sqrt{c^{2} x^{2}+1}}{225}\right)}{c^{3}}"," ",0,"1/c^3*(d*a*(1/5*c^5*x^5+1/3*c^3*x^3)+d*b*(1/5*arcsinh(c*x)*c^5*x^5+1/3*arcsinh(c*x)*c^3*x^3-1/25*c^4*x^4*(c^2*x^2+1)^(1/2)-13/225*c^2*x^2*(c^2*x^2+1)^(1/2)+26/225*(c^2*x^2+1)^(1/2)))","A"
4,1,94,75,0.008000," ","int(x*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","\frac{d a \left(\frac{1}{4} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d b \left(\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}+\frac{\arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{16}-\frac{5 c x \sqrt{c^{2} x^{2}+1}}{32}+\frac{5 \arcsinh \left(c x \right)}{32}\right)}{c^{2}}"," ",0,"1/c^2*(d*a*(1/4*c^4*x^4+1/2*c^2*x^2)+d*b*(1/4*arcsinh(c*x)*c^4*x^4+1/2*arcsinh(c*x)*c^2*x^2-1/16*c^3*x^3*(c^2*x^2+1)^(1/2)-5/32*c*x*(c^2*x^2+1)^(1/2)+5/32*arcsinh(c*x)))","A"
5,1,76,65,0.007000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","\frac{d a \left(\frac{1}{3} c^{3} x^{3}+c x \right)+d b \left(\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}+\arcsinh \left(c x \right) c x -\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{9}-\frac{7 \sqrt{c^{2} x^{2}+1}}{9}\right)}{c}"," ",0,"1/c*(d*a*(1/3*c^3*x^3+c*x)+d*b*(1/3*arcsinh(c*x)*c^3*x^3+arcsinh(c*x)*c*x-1/9*c^2*x^2*(c^2*x^2+1)^(1/2)-7/9*(c^2*x^2+1)^(1/2)))","A"
6,1,162,117,0.272000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x,x)","\frac{d a \,c^{2} x^{2}}{2}+d a \ln \left(c x \right)-\frac{d b \arcsinh \left(c x \right)^{2}}{2}+\frac{d b \arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{b c d x \sqrt{c^{2} x^{2}+1}}{4}+\frac{b d \arcsinh \left(c x \right)}{4}+d b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+d b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+d b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+d b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)"," ",0,"1/2*d*a*c^2*x^2+d*a*ln(c*x)-1/2*d*b*arcsinh(c*x)^2+1/2*d*b*arcsinh(c*x)*c^2*x^2-1/4*b*c*d*x*(c^2*x^2+1)^(1/2)+1/4*b*d*arcsinh(c*x)+d*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+d*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+d*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+d*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
7,1,69,62,0.010000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x^2,x)","c \left(d a \left(c x -\frac{1}{c x}\right)+d b \left(\arcsinh \left(c x \right) c x -\frac{\arcsinh \left(c x \right)}{c x}-\sqrt{c^{2} x^{2}+1}-\arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)\right)\right)"," ",0,"c*(d*a*(c*x-1/c/x)+d*b*(arcsinh(c*x)*c*x-arcsinh(c*x)/c/x-(c^2*x^2+1)^(1/2)-arctanh(1/(c^2*x^2+1)^(1/2))))","A"
8,1,175,134,0.241000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x^3,x)","c^{2} d a \ln \left(c x \right)-\frac{d a}{2 x^{2}}-\frac{c^{2} d b \arcsinh \left(c x \right)^{2}}{2}-\frac{b c d \sqrt{c^{2} x^{2}+1}}{2 x}+\frac{c^{2} d b}{2}-\frac{d b \arcsinh \left(c x \right)}{2 x^{2}}+c^{2} d b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+c^{2} d b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+c^{2} d b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+c^{2} d b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)"," ",0,"c^2*d*a*ln(c*x)-1/2*d*a/x^2-1/2*c^2*d*b*arcsinh(c*x)^2-1/2*b*c*d*(c^2*x^2+1)^(1/2)/x+1/2*c^2*d*b-1/2*d*b*arcsinh(c*x)/x^2+c^2*d*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+c^2*d*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+c^2*d*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+c^2*d*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
9,1,87,70,0.014000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x^4,x)","c^{3} \left(d a \left(-\frac{1}{c x}-\frac{1}{3 c^{3} x^{3}}\right)+d b \left(-\frac{\arcsinh \left(c x \right)}{c x}-\frac{\arcsinh \left(c x \right)}{3 c^{3} x^{3}}-\frac{5 \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{6}-\frac{\sqrt{c^{2} x^{2}+1}}{6 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(d*a*(-1/c/x-1/3/c^3/x^3)+d*b*(-arcsinh(c*x)/c/x-1/3*arcsinh(c*x)/c^3/x^3-5/6*arctanh(1/(c^2*x^2+1)^(1/2))-1/6/c^2/x^2*(c^2*x^2+1)^(1/2)))","A"
10,1,167,155,0.014000," ","int(x^4*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{9} c^{9} x^{9}+\frac{2}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{2} b \left(\frac{\arcsinh \left(c x \right) c^{9} x^{9}}{9}+\frac{2 \arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{81}-\frac{106 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{3969}-\frac{263 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{33075}+\frac{1052 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{99225}-\frac{2104 \sqrt{c^{2} x^{2}+1}}{99225}\right)}{c^{5}}"," ",0,"1/c^5*(d^2*a*(1/9*c^9*x^9+2/7*c^7*x^7+1/5*c^5*x^5)+d^2*b*(1/9*arcsinh(c*x)*c^9*x^9+2/7*arcsinh(c*x)*c^7*x^7+1/5*arcsinh(c*x)*c^5*x^5-1/81*c^8*x^8*(c^2*x^2+1)^(1/2)-106/3969*c^6*x^6*(c^2*x^2+1)^(1/2)-263/33075*c^4*x^4*(c^2*x^2+1)^(1/2)+1052/99225*c^2*x^2*(c^2*x^2+1)^(1/2)-2104/99225*(c^2*x^2+1)^(1/2)))","A"
11,1,156,156,0.011000," ","int(x^3*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{8} c^{8} x^{8}+\frac{1}{3} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d^{2} b \left(\frac{\arcsinh \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{3}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}-\frac{c^{7} x^{7} \sqrt{c^{2} x^{2}+1}}{64}-\frac{43 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{1152}-\frac{73 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{4608}+\frac{73 c x \sqrt{c^{2} x^{2}+1}}{3072}-\frac{73 \arcsinh \left(c x \right)}{3072}\right)}{c^{4}}"," ",0,"1/c^4*(d^2*a*(1/8*c^8*x^8+1/3*c^6*x^6+1/4*c^4*x^4)+d^2*b*(1/8*arcsinh(c*x)*c^8*x^8+1/3*arcsinh(c*x)*c^6*x^6+1/4*arcsinh(c*x)*c^4*x^4-1/64*c^7*x^7*(c^2*x^2+1)^(1/2)-43/1152*c^5*x^5*(c^2*x^2+1)^(1/2)-73/4608*c^3*x^3*(c^2*x^2+1)^(1/2)+73/3072*c*x*(c^2*x^2+1)^(1/2)-73/3072*arcsinh(c*x)))","A"
12,1,148,135,0.008000," ","int(x^2*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{7} c^{7} x^{7}+\frac{2}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{2} b \left(\frac{\arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{2 \arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}-\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{49}-\frac{68 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1225}-\frac{409 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{11025}+\frac{818 \sqrt{c^{2} x^{2}+1}}{11025}\right)}{c^{3}}"," ",0,"1/c^3*(d^2*a*(1/7*c^7*x^7+2/5*c^5*x^5+1/3*c^3*x^3)+d^2*b*(1/7*arcsinh(c*x)*c^7*x^7+2/5*arcsinh(c*x)*c^5*x^5+1/3*arcsinh(c*x)*c^3*x^3-1/49*c^6*x^6*(c^2*x^2+1)^(1/2)-68/1225*c^4*x^4*(c^2*x^2+1)^(1/2)-409/11025*c^2*x^2*(c^2*x^2+1)^(1/2)+818/11025*(c^2*x^2+1)^(1/2)))","A"
13,1,137,104,0.005000," ","int(x*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{6} c^{6} x^{6}+\frac{1}{2} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d^{2} b \left(\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{6}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{2}+\frac{\arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{36}-\frac{13 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{144}-\frac{11 c x \sqrt{c^{2} x^{2}+1}}{96}+\frac{11 \arcsinh \left(c x \right)}{96}\right)}{c^{2}}"," ",0,"1/c^2*(d^2*a*(1/6*c^6*x^6+1/2*c^4*x^4+1/2*c^2*x^2)+d^2*b*(1/6*arcsinh(c*x)*c^6*x^6+1/2*arcsinh(c*x)*c^4*x^4+1/2*arcsinh(c*x)*c^2*x^2-1/36*c^5*x^5*(c^2*x^2+1)^(1/2)-13/144*c^3*x^3*(c^2*x^2+1)^(1/2)-11/96*c*x*(c^2*x^2+1)^(1/2)+11/96*arcsinh(c*x)))","A"
14,1,119,112,0.007000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\frac{d^{2} a \left(\frac{1}{5} c^{5} x^{5}+\frac{2}{3} c^{3} x^{3}+c x \right)+d^{2} b \left(\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{2 \arcsinh \left(c x \right) c^{3} x^{3}}{3}+\arcsinh \left(c x \right) c x -\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{25}-\frac{38 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{225}-\frac{149 \sqrt{c^{2} x^{2}+1}}{225}\right)}{c}"," ",0,"1/c*(d^2*a*(1/5*c^5*x^5+2/3*c^3*x^3+c*x)+d^2*b*(1/5*arcsinh(c*x)*c^5*x^5+2/3*arcsinh(c*x)*c^3*x^3+arcsinh(c*x)*c*x-1/25*c^4*x^4*(c^2*x^2+1)^(1/2)-38/225*c^2*x^2*(c^2*x^2+1)^(1/2)-149/225*(c^2*x^2+1)^(1/2)))","A"
15,1,231,172,0.165000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x,x)","\frac{d^{2} a \,c^{4} x^{4}}{4}+d^{2} a \,c^{2} x^{2}+d^{2} a \ln \left(c x \right)+d^{2} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+d^{2} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{2} b \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{16}-\frac{13 b c \,d^{2} x \sqrt{c^{2} x^{2}+1}}{32}+\frac{d^{2} b \arcsinh \left(c x \right) c^{4} x^{4}}{4}+d^{2} b \arcsinh \left(c x \right) c^{2} x^{2}+\frac{13 b \,d^{2} \arcsinh \left(c x \right)}{32}+d^{2} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+d^{2} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{2} b \arcsinh \left(c x \right)^{2}}{2}"," ",0,"1/4*d^2*a*c^4*x^4+d^2*a*c^2*x^2+d^2*a*ln(c*x)+d^2*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+d^2*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-1/16*d^2*b*c^3*x^3*(c^2*x^2+1)^(1/2)-13/32*b*c*d^2*x*(c^2*x^2+1)^(1/2)+1/4*d^2*b*arcsinh(c*x)*c^4*x^4+d^2*b*arcsinh(c*x)*c^2*x^2+13/32*b*d^2*arcsinh(c*x)+d^2*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))+d^2*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-1/2*d^2*b*arcsinh(c*x)^2","A"
16,1,114,108,0.011000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x^2,x)","c \left(d^{2} a \left(\frac{c^{3} x^{3}}{3}+2 c x -\frac{1}{c x}\right)+d^{2} b \left(\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}+2 \arcsinh \left(c x \right) c x -\frac{\arcsinh \left(c x \right)}{c x}-\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{9}-\frac{16 \sqrt{c^{2} x^{2}+1}}{9}-\arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)\right)\right)"," ",0,"c*(d^2*a*(1/3*c^3*x^3+2*c*x-1/c/x)+d^2*b*(1/3*arcsinh(c*x)*c^3*x^3+2*arcsinh(c*x)*c*x-arcsinh(c*x)/c/x-1/9*c^2*x^2*(c^2*x^2+1)^(1/2)-16/9*(c^2*x^2+1)^(1/2)-arctanh(1/(c^2*x^2+1)^(1/2))))","A"
17,1,262,193,0.320000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x^3,x)","\frac{c^{4} d^{2} a \,x^{2}}{2}+2 c^{2} d^{2} a \ln \left(c x \right)-\frac{d^{2} a}{2 x^{2}}-c^{2} d^{2} b \arcsinh \left(c x \right)^{2}+\frac{c^{4} d^{2} b \arcsinh \left(c x \right) x^{2}}{2}-\frac{b \,c^{3} d^{2} x \sqrt{c^{2} x^{2}+1}}{4}+\frac{b \,c^{2} d^{2} \arcsinh \left(c x \right)}{4}+\frac{d^{2} b \,c^{2}}{2}-\frac{c \,d^{2} b \sqrt{c^{2} x^{2}+1}}{2 x}-\frac{d^{2} b \arcsinh \left(c x \right)}{2 x^{2}}+2 c^{2} d^{2} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d^{2} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d^{2} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d^{2} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)"," ",0,"1/2*c^4*d^2*a*x^2+2*c^2*d^2*a*ln(c*x)-1/2*d^2*a/x^2-c^2*d^2*b*arcsinh(c*x)^2+1/2*c^4*d^2*b*arcsinh(c*x)*x^2-1/4*b*c^3*d^2*x*(c^2*x^2+1)^(1/2)+1/4*b*c^2*d^2*arcsinh(c*x)+1/2*d^2*b*c^2-1/2*c*d^2*b/x*(c^2*x^2+1)^(1/2)-1/2*d^2*b*arcsinh(c*x)/x^2+2*c^2*d^2*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*c^2*d^2*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*c^2*d^2*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*c^2*d^2*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
18,1,114,114,0.013000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x^4,x)","c^{3} \left(d^{2} a \left(c x -\frac{2}{c x}-\frac{1}{3 c^{3} x^{3}}\right)+d^{2} b \left(\arcsinh \left(c x \right) c x -\frac{2 \arcsinh \left(c x \right)}{c x}-\frac{\arcsinh \left(c x \right)}{3 c^{3} x^{3}}-\sqrt{c^{2} x^{2}+1}-\frac{11 \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{6}-\frac{\sqrt{c^{2} x^{2}+1}}{6 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(d^2*a*(c*x-2/c/x-1/3/c^3/x^3)+d^2*b*(arcsinh(c*x)*c*x-2*arcsinh(c*x)/c/x-1/3*arcsinh(c*x)/c^3/x^3-(c^2*x^2+1)^(1/2)-11/6*arctanh(1/(c^2*x^2+1)^(1/2))-1/6/c^2/x^2*(c^2*x^2+1)^(1/2)))","A"
19,1,206,194,0.020000," ","int(x^4*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\frac{d^{3} a \left(\frac{1}{11} c^{11} x^{11}+\frac{1}{3} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{11} x^{11}}{11}+\frac{\arcsinh \left(c x \right) c^{9} x^{9}}{3}+\frac{3 \arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{10} x^{10} \sqrt{c^{2} x^{2}+1}}{121}-\frac{91 c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{3267}-\frac{4705 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{160083}-\frac{6311 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1334025}+\frac{25244 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{4002075}-\frac{50488 \sqrt{c^{2} x^{2}+1}}{4002075}\right)}{c^{5}}"," ",0,"1/c^5*(d^3*a*(1/11*c^11*x^11+1/3*c^9*x^9+3/7*c^7*x^7+1/5*c^5*x^5)+d^3*b*(1/11*arcsinh(c*x)*c^11*x^11+1/3*arcsinh(c*x)*c^9*x^9+3/7*arcsinh(c*x)*c^7*x^7+1/5*arcsinh(c*x)*c^5*x^5-1/121*c^10*x^10*(c^2*x^2+1)^(1/2)-91/3267*c^8*x^8*(c^2*x^2+1)^(1/2)-4705/160083*c^6*x^6*(c^2*x^2+1)^(1/2)-6311/1334025*c^4*x^4*(c^2*x^2+1)^(1/2)+25244/4002075*c^2*x^2*(c^2*x^2+1)^(1/2)-50488/4002075*(c^2*x^2+1)^(1/2)))","A"
20,1,195,173,0.017000," ","int(x^3*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\frac{d^{3} a \left(\frac{1}{10} c^{10} x^{10}+\frac{3}{8} c^{8} x^{8}+\frac{1}{2} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{10} x^{10}}{10}+\frac{3 \arcsinh \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{2}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}-\frac{c^{9} x^{9} \sqrt{c^{2} x^{2}+1}}{100}-\frac{57 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}}{1600}-\frac{401 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{9600}-\frac{79 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{7680}+\frac{79 c x \sqrt{c^{2} x^{2}+1}}{5120}-\frac{79 \arcsinh \left(c x \right)}{5120}\right)}{c^{4}}"," ",0,"1/c^4*(d^3*a*(1/10*c^10*x^10+3/8*c^8*x^8+1/2*c^6*x^6+1/4*c^4*x^4)+d^3*b*(1/10*arcsinh(c*x)*c^10*x^10+3/8*arcsinh(c*x)*c^8*x^8+1/2*arcsinh(c*x)*c^6*x^6+1/4*arcsinh(c*x)*c^4*x^4-1/100*c^9*x^9*(c^2*x^2+1)^(1/2)-57/1600*c^7*x^7*(c^2*x^2+1)^(1/2)-401/9600*c^5*x^5*(c^2*x^2+1)^(1/2)-79/7680*c^3*x^3*(c^2*x^2+1)^(1/2)+79/5120*c*x*(c^2*x^2+1)^(1/2)-79/5120*arcsinh(c*x)))","A"
21,1,187,174,0.009000," ","int(x^2*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\frac{d^{3} a \left(\frac{1}{9} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{9} x^{9}}{9}+\frac{3 \arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{3 \arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}-\frac{c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{81}-\frac{187 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{3969}-\frac{2099 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{33075}-\frac{2629 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{99225}+\frac{5258 \sqrt{c^{2} x^{2}+1}}{99225}\right)}{c^{3}}"," ",0,"1/c^3*(d^3*a*(1/9*c^9*x^9+3/7*c^7*x^7+3/5*c^5*x^5+1/3*c^3*x^3)+d^3*b*(1/9*arcsinh(c*x)*c^9*x^9+3/7*arcsinh(c*x)*c^7*x^7+3/5*arcsinh(c*x)*c^5*x^5+1/3*arcsinh(c*x)*c^3*x^3-1/81*c^8*x^8*(c^2*x^2+1)^(1/2)-187/3969*c^6*x^6*(c^2*x^2+1)^(1/2)-2099/33075*c^4*x^4*(c^2*x^2+1)^(1/2)-2629/99225*c^2*x^2*(c^2*x^2+1)^(1/2)+5258/99225*(c^2*x^2+1)^(1/2)))","A"
22,1,176,125,0.007000," ","int(x*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\frac{d^{3} a \left(\frac{1}{8} c^{8} x^{8}+\frac{1}{2} c^{6} x^{6}+\frac{3}{4} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{2}+\frac{3 \arcsinh \left(c x \right) c^{4} x^{4}}{4}+\frac{\arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{c^{7} x^{7} \sqrt{c^{2} x^{2}+1}}{64}-\frac{25 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{384}-\frac{163 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{1536}-\frac{93 c x \sqrt{c^{2} x^{2}+1}}{1024}+\frac{93 \arcsinh \left(c x \right)}{1024}\right)}{c^{2}}"," ",0,"1/c^2*(d^3*a*(1/8*c^8*x^8+1/2*c^6*x^6+3/4*c^4*x^4+1/2*c^2*x^2)+d^3*b*(1/8*arcsinh(c*x)*c^8*x^8+1/2*arcsinh(c*x)*c^6*x^6+3/4*arcsinh(c*x)*c^4*x^4+1/2*arcsinh(c*x)*c^2*x^2-1/64*c^7*x^7*(c^2*x^2+1)^(1/2)-25/384*c^5*x^5*(c^2*x^2+1)^(1/2)-163/1536*c^3*x^3*(c^2*x^2+1)^(1/2)-93/1024*c*x*(c^2*x^2+1)^(1/2)+93/1024*arcsinh(c*x)))","A"
23,1,156,150,0.007000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\frac{d^{3} a \left(\frac{1}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}+c^{3} x^{3}+c x \right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{3 \arcsinh \left(c x \right) c^{5} x^{5}}{5}+\arcsinh \left(c x \right) c^{3} x^{3}+\arcsinh \left(c x \right) c x -\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{49}-\frac{117 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1225}-\frac{757 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3675}-\frac{2161 \sqrt{c^{2} x^{2}+1}}{3675}\right)}{c}"," ",0,"1/c*(d^3*a*(1/7*c^7*x^7+3/5*c^5*x^5+c^3*x^3+c*x)+d^3*b*(1/7*arcsinh(c*x)*c^7*x^7+3/5*arcsinh(c*x)*c^5*x^5+arcsinh(c*x)*c^3*x^3+arcsinh(c*x)*c*x-1/49*c^6*x^6*(c^2*x^2+1)^(1/2)-117/1225*c^4*x^4*(c^2*x^2+1)^(1/2)-757/3675*c^2*x^2*(c^2*x^2+1)^(1/2)-2161/3675*(c^2*x^2+1)^(1/2)))","A"
24,1,284,215,0.198000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x,x)","\frac{d^{3} a \,c^{6} x^{6}}{6}+\frac{3 d^{3} a \,c^{4} x^{4}}{4}+\frac{3 d^{3} a \,c^{2} x^{2}}{2}+d^{3} a \ln \left(c x \right)-\frac{d^{3} b \,c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{36}-\frac{11 d^{3} b \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{72}-\frac{25 b c \,d^{3} x \sqrt{c^{2} x^{2}+1}}{48}+d^{3} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+d^{3} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+\frac{d^{3} b \arcsinh \left(c x \right) c^{6} x^{6}}{6}+\frac{3 d^{3} b \arcsinh \left(c x \right) c^{4} x^{4}}{4}+\frac{3 d^{3} b \arcsinh \left(c x \right) c^{2} x^{2}}{2}+\frac{25 b \,d^{3} \arcsinh \left(c x \right)}{48}+d^{3} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+d^{3} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{3} b \arcsinh \left(c x \right)^{2}}{2}"," ",0,"1/6*d^3*a*c^6*x^6+3/4*d^3*a*c^4*x^4+3/2*d^3*a*c^2*x^2+d^3*a*ln(c*x)-1/36*d^3*b*c^5*x^5*(c^2*x^2+1)^(1/2)-11/72*d^3*b*c^3*x^3*(c^2*x^2+1)^(1/2)-25/48*b*c*d^3*x*(c^2*x^2+1)^(1/2)+d^3*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+d^3*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+1/6*d^3*b*arcsinh(c*x)*c^6*x^6+3/4*d^3*b*arcsinh(c*x)*c^4*x^4+3/2*d^3*b*arcsinh(c*x)*c^2*x^2+25/48*b*d^3*arcsinh(c*x)+d^3*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+d^3*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))-1/2*d^3*b*arcsinh(c*x)^2","A"
25,1,151,144,0.012000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x^2,x)","c \left(d^{3} a \left(\frac{c^{5} x^{5}}{5}+c^{3} x^{3}+3 c x -\frac{1}{c x}\right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}+\arcsinh \left(c x \right) c^{3} x^{3}+3 \arcsinh \left(c x \right) c x -\frac{\arcsinh \left(c x \right)}{c x}-\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{25}-\frac{7 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{25}-\frac{61 \sqrt{c^{2} x^{2}+1}}{25}-\arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)\right)\right)"," ",0,"c*(d^3*a*(1/5*c^5*x^5+c^3*x^3+3*c*x-1/c/x)+d^3*b*(1/5*arcsinh(c*x)*c^5*x^5+arcsinh(c*x)*c^3*x^3+3*arcsinh(c*x)*c*x-arcsinh(c*x)/c/x-1/25*c^4*x^4*(c^2*x^2+1)^(1/2)-7/25*c^2*x^2*(c^2*x^2+1)^(1/2)-61/25*(c^2*x^2+1)^(1/2)-arctanh(1/(c^2*x^2+1)^(1/2))))","A"
26,1,313,243,0.386000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x^3,x)","\frac{c^{6} d^{3} a \,x^{4}}{4}+\frac{3 c^{4} d^{3} a \,x^{2}}{2}+3 c^{2} d^{3} a \ln \left(c x \right)-\frac{d^{3} a}{2 x^{2}}+\frac{d^{3} b \,c^{2}}{2}+\frac{c^{6} d^{3} b \arcsinh \left(c x \right) x^{4}}{4}+\frac{3 c^{4} d^{3} b \arcsinh \left(c x \right) x^{2}}{2}-\frac{d^{3} b \arcsinh \left(c x \right)}{2 x^{2}}+\frac{21 b \,c^{2} d^{3} \arcsinh \left(c x \right)}{32}-\frac{c \,d^{3} b \sqrt{c^{2} x^{2}+1}}{2 x}+3 c^{2} d^{3} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+3 c^{2} d^{3} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+3 c^{2} d^{3} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+3 c^{2} d^{3} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-\frac{3 c^{2} d^{3} b \arcsinh \left(c x \right)^{2}}{2}-\frac{c^{5} d^{3} b \,x^{3} \sqrt{c^{2} x^{2}+1}}{16}-\frac{21 b \,c^{3} d^{3} x \sqrt{c^{2} x^{2}+1}}{32}"," ",0,"1/4*c^6*d^3*a*x^4+3/2*c^4*d^3*a*x^2+3*c^2*d^3*a*ln(c*x)-1/2*d^3*a/x^2+1/2*d^3*b*c^2+1/4*c^6*d^3*b*arcsinh(c*x)*x^4+3/2*c^4*d^3*b*arcsinh(c*x)*x^2-1/2*d^3*b*arcsinh(c*x)/x^2+21/32*b*c^2*d^3*arcsinh(c*x)-1/2*c*d^3*b/x*(c^2*x^2+1)^(1/2)+3*c^2*d^3*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+3*c^2*d^3*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+3*c^2*d^3*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))+3*c^2*d^3*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-3/2*c^2*d^3*b*arcsinh(c*x)^2-1/16*c^5*d^3*b*x^3*(c^2*x^2+1)^(1/2)-21/32*b*c^3*d^3*x*(c^2*x^2+1)^(1/2)","A"
27,1,155,154,0.013000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x^4,x)","c^{3} \left(d^{3} a \left(\frac{c^{3} x^{3}}{3}+3 c x -\frac{3}{c x}-\frac{1}{3 c^{3} x^{3}}\right)+d^{3} b \left(\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}+3 \arcsinh \left(c x \right) c x -\frac{3 \arcsinh \left(c x \right)}{c x}-\frac{\arcsinh \left(c x \right)}{3 c^{3} x^{3}}-\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{9}-\frac{25 \sqrt{c^{2} x^{2}+1}}{9}-\frac{17 \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{6}-\frac{\sqrt{c^{2} x^{2}+1}}{6 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(d^3*a*(1/3*c^3*x^3+3*c*x-3/c/x-1/3/c^3/x^3)+d^3*b*(1/3*arcsinh(c*x)*c^3*x^3+3*arcsinh(c*x)*c*x-3*arcsinh(c*x)/c/x-1/3*arcsinh(c*x)/c^3/x^3-1/9*c^2*x^2*(c^2*x^2+1)^(1/2)-25/9*(c^2*x^2+1)^(1/2)-17/6*arctanh(1/(c^2*x^2+1)^(1/2))-1/6/c^2/x^2*(c^2*x^2+1)^(1/2)))","A"
28,1,266,169,0.135000," ","int(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","\frac{a \,x^{3}}{3 c^{2} d}-\frac{a x}{c^{4} d}+\frac{a \arctan \left(c x \right)}{c^{5} d}+\frac{b \arcsinh \left(c x \right) x^{3}}{3 c^{2} d}-\frac{b \arcsinh \left(c x \right) x}{c^{4} d}+\frac{b \arcsinh \left(c x \right) \arctan \left(c x \right)}{c^{5} d}-\frac{b \,x^{2} \sqrt{c^{2} x^{2}+1}}{9 c^{3} d}+\frac{11 b \sqrt{c^{2} x^{2}+1}}{9 c^{5} d}+\frac{b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d}-\frac{b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d}-\frac{i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d}+\frac{i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{5} d}"," ",0,"1/3/c^2*a/d*x^3-1/c^4*a/d*x+1/c^5*a/d*arctan(c*x)+1/3/c^2*b/d*arcsinh(c*x)*x^3-1/c^4*b/d*arcsinh(c*x)*x+1/c^5*b/d*arcsinh(c*x)*arctan(c*x)-1/9/c^3*b/d*x^2*(c^2*x^2+1)^(1/2)+11/9*b*(c^2*x^2+1)^(1/2)/c^5/d+1/c^5*b/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^5*b/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^5*b/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^5*b/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
29,1,161,141,0.125000," ","int(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","\frac{a \,x^{2}}{2 c^{2} d}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d}+\frac{b \arcsinh \left(c x \right)^{2}}{2 c^{4} d}+\frac{b \arcsinh \left(c x \right) x^{2}}{2 c^{2} d}-\frac{b x \sqrt{c^{2} x^{2}+1}}{4 c^{3} d}+\frac{b \arcsinh \left(c x \right)}{4 c^{4} d}-\frac{b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}-\frac{b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d}"," ",0,"1/2/c^2*a/d*x^2-1/2/c^4*a/d*ln(c^2*x^2+1)+1/2/c^4*b/d*arcsinh(c*x)^2+1/2/c^2*b/d*arcsinh(c*x)*x^2-1/4*b*x*(c^2*x^2+1)^(1/2)/c^3/d+1/4*b*arcsinh(c*x)/c^4/d-1/c^4*b/d*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/c^4/d","A"
30,1,215,129,0.013000," ","int(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","\frac{a x}{c^{2} d}-\frac{a \arctan \left(c x \right)}{c^{3} d}-\frac{b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}-\frac{i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3} d}-\frac{b \arcsinh \left(c x \right) \arctan \left(c x \right)}{c^{3} d}+\frac{b \arcsinh \left(c x \right) x}{c^{2} d}-\frac{b \sqrt{c^{2} x^{2}+1}}{c^{3} d}"," ",0,"1/c^2*a/d*x-1/c^3*a/d*arctan(c*x)-1/c^3*b/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c^3*b/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I/c^3*b/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c^3*b/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c^3*b/d*arcsinh(c*x)*arctan(c*x)+1/c^2*b/d*arcsinh(c*x)*x-b*(c^2*x^2+1)^(1/2)/c^3/d","A"
31,1,98,87,0.046000," ","int(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 c^{2} d}-\frac{b \arcsinh \left(c x \right)^{2}}{2 c^{2} d}+\frac{b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}+\frac{b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{2} d}"," ",0,"1/2/c^2*a/d*ln(c^2*x^2+1)-1/2/c^2*b/d*arcsinh(c*x)^2+1/c^2*b/d*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/c^2/d","A"
32,1,171,93,0.006000," ","int((a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","\frac{a \arctan \left(c x \right)}{c d}+\frac{i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c d}+\frac{b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c d}-\frac{b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c d}-\frac{i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{c d}+\frac{b \arcsinh \left(c x \right) \arctan \left(c x \right)}{c d}"," ",0,"1/c*a/d*arctan(c*x)+I/c*b/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c*b/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/c*b/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I/c*b/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/c*b/d*arcsinh(c*x)*arctan(c*x)","A"
33,1,74,84,0.066000," ","int((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 d}+\frac{b \dilog \left(\frac{1}{\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}}\right)}{d}-\frac{b \dilog \left(\frac{1}{\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}}\right)}{4 d}"," ",0,"a/d*ln(c*x)-1/2*a/d*ln(c^2*x^2+1)+b/d*dilog(1/(c*x+(c^2*x^2+1)^(1/2))^2)-1/4*b/d*dilog(1/(c*x+(c^2*x^2+1)^(1/2))^4)","A"
34,1,202,124,0.015000," ","int((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d),x)","-\frac{a}{d x}-\frac{c a \arctan \left(c x \right)}{d}-\frac{b \arcsinh \left(c x \right)}{d x}-\frac{c b \arcsinh \left(c x \right) \arctan \left(c x \right)}{d}-\frac{c b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{c b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{c b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{i c b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{i c b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}"," ",0,"-a/d/x-c*a/d*arctan(c*x)-b/d*arcsinh(c*x)/x-c*b/d*arcsinh(c*x)*arctan(c*x)-c*b/d*arctanh(1/(c^2*x^2+1)^(1/2))-c*b/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+c*b/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*c*b/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I*c*b/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
35,1,266,133,0.126000," ","int((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d),x)","-\frac{a}{2 d \,x^{2}}-\frac{c^{2} a \ln \left(c x \right)}{d}+\frac{c^{2} a \ln \left(c^{2} x^{2}+1\right)}{2 d}-\frac{b c \sqrt{c^{2} x^{2}+1}}{2 d x}+\frac{c^{2} b}{2 d}-\frac{b \arcsinh \left(c x \right)}{2 d \,x^{2}}+\frac{c^{2} b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{b \,c^{2} \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d}-\frac{c^{2} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{c^{2} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{c^{2} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{c^{2} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d}"," ",0,"-1/2*a/d/x^2-c^2*a/d*ln(c*x)+1/2*c^2*a/d*ln(c^2*x^2+1)-1/2*b*c*(c^2*x^2+1)^(1/2)/d/x+1/2*c^2*b/d-1/2*b/d*arcsinh(c*x)/x^2+c^2*b/d*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b*c^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/d-c^2*b/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-c^2*b/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-c^2*b/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-c^2*b/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
36,1,261,172,0.019000," ","int((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d),x)","-\frac{a}{3 d \,x^{3}}+\frac{c^{2} a}{d x}+\frac{c^{3} a \arctan \left(c x \right)}{d}-\frac{b \arcsinh \left(c x \right)}{3 d \,x^{3}}+\frac{c^{2} b \arcsinh \left(c x \right)}{d x}+\frac{c^{3} b \arcsinh \left(c x \right) \arctan \left(c x \right)}{d}-\frac{b c \sqrt{c^{2} x^{2}+1}}{6 d \,x^{2}}+\frac{7 c^{3} b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{6 d}+\frac{c^{3} b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{c^{3} b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}-\frac{i c^{3} b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}+\frac{i c^{3} b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{d}"," ",0,"-1/3*a/d/x^3+c^2*a/d/x+c^3*a/d*arctan(c*x)-1/3*b/d*arcsinh(c*x)/x^3+c^2*b/d*arcsinh(c*x)/x+c^3*b/d*arcsinh(c*x)*arctan(c*x)-1/6*b*c*(c^2*x^2+1)^(1/2)/d/x^2+7/6*c^3*b/d*arctanh(1/(c^2*x^2+1)^(1/2))+c^3*b/d*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-c^3*b/d*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-I*c^3*b/d*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*c^3*b/d*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
37,1,285,180,0.021000," ","int(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","\frac{a x}{c^{4} d^{2}}+\frac{a x}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{3 a \arctan \left(c x \right)}{2 c^{5} d^{2}}+\frac{b \arcsinh \left(c x \right) x}{c^{4} d^{2}}+\frac{b \arcsinh \left(c x \right) x}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{3 b \arcsinh \left(c x \right) \arctan \left(c x \right)}{2 c^{5} d^{2}}-\frac{b \,x^{2}}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b}{2 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{3 b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{5} d^{2}}+\frac{3 b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{5} d^{2}}+\frac{3 i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{5} d^{2}}-\frac{3 i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{5} d^{2}}"," ",0,"1/c^4*a/d^2*x+1/2/c^4*a/d^2*x/(c^2*x^2+1)-3/2/c^5*a/d^2*arctan(c*x)+1/c^4*b/d^2*arcsinh(c*x)*x+1/2/c^4*b/d^2*arcsinh(c*x)*x/(c^2*x^2+1)-3/2/c^5*b/d^2*arcsinh(c*x)*arctan(c*x)-1/c^3*b/d^2*x^2/(c^2*x^2+1)^(1/2)-1/2*b/c^5/d^2/(c^2*x^2+1)^(1/2)-3/2/c^5*b/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2/c^5*b/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I/c^5*b/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I/c^5*b/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
38,1,206,151,0.213000," ","int(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","\frac{a}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d^{2}}-\frac{b \arcsinh \left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{b x}{2 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{b \,x^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right)}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}+\frac{b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d^{2}}"," ",0,"1/2/c^4*a/d^2/(c^2*x^2+1)+1/2/c^4*a/d^2*ln(c^2*x^2+1)-1/2/c^4*b/d^2*arcsinh(c*x)^2-1/2*b*x/c^3/d^2/(c^2*x^2+1)^(1/2)+1/2/c^2*b/d^2*x^2/(c^2*x^2+1)+1/2/c^4*b/d^2*arcsinh(c*x)/(c^2*x^2+1)+1/2/c^4*b/d^2/(c^2*x^2+1)+1/c^4*b/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/c^4/d^2","A"
39,1,240,140,0.013000," ","int(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","-\frac{a x}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a \arctan \left(c x \right)}{2 c^{3} d^{2}}-\frac{b \arcsinh \left(c x \right) x}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right) \arctan \left(c x \right)}{2 c^{3} d^{2}}+\frac{b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{3} d^{2}}-\frac{b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{3} d^{2}}-\frac{i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{3} d^{2}}+\frac{i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c^{3} d^{2}}-\frac{b}{2 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2/c^2*a/d^2*x/(c^2*x^2+1)+1/2/c^3*a/d^2*arctan(c*x)-1/2/c^2*b/d^2*arcsinh(c*x)*x/(c^2*x^2+1)+1/2/c^3*b/d^2*arcsinh(c*x)*arctan(c*x)+1/2/c^3*b/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c^3*b/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I/c^3*b/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I/c^3*b/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*b/c^3/d^2/(c^2*x^2+1)^(1/2)","A"
40,1,61,52,0.005000," ","int(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","\frac{-\frac{a}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \left(-\frac{\arcsinh \left(c x \right)}{2 \left(c^{2} x^{2}+1\right)}+\frac{c x}{2 \sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}}{c^{2}}"," ",0,"1/c^2*(-1/2*a/d^2/(c^2*x^2+1)+b/d^2*(-1/2/(c^2*x^2+1)*arcsinh(c*x)+1/2*c*x/(c^2*x^2+1)^(1/2)))","A"
41,1,234,137,0.011000," ","int((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","\frac{a x}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a \arctan \left(c x \right)}{2 c \,d^{2}}+\frac{b \arcsinh \left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right) \arctan \left(c x \right)}{2 c \,d^{2}}+\frac{b}{2 c \,d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c \,d^{2}}-\frac{b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c \,d^{2}}-\frac{i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c \,d^{2}}+\frac{i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c \,d^{2}}"," ",0,"1/2*a/d^2*x/(c^2*x^2+1)+1/2/c*a/d^2*arctan(c*x)+1/2*b/d^2*arcsinh(c*x)*x/(c^2*x^2+1)+1/2/c*b/d^2*arcsinh(c*x)*arctan(c*x)+1/2*b/c/d^2/(c^2*x^2+1)^(1/2)+1/2/c*b/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2/c*b/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*I/c*b/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I/c*b/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
42,1,283,127,0.120000," ","int((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^2,x)","\frac{a \ln \left(c x \right)}{d^{2}}+\frac{a}{2 d^{2} \left(c^{2} x^{2}+1\right)}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}-\frac{b c x}{2 d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{b \,c^{2} x^{2}}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right)}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b}{2 d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{2}}+\frac{b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}"," ",0,"a/d^2*ln(c*x)+1/2*a/d^2/(c^2*x^2+1)-1/2*a/d^2*ln(c^2*x^2+1)-1/2*b*c*x/d^2/(c^2*x^2+1)^(1/2)+1/2*b/d^2*c^2*x^2/(c^2*x^2+1)+1/2*b/d^2*arcsinh(c*x)/(c^2*x^2+1)+1/2*b/d^2/(c^2*x^2+1)-b/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^2+b/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+b/d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+b/d^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+b/d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))","B"
43,1,267,181,0.020000," ","int((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^2,x)","-\frac{a}{d^{2} x}-\frac{a \,c^{2} x}{2 d^{2} \left(c^{2} x^{2}+1\right)}-\frac{3 c a \arctan \left(c x \right)}{2 d^{2}}-\frac{b \arcsinh \left(c x \right)}{d^{2} x}-\frac{b \arcsinh \left(c x \right) c^{2} x}{2 d^{2} \left(c^{2} x^{2}+1\right)}-\frac{3 c b \arcsinh \left(c x \right) \arctan \left(c x \right)}{2 d^{2}}-\frac{3 c b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}+\frac{3 c b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}+\frac{3 i c b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}-\frac{3 i c b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}-\frac{b c}{2 d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{c b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{2}}"," ",0,"-a/d^2/x-1/2*a/d^2*c^2*x/(c^2*x^2+1)-3/2*c*a/d^2*arctan(c*x)-b/d^2*arcsinh(c*x)/x-1/2*b/d^2*arcsinh(c*x)*c^2*x/(c^2*x^2+1)-3/2*c*b/d^2*arcsinh(c*x)*arctan(c*x)-3/2*c*b/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*c*b/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*c*b/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*I*c*b/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/2*b*c/d^2/(c^2*x^2+1)^(1/2)-c*b/d^2*arctanh(1/(c^2*x^2+1)^(1/2))","A"
44,1,311,170,0.145000," ","int((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^2,x)","-\frac{a}{2 d^{2} x^{2}}-\frac{2 c^{2} a \ln \left(c x \right)}{d^{2}}-\frac{c^{2} a}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{c^{2} a \ln \left(c^{2} x^{2}+1\right)}{d^{2}}-\frac{c^{2} b \arcsinh \left(c x \right)}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b c}{2 d^{2} x \sqrt{c^{2} x^{2}+1}}-\frac{b \arcsinh \left(c x \right)}{2 d^{2} x^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 c^{2} b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{b \,c^{2} \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{2 c^{2} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 c^{2} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 c^{2} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 c^{2} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}"," ",0,"-1/2*a/d^2/x^2-2*c^2*a/d^2*ln(c*x)-1/2*c^2*a/d^2/(c^2*x^2+1)+c^2*a/d^2*ln(c^2*x^2+1)-c^2*b/d^2*arcsinh(c*x)/(c^2*x^2+1)-1/2*b*c/d^2/x/(c^2*x^2+1)^(1/2)-1/2*b/d^2/x^2/(c^2*x^2+1)*arcsinh(c*x)+2*c^2*b/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+b*c^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^2-2*c^2*b/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*c^2*b/d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*c^2*b/d^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-2*c^2*b/d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
45,1,332,243,0.020000," ","int((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^2,x)","-\frac{a}{3 d^{2} x^{3}}+\frac{2 c^{2} a}{d^{2} x}+\frac{c^{4} a x}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 c^{3} a \arctan \left(c x \right)}{2 d^{2}}-\frac{b \arcsinh \left(c x \right)}{3 d^{2} x^{3}}+\frac{2 c^{2} b \arcsinh \left(c x \right)}{d^{2} x}+\frac{c^{4} b \arcsinh \left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 c^{3} b \arcsinh \left(c x \right) \arctan \left(c x \right)}{2 d^{2}}+\frac{b \,c^{3}}{3 d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{13 c^{3} b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{6 d^{2}}-\frac{b c}{6 d^{2} x^{2} \sqrt{c^{2} x^{2}+1}}+\frac{5 c^{3} b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}-\frac{5 c^{3} b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}-\frac{5 i c^{3} b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}+\frac{5 i c^{3} b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{2 d^{2}}"," ",0,"-1/3*a/d^2/x^3+2*c^2*a/d^2/x+1/2*c^4*a/d^2*x/(c^2*x^2+1)+5/2*c^3*a/d^2*arctan(c*x)-1/3*b/d^2*arcsinh(c*x)/x^3+2*c^2*b/d^2*arcsinh(c*x)/x+1/2*c^4*b/d^2*arcsinh(c*x)*x/(c^2*x^2+1)+5/2*c^3*b/d^2*arcsinh(c*x)*arctan(c*x)+1/3*b*c^3/d^2/(c^2*x^2+1)^(1/2)+13/6*c^3*b/d^2*arctanh(1/(c^2*x^2+1)^(1/2))-1/6*b*c/d^2/x^2/(c^2*x^2+1)^(1/2)+5/2*c^3*b/d^2*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-5/2*c^3*b/d^2*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-5/2*I*c^3*b/d^2*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+5/2*I*c^3*b/d^2*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
46,1,313,191,0.016000," ","int(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","-\frac{5 a \,x^{3}}{8 c^{2} d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{3 a x}{8 c^{4} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{3 a \arctan \left(c x \right)}{8 c^{5} d^{3}}-\frac{5 b \arcsinh \left(c x \right) x^{3}}{8 c^{2} d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{3 b \arcsinh \left(c x \right) x}{8 c^{4} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{3 b \arcsinh \left(c x \right) \arctan \left(c x \right)}{8 c^{5} d^{3}}+\frac{3 b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{5} d^{3}}-\frac{3 b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{5} d^{3}}-\frac{3 i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{5} d^{3}}+\frac{3 i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{5} d^{3}}-\frac{5 b \,x^{2}}{8 c^{3} d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{13 b}{24 c^{5} d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-5/8/c^2*a/d^3*x^3/(c^2*x^2+1)^2-3/8/c^4*a/d^3*x/(c^2*x^2+1)^2+3/8/c^5*a/d^3*arctan(c*x)-5/8/c^2*b/d^3*arcsinh(c*x)*x^3/(c^2*x^2+1)^2-3/8/c^4*b/d^3*arcsinh(c*x)*x/(c^2*x^2+1)^2+3/8/c^5*b/d^3*arcsinh(c*x)*arctan(c*x)+3/8/c^5*b/d^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/8/c^5*b/d^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/8*I/c^5*b/d^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/8*I/c^5*b/d^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-5/8/c^3*b/d^3*x^2/(c^2*x^2+1)^(3/2)-13/24*b/c^5/d^3/(c^2*x^2+1)^(3/2)","A"
47,1,108,85,0.015000," ","int(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","\frac{\frac{a \left(-\frac{1}{2 \left(c^{2} x^{2}+1\right)}+\frac{1}{4 \left(c^{2} x^{2}+1\right)^{2}}\right)}{d^{3}}+\frac{b \left(-\frac{\arcsinh \left(c x \right)}{2 \left(c^{2} x^{2}+1\right)}+\frac{\arcsinh \left(c x \right)}{4 \left(c^{2} x^{2}+1\right)^{2}}-\frac{c x}{12 \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{c x}{3 \sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}}{c^{4}}"," ",0,"1/c^4*(a/d^3*(-1/2/(c^2*x^2+1)+1/4/(c^2*x^2+1)^2)+b/d^3*(-1/2/(c^2*x^2+1)*arcsinh(c*x)+1/4/(c^2*x^2+1)^2*arcsinh(c*x)-1/12/(c^2*x^2+1)^(3/2)*c*x+1/3*c*x/(c^2*x^2+1)^(1/2)))","A"
48,1,307,189,0.014000," ","int(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","\frac{a \,x^{3}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{a x}{8 c^{2} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{a \arctan \left(c x \right)}{8 c^{3} d^{3}}+\frac{b \arcsinh \left(c x \right) x^{3}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{b \arcsinh \left(c x \right) x}{8 c^{2} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \arcsinh \left(c x \right) \arctan \left(c x \right)}{8 c^{3} d^{3}}+\frac{b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{3} d^{3}}-\frac{b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{3} d^{3}}-\frac{i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{3} d^{3}}+\frac{i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c^{3} d^{3}}+\frac{b \,x^{2}}{8 c \,d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{b}{24 c^{3} d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/8*a/d^3*x^3/(c^2*x^2+1)^2-1/8/c^2*a/d^3*x/(c^2*x^2+1)^2+1/8/c^3*a/d^3*arctan(c*x)+1/8*b/d^3*arcsinh(c*x)*x^3/(c^2*x^2+1)^2-1/8/c^2*b/d^3*arcsinh(c*x)*x/(c^2*x^2+1)^2+1/8/c^3*b/d^3*arcsinh(c*x)*arctan(c*x)+1/8/c^3*b/d^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/8/c^3*b/d^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-1/8*I/c^3*b/d^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/8*I/c^3*b/d^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/8/c*b/d^3*x^2/(c^2*x^2+1)^(3/2)+1/24*b/c^3/d^3/(c^2*x^2+1)^(3/2)","A"
49,1,76,73,0.009000," ","int(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","\frac{-\frac{a}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \left(-\frac{\arcsinh \left(c x \right)}{4 \left(c^{2} x^{2}+1\right)^{2}}+\frac{c x}{12 \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{c x}{6 \sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}}{c^{2}}"," ",0,"1/c^2*(-1/4*a/d^3/(c^2*x^2+1)^2+b/d^3*(-1/4/(c^2*x^2+1)^2*arcsinh(c*x)+1/12/(c^2*x^2+1)^(3/2)*c*x+1/6*c*x/(c^2*x^2+1)^(1/2)))","A"
50,1,295,183,0.012000," ","int((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","\frac{a x}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{3 a x}{8 d^{3} \left(c^{2} x^{2}+1\right)}+\frac{3 a \arctan \left(c x \right)}{8 c \,d^{3}}+\frac{b \arcsinh \left(c x \right) x}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{3 b \arcsinh \left(c x \right) x}{8 d^{3} \left(c^{2} x^{2}+1\right)}+\frac{3 b \arcsinh \left(c x \right) \arctan \left(c x \right)}{8 c \,d^{3}}+\frac{3 c b \,x^{2}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{11 b}{24 c \,d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{3 b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c \,d^{3}}-\frac{3 b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c \,d^{3}}-\frac{3 i b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c \,d^{3}}+\frac{3 i b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 c \,d^{3}}"," ",0,"1/4*a/d^3*x/(c^2*x^2+1)^2+3/8*a/d^3*x/(c^2*x^2+1)+3/8/c*a/d^3*arctan(c*x)+1/4*b/d^3*arcsinh(c*x)*x/(c^2*x^2+1)^2+3/8*b/d^3*arcsinh(c*x)*x/(c^2*x^2+1)+3/8/c*b/d^3*arcsinh(c*x)*arctan(c*x)+3/8*c*b/d^3*x^2/(c^2*x^2+1)^(3/2)+11/24*b/c/d^3/(c^2*x^2+1)^(3/2)+3/8/c*b/d^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/8/c*b/d^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/8*I/c*b/d^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/8*I/c*b/d^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
51,1,451,170,0.197000," ","int((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^3,x)","\frac{a \ln \left(c x \right)}{d^{3}}+\frac{a}{2 d^{3} \left(c^{2} x^{2}+1\right)}+\frac{a}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{a \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}-\frac{2 b \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{2 b \,c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right) c^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{3 b c x \sqrt{c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 b \,c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{3 b \arcsinh \left(c x \right)}{4 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{2 b}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}+\frac{b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}"," ",0,"a/d^3*ln(c*x)+1/2*a/d^3/(c^2*x^2+1)+1/4*a/d^3/(c^2*x^2+1)^2-1/2*a/d^3*ln(c^2*x^2+1)-2/3*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c^3*x^3*(c^2*x^2+1)^(1/2)+2/3*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c^4*x^4+1/2*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*c^2*x^2-3/4*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c*x*(c^2*x^2+1)^(1/2)+4/3*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c^2*x^2+3/4*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)+2/3*b/d^3/(c^4*x^4+2*c^2*x^2+1)-b/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^3+b/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+b/d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+b/d^3*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+b/d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))","B"
52,1,357,227,0.020000," ","int((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^3,x)","-\frac{a}{d^{3} x}-\frac{7 a \,c^{4} x^{3}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{9 a \,c^{2} x}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{15 c a \arctan \left(c x \right)}{8 d^{3}}-\frac{b \arcsinh \left(c x \right)}{d^{3} x}-\frac{7 b \arcsinh \left(c x \right) c^{4} x^{3}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{9 b \arcsinh \left(c x \right) c^{2} x}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{15 c b \arcsinh \left(c x \right) \arctan \left(c x \right)}{8 d^{3}}-\frac{15 c b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}+\frac{15 c b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}+\frac{15 i c b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}-\frac{15 i c b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}-\frac{15 b \,c^{3} x^{2}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{47 b c}{24 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{b c}{d^{3} \sqrt{c^{2} x^{2}+1}}-\frac{c b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{d^{3}}"," ",0,"-a/d^3/x-7/8*a/d^3*c^4*x^3/(c^2*x^2+1)^2-9/8*a/d^3*c^2*x/(c^2*x^2+1)^2-15/8*c*a/d^3*arctan(c*x)-b/d^3*arcsinh(c*x)/x-7/8*b/d^3*arcsinh(c*x)*c^4*x^3/(c^2*x^2+1)^2-9/8*b/d^3*arcsinh(c*x)*c^2*x/(c^2*x^2+1)^2-15/8*c*b/d^3*arcsinh(c*x)*arctan(c*x)-15/8*c*b/d^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+15/8*c*b/d^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+15/8*I*c*b/d^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-15/8*I*c*b/d^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-15/8*b/d^3*c^3*x^2/(c^2*x^2+1)^(3/2)-47/24*b*c/d^3/(c^2*x^2+1)^(3/2)+b*c/d^3/(c^2*x^2+1)^(1/2)-c*b/d^3*arctanh(1/(c^2*x^2+1)^(1/2))","A"
53,1,575,240,0.261000," ","int((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^3,x)","-\frac{a}{2 d^{3} x^{2}}-\frac{3 c^{2} a \ln \left(c x \right)}{d^{3}}-\frac{c^{2} a}{d^{3} \left(c^{2} x^{2}+1\right)}-\frac{c^{2} a}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{3 c^{2} a \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}+\frac{2 c^{5} b \,x^{3} \sqrt{c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{2 c^{6} b \,x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{3 c^{4} b \arcsinh \left(c x \right) x^{2}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{c^{3} b x \sqrt{c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{4 c^{4} b \,x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{9 c^{2} b \arcsinh \left(c x \right)}{4 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) x}-\frac{2 c^{2} b}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) x^{2}}+\frac{3 c^{2} b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{3 b \,c^{2} \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}-\frac{3 c^{2} b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 c^{2} b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 c^{2} b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 c^{2} b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}"," ",0,"-1/2*a/d^3/x^2-3*c^2*a/d^3*ln(c*x)-c^2*a/d^3/(c^2*x^2+1)-1/4*c^2*a/d^3/(c^2*x^2+1)^2+3/2*c^2*a/d^3*ln(c^2*x^2+1)+2/3*c^5*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x^3*(c^2*x^2+1)^(1/2)-2/3*c^6*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x^4-3/2*c^4*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^2+1/4*c^3*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x*(c^2*x^2+1)^(1/2)-4/3*c^4*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x^2-9/4*c^2*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)-1/2*c*b/d^3/(c^4*x^4+2*c^2*x^2+1)/x*(c^2*x^2+1)^(1/2)-2/3*c^2*b/d^3/(c^4*x^4+2*c^2*x^2+1)-1/2*b/d^3/(c^4*x^4+2*c^2*x^2+1)/x^2*arcsinh(c*x)+3*c^2*b/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+3/2*b*c^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^3-3*c^2*b/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-3*c^2*b/d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-3*c^2*b/d^3*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-3*c^2*b/d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))","B"
54,1,425,291,0.020000," ","int((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^3,x)","-\frac{a}{3 d^{3} x^{3}}+\frac{3 c^{2} a}{d^{3} x}+\frac{11 c^{6} a \,x^{3}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{13 c^{4} a x}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{35 c^{3} a \arctan \left(c x \right)}{8 d^{3}}-\frac{b \arcsinh \left(c x \right)}{3 d^{3} x^{3}}+\frac{3 c^{2} b \arcsinh \left(c x \right)}{d^{3} x}+\frac{11 c^{6} b \arcsinh \left(c x \right) x^{3}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{13 c^{4} b \arcsinh \left(c x \right) x}{8 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{35 c^{3} b \arcsinh \left(c x \right) \arctan \left(c x \right)}{8 d^{3}}+\frac{35 c^{5} b \,x^{2}}{8 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{103 b \,c^{3}}{24 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{19 b \,c^{3}}{6 d^{3} \sqrt{c^{2} x^{2}+1}}+\frac{19 c^{3} b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{6 d^{3}}-\frac{b c}{6 d^{3} x^{2} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{35 c^{3} b \arctan \left(c x \right) \ln \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}-\frac{35 c^{3} b \arctan \left(c x \right) \ln \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}+\frac{35 i c^{3} b \dilog \left(1-\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}-\frac{35 i c^{3} b \dilog \left(1+\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)}{8 d^{3}}"," ",0,"-1/3*a/d^3/x^3+3*c^2*a/d^3/x+11/8*c^6*a/d^3*x^3/(c^2*x^2+1)^2+13/8*c^4*a/d^3*x/(c^2*x^2+1)^2+35/8*c^3*a/d^3*arctan(c*x)-1/3*b/d^3*arcsinh(c*x)/x^3+3*c^2*b/d^3*arcsinh(c*x)/x+11/8*c^6*b/d^3*arcsinh(c*x)*x^3/(c^2*x^2+1)^2+13/8*c^4*b/d^3*arcsinh(c*x)*x/(c^2*x^2+1)^2+35/8*c^3*b/d^3*arcsinh(c*x)*arctan(c*x)+35/8*c^5*b/d^3*x^2/(c^2*x^2+1)^(3/2)+103/24*b*c^3/d^3/(c^2*x^2+1)^(3/2)-19/6*b*c^3/d^3/(c^2*x^2+1)^(1/2)+19/6*c^3*b/d^3*arctanh(1/(c^2*x^2+1)^(1/2))-1/6*b*c/d^3/x^2/(c^2*x^2+1)^(3/2)+35/8*c^3*b/d^3*arctan(c*x)*ln(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-35/8*c^3*b/d^3*arctan(c*x)*ln(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))+35/8*I*c^3*b/d^3*dilog(1-I*(1+I*c*x)/(c^2*x^2+1)^(1/2))-35/8*I*c^3*b/d^3*dilog(1+I*(1+I*c*x)/(c^2*x^2+1)^(1/2))","A"
55,1,164,89,0.152000," ","int(x^3*(a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2),x)","a \left(\frac{x^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{5 \pi  \,c^{2}}-\frac{2 \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{15 \pi  \,c^{4}}\right)+\frac{b \sqrt{\pi}\, \left(45 \arcsinh \left(c x \right) c^{6} x^{6}+60 \arcsinh \left(c x \right) c^{4} x^{4}-9 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}-15 \arcsinh \left(c x \right) c^{2} x^{2}-5 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-30 \arcsinh \left(c x \right)+30 c x \sqrt{c^{2} x^{2}+1}\right)}{225 c^{4} \sqrt{c^{2} x^{2}+1}}"," ",0,"a*(1/5*x^2*(Pi*c^2*x^2+Pi)^(3/2)/Pi/c^2-2/15/Pi/c^4*(Pi*c^2*x^2+Pi)^(3/2))+1/225*b/c^4*Pi^(1/2)/(c^2*x^2+1)^(1/2)*(45*arcsinh(c*x)*c^6*x^6+60*arcsinh(c*x)*c^4*x^4-9*c^5*x^5*(c^2*x^2+1)^(1/2)-15*arcsinh(c*x)*c^2*x^2-5*c^3*x^3*(c^2*x^2+1)^(1/2)-30*arcsinh(c*x)+30*c*x*(c^2*x^2+1)^(1/2))","A"
56,1,170,97,0.067000," ","int(x^2*(a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{4 \pi  \,c^{2}}-\frac{a x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{8 c^{2}}-\frac{a \pi  \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{8 c^{2} \sqrt{\pi  \,c^{2}}}+\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{4}-\frac{b c \,x^{4} \sqrt{\pi}}{16}+\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{8 c^{2}}-\frac{b \,x^{2} \sqrt{\pi}}{16 c}-\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right)^{2}}{16 c^{3}}"," ",0,"1/4*a*x*(Pi*c^2*x^2+Pi)^(3/2)/Pi/c^2-1/8*a/c^2*x*(Pi*c^2*x^2+Pi)^(1/2)-1/8*a/c^2*Pi*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/4*b*Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-1/16*b*c*x^4*Pi^(1/2)+1/8*b*Pi^(1/2)/c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/16*b*x^2*Pi^(1/2)/c-1/16*b*Pi^(1/2)/c^3*arcsinh(c*x)^2","A"
57,1,108,49,0.059000," ","int(x*(a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{3 \pi  \,c^{2}}+\frac{b \sqrt{\pi}\, \left(3 \arcsinh \left(c x \right) c^{4} x^{4}+6 \arcsinh \left(c x \right) c^{2} x^{2}-c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+3 \arcsinh \left(c x \right)-3 c x \sqrt{c^{2} x^{2}+1}\right)}{9 c^{2} \sqrt{c^{2} x^{2}+1}}"," ",0,"1/3*a/Pi/c^2*(Pi*c^2*x^2+Pi)^(3/2)+1/9*b/c^2*Pi^(1/2)/(c^2*x^2+1)^(1/2)*(3*arcsinh(c*x)*c^4*x^4+6*arcsinh(c*x)*c^2*x^2-c^3*x^3*(c^2*x^2+1)^(1/2)+3*arcsinh(c*x)-3*c*x*(c^2*x^2+1)^(1/2))","B"
58,1,112,55,0.057000," ","int((a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{x a \sqrt{\pi  \,c^{2} x^{2}+\pi}}{2}+\frac{a \pi  \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 \sqrt{\pi  \,c^{2}}}+\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2}-\frac{b c \,x^{2} \sqrt{\pi}}{4}+\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right)^{2}}{4 c}-\frac{b \sqrt{\pi}}{4 c}"," ",0,"1/2*x*a*(Pi*c^2*x^2+Pi)^(1/2)+1/2*a*Pi*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b*Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/4*b*c*x^2*Pi^(1/2)+1/4*b*Pi^(1/2)/c*arcsinh(c*x)^2-1/4*b*Pi^(1/2)/c","B"
59,1,171,107,0.215000," ","int((a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2)/x,x)","-\sqrt{\pi}\, \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right) a +a \sqrt{\pi  \,c^{2} x^{2}+\pi}+\sqrt{\pi}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) b +\sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, b -\sqrt{\pi}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) b -b c x \sqrt{\pi}+b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) \sqrt{\pi}-b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) \sqrt{\pi}"," ",0,"-Pi^(1/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))*a+a*(Pi*c^2*x^2+Pi)^(1/2)+Pi^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*b+Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*b-Pi^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*b-b*c*x*Pi^(1/2)+b*polylog(2,c*x+(c^2*x^2+1)^(1/2))*Pi^(1/2)-b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*Pi^(1/2)","A"
60,1,155,53,0.165000," ","int((a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2)/x^2,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{\pi  x}+a \,c^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}+\frac{a \,c^{2} \pi  \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{\sqrt{\pi  \,c^{2}}}+\frac{b c \sqrt{\pi}\, \arcsinh \left(c x \right)^{2}}{2}-b c \sqrt{\pi}\, \arcsinh \left(c x \right)-\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}+b c \sqrt{\pi}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)"," ",0,"-a/Pi/x*(Pi*c^2*x^2+Pi)^(3/2)+a*c^2*x*(Pi*c^2*x^2+Pi)^(1/2)+a*c^2*Pi*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b*c*Pi^(1/2)*arcsinh(c*x)^2-b*c*Pi^(1/2)*arcsinh(c*x)-b*Pi^(1/2)*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)+b*c*Pi^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
61,1,243,123,0.300000," ","int((a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2)/x^3,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{2 \pi  \,x^{2}}-\frac{a \sqrt{\pi}\, \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right) c^{2}}{2}+\frac{a \sqrt{\pi  \,c^{2} x^{2}+\pi}\, c^{2}}{2}-\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b c \sqrt{\pi}}{2 x}-\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right)}{2 \sqrt{c^{2} x^{2}+1}\, x^{2}}-\frac{b \,c^{2} \sqrt{\pi}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2}-\frac{b \,c^{2} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) \sqrt{\pi}}{2}+\frac{b \,c^{2} \sqrt{\pi}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{2}+\frac{b \,c^{2} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) \sqrt{\pi}}{2}"," ",0,"-1/2*a/Pi/x^2*(Pi*c^2*x^2+Pi)^(3/2)-1/2*a*Pi^(1/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))*c^2+1/2*a*(Pi*c^2*x^2+Pi)^(1/2)*c^2-1/2*b*Pi^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^2-1/2*b*c*Pi^(1/2)/x-1/2*b*Pi^(1/2)/(c^2*x^2+1)^(1/2)/x^2*arcsinh(c*x)-1/2*b*c^2*Pi^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-1/2*b*c^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*Pi^(1/2)+1/2*b*c^2*Pi^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+1/2*b*c^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))*Pi^(1/2)","A"
62,1,501,50,0.306000," ","int((a+b*arcsinh(c*x))*(Pi*c^2*x^2+Pi)^(1/2)/x^4,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{3 \pi  \,x^{3}}-\frac{2 b \,c^{3} \sqrt{\pi}\, \arcsinh \left(c x \right)}{3}+\frac{b \sqrt{\pi}\, x^{4} \arcsinh \left(c x \right) c^{7}}{3 c^{4} x^{4}+3 c^{2} x^{2}+1}-\frac{b \sqrt{\pi}\, x^{3} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{6}}{3 c^{4} x^{4}+3 c^{2} x^{2}+1}+\frac{b \sqrt{\pi}\, x^{4} c^{7}}{18 c^{4} x^{4}+18 c^{2} x^{2}+6}-\frac{b \sqrt{\pi}\, x^{2} \left(c^{2} x^{2}+1\right) c^{5}}{6 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right)}+\frac{b \sqrt{\pi}\, x^{2} \arcsinh \left(c x \right) c^{5}}{3 c^{4} x^{4}+3 c^{2} x^{2}+1}-\frac{2 b \sqrt{\pi}\, x \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4}}{3 c^{4} x^{4}+3 c^{2} x^{2}+1}-\frac{b \sqrt{\pi}\, \left(c^{2} x^{2}+1\right) c^{3}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right)}+\frac{b \,c^{3} \sqrt{\pi}\, \arcsinh \left(c x \right)}{9 c^{4} x^{4}+9 c^{2} x^{2}+3}-\frac{4 b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x}-\frac{b \sqrt{\pi}\, \left(c^{2} x^{2}+1\right) c}{6 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{2}}-\frac{b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{3}}+\frac{b \,c^{3} \sqrt{\pi}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{3}"," ",0,"-1/3*a/Pi/x^3*(Pi*c^2*x^2+Pi)^(3/2)-2/3*b*c^3*Pi^(1/2)*arcsinh(c*x)+b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^4*arcsinh(c*x)*c^7-b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^6+1/6*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^4*c^7-1/6*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2*(c^2*x^2+1)*c^5+b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2*arcsinh(c*x)*c^5-2*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4-1/3*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*(c^2*x^2+1)*c^3+1/3*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*arcsinh(c*x)*c^3-4/3*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2-1/6*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^2*(c^2*x^2+1)*c-1/3*b*Pi^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+1/3*b*c^3*Pi^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
63,1,195,101,0.111000," ","int(x^3*(Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x)),x)","a \left(\frac{x^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{7 \pi  \,c^{2}}-\frac{2 \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{35 \pi  \,c^{4}}\right)+\frac{b \,\pi^{\frac{3}{2}} \left(525 \arcsinh \left(c x \right) c^{8} x^{8}+1365 \arcsinh \left(c x \right) c^{6} x^{6}-75 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+945 \arcsinh \left(c x \right) c^{4} x^{4}-168 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}-105 \arcsinh \left(c x \right) c^{2} x^{2}-35 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-210 \arcsinh \left(c x \right)+210 c x \sqrt{c^{2} x^{2}+1}\right)}{3675 c^{4} \sqrt{c^{2} x^{2}+1}}"," ",0,"a*(1/7*x^2*(Pi*c^2*x^2+Pi)^(5/2)/Pi/c^2-2/35/Pi/c^4*(Pi*c^2*x^2+Pi)^(5/2))+1/3675*b/c^4*Pi^(3/2)/(c^2*x^2+1)^(1/2)*(525*arcsinh(c*x)*c^8*x^8+1365*arcsinh(c*x)*c^6*x^6-75*c^7*x^7*(c^2*x^2+1)^(1/2)+945*arcsinh(c*x)*c^4*x^4-168*c^5*x^5*(c^2*x^2+1)^(1/2)-105*arcsinh(c*x)*c^2*x^2-35*c^3*x^3*(c^2*x^2+1)^(1/2)-210*arcsinh(c*x)+210*c*x*(c^2*x^2+1)^(1/2))","A"
64,1,240,135,0.113000," ","int(x^2*(Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x)),x)","\frac{a x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{6 \pi  \,c^{2}}-\frac{a x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{24 c^{2}}-\frac{a \pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{16 c^{2}}-\frac{a \,\pi^{2} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{16 c^{2} \sqrt{\pi  \,c^{2}}}+\frac{b \,\pi^{\frac{3}{2}} c^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{5}}{6}-\frac{b \,c^{3} \pi^{\frac{3}{2}} x^{6}}{36}+\frac{7 b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{24}-\frac{7 b c \,\pi^{\frac{3}{2}} x^{4}}{96}+\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{16 c^{2}}-\frac{b \,\pi^{\frac{3}{2}} x^{2}}{32 c}-\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{2}}{32 c^{3}}+\frac{b \,\pi^{\frac{3}{2}}}{72 c^{3}}"," ",0,"1/6*a*x*(Pi*c^2*x^2+Pi)^(5/2)/Pi/c^2-1/24*a/c^2*x*(Pi*c^2*x^2+Pi)^(3/2)-1/16*a/c^2*Pi*x*(Pi*c^2*x^2+Pi)^(1/2)-1/16*a/c^2*Pi^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/6*b*Pi^(3/2)*c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^5-1/36*b*c^3*Pi^(3/2)*x^6+7/24*b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-7/96*b*c*Pi^(3/2)*x^4+1/16*b*Pi^(3/2)/c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/32*b*Pi^(3/2)*x^2/c-1/32*b*Pi^(3/2)/c^3*arcsinh(c*x)^2+1/72*b*Pi^(3/2)/c^3","A"
65,1,139,61,0.065000," ","int(x*(Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x)),x)","\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{5 \pi  \,c^{2}}+\frac{b \,\pi^{\frac{3}{2}} \left(15 \arcsinh \left(c x \right) c^{6} x^{6}+45 \arcsinh \left(c x \right) c^{4} x^{4}-3 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+45 \arcsinh \left(c x \right) c^{2} x^{2}-10 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+15 \arcsinh \left(c x \right)-15 c x \sqrt{c^{2} x^{2}+1}\right)}{75 c^{2} \sqrt{c^{2} x^{2}+1}}"," ",0,"1/5*a/Pi/c^2*(Pi*c^2*x^2+Pi)^(5/2)+1/75*b/c^2*Pi^(3/2)/(c^2*x^2+1)^(1/2)*(15*arcsinh(c*x)*c^6*x^6+45*arcsinh(c*x)*c^4*x^4-3*c^5*x^5*(c^2*x^2+1)^(1/2)+45*arcsinh(c*x)*c^2*x^2-10*c^3*x^3*(c^2*x^2+1)^(1/2)+15*arcsinh(c*x)-15*c*x*(c^2*x^2+1)^(1/2))","B"
66,1,170,91,0.063000," ","int((Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x)),x)","\frac{x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}} a}{4}+\frac{3 a \pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{8}+\frac{3 a \,\pi^{2} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{8 \sqrt{\pi  \,c^{2}}}+\frac{b \,\pi^{\frac{3}{2}} c^{2} \sqrt{c^{2} x^{2}+1}\, \arcsinh \left(c x \right) x^{3}}{4}-\frac{b \,c^{3} \pi^{\frac{3}{2}} x^{4}}{16}+\frac{5 b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{8}-\frac{5 b c \,\pi^{\frac{3}{2}} x^{2}}{16}+\frac{3 b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{2}}{16 c}-\frac{b \,\pi^{\frac{3}{2}}}{4 c}"," ",0,"1/4*x*(Pi*c^2*x^2+Pi)^(3/2)*a+3/8*a*Pi*x*(Pi*c^2*x^2+Pi)^(1/2)+3/8*a*Pi^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/4*b*Pi^(3/2)*c^2*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^3-1/16*b*c^3*Pi^(3/2)*x^4+5/8*b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-5/16*b*c*Pi^(3/2)*x^2+3/16*b*Pi^(3/2)/c*arcsinh(c*x)^2-1/4*b*Pi^(3/2)/c","A"
67,1,227,142,0.271000," ","int((Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x))/x,x)","\frac{\left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}} a}{3}-a \,\pi^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)+a \sqrt{\pi  \,c^{2} x^{2}+\pi}\, \pi +\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2} c^{2}}{3}-b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)-b \,\pi^{\frac{3}{2}} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)-\frac{b \,c^{3} \pi^{\frac{3}{2}} x^{3}}{9}+\frac{4 b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3}-\frac{4 b c \,\pi^{\frac{3}{2}} x}{3}+b \,\pi^{\frac{3}{2}} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)"," ",0,"1/3*(Pi*c^2*x^2+Pi)^(3/2)*a-a*Pi^(3/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+a*(Pi*c^2*x^2+Pi)^(1/2)*Pi+1/3*b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2*c^2-b*Pi^(3/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-b*Pi^(3/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+b*Pi^(3/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-1/9*b*c^3*Pi^(3/2)*x^3+4/3*b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-4/3*b*c*Pi^(3/2)*x+b*Pi^(3/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
68,1,222,92,0.224000," ","int((Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x))/x^2,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{\pi  x}+a \,c^{2} x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}+\frac{3 a \,c^{2} \pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{2}+\frac{3 a \,c^{2} \pi^{2} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 \sqrt{\pi  \,c^{2}}}+\frac{3 b c \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{2}}{4}+\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x \,c^{2}}{2}-\frac{b \,c^{3} \pi^{\frac{3}{2}} x^{2}}{4}-b c \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right)-\frac{b \,\pi^{\frac{3}{2}} c}{8}-\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}+b c \,\pi^{\frac{3}{2}} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)"," ",0,"-a/Pi/x*(Pi*c^2*x^2+Pi)^(5/2)+a*c^2*x*(Pi*c^2*x^2+Pi)^(3/2)+3/2*a*c^2*Pi*x*(Pi*c^2*x^2+Pi)^(1/2)+3/2*a*c^2*Pi^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+3/4*b*c*Pi^(3/2)*arcsinh(c*x)^2+1/2*b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x*c^2-1/4*b*c^3*Pi^(3/2)*x^2-b*c*Pi^(3/2)*arcsinh(c*x)-1/8*b*Pi^(3/2)*c-b*Pi^(3/2)*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)+b*c*Pi^(3/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
69,1,295,159,0.523000," ","int((Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x))/x^3,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{2 \pi  \,x^{2}}+\frac{a \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{2}-\frac{3 a \,c^{2} \pi^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{2}+\frac{3 a \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}\, \pi}{2}+b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2}-b \,c^{3} \pi^{\frac{3}{2}} x -\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b c \,\pi^{\frac{3}{2}}}{2 x}-\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right)}{2 \sqrt{c^{2} x^{2}+1}\, x^{2}}-\frac{3 b \,c^{2} \pi^{\frac{3}{2}} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2}-\frac{3 b \,c^{2} \pi^{\frac{3}{2}} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{2}+\frac{3 b \,c^{2} \pi^{\frac{3}{2}} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{2}+\frac{3 b \,c^{2} \pi^{\frac{3}{2}} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{2}"," ",0,"-1/2*a/Pi/x^2*(Pi*c^2*x^2+Pi)^(5/2)+1/2*a*c^2*(Pi*c^2*x^2+Pi)^(3/2)-3/2*a*c^2*Pi^(3/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+3/2*a*c^2*(Pi*c^2*x^2+Pi)^(1/2)*Pi+b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2-b*c^3*Pi^(3/2)*x-1/2*b*Pi^(3/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^2-1/2*b*c*Pi^(3/2)/x-1/2*b*Pi^(3/2)/(c^2*x^2+1)^(1/2)/x^2*arcsinh(c*x)-3/2*b*c^2*Pi^(3/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-3/2*b*c^2*Pi^(3/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+3/2*b*c^2*Pi^(3/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+3/2*b*c^2*Pi^(3/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))","A"
70,1,622,97,0.290000," ","int((Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x))/x^4,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{3 \pi  \,x^{3}}-\frac{2 a \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{3 \pi  x}+\frac{2 a \,c^{4} x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{3}+a \,c^{4} \pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}+\frac{a \,c^{4} \pi^{2} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{\sqrt{\pi  \,c^{2}}}+\frac{b \,c^{3} \pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{2}}{2}-\frac{8 b \,c^{3} \pi^{\frac{3}{2}} \arcsinh \left(c x \right)}{3}+\frac{32 b \,\pi^{\frac{3}{2}} x^{4} \arcsinh \left(c x \right) c^{7}}{24 c^{4} x^{4}+9 c^{2} x^{2}+1}-\frac{32 b \,\pi^{\frac{3}{2}} x^{3} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{6}}{24 c^{4} x^{4}+9 c^{2} x^{2}+1}+\frac{8 b \,\pi^{\frac{3}{2}} x^{4} c^{7}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right)}-\frac{8 b \,\pi^{\frac{3}{2}} x^{2} \left(c^{2} x^{2}+1\right) c^{5}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right)}+\frac{12 b \,\pi^{\frac{3}{2}} x^{2} \arcsinh \left(c x \right) c^{5}}{24 c^{4} x^{4}+9 c^{2} x^{2}+1}-\frac{20 b \,\pi^{\frac{3}{2}} x \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4}}{24 c^{4} x^{4}+9 c^{2} x^{2}+1}-\frac{4 b \,\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right) c^{3}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right)}+\frac{4 b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) c^{3}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right)}-\frac{13 b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) x}-\frac{b \,\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right) c}{6 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) x^{2}}-\frac{b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) x^{3}}+\frac{4 b \,c^{3} \pi^{\frac{3}{2}} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{3}"," ",0,"-1/3*a/Pi/x^3*(Pi*c^2*x^2+Pi)^(5/2)-2/3*a*c^2/Pi/x*(Pi*c^2*x^2+Pi)^(5/2)+2/3*a*c^4*x*(Pi*c^2*x^2+Pi)^(3/2)+a*c^4*Pi*x*(Pi*c^2*x^2+Pi)^(1/2)+a*c^4*Pi^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b*c^3*Pi^(3/2)*arcsinh(c*x)^2-8/3*b*c^3*Pi^(3/2)*arcsinh(c*x)+32*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*x^4*arcsinh(c*x)*c^7-32*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^6+8/3*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*x^4*c^7-8/3*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*x^2*(c^2*x^2+1)*c^5+12*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*x^2*arcsinh(c*x)*c^5-20*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4-4/3*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*(c^2*x^2+1)*c^3+4/3*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)*arcsinh(c*x)*c^3-13/3*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)/x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2-1/6*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)/x^2*(c^2*x^2+1)*c-1/3*b*Pi^(3/2)/(24*c^4*x^4+9*c^2*x^2+1)/x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+4/3*b*c^3*Pi^(3/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
71,1,226,113,0.115000," ","int(x^3*(Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x)),x)","a \left(\frac{x^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{9 \pi  \,c^{2}}-\frac{2 \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{63 \pi  \,c^{4}}\right)+\frac{b \,\pi^{\frac{5}{2}} \left(441 \arcsinh \left(c x \right) c^{10} x^{10}+1638 \arcsinh \left(c x \right) c^{8} x^{8}-49 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+2142 \arcsinh \left(c x \right) c^{6} x^{6}-171 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+1008 \arcsinh \left(c x \right) c^{4} x^{4}-189 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}-63 \arcsinh \left(c x \right) c^{2} x^{2}-21 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-126 \arcsinh \left(c x \right)+126 c x \sqrt{c^{2} x^{2}+1}\right)}{3969 c^{4} \sqrt{c^{2} x^{2}+1}}"," ",0,"a*(1/9*x^2*(Pi*c^2*x^2+Pi)^(7/2)/Pi/c^2-2/63/Pi/c^4*(Pi*c^2*x^2+Pi)^(7/2))+1/3969*b/c^4*Pi^(5/2)/(c^2*x^2+1)^(1/2)*(441*arcsinh(c*x)*c^10*x^10+1638*arcsinh(c*x)*c^8*x^8-49*c^9*x^9*(c^2*x^2+1)^(1/2)+2142*arcsinh(c*x)*c^6*x^6-171*c^7*x^7*(c^2*x^2+1)^(1/2)+1008*arcsinh(c*x)*c^4*x^4-189*c^5*x^5*(c^2*x^2+1)^(1/2)-63*arcsinh(c*x)*c^2*x^2-21*c^3*x^3*(c^2*x^2+1)^(1/2)-126*arcsinh(c*x)+126*c*x*(c^2*x^2+1)^(1/2))","A"
72,1,301,175,0.109000," ","int(x^2*(Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x)),x)","\frac{a x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{8 \pi  \,c^{2}}-\frac{a x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{48 c^{2}}-\frac{5 a \pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{192 c^{2}}-\frac{5 a \,\pi^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{128 c^{2}}-\frac{5 a \,\pi^{3} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{128 c^{2} \sqrt{\pi  \,c^{2}}}+\frac{b \,\pi^{\frac{5}{2}} c^{4} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{7}}{8}-\frac{b \,c^{5} \pi^{\frac{5}{2}} x^{8}}{64}+\frac{17 b \,\pi^{\frac{5}{2}} c^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{5}}{48}-\frac{17 b \,c^{3} \pi^{\frac{5}{2}} x^{6}}{288}+\frac{59 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{192}-\frac{59 b c \,\pi^{\frac{5}{2}} x^{4}}{768}+\frac{5 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{128 c^{2}}-\frac{5 b \,\pi^{\frac{5}{2}} x^{2}}{256 c}-\frac{5 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{2}}{256 c^{3}}+\frac{b \,\pi^{\frac{5}{2}}}{72 c^{3}}"," ",0,"1/8*a*x*(Pi*c^2*x^2+Pi)^(7/2)/Pi/c^2-1/48*a/c^2*x*(Pi*c^2*x^2+Pi)^(5/2)-5/192*a/c^2*Pi*x*(Pi*c^2*x^2+Pi)^(3/2)-5/128*a/c^2*Pi^2*x*(Pi*c^2*x^2+Pi)^(1/2)-5/128*a/c^2*Pi^3*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/8*b*Pi^(5/2)*c^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^7-1/64*b*c^5*Pi^(5/2)*x^8+17/48*b*Pi^(5/2)*c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^5-17/288*b*c^3*Pi^(5/2)*x^6+59/192*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-59/768*b*c*Pi^(5/2)*x^4+5/128*b*Pi^(5/2)/c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-5/256*b*Pi^(5/2)*x^2/c-5/256*b*Pi^(5/2)/c^3*arcsinh(c*x)^2+1/72*b*Pi^(5/2)/c^3","A"
73,1,170,73,0.072000," ","int(x*(Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x)),x)","\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{7 \pi  \,c^{2}}+\frac{b \,\pi^{\frac{5}{2}} \left(35 \arcsinh \left(c x \right) c^{8} x^{8}+140 \arcsinh \left(c x \right) c^{6} x^{6}-5 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+210 \arcsinh \left(c x \right) c^{4} x^{4}-21 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+140 \arcsinh \left(c x \right) c^{2} x^{2}-35 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+35 \arcsinh \left(c x \right)-35 c x \sqrt{c^{2} x^{2}+1}\right)}{245 c^{2} \sqrt{c^{2} x^{2}+1}}"," ",0,"1/7*a/Pi/c^2*(Pi*c^2*x^2+Pi)^(7/2)+1/245*b/c^2*Pi^(5/2)*(35*arcsinh(c*x)*c^8*x^8+140*arcsinh(c*x)*c^6*x^6-5*c^7*x^7*(c^2*x^2+1)^(1/2)+210*arcsinh(c*x)*c^4*x^4-21*c^5*x^5*(c^2*x^2+1)^(1/2)+140*arcsinh(c*x)*c^2*x^2-35*c^3*x^3*(c^2*x^2+1)^(1/2)+35*arcsinh(c*x)-35*c*x*(c^2*x^2+1)^(1/2))/(c^2*x^2+1)^(1/2)","B"
74,1,228,137,0.069000," ","int((Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x)),x)","\frac{x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}} a}{6}+\frac{5 a \pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{24}+\frac{5 a \,\pi^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{16}+\frac{5 a \,\pi^{3} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{16 \sqrt{\pi  \,c^{2}}}+\frac{b \,\pi^{\frac{5}{2}} c^{4} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{5}}{6}-\frac{b \,\pi^{\frac{5}{2}} c^{5} x^{6}}{36}+\frac{13 b \,\pi^{\frac{5}{2}} c^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{24}-\frac{13 b \,c^{3} \pi^{\frac{5}{2}} x^{4}}{96}+\frac{11 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{16}-\frac{11 b c \,\pi^{\frac{5}{2}} x^{2}}{32}+\frac{5 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{2}}{32 c}-\frac{17 b \,\pi^{\frac{5}{2}}}{72 c}"," ",0,"1/6*x*(Pi*c^2*x^2+Pi)^(5/2)*a+5/24*a*Pi*x*(Pi*c^2*x^2+Pi)^(3/2)+5/16*a*Pi^2*x*(Pi*c^2*x^2+Pi)^(1/2)+5/16*a*Pi^3*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/6*b*Pi^(5/2)*c^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^5-1/36*b*Pi^(5/2)*c^5*x^6+13/24*b*Pi^(5/2)*c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-13/96*b*c^3*Pi^(5/2)*x^4+11/16*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-11/32*b*c*Pi^(5/2)*x^2+5/32*b*Pi^(5/2)/c*arcsinh(c*x)^2-17/72*b*Pi^(5/2)/c","A"
75,1,284,179,0.357000," ","int((Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x))/x,x)","\frac{\left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}} a}{5}+\frac{a \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{3}-a \,\pi^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)+a \sqrt{\pi  \,c^{2} x^{2}+\pi}\, \pi^{2}-b \,\pi^{\frac{5}{2}} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+b \,\pi^{\frac{5}{2}} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)-\frac{b \,c^{5} \pi^{\frac{5}{2}} x^{5}}{25}-\frac{11 b \,c^{3} \pi^{\frac{5}{2}} x^{3}}{45}+\frac{23 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{15}-\frac{23 b c \,\pi^{\frac{5}{2}} x}{15}+\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{4} c^{4}}{5}+\frac{11 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2} c^{2}}{15}"," ",0,"1/5*(Pi*c^2*x^2+Pi)^(5/2)*a+1/3*a*Pi*(Pi*c^2*x^2+Pi)^(3/2)-a*Pi^(5/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+a*(Pi*c^2*x^2+Pi)^(1/2)*Pi^2-b*Pi^(5/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+b*Pi^(5/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-b*Pi^(5/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+b*Pi^(5/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-1/25*b*c^5*Pi^(5/2)*x^5-11/45*b*c^3*Pi^(5/2)*x^3+23/15*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-23/15*b*c*Pi^(5/2)*x+1/5*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4*c^4+11/15*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2*c^2","A"
76,1,283,133,0.294000," ","int((Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x))/x^2,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{\pi  x}+a \,c^{2} x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}+\frac{5 a \,c^{2} \pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{4}+\frac{15 a \,c^{2} \pi^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{8}+\frac{15 a \,c^{2} \pi^{3} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{8 \sqrt{\pi  \,c^{2}}}+\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3} c^{4}}{4}+\frac{9 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x \,c^{2}}{8}-\frac{33 b \,\pi^{\frac{5}{2}} c}{128}-\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}+b c \,\pi^{\frac{5}{2}} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)-\frac{b \,c^{5} \pi^{\frac{5}{2}} x^{4}}{16}-\frac{9 b \,c^{3} \pi^{\frac{5}{2}} x^{2}}{16}+\frac{15 b c \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{2}}{16}-b c \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right)"," ",0,"-a/Pi/x*(Pi*c^2*x^2+Pi)^(7/2)+a*c^2*x*(Pi*c^2*x^2+Pi)^(5/2)+5/4*a*c^2*Pi*x*(Pi*c^2*x^2+Pi)^(3/2)+15/8*a*c^2*Pi^2*x*(Pi*c^2*x^2+Pi)^(1/2)+15/8*a*c^2*Pi^3*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/4*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3*c^4+9/8*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x*c^2-33/128*b*Pi^(5/2)*c-b*Pi^(5/2)*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)+b*c*Pi^(5/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)-1/16*b*c^5*Pi^(5/2)*x^4-9/16*b*c^3*Pi^(5/2)*x^2+15/16*b*c*Pi^(5/2)*arcsinh(c*x)^2-b*c*Pi^(5/2)*arcsinh(c*x)","B"
77,1,356,199,0.623000," ","int((Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x))/x^3,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{2 \pi  \,x^{2}}+\frac{a \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{2}+\frac{5 a \,c^{2} \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{6}-\frac{5 a \,c^{2} \pi^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{2}+\frac{5 a \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}\, \pi^{2}}{2}+\frac{5 b \,c^{2} \pi^{\frac{5}{2}} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{2}-\frac{5 b \,c^{2} \pi^{\frac{5}{2}} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{2}-\frac{b \,c^{5} \pi^{\frac{5}{2}} x^{3}}{9}-\frac{7 b \,c^{3} \pi^{\frac{5}{2}} x}{3}-\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2} c^{4}}{3}-\frac{b c \,\pi^{\frac{5}{2}}}{2 x}-\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right)}{2 \sqrt{c^{2} x^{2}+1}\, x^{2}}+\frac{7 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2}}{3}+\frac{5 b \,c^{2} \pi^{\frac{5}{2}} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{2}-\frac{5 b \,c^{2} \pi^{\frac{5}{2}} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2}"," ",0,"-1/2*a/Pi/x^2*(Pi*c^2*x^2+Pi)^(7/2)+1/2*a*c^2*(Pi*c^2*x^2+Pi)^(5/2)+5/6*a*c^2*Pi*(Pi*c^2*x^2+Pi)^(3/2)-5/2*a*c^2*Pi^(5/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+5/2*a*c^2*(Pi*c^2*x^2+Pi)^(1/2)*Pi^2+5/2*b*c^2*Pi^(5/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-5/2*b*c^2*Pi^(5/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-1/9*b*c^5*Pi^(5/2)*x^3-7/3*b*c^3*Pi^(5/2)*x-1/2*b*Pi^(5/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^2+1/3*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2*c^4-1/2*b*c*Pi^(5/2)/x-1/2*b*Pi^(5/2)/(c^2*x^2+1)^(1/2)/x^2*arcsinh(c*x)+7/3*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2+5/2*b*c^2*Pi^(5/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-5/2*b*c^2*Pi^(5/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
78,1,692,138,0.351000," ","int((Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x))/x^4,x)","-\frac{a \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{3 \pi  \,x^{3}}-\frac{4 a \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{7}{2}}}{3 \pi  x}+\frac{4 a \,c^{4} x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{3}+\frac{5 a \,c^{4} \pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{3}+\frac{5 a \,c^{4} \pi^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{2}+\frac{5 a \,c^{4} \pi^{3} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 \sqrt{\pi  \,c^{2}}}-\frac{147 b \,\pi^{\frac{5}{2}} x^{3} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{6}}{63 c^{4} x^{4}+15 c^{2} x^{2}+1}-\frac{56 b \,\pi^{\frac{5}{2}} x \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4}}{63 c^{4} x^{4}+15 c^{2} x^{2}+1}-\frac{22 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) x}-\frac{b \,c^{5} \pi^{\frac{5}{2}} x^{2}}{4}+\frac{7 b \,c^{3} \pi^{\frac{5}{2}} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{3}-\frac{b \,\pi^{\frac{5}{2}} c^{3}}{8}+\frac{49 b \,\pi^{\frac{5}{2}} x^{4} c^{7}}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right)}+\frac{5 b \,c^{3} \pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{2}}{4}-\frac{14 b \,c^{3} \pi^{\frac{5}{2}} \arcsinh \left(c x \right)}{3}+\frac{147 b \,\pi^{\frac{5}{2}} x^{4} \arcsinh \left(c x \right) c^{7}}{63 c^{4} x^{4}+15 c^{2} x^{2}+1}-\frac{49 b \,\pi^{\frac{5}{2}} x^{2} \left(c^{2} x^{2}+1\right) c^{5}}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right)}+\frac{35 b \,\pi^{\frac{5}{2}} x^{2} \arcsinh \left(c x \right) c^{5}}{63 c^{4} x^{4}+15 c^{2} x^{2}+1}-\frac{7 b \,\pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right) c^{3}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right)}+\frac{7 b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) c^{3}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right)}-\frac{b \,\pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right) c}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) x^{2}}-\frac{b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) x^{3}}+\frac{b \arcsinh \left(c x \right) \pi^{\frac{5}{2}} \sqrt{c^{2} x^{2}+1}\, x \,c^{4}}{2}"," ",0,"-1/3*a/Pi/x^3*(Pi*c^2*x^2+Pi)^(7/2)-4/3*a*c^2/Pi/x*(Pi*c^2*x^2+Pi)^(7/2)+4/3*a*c^4*x*(Pi*c^2*x^2+Pi)^(5/2)+5/3*a*c^4*Pi*x*(Pi*c^2*x^2+Pi)^(3/2)+5/2*a*c^4*Pi^2*x*(Pi*c^2*x^2+Pi)^(1/2)+5/2*a*c^4*Pi^3*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)-147*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^6-56*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4-22/3*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)/x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2-1/4*b*c^5*Pi^(5/2)*x^2+7/3*b*c^3*Pi^(5/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)-1/8*b*Pi^(5/2)*c^3+49/6*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*x^4*c^7+5/4*b*c^3*Pi^(5/2)*arcsinh(c*x)^2-14/3*b*c^3*Pi^(5/2)*arcsinh(c*x)+147*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*x^4*arcsinh(c*x)*c^7-49/6*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*x^2*(c^2*x^2+1)*c^5+35*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*x^2*arcsinh(c*x)*c^5-7/3*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*(c^2*x^2+1)*c^3+7/3*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)*arcsinh(c*x)*c^3-1/6*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)/x^2*(c^2*x^2+1)*c-1/3*b*Pi^(5/2)/(63*c^4*x^4+15*c^2*x^2+1)/x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+1/2*b*arcsinh(c*x)*Pi^(5/2)*(c^2*x^2+1)^(1/2)*x*c^4","B"
79,1,26,24,0.037000," ","int(arcsinh(x)*(x^2+1)^(1/2),x)","\frac{x \arcsinh \left(x \right) \sqrt{x^{2}+1}}{2}+\frac{\arcsinh \left(x \right)^{2}}{4}-\frac{x^{2}}{4}-\frac{1}{4}"," ",0,"1/2*x*arcsinh(x)*(x^2+1)^(1/2)+1/4*arcsinh(x)^2-1/4*x^2-1/4","A"
80,1,193,125,0.122000," ","int(x^5*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(1/2),x)","a \left(\frac{x^{4} \sqrt{\pi  \,c^{2} x^{2}+\pi}}{5 \pi  \,c^{2}}-\frac{4 \left(\frac{x^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}{3 \pi  \,c^{2}}-\frac{2 \sqrt{\pi  \,c^{2} x^{2}+\pi}}{3 \pi  \,c^{4}}\right)}{5 c^{2}}\right)+\frac{b \left(45 \arcsinh \left(c x \right) c^{6} x^{6}-15 \arcsinh \left(c x \right) c^{4} x^{4}-9 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+60 \arcsinh \left(c x \right) c^{2} x^{2}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+120 \arcsinh \left(c x \right)-120 c x \sqrt{c^{2} x^{2}+1}\right)}{225 c^{6} \sqrt{\pi}\, \sqrt{c^{2} x^{2}+1}}"," ",0,"a*(1/5*x^4/Pi/c^2*(Pi*c^2*x^2+Pi)^(1/2)-4/5/c^2*(1/3*x^2/Pi/c^2*(Pi*c^2*x^2+Pi)^(1/2)-2/3/Pi/c^4*(Pi*c^2*x^2+Pi)^(1/2)))+1/225*b/c^6/Pi^(1/2)/(c^2*x^2+1)^(1/2)*(45*arcsinh(c*x)*c^6*x^6-15*arcsinh(c*x)*c^4*x^4-9*c^5*x^5*(c^2*x^2+1)^(1/2)+60*arcsinh(c*x)*c^2*x^2+20*c^3*x^3*(c^2*x^2+1)^(1/2)+120*arcsinh(c*x)-120*c*x*(c^2*x^2+1)^(1/2))","A"
81,1,188,106,0.107000," ","int(x^4*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a \,x^{3} \sqrt{\pi  \,c^{2} x^{2}+\pi}}{4 \pi  \,c^{2}}-\frac{3 a x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{8 c^{4} \pi}+\frac{3 a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{8 c^{4} \sqrt{\pi  \,c^{2}}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{4 c^{2} \sqrt{\pi}}-\frac{b \,x^{4}}{16 c \sqrt{\pi}}-\frac{3 b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{8 c^{4} \sqrt{\pi}}+\frac{3 b \,x^{2}}{16 c^{3} \sqrt{\pi}}+\frac{3 b \arcsinh \left(c x \right)^{2}}{16 c^{5} \sqrt{\pi}}+\frac{3 b}{16 c^{5} \sqrt{\pi}}"," ",0,"1/4*a*x^3/Pi/c^2*(Pi*c^2*x^2+Pi)^(1/2)-3/8*a/c^4*x/Pi*(Pi*c^2*x^2+Pi)^(1/2)+3/8*a/c^4*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/4*b/c^2/Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-1/16*b*x^4/c/Pi^(1/2)-3/8*b/c^4/Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x+3/16*b*x^2/c^3/Pi^(1/2)+3/16*b/c^5/Pi^(1/2)*arcsinh(c*x)^2+3/16*b/c^5/Pi^(1/2)","A"
82,1,133,82,0.106000," ","int(x^3*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(1/2),x)","a \left(\frac{x^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}{3 \pi  \,c^{2}}-\frac{2 \sqrt{\pi  \,c^{2} x^{2}+\pi}}{3 \pi  \,c^{4}}\right)+\frac{b \left(3 \arcsinh \left(c x \right) c^{4} x^{4}-3 \arcsinh \left(c x \right) c^{2} x^{2}-c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-6 \arcsinh \left(c x \right)+6 c x \sqrt{c^{2} x^{2}+1}\right)}{9 c^{4} \sqrt{\pi}\, \sqrt{c^{2} x^{2}+1}}"," ",0,"a*(1/3*x^2/Pi/c^2*(Pi*c^2*x^2+Pi)^(1/2)-2/3/Pi/c^4*(Pi*c^2*x^2+Pi)^(1/2))+1/9*b/c^4/Pi^(1/2)/(c^2*x^2+1)^(1/2)*(3*arcsinh(c*x)*c^4*x^4-3*arcsinh(c*x)*c^2*x^2-c^3*x^3*(c^2*x^2+1)^(1/2)-6*arcsinh(c*x)+6*c*x*(c^2*x^2+1)^(1/2))","A"
83,1,125,63,0.068000," ","int(x^2*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{2 \pi  \,c^{2}}-\frac{a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 c^{2} \sqrt{\pi  \,c^{2}}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 c^{2} \sqrt{\pi}}-\frac{b \,x^{2}}{4 c \sqrt{\pi}}-\frac{b \arcsinh \left(c x \right)^{2}}{4 c^{3} \sqrt{\pi}}-\frac{b}{4 c^{3} \sqrt{\pi}}"," ",0,"1/2*a*x/Pi/c^2*(Pi*c^2*x^2+Pi)^(1/2)-1/2*a/c^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b/c^2/Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/4*b*x^2/c/Pi^(1/2)-1/4*b/c^3/Pi^(1/2)*arcsinh(c*x)^2-1/4*b/c^3/Pi^(1/2)","A"
84,1,72,38,0.065000," ","int(x*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a \sqrt{\pi  \,c^{2} x^{2}+\pi}}{\pi  \,c^{2}}+\frac{b \left(\arcsinh \left(c x \right) c^{2} x^{2}+\arcsinh \left(c x \right)-c x \sqrt{c^{2} x^{2}+1}\right)}{c^{2} \sqrt{\pi}\, \sqrt{c^{2} x^{2}+1}}"," ",0,"a/Pi/c^2*(Pi*c^2*x^2+Pi)^(1/2)+b/c^2/Pi^(1/2)/(c^2*x^2+1)^(1/2)*(arcsinh(c*x)*c^2*x^2+arcsinh(c*x)-c*x*(c^2*x^2+1)^(1/2))","A"
85,1,53,21,0.054000," ","int((a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{\sqrt{\pi  \,c^{2}}}+\frac{b \arcsinh \left(c x \right)^{2}}{2 c \sqrt{\pi}}"," ",0,"a*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b/c/Pi^(1/2)*arcsinh(c*x)^2","B"
86,1,72,78,0.045000," ","int((a+b*arcsinh(c*x))/x/(Pi*c^2*x^2+Pi)^(1/2),x)","-\frac{a \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{\sqrt{\pi}}+\frac{b \left(4 \dilog \left(\frac{1}{c x +\sqrt{c^{2} x^{2}+1}}\right)-\dilog \left(\frac{1}{\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}}\right)\right)}{2 \sqrt{\pi}}"," ",0,"-a/Pi^(1/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+1/2*b*(4*dilog(1/(c*x+(c^2*x^2+1)^(1/2)))-dilog(1/(c*x+(c^2*x^2+1)^(1/2))^2))/Pi^(1/2)","A"
87,1,84,37,0.091000," ","int((a+b*arcsinh(c*x))/x^2/(Pi*c^2*x^2+Pi)^(1/2),x)","-\frac{a \sqrt{\pi  \,c^{2} x^{2}+\pi}}{\pi  x}-\frac{b c \arcsinh \left(c x \right)}{\sqrt{\pi}}-\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{\sqrt{\pi}\, x}+\frac{b c \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{\sqrt{\pi}}"," ",0,"-a/Pi/x*(Pi*c^2*x^2+Pi)^(1/2)-b*c/Pi^(1/2)*arcsinh(c*x)-b/Pi^(1/2)*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)+b*c/Pi^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
88,1,225,125,0.187000," ","int((a+b*arcsinh(c*x))/x^3/(Pi*c^2*x^2+Pi)^(1/2),x)","-\frac{a \sqrt{\pi  \,c^{2} x^{2}+\pi}}{2 \pi  \,x^{2}}+\frac{a \,c^{2} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{2 \sqrt{\pi}}-\frac{b \arcsinh \left(c x \right) c^{2}}{2 \sqrt{\pi}\, \sqrt{c^{2} x^{2}+1}}-\frac{b c}{2 x \sqrt{\pi}}-\frac{b \arcsinh \left(c x \right)}{2 \sqrt{\pi}\, \sqrt{c^{2} x^{2}+1}\, x^{2}}+\frac{b \,c^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \sqrt{\pi}}+\frac{b \,c^{2} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{2 \sqrt{\pi}}-\frac{b \,c^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{2 \sqrt{\pi}}-\frac{b \,c^{2} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \sqrt{\pi}}"," ",0,"-1/2*a/Pi/x^2*(Pi*c^2*x^2+Pi)^(1/2)+1/2*a/Pi^(1/2)*c^2*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))-1/2*b/Pi^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^2-1/2*b*c/x/Pi^(1/2)-1/2*b/Pi^(1/2)/(c^2*x^2+1)^(1/2)/x^2*arcsinh(c*x)+1/2*b*c^2/Pi^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+1/2*b*c^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))/Pi^(1/2)-1/2*b*c^2/Pi^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-1/2*b*c^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))/Pi^(1/2)","A"
89,1,372,81,0.118000," ","int((a+b*arcsinh(c*x))/x^4/(Pi*c^2*x^2+Pi)^(1/2),x)","-\frac{a \sqrt{\pi  \,c^{2} x^{2}+\pi}}{3 \pi  \,x^{3}}+\frac{2 a \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}{3 \pi  x}+\frac{4 b \,c^{3} \arcsinh \left(c x \right)}{3 \sqrt{\pi}}-\frac{2 b \,x^{4} c^{7}}{3 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right)}+\frac{2 b \,x^{2} \left(c^{2} x^{2}+1\right) c^{5}}{3 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right)}-\frac{2 b \,x^{2} \arcsinh \left(c x \right) c^{5}}{\sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right)}+\frac{2 b x \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4}}{\sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right)}-\frac{2 b \left(c^{2} x^{2}+1\right) c^{3}}{3 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right)}+\frac{2 b \arcsinh \left(c x \right) c^{3}}{3 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right)}-\frac{5 b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2}}{3 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right) x}+\frac{b \left(c^{2} x^{2}+1\right) c}{6 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right) x^{2}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \sqrt{\pi}\, \left(3 c^{2} x^{2}-1\right) x^{3}}-\frac{2 b \,c^{3} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{3 \sqrt{\pi}}"," ",0,"-1/3*a/Pi/x^3*(Pi*c^2*x^2+Pi)^(1/2)+2/3*a/Pi*c^2/x*(Pi*c^2*x^2+Pi)^(1/2)+4/3*b*c^3/Pi^(1/2)*arcsinh(c*x)-2/3*b/Pi^(1/2)/(3*c^2*x^2-1)*x^4*c^7+2/3*b/Pi^(1/2)/(3*c^2*x^2-1)*x^2*(c^2*x^2+1)*c^5-2*b/Pi^(1/2)/(3*c^2*x^2-1)*x^2*arcsinh(c*x)*c^5+2*b/Pi^(1/2)/(3*c^2*x^2-1)*x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4-2/3*b/Pi^(1/2)/(3*c^2*x^2-1)*(c^2*x^2+1)*c^3+2/3*b/Pi^(1/2)/(3*c^2*x^2-1)*arcsinh(c*x)*c^3-5/3*b/Pi^(1/2)/(3*c^2*x^2-1)/x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2+1/6*b/Pi^(1/2)/(3*c^2*x^2-1)/x^2*(c^2*x^2+1)*c+1/3*b/Pi^(1/2)/(3*c^2*x^2-1)/x^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2/3*b*c^3/Pi^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
90,1,224,121,0.319000," ","int(x^5*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(3/2),x)","\frac{a \,x^{4}}{3 \pi  \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{4 a \,x^{2}}{3 c^{4} \pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{8 a}{3 c^{6} \pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{5 b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \pi^{\frac{3}{2}} c^{6}}-\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{c^{6} \pi^{\frac{3}{2}}}+\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{c^{6} \pi^{\frac{3}{2}}}-\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}\, c^{6}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \pi^{\frac{3}{2}} c^{4}}-\frac{b \,x^{3}}{9 c^{3} \pi^{\frac{3}{2}}}+\frac{5 b x}{3 c^{5} \pi^{\frac{3}{2}}}"," ",0,"1/3*a*x^4/Pi/c^2/(Pi*c^2*x^2+Pi)^(1/2)-4/3*a/c^4*x^2/Pi/(Pi*c^2*x^2+Pi)^(1/2)-8/3*a/c^6/Pi/(Pi*c^2*x^2+Pi)^(1/2)-5/3*b/Pi^(3/2)/c^6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-I*b/c^6/Pi^(3/2)*ln(c*x+(c^2*x^2+1)^(1/2)-I)+I*b/c^6/Pi^(3/2)*ln(c*x+(c^2*x^2+1)^(1/2)+I)-b/Pi^(3/2)/(c^2*x^2+1)^(1/2)/c^6*arcsinh(c*x)+1/3*b/Pi^(3/2)/c^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2-1/9*b*x^3/c^3/Pi^(3/2)+5/3*b*x/c^5/Pi^(3/2)","C"
91,1,269,113,0.327000," ","int(x^4*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(3/2),x)","\frac{a \,x^{3}}{2 \pi  \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{3 a x}{2 c^{4} \pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{3 a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 c^{4} \pi  \sqrt{\pi  \,c^{2}}}-\frac{3 b \arcsinh \left(c x \right)^{2}}{4 c^{5} \pi^{\frac{3}{2}}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 \pi^{\frac{3}{2}} c^{4}}-\frac{b \,x^{2}}{4 c^{3} \pi^{\frac{3}{2}}}+\frac{2 b \arcsinh \left(c x \right)}{c^{5} \pi^{\frac{3}{2}}}-\frac{b}{8 \pi^{\frac{3}{2}} c^{5}}-\frac{b \arcsinh \left(c x \right) x^{2}}{\pi^{\frac{3}{2}} c^{3} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right) x}{\pi^{\frac{3}{2}} c^{4} \sqrt{c^{2} x^{2}+1}}-\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} c^{5} \left(c^{2} x^{2}+1\right)}-\frac{b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{5} \pi^{\frac{3}{2}}}"," ",0,"1/2*a*x^3/Pi/c^2/(Pi*c^2*x^2+Pi)^(1/2)+3/2*a/c^4*x/Pi/(Pi*c^2*x^2+Pi)^(1/2)-3/2*a/c^4/Pi*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)-3/4*b/c^5/Pi^(3/2)*arcsinh(c*x)^2+1/2*b/Pi^(3/2)/c^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/4*b*x^2/c^3/Pi^(3/2)+2*b/c^5/Pi^(3/2)*arcsinh(c*x)-1/8*b/Pi^(3/2)/c^5-b/Pi^(3/2)*arcsinh(c*x)/c^3/(c^2*x^2+1)*x^2+b/Pi^(3/2)*arcsinh(c*x)/c^4/(c^2*x^2+1)^(1/2)*x-b/Pi^(3/2)*arcsinh(c*x)/c^5/(c^2*x^2+1)-b/c^5/Pi^(3/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
92,1,158,78,0.343000," ","int(x^3*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(3/2),x)","\frac{a \,x^{2}}{\pi  \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{2 a}{\pi  \,c^{4} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{\pi^{\frac{3}{2}} c^{4}}-\frac{b x}{c^{3} \pi^{\frac{3}{2}}}+\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}\, c^{4}}+\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{c^{4} \pi^{\frac{3}{2}}}-\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{c^{4} \pi^{\frac{3}{2}}}"," ",0,"a*x^2/Pi/c^2/(Pi*c^2*x^2+Pi)^(1/2)+2*a/Pi/c^4/(Pi*c^2*x^2+Pi)^(1/2)+b/Pi^(3/2)/c^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-b*x/c^3/Pi^(3/2)+b/Pi^(3/2)/(c^2*x^2+1)^(1/2)/c^4*arcsinh(c*x)+I*b/c^4/Pi^(3/2)*ln(c*x+(c^2*x^2+1)^(1/2)-I)-I*b/c^4/Pi^(3/2)*ln(c*x+(c^2*x^2+1)^(1/2)+I)","C"
93,1,196,70,0.158000," ","int(x^2*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(3/2),x)","-\frac{a x}{\pi  \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{\pi  \,c^{2} \sqrt{\pi  \,c^{2}}}+\frac{b \arcsinh \left(c x \right)^{2}}{2 c^{3} \pi^{\frac{3}{2}}}-\frac{2 b \arcsinh \left(c x \right)}{c^{3} \pi^{\frac{3}{2}}}+\frac{b \arcsinh \left(c x \right) x^{2}}{\pi^{\frac{3}{2}} c \left(c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right) x}{\pi^{\frac{3}{2}} c^{2} \sqrt{c^{2} x^{2}+1}}+\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} c^{3} \left(c^{2} x^{2}+1\right)}+\frac{b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{3} \pi^{\frac{3}{2}}}"," ",0,"-a*x/Pi/c^2/(Pi*c^2*x^2+Pi)^(1/2)+a/Pi/c^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b/c^3/Pi^(3/2)*arcsinh(c*x)^2-2*b/c^3/Pi^(3/2)*arcsinh(c*x)+b/Pi^(3/2)*arcsinh(c*x)/c/(c^2*x^2+1)*x^2-b/Pi^(3/2)*arcsinh(c*x)/c^2/(c^2*x^2+1)^(1/2)*x+b/Pi^(3/2)*arcsinh(c*x)/c^3/(c^2*x^2+1)+b/c^3/Pi^(3/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
94,1,103,43,0.092000," ","int(x*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(3/2),x)","-\frac{a}{\pi  \,c^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}\, c^{2}}+\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{c^{2} \pi^{\frac{3}{2}}}-\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{c^{2} \pi^{\frac{3}{2}}}"," ",0,"-a/Pi/c^2/(Pi*c^2*x^2+Pi)^(1/2)-b/Pi^(3/2)/(c^2*x^2+1)^(1/2)/c^2*arcsinh(c*x)+I*b/c^2/Pi^(3/2)*ln(c*x+(c^2*x^2+1)^(1/2)+I)-I*b/c^2/Pi^(3/2)*ln(c*x+(c^2*x^2+1)^(1/2)-I)","C"
95,1,132,45,0.082000," ","int((a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(3/2),x)","\frac{a x}{\pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{2 b \arcsinh \left(c x \right)}{c \,\pi^{\frac{3}{2}}}-\frac{b \arcsinh \left(c x \right) c \,x^{2}}{\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right)}+\frac{b \arcsinh \left(c x \right) x}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}}-\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} c \left(c^{2} x^{2}+1\right)}-\frac{b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c \,\pi^{\frac{3}{2}}}"," ",0,"a/Pi*x/(Pi*c^2*x^2+Pi)^(1/2)+2*b/c/Pi^(3/2)*arcsinh(c*x)-b/Pi^(3/2)*arcsinh(c*x)*c/(c^2*x^2+1)*x^2+b/Pi^(3/2)*arcsinh(c*x)/(c^2*x^2+1)^(1/2)*x-b/Pi^(3/2)*arcsinh(c*x)/c/(c^2*x^2+1)-b/c/Pi^(3/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
96,1,156,112,0.229000," ","int((a+b*arcsinh(c*x))/x/(Pi*c^2*x^2+Pi)^(3/2),x)","\frac{a}{\pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{a \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{\pi^{\frac{3}{2}}}+\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}}-\frac{2 b \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{3}{2}}}-\frac{b \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{3}{2}}}-\frac{b \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{3}{2}}}-\frac{b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{3}{2}}}"," ",0,"a/Pi/(Pi*c^2*x^2+Pi)^(1/2)-a/Pi^(3/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+b/Pi^(3/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-2*b/Pi^(3/2)*arctan(c*x+(c^2*x^2+1)^(1/2))-b/Pi^(3/2)*dilog(c*x+(c^2*x^2+1)^(1/2))-b/Pi^(3/2)*dilog(1+c*x+(c^2*x^2+1)^(1/2))-b/Pi^(3/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
97,1,180,85,0.148000," ","int((a+b*arcsinh(c*x))/x^2/(Pi*c^2*x^2+Pi)^(3/2),x)","-\frac{a}{\pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{2 a \,c^{2} x}{\pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{4 b c \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}}}+\frac{2 b \arcsinh \left(c x \right) x^{2} c^{3}}{\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right)}-\frac{2 b \arcsinh \left(c x \right) x \,c^{2}}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}}+\frac{2 b \arcsinh \left(c x \right) c}{\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} x \sqrt{c^{2} x^{2}+1}}+\frac{b c \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}-1\right)}{\pi^{\frac{3}{2}}}"," ",0,"-a/Pi/x/(Pi*c^2*x^2+Pi)^(1/2)-2*a/Pi*c^2*x/(Pi*c^2*x^2+Pi)^(1/2)-4*b*c/Pi^(3/2)*arcsinh(c*x)+2*b/Pi^(3/2)*arcsinh(c*x)*x^2/(c^2*x^2+1)*c^3-2*b/Pi^(3/2)*arcsinh(c*x)*x/(c^2*x^2+1)^(1/2)*c^2+2*b/Pi^(3/2)*arcsinh(c*x)/(c^2*x^2+1)*c-b/Pi^(3/2)*arcsinh(c*x)/x/(c^2*x^2+1)^(1/2)+b*c/Pi^(3/2)*ln((c*x+(c^2*x^2+1)^(1/2))^4-1)","B"
98,1,234,169,0.304000," ","int((a+b*arcsinh(c*x))/x^3/(Pi*c^2*x^2+Pi)^(3/2),x)","-\frac{a}{2 \pi  \,x^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{3 a \,c^{2}}{2 \pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{3 a \,c^{2} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{2 \pi^{\frac{3}{2}}}-\frac{3 b \arcsinh \left(c x \right) c^{2}}{2 \pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}}-\frac{b c}{2 \pi^{\frac{3}{2}} x}-\frac{b \arcsinh \left(c x \right)}{2 \pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}\, x^{2}}+\frac{2 b \,c^{2} \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{3}{2}}}+\frac{3 b \,c^{2} \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \pi^{\frac{3}{2}}}+\frac{3 b \,c^{2} \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \pi^{\frac{3}{2}}}+\frac{3 b \,c^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \pi^{\frac{3}{2}}}"," ",0,"-1/2*a/Pi/x^2/(Pi*c^2*x^2+Pi)^(1/2)-3/2*a*c^2/Pi/(Pi*c^2*x^2+Pi)^(1/2)+3/2*a*c^2/Pi^(3/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))-3/2*b/Pi^(3/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^2-1/2*b*c/Pi^(3/2)/x-1/2*b/Pi^(3/2)/(c^2*x^2+1)^(1/2)/x^2*arcsinh(c*x)+2*b*c^2/Pi^(3/2)*arctan(c*x+(c^2*x^2+1)^(1/2))+3/2*b*c^2/Pi^(3/2)*dilog(c*x+(c^2*x^2+1)^(1/2))+3/2*b*c^2/Pi^(3/2)*dilog(1+c*x+(c^2*x^2+1)^(1/2))+3/2*b*c^2/Pi^(3/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
99,1,601,132,0.324000," ","int((a+b*arcsinh(c*x))/x^4/(Pi*c^2*x^2+Pi)^(3/2),x)","-\frac{a}{3 \pi  \,x^{3} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{4 a \,c^{2}}{3 \pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{8 a \,c^{4} x}{3 \pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{16 b \,c^{3} \arcsinh \left(c x \right)}{3 \pi^{\frac{3}{2}}}-\frac{32 b \,x^{8} c^{11}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{32 b \,x^{6} c^{9}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right)}-\frac{64 b \,x^{6} c^{9}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{32 b \,x^{4} c^{7}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right)}-\frac{64 b \,x^{4} \arcsinh \left(c x \right) c^{7}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{64 b \,x^{3} \arcsinh \left(c x \right) c^{6}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \sqrt{c^{2} x^{2}+1}}-\frac{32 b \,x^{4} c^{7}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}-\frac{56 b \,x^{2} \arcsinh \left(c x \right) c^{5}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{8 b x \arcsinh \left(c x \right) c^{4}}{\pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \sqrt{c^{2} x^{2}+1}}-\frac{4 b \,c^{3}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right)}+\frac{8 b \arcsinh \left(c x \right) c^{3}}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}-\frac{4 b \arcsinh \left(c x \right) c^{2}}{\pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) x \sqrt{c^{2} x^{2}+1}}+\frac{b c}{6 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) x^{2}}+\frac{b \arcsinh \left(c x \right)}{3 \pi^{\frac{3}{2}} \left(8 c^{2} x^{2}-1\right) x^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \,c^{3} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\pi^{\frac{3}{2}}}-\frac{5 b \,c^{3} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{3 \pi^{\frac{3}{2}}}"," ",0,"-1/3*a/Pi/x^3/(Pi*c^2*x^2+Pi)^(1/2)+4/3*a*c^2/Pi/x/(Pi*c^2*x^2+Pi)^(1/2)+8/3*a*c^4/Pi*x/(Pi*c^2*x^2+Pi)^(1/2)+16/3*b*c^3/Pi^(3/2)*arcsinh(c*x)-32/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^8/(c^2*x^2+1)*c^11+32/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^6*c^9-64/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^6/(c^2*x^2+1)*c^9+32/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^4*c^7-64/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^4/(c^2*x^2+1)*arcsinh(c*x)*c^7+64/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^6-32/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^4/(c^2*x^2+1)*c^7-56/3*b/Pi^(3/2)/(8*c^2*x^2-1)*x^2/(c^2*x^2+1)*arcsinh(c*x)*c^5+8*b/Pi^(3/2)/(8*c^2*x^2-1)*x/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^4-4/3*b/Pi^(3/2)/(8*c^2*x^2-1)*c^3+8/3*b/Pi^(3/2)/(8*c^2*x^2-1)/(c^2*x^2+1)*arcsinh(c*x)*c^3-4*b/Pi^(3/2)/(8*c^2*x^2-1)/x/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^2+1/6*b/Pi^(3/2)/(8*c^2*x^2-1)/x^2*c+1/3*b/Pi^(3/2)/(8*c^2*x^2-1)/x^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-b*c^3/Pi^(3/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-5/3*b*c^3/Pi^(3/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
100,1,970,164,0.510000," ","int(x^6*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{49 b c \,x^{8}}{6 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{98 b \,x^{6}}{3 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c}-\frac{49 b \,x^{4}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c^{3}}-\frac{98 b \,x^{2}}{3 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c^{5}}+\frac{49 b \,x^{6}}{6 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right) c}+\frac{14 b \,x^{4}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right) c^{3}}+\frac{6 b \,x^{2}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right) c^{5}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 \pi^{\frac{5}{2}} c^{6}}-\frac{343 b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c^{7}}+\frac{147 b \arcsinh \left(c x \right) x^{7}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b \,x^{2}}{4 c^{5} \pi^{\frac{5}{2}}}-\frac{7 b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{7} \pi^{\frac{5}{2}}}+\frac{14 b \arcsinh \left(c x \right)}{3 c^{7} \pi^{\frac{5}{2}}}-\frac{5 b \arcsinh \left(c x \right)^{2}}{4 c^{7} \pi^{\frac{5}{2}}}+\frac{a \,x^{5}}{2 \pi  \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{1463 b \arcsinh \left(c x \right) x^{2}}{3 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c^{5}}+\frac{385 b \arcsinh \left(c x \right) x^{5}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{2}}+\frac{1009 b \arcsinh \left(c x \right) x^{3}}{3 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{4}}+\frac{98 b \arcsinh \left(c x \right) x}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{6}}-\frac{147 b c \arcsinh \left(c x \right) x^{8}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{553 b \arcsinh \left(c x \right) x^{6}}{\pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c}-\frac{2338 b \arcsinh \left(c x \right) x^{4}}{3 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c^{3}}+\frac{5 a \,x^{3}}{6 c^{4} \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{5 a x}{2 c^{6} \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{5 a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 c^{6} \pi^{2} \sqrt{\pi  \,c^{2}}}-\frac{49 b}{6 \pi^{\frac{5}{2}} \left(63 c^{4} x^{4}+111 c^{2} x^{2}+49\right) \left(c^{2} x^{2}+1\right)^{2} c^{7}}-\frac{b}{8 \pi^{\frac{5}{2}} c^{7}}"," ",0,"1/2*b/Pi^(5/2)/c^6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-49/6*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2*c*x^8-98/3*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c*x^6-49*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c^3*x^4-98/3*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c^5*x^2-343/3*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c^7*arcsinh(c*x)+49/6*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)/c*x^6+14*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)/c^3*x^4+6*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)/c^5*x^2+147*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^7-1/4*b*x^2/c^5/Pi^(5/2)+14/3*b/c^7/Pi^(5/2)*arcsinh(c*x)-5/4*b/c^7/Pi^(5/2)*arcsinh(c*x)^2-7/3*b/c^7/Pi^(5/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*a*x^5/Pi/c^2/(Pi*c^2*x^2+Pi)^(3/2)-1463/3*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c^5*arcsinh(c*x)*x^2+385*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^(3/2)/c^2*arcsinh(c*x)*x^5+1009/3*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^(3/2)/c^4*arcsinh(c*x)*x^3+98*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^(3/2)/c^6*arcsinh(c*x)*x-147*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2*c*arcsinh(c*x)*x^8-553*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c*arcsinh(c*x)*x^6-2338/3*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c^3*arcsinh(c*x)*x^4+5/6*a/c^4*x^3/Pi/(Pi*c^2*x^2+Pi)^(3/2)+5/2*a/c^6/Pi^2*x/(Pi*c^2*x^2+Pi)^(1/2)-5/2*a/c^6/Pi^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)-49/6*b/Pi^(5/2)/(63*c^4*x^4+111*c^2*x^2+49)/(c^2*x^2+1)^2/c^7-1/8*b/Pi^(5/2)/c^7","B"
101,1,231,131,0.484000," ","int(x^5*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","\frac{a \,x^{4}}{\pi  \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{4 a \,x^{2}}{c^{4} \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{8 a}{3 c^{6} \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{b \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{\pi^{\frac{5}{2}} c^{6}}-\frac{b x}{c^{5} \pi^{\frac{5}{2}}}+\frac{2 b \arcsinh \left(c x \right) x^{2}}{\pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{4}}+\frac{b x}{6 c^{5} \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)}+\frac{5 b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{6}}+\frac{11 i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{6 c^{6} \pi^{\frac{5}{2}}}-\frac{11 i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{6 c^{6} \pi^{\frac{5}{2}}}"," ",0,"a*x^4/Pi/c^2/(Pi*c^2*x^2+Pi)^(3/2)+4*a/c^4*x^2/Pi/(Pi*c^2*x^2+Pi)^(3/2)+8/3*a/c^6/Pi/(Pi*c^2*x^2+Pi)^(3/2)+b/Pi^(5/2)/c^6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-b*x/c^5/Pi^(5/2)+2*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)/c^4*arcsinh(c*x)*x^2+1/6*b*x/c^5/Pi^(5/2)/(c^2*x^2+1)+5/3*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)/c^6*arcsinh(c*x)+11/6*I*b/c^6/Pi^(5/2)*ln(c*x+(c^2*x^2+1)^(1/2)-I)-11/6*I*b/c^6/Pi^(5/2)*ln(c*x+(c^2*x^2+1)^(1/2)+I)","C"
102,1,897,121,0.355000," ","int(x^4*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{a \,x^{3}}{3 \pi  \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{a x}{\pi^{2} c^{4} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{a \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{\pi^{2} c^{4} \sqrt{\pi  \,c^{2}}}+\frac{b \arcsinh \left(c x \right)^{2}}{2 c^{5} \pi^{\frac{5}{2}}}-\frac{8 b \arcsinh \left(c x \right)}{3 c^{5} \pi^{\frac{5}{2}}}+\frac{32 b \,c^{3} \arcsinh \left(c x \right) x^{8}}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{32 b \,c^{2} \arcsinh \left(c x \right) x^{7}}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 b \,c^{3} x^{8}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{8 b c \,x^{6}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)}+\frac{116 b c \arcsinh \left(c x \right) x^{6}}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{76 b \arcsinh \left(c x \right) x^{5}}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{32 b c \,x^{6}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{4 b \,x^{4}}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right) c}+\frac{472 b \arcsinh \left(c x \right) x^{4}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2} c}-\frac{181 b \arcsinh \left(c x \right) x^{3}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{2}}+\frac{16 b \,x^{4}}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2} c}-\frac{3 b \,x^{2}}{2 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right) c^{3}}+\frac{284 b \arcsinh \left(c x \right) x^{2}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2} c^{3}}-\frac{16 b \arcsinh \left(c x \right) x}{\pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{4}}+\frac{32 b \,x^{2}}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2} c^{3}}+\frac{64 b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2} c^{5}}+\frac{8 b}{3 \pi^{\frac{5}{2}} \left(24 c^{4} x^{4}+39 c^{2} x^{2}+16\right) \left(c^{2} x^{2}+1\right)^{2} c^{5}}+\frac{4 b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{5} \pi^{\frac{5}{2}}}"," ",0,"-1/3*a*x^3/Pi/c^2/(Pi*c^2*x^2+Pi)^(3/2)-a/Pi^2/c^4*x/(Pi*c^2*x^2+Pi)^(1/2)+a/Pi^2/c^4*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b/c^5/Pi^(5/2)*arcsinh(c*x)^2-8/3*b/c^5/Pi^(5/2)*arcsinh(c*x)+32*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2*c^3*arcsinh(c*x)*x^8-32*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^(3/2)*c^2*arcsinh(c*x)*x^7+8/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2*c^3*x^8-8/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)*c*x^6+116*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2*c*arcsinh(c*x)*x^6-76*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^5+32/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2*c*x^6-4*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)/c*x^4+472/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2/c*arcsinh(c*x)*x^4-181/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^(3/2)/c^2*arcsinh(c*x)*x^3+16*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2/c*x^4-3/2*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)/c^3*x^2+284/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2/c^3*arcsinh(c*x)*x^2-16*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^(3/2)/c^4*arcsinh(c*x)*x+32/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2/c^3*x^2+64/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2/c^5*arcsinh(c*x)+8/3*b/Pi^(5/2)/(24*c^4*x^4+39*c^2*x^2+16)/(c^2*x^2+1)^2/c^5+4/3*b/c^5/Pi^(5/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
103,1,175,93,0.516000," ","int(x^3*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{a \,x^{2}}{\pi  \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{2 a}{3 \pi  \,c^{4} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{b \arcsinh \left(c x \right) x^{2}}{\pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{2}}-\frac{b x}{6 c^{3} \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)}-\frac{2 b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{4}}+\frac{5 i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{6 c^{4} \pi^{\frac{5}{2}}}-\frac{5 i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{6 c^{4} \pi^{\frac{5}{2}}}"," ",0,"-a*x^2/Pi/c^2/(Pi*c^2*x^2+Pi)^(3/2)-2/3*a/Pi/c^4/(Pi*c^2*x^2+Pi)^(3/2)-b/Pi^(5/2)/(c^2*x^2+1)^(3/2)/c^2*arcsinh(c*x)*x^2-1/6*b*x/c^3/Pi^(5/2)/(c^2*x^2+1)-2/3*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)/c^4*arcsinh(c*x)+5/6*I*b/c^4/Pi^(5/2)*ln(c*x+(c^2*x^2+1)^(1/2)+I)-5/6*I*b/c^4/Pi^(5/2)*ln(c*x+(c^2*x^2+1)^(1/2)-I)","C"
104,1,707,68,0.297000," ","int(x^2*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{a x}{3 c^{2} \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{a x}{3 c^{2} \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{2 b \arcsinh \left(c x \right)}{3 c^{3} \pi^{\frac{5}{2}}}-\frac{b \,c^{5} \arcsinh \left(c x \right) x^{8}}{\pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \,c^{4} \arcsinh \left(c x \right) x^{7}}{\pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b \,c^{5} x^{8}}{6 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \,c^{3} x^{6}}{6 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{3 b \,c^{3} \arcsinh \left(c x \right) x^{6}}{\pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \,c^{2} \arcsinh \left(c x \right) x^{5}}{\pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{2 b \,c^{3} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{10 b c \arcsinh \left(c x \right) x^{4}}{3 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \arcsinh \left(c x \right) x^{3}}{3 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b c \,x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{5 b \arcsinh \left(c x \right) x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2} c}-\frac{2 b \,x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2} c}-\frac{b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2} c^{3}}-\frac{b}{6 \pi^{\frac{5}{2}} \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)^{2} c^{3}}-\frac{b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{3} \pi^{\frac{5}{2}}}"," ",0,"-1/3*a/c^2/Pi*x/(Pi*c^2*x^2+Pi)^(3/2)+1/3*a/c^2/Pi^2*x/(Pi*c^2*x^2+Pi)^(1/2)+2/3*b/c^3/Pi^(5/2)*arcsinh(c*x)-b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2*c^5*arcsinh(c*x)*x^8+b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(3/2)*c^4*arcsinh(c*x)*x^7-1/6*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2*c^5*x^8+1/6*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)*c^3*x^6-3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2*c^3*arcsinh(c*x)*x^6+b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(3/2)*c^2*arcsinh(c*x)*x^5-2/3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2*c^3*x^6-10/3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2*c*arcsinh(c*x)*x^4+1/3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^3-b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2*c*x^4-5/3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2/c*arcsinh(c*x)*x^2-2/3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2/c*x^2-1/3*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2/c^3*arcsinh(c*x)-1/6*b/Pi^(5/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^2/c^3-1/3*b/c^3/Pi^(5/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
105,1,124,66,0.108000," ","int(x*(a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{a}{3 \pi  \,c^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{b x}{6 c \,\pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{2}}+\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{6 c^{2} \pi^{\frac{5}{2}}}-\frac{i b \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{6 c^{2} \pi^{\frac{5}{2}}}"," ",0,"-1/3*a/Pi/c^2/(Pi*c^2*x^2+Pi)^(3/2)+1/6*b*x/c/Pi^(5/2)/(c^2*x^2+1)-1/3*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)/c^2*arcsinh(c*x)+1/6*I*b/c^2/Pi^(5/2)*ln(c*x+(c^2*x^2+1)^(1/2)+I)-1/6*I*b/c^2/Pi^(5/2)*ln(c*x+(c^2*x^2+1)^(1/2)-I)","C"
106,1,618,92,0.115000," ","int((a+b*arcsinh(c*x))/(Pi*c^2*x^2+Pi)^(5/2),x)","\frac{a x}{3 \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{2 a x}{3 \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{4 b \arcsinh \left(c x \right)}{3 c \,\pi^{\frac{5}{2}}}+\frac{2 b \,c^{7} x^{8}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{2 b \,c^{5} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{2 b \,c^{5} \arcsinh \left(c x \right) x^{6}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{2 b \,c^{4} \arcsinh \left(c x \right) x^{5}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 b \,c^{5} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{2 b \,c^{3} x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{20 b \,c^{3} \arcsinh \left(c x \right) x^{4}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{17 b \,c^{2} \arcsinh \left(c x \right) x^{3}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{4 b \,c^{3} x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{3 b c \,x^{2}}{2 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{22 b c \arcsinh \left(c x \right) x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 b \arcsinh \left(c x \right) x}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 b c \,x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{8 b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{2 b}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{2 b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c \,\pi^{\frac{5}{2}}}"," ",0,"1/3*a/Pi*x/(Pi*c^2*x^2+Pi)^(3/2)+2/3*a/Pi^2*x/(Pi*c^2*x^2+Pi)^(1/2)+4/3*b/c/Pi^(5/2)*arcsinh(c*x)+2/3*b/Pi^(5/2)*c^7/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^8-2/3*b/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)*x^6-2*b/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^6+2*b/Pi^(5/2)*c^4/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^5+8/3*b/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^6-2*b/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)*x^4-20/3*b/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^4+17/3*b/Pi^(5/2)*c^2/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^3+4*b/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^4-3/2*b/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)*x^2-22/3*b/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^2+4*b/Pi^(5/2)/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x+8/3*b/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^2-8/3*b/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)+2/3*b/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2-2/3*b/c/Pi^(5/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
107,1,220,156,0.261000," ","int((a+b*arcsinh(c*x))/x/(Pi*c^2*x^2+Pi)^(5/2),x)","\frac{a}{3 \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{a}{\pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{a \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{\pi^{\frac{5}{2}}}+\frac{b \arcsinh \left(c x \right) x^{2} c^{2}}{\pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b c x}{6 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)}+\frac{4 b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{7 b \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{3 \pi^{\frac{5}{2}}}-\frac{b \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{5}{2}}}-\frac{b \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{5}{2}}}-\frac{b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\pi^{\frac{5}{2}}}"," ",0,"1/3*a/Pi/(Pi*c^2*x^2+Pi)^(3/2)+a/Pi^2/(Pi*c^2*x^2+Pi)^(1/2)-a/Pi^(5/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))+b/Pi^(5/2)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^2*c^2-1/6*b*c*x/Pi^(5/2)/(c^2*x^2+1)+4/3*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)-7/3*b/Pi^(5/2)*arctan(c*x+(c^2*x^2+1)^(1/2))-b/Pi^(5/2)*dilog(c*x+(c^2*x^2+1)^(1/2))-b/Pi^(5/2)*dilog(1+c*x+(c^2*x^2+1)^(1/2))-b/Pi^(5/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
108,1,778,132,0.293000," ","int((a+b*arcsinh(c*x))/x^2/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{a}{\pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{4 a \,c^{2} x}{3 \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{8 a \,c^{2} x}{3 \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{16 b c \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}}}+\frac{32 b \,x^{10} c^{11}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{32 b \,x^{8} c^{9}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)}+\frac{128 b \,x^{8} c^{9}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{32 b \,x^{6} c^{7}}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)}+\frac{64 b \,x^{6} \arcsinh \left(c x \right) c^{7}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{64 b \,x^{5} \arcsinh \left(c x \right) c^{6}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{64 b \,x^{6} c^{7}}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{32 b \,x^{4} c^{5}}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)}+\frac{200 b \,x^{4} \arcsinh \left(c x \right) c^{5}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{56 b \,x^{3} \arcsinh \left(c x \right) c^{4}}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{128 b \,x^{4} c^{5}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{12 b \,x^{2} c^{3}}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)}+\frac{208 b \,x^{2} \arcsinh \left(c x \right) c^{3}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{44 b x \arcsinh \left(c x \right) c^{2}}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{32 b \,x^{2} c^{3}}{3 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{3 b c}{2 \pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)}+\frac{24 b \arcsinh \left(c x \right) c}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{9 b \arcsinh \left(c x \right)}{\pi^{\frac{5}{2}} \left(8 c^{2} x^{2}+9\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} x}+\frac{5 b c \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \pi^{\frac{5}{2}}}+\frac{b c \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right)}{\pi^{\frac{5}{2}}}"," ",0,"-a/Pi/x/(Pi*c^2*x^2+Pi)^(3/2)-4/3*a*c^2/Pi*x/(Pi*c^2*x^2+Pi)^(3/2)-8/3*a*c^2/Pi^2*x/(Pi*c^2*x^2+Pi)^(1/2)-16/3*b*c/Pi^(5/2)*arcsinh(c*x)+32/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^10*c^11-32/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)*x^8*c^9+128/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^8*c^9-32*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)*x^6*c^7+64/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^6*arcsinh(c*x)*c^7-64/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^(3/2)*x^5*arcsinh(c*x)*c^6+64*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^6*c^7-32*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)*x^4*c^5+200/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^4*arcsinh(c*x)*c^5-56*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^(3/2)*x^3*arcsinh(c*x)*c^4+128/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^4*c^5-12*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)*x^2*c^3+208/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^2*arcsinh(c*x)*c^3-44*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^(3/2)*x*arcsinh(c*x)*c^2+32/3*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*x^2*c^3-3/2*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)*c+24*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^2*arcsinh(c*x)*c-9*b/Pi^(5/2)/(8*c^2*x^2+9)/(c^2*x^2+1)^(3/2)/x*arcsinh(c*x)+5/3*b*c/Pi^(5/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+b*c/Pi^(5/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)","B"
109,1,314,240,0.340000," ","int((a+b*arcsinh(c*x))/x^3/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{a}{2 \pi  \,x^{2} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{5 a \,c^{2}}{6 \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{5 a \,c^{2}}{2 \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{5 a \,c^{2} \arctanh \left(\frac{\sqrt{\pi}}{\sqrt{\pi  \,c^{2} x^{2}+\pi}}\right)}{2 \pi^{\frac{5}{2}}}-\frac{5 b \,x^{2} \arcsinh \left(c x \right) c^{4}}{2 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b \,c^{3} x}{3 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)}-\frac{10 b \arcsinh \left(c x \right) c^{2}}{3 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b c}{2 \pi^{\frac{5}{2}} x \left(c^{2} x^{2}+1\right)}-\frac{b \arcsinh \left(c x \right)}{2 \pi^{\frac{5}{2}} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} x^{2}}+\frac{13 b \,c^{2} \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{3 \pi^{\frac{5}{2}}}+\frac{5 b \,c^{2} \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \pi^{\frac{5}{2}}}+\frac{5 b \,c^{2} \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \pi^{\frac{5}{2}}}+\frac{5 b \,c^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{2 \pi^{\frac{5}{2}}}"," ",0,"-1/2*a/Pi/x^2/(Pi*c^2*x^2+Pi)^(3/2)-5/6*a*c^2/Pi/(Pi*c^2*x^2+Pi)^(3/2)-5/2*a*c^2/Pi^2/(Pi*c^2*x^2+Pi)^(1/2)+5/2*a*c^2/Pi^(5/2)*arctanh(Pi^(1/2)/(Pi*c^2*x^2+Pi)^(1/2))-5/2*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)*x^2*arcsinh(c*x)*c^4-1/3*b*c^3*x/Pi^(5/2)/(c^2*x^2+1)-10/3*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*c^2-1/2*b*c/Pi^(5/2)/x/(c^2*x^2+1)-1/2*b/Pi^(5/2)/(c^2*x^2+1)^(3/2)/x^2*arcsinh(c*x)+13/3*b*c^2/Pi^(5/2)*arctan(c*x+(c^2*x^2+1)^(1/2))+5/2*b*c^2/Pi^(5/2)*dilog(c*x+(c^2*x^2+1)^(1/2))+5/2*b*c^2/Pi^(5/2)*dilog(1+c*x+(c^2*x^2+1)^(1/2))+5/2*b*c^2/Pi^(5/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
110,1,1153,181,0.254000," ","int((a+b*arcsinh(c*x))/x^4/(Pi*c^2*x^2+Pi)^(5/2),x)","\frac{32 b \,c^{3} \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}}}-\frac{a}{3 \pi  \,x^{3} \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}-\frac{8 b \,c^{3} \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}-1\right)}{3 \pi^{\frac{5}{2}}}-\frac{64 b \,x^{8} \arcsinh \left(c x \right) c^{11}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{192 b \,x^{6} \arcsinh \left(c x \right) c^{9}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{560 b \,x^{4} \arcsinh \left(c x \right) c^{7}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{160 b \,x^{2} \arcsinh \left(c x \right) c^{5}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{160 b \,x^{5} \arcsinh \left(c x \right) c^{8}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{344 b \,x^{3} \arcsinh \left(c x \right) c^{6}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{12 b x \arcsinh \left(c x \right) c^{4}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{6 b \arcsinh \left(c x \right) c^{2}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} x}+\frac{64 b \,x^{7} \arcsinh \left(c x \right) c^{10}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{128 b \,x^{10} c^{13}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{128 b \,x^{8} c^{11}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{128 b \,x^{6} c^{9}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{128 b \,x^{4} c^{7}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}-\frac{2 b \,x^{2} c^{5}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{b c}{6 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right) x^{2}}-\frac{128 b \,x^{12} c^{15}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{512 b \,x^{10} c^{13}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{256 b \,x^{8} c^{11}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{512 b \,x^{6} c^{9}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{128 b \,x^{4} c^{7}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} x^{3}}+\frac{16 b \arcsinh \left(c x \right) c^{3}}{3 \pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{2 b \,c^{3}}{\pi^{\frac{5}{2}} \left(12 c^{4} x^{4}+12 c^{2} x^{2}-1\right) \left(c^{2} x^{2}+1\right)}+\frac{2 a \,c^{2}}{\pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{8 a \,c^{4} x}{3 \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{16 a \,c^{4} x}{3 \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}"," ",0,"-1/3*a/Pi/x^3/(Pi*c^2*x^2+Pi)^(3/2)-8/3*b*c^3/Pi^(5/2)*ln((c*x+(c^2*x^2+1)^(1/2))^4-1)+32/3*b*c^3/Pi^(5/2)*arcsinh(c*x)-64*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^8*arcsinh(c*x)*c^11-192*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^6*arcsinh(c*x)*c^9-560/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^4*arcsinh(c*x)*c^7-160/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^2*arcsinh(c*x)*c^5+160*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^(3/2)*x^5*arcsinh(c*x)*c^8+344/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^(3/2)*x^3*arcsinh(c*x)*c^6+12*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^(3/2)*x*arcsinh(c*x)*c^4-6*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^(3/2)/x*arcsinh(c*x)*c^2+64*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^(3/2)*x^7*arcsinh(c*x)*c^10+128/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)*x^10*c^13+128*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)*x^8*c^11+128*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)*x^6*c^9+128/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)*x^4*c^7-2*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)*x^2*c^5+1/6*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)/x^2*c+1/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^(3/2)/x^3*arcsinh(c*x)+16/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*arcsinh(c*x)*c^3-128/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^12*c^15-512/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^10*c^13-256*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^8*c^11-512/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^6*c^9-128/3*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)^2*x^4*c^7-2*b/Pi^(5/2)/(12*c^4*x^4+12*c^2*x^2-1)/(c^2*x^2+1)*c^3+2*a*c^2/Pi/x/(Pi*c^2*x^2+Pi)^(3/2)+8/3*a*c^4/Pi*x/(Pi*c^2*x^2+Pi)^(3/2)+16/3*a*c^4/Pi^2*x/(Pi*c^2*x^2+Pi)^(1/2)","B"
111,1,363,170,0.219000," ","int(arcsinh(a*x)/(a^2*c*x^2+c)^(7/2),x)","\frac{16 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}-8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+20 x^{3} a^{3}-16 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+15 a x -8 \sqrt{a^{2} x^{2}+1}\right) \left(-64 x^{8} a^{8}-64 \sqrt{a^{2} x^{2}+1}\, x^{7} a^{7}-280 x^{6} a^{6}-248 \sqrt{a^{2} x^{2}+1}\, x^{5} a^{5}+160 \arcsinh \left(a x \right) x^{4} a^{4}-456 x^{4} a^{4}-340 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+380 \arcsinh \left(a x \right) x^{2} a^{2}-328 a^{2} x^{2}-165 \sqrt{a^{2} x^{2}+1}\, x a +256 \arcsinh \left(a x \right)-88\right)}{60 \left(40 a^{10} x^{10}+215 x^{8} a^{8}+469 x^{6} a^{6}+517 x^{4} a^{4}+287 a^{2} x^{2}+64\right) a \,c^{4}}-\frac{8 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}"," ",0,"16/15*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*arcsinh(a*x)+1/60*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5-8*(a^2*x^2+1)^(1/2)*x^4*a^4+20*x^3*a^3-16*(a^2*x^2+1)^(1/2)*x^2*a^2+15*a*x-8*(a^2*x^2+1)^(1/2))*(-64*x^8*a^8-64*(a^2*x^2+1)^(1/2)*x^7*a^7-280*x^6*a^6-248*(a^2*x^2+1)^(1/2)*x^5*a^5+160*arcsinh(a*x)*x^4*a^4-456*x^4*a^4-340*(a^2*x^2+1)^(1/2)*x^3*a^3+380*arcsinh(a*x)*x^2*a^2-328*a^2*x^2-165*(a^2*x^2+1)^(1/2)*x*a+256*arcsinh(a*x)-88)/(40*a^10*x^10+215*a^8*x^8+469*a^6*x^6+517*a^4*x^4+287*a^2*x^2+64)/a/c^4-8/15*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)","B"
112,1,74,72,0.076000," ","int(x^4*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{4 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-x^{4} a^{4}-6 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +3 a^{2} x^{2}+3 \arcsinh \left(a x \right)^{2}+3}{16 a^{5}}"," ",0,"1/16*(4*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3-x^4*a^4-6*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+3*a^2*x^2+3*arcsinh(a*x)^2+3)/a^5","A"
113,1,82,58,0.046000," ","int(x^3*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{3 \arcsinh \left(a x \right) x^{4} a^{4}-3 \arcsinh \left(a x \right) x^{2} a^{2}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}-6 \arcsinh \left(a x \right)+6 \sqrt{a^{2} x^{2}+1}\, x a}{9 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/9/a^4*(3*arcsinh(a*x)*x^4*a^4-3*arcsinh(a*x)*x^2*a^2-(a^2*x^2+1)^(1/2)*x^3*a^3-6*arcsinh(a*x)+6*(a^2*x^2+1)^(1/2)*x*a)/(a^2*x^2+1)^(1/2)","A"
114,1,40,41,0.041000," ","int(x^2*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","-\frac{-2 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +a^{2} x^{2}+\arcsinh \left(a x \right)^{2}+1}{4 a^{3}}"," ",0,"-1/4*(-2*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+a^2*x^2+arcsinh(a*x)^2+1)/a^3","A"
115,1,47,26,0.040000," ","int(x*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right) x^{2} a^{2}+\arcsinh \left(a x \right)-\sqrt{a^{2} x^{2}+1}\, x a}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/a^2/(a^2*x^2+1)^(1/2)*(arcsinh(a*x)*x^2*a^2+arcsinh(a*x)-(a^2*x^2+1)^(1/2)*x*a)","A"
116,1,12,11,0.005000," ","int(arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{2}}{2 a}"," ",0,"1/2*arcsinh(a*x)^2/a","A"
117,1,42,62,0.056000," ","int(arcsinh(a*x)/x/(a^2*x^2+1)^(1/2),x)","2 \dilog \left(\frac{1}{a x +\sqrt{a^{2} x^{2}+1}}\right)-\frac{\dilog \left(\frac{1}{\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}}\right)}{2}"," ",0,"2*dilog(1/(a*x+(a^2*x^2+1)^(1/2)))-1/2*dilog(1/(a*x+(a^2*x^2+1)^(1/2))^2)","A"
118,1,56,25,0.082000," ","int(arcsinh(a*x)/x^2/(a^2*x^2+1)^(1/2),x)","-2 a \arcsinh \left(a x \right)+\frac{\left(a x -\sqrt{a^{2} x^{2}+1}\right) \arcsinh \left(a x \right)}{x}+a \ln \left(\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}-1\right)"," ",0,"-2*a*arcsinh(a*x)+(a*x-(a^2*x^2+1)^(1/2))/x*arcsinh(a*x)+a*ln((a*x+(a^2*x^2+1)^(1/2))^2-1)","B"
119,1,150,98,0.092000," ","int(arcsinh(a*x)/x^3/(a^2*x^2+1)^(1/2),x)","-\frac{\arcsinh \left(a x \right) x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, x a +\arcsinh \left(a x \right)}{2 \sqrt{a^{2} x^{2}+1}\, x^{2}}+\frac{a^{2} \arcsinh \left(a x \right) \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)}{2}+\frac{a^{2} \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-\frac{a^{2} \arcsinh \left(a x \right) \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-\frac{a^{2} \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)}{2}"," ",0,"-1/2/(a^2*x^2+1)^(1/2)*(arcsinh(a*x)*x^2*a^2+(a^2*x^2+1)^(1/2)*x*a+arcsinh(a*x))/x^2+1/2*a^2*arcsinh(a*x)*ln(1+a*x+(a^2*x^2+1)^(1/2))+1/2*a^2*polylog(2,-a*x-(a^2*x^2+1)^(1/2))-1/2*a^2*arcsinh(a*x)*ln(1-a*x-(a^2*x^2+1)^(1/2))-1/2*a^2*polylog(2,a*x+(a^2*x^2+1)^(1/2))","A"
120,1,578,149,0.262000," ","int(x^3*(a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x)","a \left(\frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}-\frac{2 \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}\right)+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right)}{800 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{288 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{288 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right)}{800 c^{4} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a*(1/5*x^2*(c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(c^2*d*x^2+d)^(3/2))+b*(1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))/c^4/(c^2*x^2+1)-1/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^4/(c^2*x^2+1)-1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^4/(c^2*x^2+1)-1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^4/(c^2*x^2+1)-1/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^4/(c^2*x^2+1)+1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))/c^4/(c^2*x^2+1))","B"
121,1,320,155,0.227000," ","int(x^2*(a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x)","\frac{a x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}-\frac{a x \sqrt{c^{2} d \,x^{2}+d}}{8 c^{2}}-\frac{a d \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{b \sqrt{d \left(c^{2} x^{2}+1\right)}}{128 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{16 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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)}\, c \,x^{4}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \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)}\, x^{2}}{16 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}+1\right)}"," ",0,"1/4*a*x*(c^2*d*x^2+d)^(3/2)/c^2/d-1/8*a/c^2*x*(c^2*d*x^2+d)^(1/2)-1/8*a/c^2*d*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-1/128*b*(d*(c^2*x^2+1))^(1/2)/c^3/(c^2*x^2+1)^(1/2)-1/16*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^2+1/4*b*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/16*b*(d*(c^2*x^2+1))^(1/2)*c/(c^2*x^2+1)^(1/2)*x^4+3/8*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/16*b*(d*(c^2*x^2+1))^(1/2)/c/(c^2*x^2+1)^(1/2)*x^2+1/8*b*(d*(c^2*x^2+1))^(1/2)/c^2/(c^2*x^2+1)*arcsinh(c*x)*x","B"
122,1,321,89,0.138000," ","int(x*(a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x)","\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"1/3*a/c^2/d*(c^2*d*x^2+d)^(3/2)+b*(1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^2/(c^2*x^2+1)+1/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^2/(c^2*x^2+1)+1/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^2/(c^2*x^2+1)+1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^2/(c^2*x^2+1))","B"
123,1,222,95,0.139000," ","int((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x)","\frac{a x \sqrt{c^{2} d \,x^{2}+d}}{2}+\frac{a d \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)}\, \arcsinh \left(c x \right)^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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)}\, c \,x^{2}}{4 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{2 c^{2} x^{2}+2}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}}{8 c \sqrt{c^{2} x^{2}+1}}"," ",0,"1/2*a*x*(c^2*d*x^2+d)^(1/2)+1/2*a*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)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^2+1/2*b*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)*c/(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*x-1/8*b*(d*(c^2*x^2+1))^(1/2)/c/(c^2*x^2+1)^(1/2)","B"
124,1,331,187,0.182000," ","int((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x,x)","-\sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right) a +a \sqrt{c^{2} d \,x^{2}+d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2} c^{2}}{c^{2} x^{2}+1}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c x}{\sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{2} x^{2}+1}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}"," ",0,"-d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)*a+a*(c^2*d*x^2+d)^(1/2)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*x^2*c^2-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*c*x+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-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)*polylog(2,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)*arcsinh(c*x)*ln(1+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)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))","A"
125,1,263,93,0.175000," ","int((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x^2,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{d x}+a \,c^{2} x \sqrt{c^{2} d \,x^{2}+d}+\frac{a \,c^{2} d \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} c}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{\sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2}}{c^{2} x^{2}+1}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{x \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c}{\sqrt{c^{2} x^{2}+1}}"," ",0,"-a/d/x*(c^2*d*x^2+d)^(3/2)+a*c^2*x*(c^2*d*x^2+d)^(1/2)+a*c^2*d*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)*arcsinh(c*x)^2*c-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)*x/(c^2*x^2+1)*c^2-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/x/(c^2*x^2+1)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c","B"
126,1,377,203,0.239000," ","int((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x^3,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2 d \,x^{2}}-\frac{a \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right) c^{2}}{2}+\frac{a \sqrt{c^{2} d \,x^{2}+d}\, c^{2}}{2}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{2 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{2 x \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{2 x^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2*a/d/x^2*(c^2*d*x^2+d)^(3/2)-1/2*a*d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)*c^2+1/2*a*(c^2*d*x^2+d)^(1/2)*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/x/(c^2*x^2+1)^(1/2)*c-1/2*b*(d*(c^2*x^2+1))^(1/2)/x^2/(c^2*x^2+1)*arcsinh(c*x)+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2","A"
127,1,946,90,0.257000," ","int((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x^4,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 d \,x^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{8}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4} \arcsinh \left(c x \right) c^{7}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{6 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{18 c^{4} x^{4}+18 c^{2} x^{2}+6}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) c^{5}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} c^{5}}{2 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{18 c^{4} x^{4}+18 c^{2} x^{2}+6}-\frac{10 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{6 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3}}{2 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{6 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/3*a/d/x^3*(c^2*d*x^2+d)^(3/2)-2/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8+b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^7-1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8+1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3*c^6-3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6+b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-1/2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x*c^4-10/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-1/2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3-5/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)*c^2-1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*c-1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)+1/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c^3","B"
128,1,872,185,0.273000," ","int(x^3*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","a \left(\frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}-\frac{2 \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}\right)+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+7 \arcsinh \left(c x \right)\right) d}{6272 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right) d}{3200 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d}{384 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d}{384 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right) d}{3200 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+7 \arcsinh \left(c x \right)\right) d}{6272 c^{4} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a*(1/7*x^2*(c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(c^2*d*x^2+d)^(5/2))+b*(1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+7*arcsinh(c*x))*d/c^4/(c^2*x^2+1)+1/3200*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))*d/c^4/(c^2*x^2+1)-1/384*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d/c^4/(c^2*x^2+1)-3/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d/c^4/(c^2*x^2+1)-3/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d/c^4/(c^2*x^2+1)-1/384*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d/c^4/(c^2*x^2+1)+1/3200*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))*d/c^4/(c^2*x^2+1)+1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(1+7*arcsinh(c*x))*d/c^4/(c^2*x^2+1))","B"
129,1,421,218,0.296000," ","int(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","\frac{a x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6 c^{2} d}-\frac{a x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}-\frac{a d x \sqrt{c^{2} d \,x^{2}+d}}{16 c^{2}}-\frac{a \,d^{2} \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{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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^{3} x^{6}}{36 \sqrt{c^{2} x^{2}+1}}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right) x^{5}}{24 \left(c^{2} x^{2}+1\right)}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \,x^{4}}{96 \sqrt{c^{2} x^{2}+1}}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{3}}{48 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{2}}{32 c \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x}{16 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d}{32 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{2304 c^{3} \sqrt{c^{2} x^{2}+1}}"," ",0,"1/6*a*x*(c^2*d*x^2+d)^(5/2)/c^2/d-1/24*a/c^2*x*(c^2*d*x^2+d)^(3/2)-1/16*a/c^2*d*x*(c^2*d*x^2+d)^(1/2)-1/16*a/c^2*d^2*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/6*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7-1/36*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^6+11/24*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5-7/96*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*x^4+17/48*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/32*b*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)*x^2+1/16*b*(d*(c^2*x^2+1))^(1/2)*d/c^2/(c^2*x^2+1)*arcsinh(c*x)*x-1/32*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^2*d+7/2304*b*(d*(c^2*x^2+1))^(1/2)*d/c^3/(c^2*x^2+1)^(1/2)","A"
130,1,559,124,0.168000," ","int(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right) d}{800 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d}{96 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d}{96 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right) d}{800 c^{2} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"1/5*a/c^2/d*(c^2*d*x^2+d)^(5/2)+b*(1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/96*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/96*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))*d/c^2/(c^2*x^2+1))","B"
131,1,318,154,0.168000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","\frac{x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a}{4}+\frac{3 a d x \sqrt{c^{2} d \,x^{2}+d}}{8}+\frac{3 a \,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{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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)}\, d \,c^{3} x^{4}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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)}\, d c \,x^{2}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x}{8 \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d}{16 \sqrt{c^{2} x^{2}+1}\, c}-\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{128 c \sqrt{c^{2} x^{2}+1}}"," ",0,"1/4*x*(c^2*d*x^2+d)^(3/2)*a+3/8*a*d*x*(c^2*d*x^2+d)^(1/2)+3/8*a*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*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/16*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^4+7/8*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-5/16*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*x^2+5/8*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x+3/16*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^2*d-17/128*b*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)","B"
132,1,428,247,0.207000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x,x)","\frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a}{3}-a \,d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)+a \sqrt{c^{2} d \,x^{2}+d}\, d +\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{3 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\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)}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c x}{3 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{4} c^{4}}{3 c^{2} x^{2}+3}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{3}}{9 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}"," ",0,"1/3*(c^2*d*x^2+d)^(3/2)*a-a*d^(3/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+a*(c^2*d*x^2+d)^(1/2)*d+4/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d+5/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x^2*c^2-4/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)*c*x+1/3*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x^4*c^4-1/9*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)*c^3*x^3+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d","A"
133,1,392,155,0.208000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x^2,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{d x}+a \,c^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}+\frac{3 a \,c^{2} d x \sqrt{c^{2} d \,x^{2}+d}}{2}+\frac{3 a \,c^{2} d^{2} \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{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d c}{4 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right) x^{3}}{2 c^{2} x^{2}+2}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{2}}{4 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right) x}{2 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c}{8 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d}{x \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) d c}{\sqrt{c^{2} x^{2}+1}}"," ",0,"-a/d/x*(c^2*d*x^2+d)^(5/2)+a*c^2*x*(c^2*d*x^2+d)^(3/2)+3/2*a*c^2*d*x*(c^2*d*x^2+d)^(1/2)+3/2*a*c^2*d^2*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)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d*c+1/2*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^2-1/2*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x-b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/8*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)*d/x/(c^2*x^2+1)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d*c","B"
134,1,472,264,0.270000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x^3,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2 d \,x^{2}}+\frac{a \,c^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2}-\frac{3 a \,c^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2}+\frac{3 a \,c^{2} \sqrt{c^{2} d \,x^{2}+d}\, d}{2}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} d \arcsinh \left(c x \right) x^{2}}{c^{2} x^{2}+1}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} d x}{\sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} d \arcsinh \left(c x \right)}{2 c^{2} x^{2}+2}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c}{2 x \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{2 x^{2} \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{2 \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{2 \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{2 \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{2 \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2*a/d/x^2*(c^2*d*x^2+d)^(5/2)+1/2*a*c^2*(c^2*d*x^2+d)^(3/2)-3/2*a*c^2*d^(3/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+3/2*a*c^2*(c^2*d*x^2+d)^(1/2)*d+b*(d*(c^2*x^2+1))^(1/2)*c^4*d/(c^2*x^2+1)*arcsinh(c*x)*x^2-b*(d*(c^2*x^2+1))^(1/2)*c^3*d/(c^2*x^2+1)^(1/2)*x+1/2*b*(d*(c^2*x^2+1))^(1/2)*c^2*d/(c^2*x^2+1)*arcsinh(c*x)-1/2*b*(d*(c^2*x^2+1))^(1/2)*d/x/(c^2*x^2+1)^(1/2)*c-1/2*b*(d*(c^2*x^2+1))^(1/2)*d/x^2/(c^2*x^2+1)*arcsinh(c*x)+3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2*d+3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2*d-3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2*d-3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2*d","A"
135,1,1107,160,0.260000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x^4,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3 d \,x^{3}}-\frac{2 a \,c^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3 d x}+\frac{2 a \,c^{4} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}+a \,c^{4} d x \sqrt{c^{2} d \,x^{2}+d}+\frac{a \,c^{4} d^{2} \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} d \,c^{3}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d \,c^{3}}{3 \sqrt{c^{2} x^{2}+1}}-\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{5} \arcsinh \left(c x \right) c^{8}}{\left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{4} \arcsinh \left(c x \right) c^{7}}{\left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{5} c^{8}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{3} c^{6}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right)}-\frac{52 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{3} \arcsinh \left(c x \right) c^{6}}{\left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{12 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{2} \arcsinh \left(c x \right) c^{5}}{\left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{10 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{3} c^{6}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{2} c^{5}}{\left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d x \,c^{4}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right)}-\frac{73 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d x \arcsinh \left(c x \right) c^{4}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) c^{3}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d x \,c^{4}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3}}{2 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{14 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) c^{2}}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c}{6 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) x^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{3 \left(24 c^{4} x^{4}+9 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}+1\right)}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) d \,c^{3}}{3 \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/3*a/d/x^3*(c^2*d*x^2+d)^(5/2)-2/3*a*c^2/d/x*(c^2*d*x^2+d)^(5/2)+2/3*a*c^4*x*(c^2*d*x^2+d)^(3/2)+a*c^4*d*x*(c^2*d*x^2+d)^(1/2)+a*c^4*d^2*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)*arcsinh(c*x)^2*d*c^3-8/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*d*c^3-32*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8+32*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^7-8/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8+8/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3*c^6-52*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6+12*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-10/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-4*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+2/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x*c^4-73/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4+4/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-2/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-3/2*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3-14/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)*c^2-1/6*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*c-1/3*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)+4/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d*c^3","B"
136,1,996,228,0.279000," ","int(x^3*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","a \left(\frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}-\frac{2 \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}\right)+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(256 c^{10} x^{10}+256 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+704 c^{8} x^{8}+576 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+688 c^{6} x^{6}+432 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+280 c^{4} x^{4}+120 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+41 c^{2} x^{2}+9 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+9 \arcsinh \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+7 \arcsinh \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+7 \arcsinh \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(256 c^{10} x^{10}-256 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+704 c^{8} x^{8}-576 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+688 c^{6} x^{6}-432 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+280 c^{4} x^{4}-120 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+41 c^{2} x^{2}-9 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+9 \arcsinh \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a*(1/9*x^2*(c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(c^2*d*x^2+d)^(7/2))+b*(1/41472*(d*(c^2*x^2+1))^(1/2)*(256*c^10*x^10+256*c^9*x^9*(c^2*x^2+1)^(1/2)+704*c^8*x^8+576*c^7*x^7*(c^2*x^2+1)^(1/2)+688*c^6*x^6+432*c^5*x^5*(c^2*x^2+1)^(1/2)+280*c^4*x^4+120*c^3*x^3*(c^2*x^2+1)^(1/2)+41*c^2*x^2+9*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+9*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)+3/25088*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+7*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-1/576*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-3/256*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-3/256*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-1/576*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)+3/25088*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(1+7*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)+1/41472*(d*(c^2*x^2+1))^(1/2)*(256*c^10*x^10-256*c^9*x^9*(c^2*x^2+1)^(1/2)+704*c^8*x^8-576*c^7*x^7*(c^2*x^2+1)^(1/2)+688*c^6*x^6-432*c^5*x^5*(c^2*x^2+1)^(1/2)+280*c^4*x^4-120*c^3*x^3*(c^2*x^2+1)^(1/2)+41*c^2*x^2-9*c*x*(c^2*x^2+1)^(1/2)+1)*(1+9*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1))","B"
137,1,537,291,0.338000," ","int(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","\frac{a x \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 c^{2} d}-\frac{a x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{48 c^{2}}-\frac{5 a d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{192 c^{2}}-\frac{5 a \,d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{128 c^{2}}-\frac{5 a \,d^{3} \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{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2}}{256 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{359 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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^{9}}{8 c^{2} x^{2}+8}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{8}}{64 \sqrt{c^{2} x^{2}+1}}+\frac{23 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{7}}{48 \left(c^{2} x^{2}+1\right)}-\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{6}}{288 \sqrt{c^{2} x^{2}+1}}+\frac{127 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right) x^{5}}{192 \left(c^{2} x^{2}+1\right)}-\frac{59 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \,x^{4}}{768 \sqrt{c^{2} x^{2}+1}}+\frac{133 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{3}}{384 \left(c^{2} x^{2}+1\right)}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{2}}{256 c \sqrt{c^{2} x^{2}+1}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x}{128 c^{2} \left(c^{2} x^{2}+1\right)}"," ",0,"1/8*a*x*(c^2*d*x^2+d)^(7/2)/c^2/d-1/48*a/c^2*x*(c^2*d*x^2+d)^(5/2)-5/192*a/c^2*d*x*(c^2*d*x^2+d)^(3/2)-5/128*a/c^2*d^2*x*(c^2*d*x^2+d)^(1/2)-5/128*a/c^2*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-5/256*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^2*d^2+359/73728*b*(d*(c^2*x^2+1))^(1/2)*d^2/c^3/(c^2*x^2+1)^(1/2)+1/8*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^9-1/64*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^8+23/48*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7-17/288*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^6+127/192*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5-59/768*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*x^4+133/384*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-5/256*b*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)*x^2+5/128*b*(d*(c^2*x^2+1))^(1/2)*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x","A"
138,1,863,165,0.206000," ","int(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+7 \arcsinh \left(c x \right)\right) d^{2}}{6272 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right) d^{2}}{640 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right) d^{2}}{640 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+7 \arcsinh \left(c x \right)\right) d^{2}}{6272 c^{2} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"1/7*a/c^2/d*(c^2*d*x^2+d)^(7/2)+b*(1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+7*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/640*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/128*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+5/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+5/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/128*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/640*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(1+7*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1))","B"
139,1,427,218,0.209000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","\frac{x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a}{6}+\frac{5 a d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a \,d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,d^{3} \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{299 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2}}{2304 c \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}}{6 c^{2} x^{2}+6}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, 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)}\, 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)}\, 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)}\, 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)}\, d^{2} c \,x^{2}}{32 \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}{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}}{32 \sqrt{c^{2} x^{2}+1}\, c}"," ",0,"1/6*x*(c^2*d*x^2+d)^(5/2)*a+5/24*a*d*x*(c^2*d*x^2+d)^(3/2)+5/16*a*d^2*x*(c^2*d*x^2+d)^(1/2)+5/16*a*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-299/2304*b*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)+1/6*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^7-1/36*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^6+17/24*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5-13/96*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^4+59/48*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-11/32*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*x^2+11/16*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x+5/32*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^2*d^2","A"
140,1,540,317,0.248000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x,x)","\frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a}{5}+\frac{a d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-a \,d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)+a \sqrt{c^{2} d \,x^{2}+d}\, d^{2}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{6} c^{6}}{5 c^{2} x^{2}+5}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{5}}{25 \sqrt{c^{2} x^{2}+1}}+\frac{14 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{4} c^{4}}{15 \left(c^{2} x^{2}+1\right)}-\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{3}}{45 \sqrt{c^{2} x^{2}+1}}+\frac{34 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{2} c^{2}}{15 \left(c^{2} x^{2}+1\right)}-\frac{23 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c x}{15 \sqrt{c^{2} x^{2}+1}}+\frac{23 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)}{15 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}"," ",0,"1/5*(c^2*d*x^2+d)^(5/2)*a+1/3*a*d*(c^2*d*x^2+d)^(3/2)-a*d^(5/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+a*(c^2*d*x^2+d)^(1/2)*d^2+1/5*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^6*c^6-1/25*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*c^5*x^5+14/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^4*c^4-11/45*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*c^3*x^3+34/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2*c^2-23/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*c*x+23/15*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2","A"
141,1,506,225,0.241000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x^2,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{d x}+a \,c^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}+\frac{5 a \,c^{2} d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{15 a \,c^{2} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{8}+\frac{15 a \,c^{2} d^{3} \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{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}+\frac{15 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2} c}{16 \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^{5}}{4 c^{2} x^{2}+4}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{4}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}+1\right)}-\frac{9 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{2}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right) x}{8 c^{2} x^{2}+8}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d^{2}}{x \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}-\frac{33 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c}{128 \sqrt{c^{2} x^{2}+1}}"," ",0,"-a/d/x*(c^2*d*x^2+d)^(7/2)+a*c^2*x*(c^2*d*x^2+d)^(5/2)+5/4*a*c^2*d*x*(c^2*d*x^2+d)^(3/2)+15/8*a*c^2*d^2*x*(c^2*d*x^2+d)^(1/2)+15/8*a*c^2*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*d^2*c+15/16*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d^2*c+1/4*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/16*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^4+11/8*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^3-9/16*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^2+1/8*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)*d^2/x/(c^2*x^2+1)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d^2*c-33/128*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)","B"
142,1,588,337,0.302000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x^3,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{2 d \,x^{2}}+\frac{a \,c^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2}+\frac{5 a \,c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6}-\frac{5 a \,c^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2}+\frac{5 a \,c^{2} \sqrt{c^{2} d \,x^{2}+d}\, d^{2}}{2}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{11 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} d^{2} \arcsinh \left(c x \right)}{6 \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)}{2 x^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{6} d^{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)}\, c^{5} d^{2} x^{3}}{9 \sqrt{c^{2} x^{2}+1}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} d^{2} \arcsinh \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}+1\right)}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} d^{2} x}{3 \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c}{2 x \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2*a/d/x^2*(c^2*d*x^2+d)^(7/2)+1/2*a*c^2*(c^2*d*x^2+d)^(5/2)+5/6*a*c^2*d*(c^2*d*x^2+d)^(3/2)-5/2*a*c^2*d^(5/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+5/2*a*c^2*(c^2*d*x^2+d)^(1/2)*d^2+5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2*d^2-5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2*d^2+5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2*d^2-5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2*d^2+11/6*b*(d*(c^2*x^2+1))^(1/2)*c^2*d^2/(c^2*x^2+1)*arcsinh(c*x)-1/2*b*(d*(c^2*x^2+1))^(1/2)*d^2/x^2/(c^2*x^2+1)*arcsinh(c*x)+1/3*b*(d*(c^2*x^2+1))^(1/2)*c^6*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-1/9*b*(d*(c^2*x^2+1))^(1/2)*c^5*d^2/(c^2*x^2+1)^(1/2)*x^3+8/3*b*(d*(c^2*x^2+1))^(1/2)*c^4*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2-7/3*b*(d*(c^2*x^2+1))^(1/2)*c^3*d^2/(c^2*x^2+1)^(1/2)*x-1/2*b*(d*(c^2*x^2+1))^(1/2)*d^2/x/(c^2*x^2+1)^(1/2)*c","A"
143,1,1316,230,0.303000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x^4,x)","-\frac{a \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{3 d \,x^{3}}+\frac{4 a \,c^{4} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3}-\frac{4 a \,c^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{3 d x}+\frac{147 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{4} \arcsinh \left(c x \right) c^{7}}{\left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{35 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{2} \arcsinh \left(c x \right) c^{5}}{\left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{147 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{5} \arcsinh \left(c x \right) c^{8}}{\left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{203 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{3} \arcsinh \left(c x \right) c^{6}}{\left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{190 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x \arcsinh \left(c x \right) c^{4}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{23 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) c^{2}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{3} \arcsinh \left(c x \right) c^{6}}{2 c^{2} x^{2}+2}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x \arcsinh \left(c x \right) c^{4}}{2 c^{2} x^{2}+2}+\frac{5 a \,c^{4} d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}+\frac{5 a \,c^{4} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{2}+\frac{5 a \,c^{4} d^{3} \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)}\, d^{2} c^{3}}{8 \sqrt{c^{2} x^{2}+1}}-\frac{49 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{5} c^{8}}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{28 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{3} c^{6}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x \,c^{4}}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{21 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{2} c^{5}}{2 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) x^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}+1\right)}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) c^{3}}{3 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3}}{2 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{2}}{4 \sqrt{c^{2} x^{2}+1}}+\frac{49 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{3} c^{6}}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right)}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x \,c^{4}}{6 \left(63 c^{4} x^{4}+15 c^{2} x^{2}+1\right)}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) d^{2} c^{3}}{3 \sqrt{c^{2} x^{2}+1}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2} c^{3}}{4 \sqrt{c^{2} x^{2}+1}}-\frac{14 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d^{2} c^{3}}{3 \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/3*a/d/x^3*(c^2*d*x^2+d)^(7/2)+4/3*a*c^4*x*(c^2*d*x^2+d)^(5/2)-4/3*a*c^2/d/x*(c^2*d*x^2+d)^(7/2)+5/3*a*c^4*d*x*(c^2*d*x^2+d)^(3/2)+5/2*a*c^4*d^2*x*(c^2*d*x^2+d)^(1/2)+5/2*a*c^4*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-1/8*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)+147*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^7+35*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-147*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8-203*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-190/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-23/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)*c^2-1/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)+1/2*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^3+1/2*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x-49/6*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-28/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-7/6*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-21/2*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5-1/6*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*c+7/3*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-5/2*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3-1/4*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^2+49/6*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3*c^6+7/6*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x*c^4+5/4*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d^2*c^3+7/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d^2*c^3-14/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*d^2*c^3","B"
144,1,26,24,0.000000," ","int(arcsinh(x)*(x^2+1)^(1/2),x)","\frac{x \arcsinh \left(x \right) \sqrt{x^{2}+1}}{2}+\frac{\arcsinh \left(x \right)^{2}}{4}-\frac{x^{2}}{4}-\frac{1}{4}"," ",0,"1/2*x*arcsinh(x)*(x^2+1)^(1/2)+1/4*arcsinh(x)^2-1/4*x^2-1/4","A"
145,1,625,185,0.291000," ","int(x^5*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","a \left(\frac{x^{4} \sqrt{c^{2} d \,x^{2}+d}}{5 c^{2} d}-\frac{4 \left(\frac{x^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)}{5 c^{2}}\right)+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}+1\right)}-\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}+1\right)}-\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a*(1/5*x^4/c^2/d*(c^2*d*x^2+d)^(1/2)-4/5/c^2*(1/3*x^2/c^2/d*(c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(c^2*d*x^2+d)^(1/2)))+b*(1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))/c^6/d/(c^2*x^2+1)-5/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^6/d/(c^2*x^2+1)+5/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^6/d/(c^2*x^2+1)+5/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^6/d/(c^2*x^2+1)-5/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^6/d/(c^2*x^2+1)+1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))/c^6/d/(c^2*x^2+1))","B"
146,1,347,166,0.337000," ","int(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","\frac{a \,x^{3} \sqrt{c^{2} d \,x^{2}+d}}{4 c^{2} d}-\frac{3 a x \sqrt{c^{2} d \,x^{2}+d}}{8 c^{4} d}+\frac{3 a \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{8 c^{4} \sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{5}}{4 d \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4}}{16 c d \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{8 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{16 c^{3} d \sqrt{c^{2} x^{2}+1}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{8 c^{4} d \left(c^{2} x^{2}+1\right)}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{16 \sqrt{c^{2} x^{2}+1}\, c^{5} d}+\frac{15 b \sqrt{d \left(c^{2} x^{2}+1\right)}}{128 c^{5} d \sqrt{c^{2} x^{2}+1}}"," ",0,"1/4*a*x^3/c^2/d*(c^2*d*x^2+d)^(1/2)-3/8*a/c^4*x/d*(c^2*d*x^2+d)^(1/2)+3/8*a/c^4*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)/d/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/16*b*(d*(c^2*x^2+1))^(1/2)/c/d/(c^2*x^2+1)^(1/2)*x^4-1/8*b*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x^3+3/16*b*(d*(c^2*x^2+1))^(1/2)/c^3/d/(c^2*x^2+1)^(1/2)*x^2-3/8*b*(d*(c^2*x^2+1))^(1/2)/c^4/d/(c^2*x^2+1)*arcsinh(c*x)*x+3/16*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d*arcsinh(c*x)^2+15/128*b*(d*(c^2*x^2+1))^(1/2)/c^5/d/(c^2*x^2+1)^(1/2)","B"
147,1,358,122,0.234000," ","int(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","a \left(\frac{x^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a*(1/3*x^2/c^2/d*(c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(c^2*d*x^2+d)^(1/2))+b*(1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^4/d/(c^2*x^2+1)-3/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^4/d/(c^2*x^2+1)-3/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^4/d/(c^2*x^2+1)+1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^4/d/(c^2*x^2+1))","B"
148,1,247,103,0.250000," ","int(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","\frac{a x \sqrt{c^{2} d \,x^{2}+d}}{2 c^{2} d}-\frac{a \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{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c^{3} d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \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)}\, x^{2}}{4 c d \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{2 c^{2} d \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}}{8 c^{3} d \sqrt{c^{2} x^{2}+1}}"," ",0,"1/2*a*x/c^2/d*(c^2*d*x^2+d)^(1/2)-1/2*a/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)-1/4*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d*arcsinh(c*x)^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)/c/d/(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x-1/8*b*(d*(c^2*x^2+1))^(1/2)/c^3/d/(c^2*x^2+1)^(1/2)","B"
149,1,148,58,0.117000," ","int(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","\frac{a \sqrt{c^{2} d \,x^{2}+d}}{c^{2} d}+b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a/c^2/d*(c^2*d*x^2+d)^(1/2)+b*(1/2*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^2/d/(c^2*x^2+1)+1/2*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^2/d/(c^2*x^2+1))","B"
150,1,77,41,0.047000," ","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"
151,1,234,138,0.162000," ","int((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^(1/2),x)","-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{\sqrt{d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-a/d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1-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)/d*polylog(2,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)/d*arcsinh(c*x)*ln(1+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)/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))","A"
152,1,183,57,0.171000," ","int((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{c^{2} d \,x^{2}+d}}{d x}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}+1\right) d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(c^{2} x^{2}+1\right) d x}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c}{\sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-a/d/x*(c^2*d*x^2+d)^(1/2)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*c-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d*x*c^2-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d/x+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c","B"
153,1,380,205,0.326000," ","int((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{c^{2} d \,x^{2}+d}}{2 d \,x^{2}}+\frac{a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2 \sqrt{d}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{2 d \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{2 x d \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{2 x^{2} d \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-1/2*a/d/x^2*(c^2*d*x^2+d)^(1/2)+1/2*a*c^2/d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)-1/2*b*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/x/d/(c^2*x^2+1)^(1/2)*c-1/2*b*(d*(c^2*x^2+1))^(1/2)/x^2/d/(c^2*x^2+1)*arcsinh(c*x)-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2","A"
154,1,791,121,0.277000," ","int((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{c^{2} d \,x^{2}+d}}{3 d \,x^{3}}+\frac{2 a \,c^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 d x}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{2 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d x}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{6 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d \,x^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d \,x^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-1/3*a/d/x^3*(c^2*d*x^2+d)^(1/2)+2/3*a*c^2/d/x*(c^2*d*x^2+d)^(1/2)+4/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*c^3+2/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^5*c^8-2/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*(c^2*x^2+1)*c^6+2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*arcsinh(c*x)*c^6-2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*c^6+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*(c^2*x^2+1)*c^4+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*arcsinh(c*x)*c^4+2/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*c^4-1/2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*c^3*(c^2*x^2+1)^(1/2)-4/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x*arcsinh(c*x)*c^2+1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x^2*c*(c^2*x^2+1)^(1/2)+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x^3*arcsinh(c*x)-2/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c^3","B"
155,1,362,190,0.293000," ","int(x^5*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","\frac{a \,x^{4}}{3 c^{2} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{4 a \,x^{2}}{3 c^{4} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{8 a}{3 c^{6} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 c^{6} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}-\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{4}}{3 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{9 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{3 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{3 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}"," ",0,"1/3*a*x^4/c^2/d/(c^2*d*x^2+d)^(1/2)-4/3*a/c^4*x^2/d/(c^2*d*x^2+d)^(1/2)-8/3*a/c^6/d/(c^2*d*x^2+d)^(1/2)-8/3*b*(d*(c^2*x^2+1))^(1/2)/c^6/d^2/(c^2*x^2+1)*arcsinh(c*x)+I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*ln(c*x+(c^2*x^2+1)^(1/2)+I)-I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-I)+1/3*b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-1/9*b*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*x^3-4/3*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2+5/3*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*x","C"
156,1,366,182,0.333000," ","int(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","\frac{a \,x^{3}}{2 c^{2} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{3 a x}{2 c^{4} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{3 a \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{2 c^{4} d \sqrt{c^{2} d}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{4 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}}{8 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}"," ",0,"1/2*a*x^3/c^2/d/(c^2*d*x^2+d)^(1/2)+3/2*a/c^4*x/d/(c^2*d*x^2+d)^(1/2)-3/2*a/c^4/d*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)/(c^2*x^2+1)^(1/2)/c^5/d^2*arcsinh(c*x)^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/4*b*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*x^2+3/2*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)*x+b*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/8*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
157,1,260,124,0.225000," ","int(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","\frac{a \,x^{2}}{c^{2} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{2 a}{d \,c^{4} \sqrt{c^{2} d \,x^{2}+d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}-\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}"," ",0,"a*x^2/c^2/d/(c^2*d*x^2+d)^(1/2)+2*a/d/c^4/(c^2*d*x^2+d)^(1/2)+b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2-b*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*x+2*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)+I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-I)-I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*ln(c*x+(c^2*x^2+1)^(1/2)+I)","C"
158,1,232,116,0.251000," ","int(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","-\frac{a x}{c^{2} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{a \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}"," ",0,"-a*x/c^2/d/(c^2*d*x^2+d)^(1/2)+a/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)+1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*arcsinh(c*x)^2-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*arcsinh(c*x)-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/c^2/d^2/(c^2*x^2+1)*x+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","A"
159,1,164,66,0.140000," ","int(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","-\frac{a}{c^{2} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}-\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}"," ",0,"-a/c^2/d/(c^2*d*x^2+d)^(1/2)-b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)+I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2)+I)-I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-I)","C"
160,1,143,68,0.111000," ","int((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","\frac{a x}{d \sqrt{c^{2} d \,x^{2}+d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}\, c \,d^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c \,d^{2}}"," ",0,"a*x/d/(c^2*d*x^2+d)^(1/2)+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^2*arcsinh(c*x)+b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/d^2/(c^2*x^2+1)*x-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
161,1,274,204,0.181000," ","int((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^(3/2),x)","\frac{a}{d \sqrt{c^{2} d \,x^{2}+d}}-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{3}{2}}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{2}}"," ",0,"a/d/(c^2*d*x^2+d)^(1/2)-a/d^(3/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+b*(d*(c^2*x^2+1))^(1/2)/d^2/(c^2*x^2+1)*arcsinh(c*x)-2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arctan(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)/d^2*dilog(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)/d^2*dilog(1+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)/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
162,1,205,131,0.171000," ","int((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^(3/2),x)","-\frac{a}{d x \sqrt{c^{2} d \,x^{2}+d}}-\frac{2 a \,c^{2} x}{d \sqrt{c^{2} d \,x^{2}+d}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}+1\right) d^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(c^{2} x^{2}+1\right) d^{2} x}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}-1\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}"," ",0,"-a/d/x/(c^2*d*x^2+d)^(1/2)-2*a*c^2/d*x/(c^2*d*x^2+d)^(1/2)-2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*c-2*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d^2*x*c^2-b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d^2/x+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*ln((c*x+(c^2*x^2+1)^(1/2))^4-1)*c","A"
163,1,389,284,0.295000," ","int((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^(3/2),x)","-\frac{a}{2 d \,x^{2} \sqrt{c^{2} d \,x^{2}+d}}-\frac{3 a \,c^{2}}{2 d \sqrt{c^{2} d \,x^{2}+d}}+\frac{3 a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{3}{2}}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{2 d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{2 d^{2} \sqrt{c^{2} x^{2}+1}\, x}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{2 d^{2} \left(c^{2} x^{2}+1\right) x^{2}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d^{2}}"," ",0,"-1/2*a/d/x^2/(c^2*d*x^2+d)^(1/2)-3/2*a*c^2/d/(c^2*d*x^2+d)^(1/2)+3/2*a*c^2/d^(3/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)-3/2*b*(d*(c^2*x^2+1))^(1/2)/d^2/(c^2*x^2+1)*arcsinh(c*x)*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/d^2/(c^2*x^2+1)^(1/2)/x*c-1/2*b*(d*(c^2*x^2+1))^(1/2)/d^2/(c^2*x^2+1)/x^2*arcsinh(c*x)+2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arctan(c*x+(c^2*x^2+1)^(1/2))*c^2+3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*dilog(c*x+(c^2*x^2+1)^(1/2))*c^2+3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*dilog(1+c*x+(c^2*x^2+1)^(1/2))*c^2+3/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2","A"
164,1,965,201,0.314000," ","int((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^(3/2),x)","-\frac{a}{3 d \,x^{3} \sqrt{c^{2} d \,x^{2}+d}}+\frac{4 a \,c^{2}}{3 d x \sqrt{c^{2} d \,x^{2}+d}}+\frac{8 a \,c^{4} x}{3 d \sqrt{c^{2} d \,x^{2}+d}}+\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} c^{10}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \left(c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{6 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x^{2}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c^{3}}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}"," ",0,"-1/3*a/d/x^3/(c^2*d*x^2+d)^(1/2)+4/3*a*c^2/d/x/(c^2*d*x^2+d)^(1/2)+8/3*a*c^4/d*x/(c^2*d*x^2+d)^(1/2)+16/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*c^3+32/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^7*c^10-32/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*(c^2*x^2+1)*c^8+16*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*c^8-16/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*(c^2*x^2+1)*c^6+64/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*arcsinh(c*x)*c^6-64/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5+4*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*c^6+4/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*(c^2*x^2+1)*c^4+8*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*arcsinh(c*x)*c^4+8/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-4/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*c^4-4/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*c^3*(c^2*x^2+1)^(1/2)-4*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x*arcsinh(c*x)*c^2+1/6*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x^2*c*(c^2*x^2+1)^(1/2)+1/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x^3*arcsinh(c*x)-b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c^3-5/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c^3","B"
165,1,1607,245,0.475000," ","int(x^6*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","\frac{a \,x^{5}}{2 c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{147 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{7}}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) d^{3}}+\frac{14 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{7} d^{3}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{4 \sqrt{c^{2} x^{2}+1}\, c^{7} d^{3}}+\frac{5 a \,x^{3}}{6 c^{4} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a x}{2 c^{6} d^{2} \sqrt{c^{2} d \,x^{2}+d}}-\frac{5 a \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{2 c^{6} d^{2} \sqrt{c^{2} d}}+\frac{49 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7}}{6 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}}{8 c^{7} d^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{4 c^{5} d^{3} \sqrt{c^{2} x^{2}+1}}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{7} d^{3}}+\frac{70 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5}}{3 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{2} d^{3}}+\frac{133 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{6 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{4} d^{3}}+\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{6} d^{3}}-\frac{49 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}}{6 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{7} d^{3}}-\frac{343 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{7} d^{3}}-\frac{147 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{6}}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c \,d^{3}}-\frac{406 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{3} d^{3}}-\frac{1120 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{5} d^{3}}-\frac{49 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x^{5}}{6 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{2} d^{3}}-\frac{21 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, x^{4}}{2 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{3} d^{3}}-\frac{91 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x^{3}}{6 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{4} d^{3}}-\frac{37 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \sqrt{c^{2} x^{2}+1}}{2 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{5} d^{3}}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{6} d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{2 c^{4} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{2 c^{6} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{385 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{5}}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{2} d^{3}}+\frac{1009 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{3 \left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{4} d^{3}}+\frac{98 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{\left(63 c^{8} x^{8}+237 c^{6} x^{6}+334 c^{4} x^{4}+209 c^{2} x^{2}+49\right) c^{6} d^{3}}"," ",0,"1/2*a*x^5/c^2/d/(c^2*d*x^2+d)^(3/2)+147*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/d^3*arcsinh(c*x)*x^7+5/6*a/c^4*x^3/d/(c^2*d*x^2+d)^(3/2)+5/2*a/c^6/d^2*x/(c^2*d*x^2+d)^(1/2)-5/2*a/c^6/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)+49/6*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/d^3*x^7-1/8*b*(d*(c^2*x^2+1))^(1/2)/c^7/d^3/(c^2*x^2+1)^(1/2)-1/4*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^3/(c^2*x^2+1)^(1/2)*x^2+14/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^7/d^3*arcsinh(c*x)-7/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^7/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+70/3*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^2/d^3*x^5+133/6*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^4/d^3*x^3+7*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^6/d^3*x-49/6*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^7/d^3*(c^2*x^2+1)^(1/2)-5/4*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^7/d^3*arcsinh(c*x)^2-147*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^6-406*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4-1120/3*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^5/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2+1/2*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^3/(c^2*x^2+1)*arcsinh(c*x)*x^3+1/2*b*(d*(c^2*x^2+1))^(1/2)/c^6/d^3/(c^2*x^2+1)*arcsinh(c*x)*x-49/6*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^2/d^3*(c^2*x^2+1)*x^5+385*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^2/d^3*arcsinh(c*x)*x^5-21/2*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^3/d^3*(c^2*x^2+1)^(1/2)*x^4-91/6*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^4/d^3*(c^2*x^2+1)*x^3+1009/3*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^4/d^3*arcsinh(c*x)*x^3-37/2*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^5/d^3*x^2*(c^2*x^2+1)^(1/2)-7*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^6/d^3*(c^2*x^2+1)*x+98*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^6/d^3*arcsinh(c*x)*x-343/3*b*(d*(c^2*x^2+1))^(1/2)/(63*c^8*x^8+237*c^6*x^6+334*c^4*x^4+209*c^2*x^2+49)/c^7/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)","B"
166,1,394,189,0.283000," ","int(x^5*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","\frac{a \,x^{4}}{c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 a \,x^{2}}{c^{4} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{8 a}{3 c^{6} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}+1\right)}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{c^{5} d^{3} \sqrt{c^{2} x^{2}+1}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{6} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{6 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{5}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{6}}+\frac{11 i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{6 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}-\frac{11 i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{6 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}"," ",0,"a*x^4/c^2/d/(c^2*d*x^2+d)^(3/2)+4*a/c^4*x^2/d/(c^2*d*x^2+d)^(3/2)+8/3*a/c^6/d/(c^2*d*x^2+d)^(3/2)+b*(d*(c^2*x^2+1))^(1/2)/c^4/d^3/(c^2*x^2+1)*arcsinh(c*x)*x^2-b*(d*(c^2*x^2+1))^(1/2)/c^5/d^3/(c^2*x^2+1)^(1/2)*x+b*(d*(c^2*x^2+1))^(1/2)/c^6/d^3/(c^2*x^2+1)*arcsinh(c*x)+2*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*arcsinh(c*x)*x^2+1/6*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c^5*x+5/3*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^6*arcsinh(c*x)+11/6*I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-I)-11/6*I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*ln(c*x+(c^2*x^2+1)^(1/2)+I)","C"
167,1,1430,179,0.374000," ","int(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","-\frac{a \,x^{3}}{3 c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a x}{c^{4} d^{2} \sqrt{c^{2} d \,x^{2}+d}}+\frac{a \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{c^{4} d^{2} \sqrt{c^{2} d}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c^{5} d^{3}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{5} d^{3}}-\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{7}}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) d^{3}}+\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{6}}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) d^{3}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{7}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) d^{3}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x^{5}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) d^{3}}-\frac{76 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{5}}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) d^{3}}+\frac{84 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c \,d^{3}}-\frac{22 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) d^{3}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c \,d^{3}}+\frac{14 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x^{3}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{2} d^{3}}-\frac{181 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{2} d^{3}}+\frac{220 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{3} d^{3}}-\frac{20 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{2} d^{3}}+\frac{13 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \sqrt{c^{2} x^{2}+1}}{2 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{3} d^{3}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{4} d^{3}}-\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{4} d^{3}}+\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{5} d^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{\left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{4} d^{3}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}}{3 \left(24 c^{8} x^{8}+87 c^{6} x^{6}+118 c^{4} x^{4}+71 c^{2} x^{2}+16\right) c^{5} d^{3}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{5} d^{3}}"," ",0,"-1/3*a*x^3/c^2/d/(c^2*d*x^2+d)^(3/2)-a/c^4/d^2*x/(c^2*d*x^2+d)^(1/2)+a/c^4/d^2*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^5/d^3*arcsinh(c*x)^2-8/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*arcsinh(c*x)-32*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*arcsinh(c*x)*x^7+32*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^6-8/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*x^7+8/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*(c^2*x^2+1)*x^5-76*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*arcsinh(c*x)*x^5+84*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4-22/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*x^5+4*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*(c^2*x^2+1)^(1/2)*x^4+14/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*(c^2*x^2+1)*x^3-181/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*arcsinh(c*x)*x^3+220/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2-20/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*x^3+13/2*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*x^2*(c^2*x^2+1)^(1/2)+2*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*(c^2*x^2+1)*x-16*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*arcsinh(c*x)*x+64/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*x+8/3*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*(c^2*x^2+1)^(1/2)+4/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
168,1,262,128,0.227000," ","int(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","-\frac{a \,x^{2}}{c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a}{3 d \,c^{4} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{6 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{5 i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{6 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}-\frac{5 i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{6 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}"," ",0,"-a*x^2/c^2/d/(c^2*d*x^2+d)^(3/2)-2/3*a/d/c^4/(c^2*d*x^2+d)^(3/2)-b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*arcsinh(c*x)*x^2-1/6*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c^3*x-2/3*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*arcsinh(c*x)+5/6*I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*ln(c*x+(c^2*x^2+1)^(1/2)+I)-5/6*I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-I)","C"
169,1,1153,103,0.277000," ","int(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","-\frac{a x}{3 c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{a x}{3 c^{2} d^{2} \sqrt{c^{2} d \,x^{2}+d}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{3} d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \arcsinh \left(c x \right) x^{7}}{\left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{6}}{\left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} x^{7}}{6 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \left(c^{2} x^{2}+1\right) x^{5}}{6 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{5}}{\left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{5}}{3 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}\, x^{4}}{2 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x^{3}}{6 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{3 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) c \,d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{6 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \sqrt{c^{2} x^{2}+1}}{2 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) c \,d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) c^{3} d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}}{6 \left(3 c^{8} x^{8}+9 c^{6} x^{6}+10 c^{4} x^{4}+5 c^{2} x^{2}+1\right) c^{3} d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{3} d^{3}}"," ",0,"-1/3*a/c^2*x/d/(c^2*d*x^2+d)^(3/2)+1/3*a/c^2/d^2*x/(c^2*d*x^2+d)^(1/2)+2/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^3*arcsinh(c*x)+b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*arcsinh(c*x)*x^7-b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^6+1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*x^7-1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*(c^2*x^2+1)*x^5+b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*arcsinh(c*x)*x^5-2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*x^5-1/2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*(c^2*x^2+1)^(1/2)*x^4-1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*(c^2*x^2+1)*x^3+1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*arcsinh(c*x)*x^3-4/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2+1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*x^3-1/2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*x^2*(c^2*x^2+1)^(1/2)-1/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-1/6*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*(c^2*x^2+1)^(1/2)-1/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
170,1,198,101,0.145000," ","int(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","-\frac{a}{3 c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{6 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}+\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{6 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}-\frac{i b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{6 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}"," ",0,"-1/3*a/c^2/d/(c^2*d*x^2+d)^(3/2)+1/6*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c*x-1/3*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*arcsinh(c*x)+1/6*I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2)+I)-1/6*I*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-I)","C"
171,1,1005,127,0.153000," ","int((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","\frac{a x}{3 d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{2 a x}{3 d^{2} \sqrt{c^{2} d \,x^{2}+d}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{6} x^{7}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \left(c^{2} x^{2}+1\right) x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \arcsinh \left(c x \right) x^{5}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \left(c^{2} x^{2}+1\right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{17 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{14 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \,x^{2} \sqrt{c^{2} x^{2}+1}}{2 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}"," ",0,"1/3*a*x/d/(c^2*d*x^2+d)^(3/2)+2/3*a/d^2*x/(c^2*d*x^2+d)^(1/2)+4/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^3*arcsinh(c*x)-2/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^6/d^3*x^7+2/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*(c^2*x^2+1)*x^5+2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*arcsinh(c*x)*x^5-2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4-7/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*x^5+5/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*(c^2*x^2+1)*x^3+17/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*arcsinh(c*x)*x^3-14/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2-8/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*x^3+1/2*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*x^2*(c^2*x^2+1)^(1/2)+b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*(c^2*x^2+1)*x+4*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*arcsinh(c*x)*x-8/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*x+2/3*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*(c^2*x^2+1)^(1/2)-2/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
172,1,364,260,0.200000," ","int((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^(5/2),x)","\frac{a}{3 d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{a}{d^{2} \sqrt{c^{2} d \,x^{2}+d}}-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{5}{2}}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2} c^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c x}{6 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{7 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{3 \sqrt{c^{2} x^{2}+1}\, d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d^{3}}"," ",0,"1/3*a/d/(c^2*d*x^2+d)^(3/2)+a/d^2/(c^2*d*x^2+d)^(1/2)-a/d^(5/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2*arcsinh(c*x)*x^2*c^2-1/6*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)*c*x+4/3*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2*arcsinh(c*x)-7/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*arctan(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)/d^3*dilog(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)/d^3*dilog(1+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)/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))","A"
173,1,1257,190,0.207000," ","int((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^(5/2),x)","-\frac{a}{d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{4 a \,c^{2} x}{3 d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{8 a \,c^{2} x}{3 d^{2} \sqrt{c^{2} d \,x^{2}+d}}-\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{3 \sqrt{c^{2} x^{2}+1}\, d^{3}}-\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{9} c^{10}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} \left(c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{112 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} c^{8}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{80 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{6}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{140 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{6}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{20 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{4}}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{56 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{4}}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{136 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{24 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{4}}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} c^{3} \sqrt{c^{2} x^{2}+1}}{3 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \left(c^{2} x^{2}+1\right) c^{2}}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{44 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{2}}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}+\frac{24 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{4 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{2}}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{3 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{2 \left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3}}-\frac{9 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(8 c^{6} x^{6}+25 c^{4} x^{4}+26 c^{2} x^{2}+9\right) d^{3} x}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c}{3 \sqrt{c^{2} x^{2}+1}\, d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{3}}"," ",0,"-a/d/x/(c^2*d*x^2+d)^(3/2)-4/3*a*c^2*x/d/(c^2*d*x^2+d)^(3/2)-8/3*a*c^2/d^2*x/(c^2*d*x^2+d)^(1/2)-16/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*arcsinh(c*x)*c-32/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^9*c^10+32/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*(c^2*x^2+1)*c^8-112/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*c^8+80/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*(c^2*x^2+1)*c^6-64/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*arcsinh(c*x)*c^6+64/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5-140/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*c^6+20*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*(c^2*x^2+1)*c^4-56*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*arcsinh(c*x)*c^4+136/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-24*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*c^4-4/3*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*c^3*(c^2*x^2+1)^(1/2)+4*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*(c^2*x^2+1)*c^2-44*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*arcsinh(c*x)*c^2+24*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c-4*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*c^2-3/2*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*c*(c^2*x^2+1)^(1/2)-9*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3/x*arcsinh(c*x)+5/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c+b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c","B"
174,1,546,379,0.306000," ","int((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^(5/2),x)","-\frac{a}{2 d \,x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{5 a \,c^{2}}{6 d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{5 a \,c^{2}}{2 d^{2} \sqrt{c^{2} d \,x^{2}+d}}+\frac{5 a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{5}{2}}}-\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) c^{4}}{2 \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{3} \sqrt{c^{2} x^{2}+1}}{3 \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) d^{3}}-\frac{10 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{3 \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) d^{3}}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{2 \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) d^{3} x}-\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{2 \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) d^{3} x^{2}}+\frac{13 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctan \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{3 \sqrt{c^{2} x^{2}+1}\, d^{3}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d^{3}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d^{3}}+\frac{5 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d^{3}}"," ",0,"-1/2*a/d/x^2/(c^2*d*x^2+d)^(3/2)-5/6*a*c^2/d/(c^2*d*x^2+d)^(3/2)-5/2*a*c^2/d^2/(c^2*d*x^2+d)^(1/2)+5/2*a*c^2/d^(5/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)-5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^4*x^4+2*c^2*x^2+1)/d^3*x^2*arcsinh(c*x)*c^4-1/3*b*(d*(c^2*x^2+1))^(1/2)/(c^4*x^4+2*c^2*x^2+1)/d^3*x*c^3*(c^2*x^2+1)^(1/2)-10/3*b*(d*(c^2*x^2+1))^(1/2)/(c^4*x^4+2*c^2*x^2+1)/d^3*arcsinh(c*x)*c^2-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^4*x^4+2*c^2*x^2+1)/d^3/x*c*(c^2*x^2+1)^(1/2)-1/2*b*(d*(c^2*x^2+1))^(1/2)/(c^4*x^4+2*c^2*x^2+1)/d^3/x^2*arcsinh(c*x)+13/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*arctan(c*x+(c^2*x^2+1)^(1/2))*c^2+5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*dilog(c*x+(c^2*x^2+1)^(1/2))*c^2+5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*dilog(1+c*x+(c^2*x^2+1)^(1/2))*c^2+5/2*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2","A"
175,1,1790,262,0.290000," ","int((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^(5/2),x)","\frac{2 a \,c^{2}}{d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a}{3 d \,x^{3} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{176 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{6} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{9}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{128 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{7}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{128 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{9} \left(c^{2} x^{2}+1\right) c^{12}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{320 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} \left(c^{2} x^{2}+1\right) c^{10}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{80 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \left(c^{2} x^{2}+1\right) c^{8}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{40 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} c^{5} \sqrt{c^{2} x^{2}+1}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{6 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3} x^{2}}+\frac{64 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} \arcsinh \left(c x \right) c^{10}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{160 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{8}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{344 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{16 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{12 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{6 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3} x}-\frac{2 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{\left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{128 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{11} c^{14}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{448 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{9} c^{12}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{560 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} c^{10}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{280 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}+\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3}}-\frac{8 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{3}}+\frac{32 b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{3}}+\frac{b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(12 c^{8} x^{8}+36 c^{6} x^{6}+35 c^{4} x^{4}+10 c^{2} x^{2}-1\right) d^{3} x^{3}}+\frac{16 a \,c^{4} x}{3 d^{2} \sqrt{c^{2} d \,x^{2}+d}}+\frac{8 a \,c^{4} x}{3 d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}"," ",0,"32/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*arcsinh(c*x)*c^3+2*a*c^2/d/x/(c^2*d*x^2+d)^(3/2)-1/3*a/d/x^3/(c^2*d*x^2+d)^(3/2)-64*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^9-128*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^7-176/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5-128/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*(c^2*x^2+1)*c^12-320/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*(c^2*x^2+1)*c^10+64*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*arcsinh(c*x)*c^10-80*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*(c^2*x^2+1)*c^8+160*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*arcsinh(c*x)*c^8-40/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*(c^2*x^2+1)*c^6+344/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*arcsinh(c*x)*c^6-2*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*c^5*(c^2*x^2+1)^(1/2)+16/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3+8/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*(c^2*x^2+1)*c^4+12*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*arcsinh(c*x)*c^4-6*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x*arcsinh(c*x)*c^2+1/6*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x^2*c*(c^2*x^2+1)^(1/2)-2*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*c^3*(c^2*x^2+1)^(1/2)+128/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^11*c^14+448/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*c^12+560/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*c^10+280/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*c^8+32/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*c^6-8/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*c^4+1/3*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x^3*arcsinh(c*x)-8/3*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^3*ln((c*x+(c^2*x^2+1)^(1/2))^4-1)*c^3+16/3*a*c^4/d^2*x/(c^2*d*x^2+d)^(1/2)+8/3*a*c^4*x/d/(c^2*d*x^2+d)^(3/2)","B"
176,1,363,170,0.002000," ","int(arcsinh(a*x)/(a^2*c*x^2+c)^(7/2),x)","\frac{16 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}-8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+20 x^{3} a^{3}-16 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+15 a x -8 \sqrt{a^{2} x^{2}+1}\right) \left(-64 x^{8} a^{8}-64 \sqrt{a^{2} x^{2}+1}\, x^{7} a^{7}-280 x^{6} a^{6}-248 \sqrt{a^{2} x^{2}+1}\, x^{5} a^{5}+160 \arcsinh \left(a x \right) x^{4} a^{4}-456 x^{4} a^{4}-340 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+380 \arcsinh \left(a x \right) x^{2} a^{2}-328 a^{2} x^{2}-165 \sqrt{a^{2} x^{2}+1}\, x a +256 \arcsinh \left(a x \right)-88\right)}{60 \left(40 a^{10} x^{10}+215 x^{8} a^{8}+469 x^{6} a^{6}+517 x^{4} a^{4}+287 a^{2} x^{2}+64\right) a \,c^{4}}-\frac{8 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}"," ",0,"16/15*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*arcsinh(a*x)+1/60*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5-8*(a^2*x^2+1)^(1/2)*x^4*a^4+20*x^3*a^3-16*(a^2*x^2+1)^(1/2)*x^2*a^2+15*a*x-8*(a^2*x^2+1)^(1/2))*(-64*x^8*a^8-64*(a^2*x^2+1)^(1/2)*x^7*a^7-280*x^6*a^6-248*(a^2*x^2+1)^(1/2)*x^5*a^5+160*arcsinh(a*x)*x^4*a^4-456*x^4*a^4-340*(a^2*x^2+1)^(1/2)*x^3*a^3+380*arcsinh(a*x)*x^2*a^2-328*a^2*x^2-165*(a^2*x^2+1)^(1/2)*x*a+256*arcsinh(a*x)-88)/(40*a^10*x^10+215*a^8*x^8+469*a^6*x^6+517*a^4*x^4+287*a^2*x^2+64)/a/c^4-8/15*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)","B"
177,1,74,72,0.002000," ","int(x^4*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{4 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-x^{4} a^{4}-6 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +3 a^{2} x^{2}+3 \arcsinh \left(a x \right)^{2}+3}{16 a^{5}}"," ",0,"1/16*(4*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3-x^4*a^4-6*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+3*a^2*x^2+3*arcsinh(a*x)^2+3)/a^5","A"
178,1,82,58,0.001000," ","int(x^3*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{3 \arcsinh \left(a x \right) x^{4} a^{4}-3 \arcsinh \left(a x \right) x^{2} a^{2}-\sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}-6 \arcsinh \left(a x \right)+6 \sqrt{a^{2} x^{2}+1}\, x a}{9 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/9/a^4*(3*arcsinh(a*x)*x^4*a^4-3*arcsinh(a*x)*x^2*a^2-(a^2*x^2+1)^(1/2)*x^3*a^3-6*arcsinh(a*x)+6*(a^2*x^2+1)^(1/2)*x*a)/(a^2*x^2+1)^(1/2)","A"
179,1,40,41,0.000000," ","int(x^2*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","-\frac{-2 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +a^{2} x^{2}+\arcsinh \left(a x \right)^{2}+1}{4 a^{3}}"," ",0,"-1/4*(-2*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+a^2*x^2+arcsinh(a*x)^2+1)/a^3","A"
180,1,47,26,0.000000," ","int(x*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right) x^{2} a^{2}+\arcsinh \left(a x \right)-\sqrt{a^{2} x^{2}+1}\, x a}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/a^2/(a^2*x^2+1)^(1/2)*(arcsinh(a*x)*x^2*a^2+arcsinh(a*x)-(a^2*x^2+1)^(1/2)*x*a)","A"
181,1,12,11,0.001000," ","int(arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{2}}{2 a}"," ",0,"1/2*arcsinh(a*x)^2/a","A"
182,1,42,62,0.000000," ","int(arcsinh(a*x)/x/(a^2*x^2+1)^(1/2),x)","2 \dilog \left(\frac{1}{a x +\sqrt{a^{2} x^{2}+1}}\right)-\frac{\dilog \left(\frac{1}{\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}}\right)}{2}"," ",0,"2*dilog(1/(a*x+(a^2*x^2+1)^(1/2)))-1/2*dilog(1/(a*x+(a^2*x^2+1)^(1/2))^2)","A"
183,1,56,25,0.000000," ","int(arcsinh(a*x)/x^2/(a^2*x^2+1)^(1/2),x)","-2 a \arcsinh \left(a x \right)+\frac{\left(a x -\sqrt{a^{2} x^{2}+1}\right) \arcsinh \left(a x \right)}{x}+a \ln \left(\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}-1\right)"," ",0,"-2*a*arcsinh(a*x)+(a*x-(a^2*x^2+1)^(1/2))/x*arcsinh(a*x)+a*ln((a*x+(a^2*x^2+1)^(1/2))^2-1)","B"
184,1,150,98,0.000000," ","int(arcsinh(a*x)/x^3/(a^2*x^2+1)^(1/2),x)","-\frac{\arcsinh \left(a x \right) x^{2} a^{2}+\sqrt{a^{2} x^{2}+1}\, x a +\arcsinh \left(a x \right)}{2 \sqrt{a^{2} x^{2}+1}\, x^{2}}+\frac{a^{2} \arcsinh \left(a x \right) \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)}{2}+\frac{a^{2} \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-\frac{a^{2} \arcsinh \left(a x \right) \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-\frac{a^{2} \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)}{2}"," ",0,"-1/2/(a^2*x^2+1)^(1/2)*(arcsinh(a*x)*x^2*a^2+(a^2*x^2+1)^(1/2)*x*a+arcsinh(a*x))/x^2+1/2*a^2*arcsinh(a*x)*ln(1+a*x+(a^2*x^2+1)^(1/2))+1/2*a^2*polylog(2,-a*x-(a^2*x^2+1)^(1/2))-1/2*a^2*arcsinh(a*x)*ln(1-a*x-(a^2*x^2+1)^(1/2))-1/2*a^2*polylog(2,a*x+(a^2*x^2+1)^(1/2))","A"
185,-2,0,303,180.000000," ","int(x^m*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right)^{3} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x)","F"
186,-2,0,209,180.000000," ","int(x^m*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right)^{2} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x)","F"
187,-2,0,122,180.000000," ","int(x^m*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right) \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x)","F"
188,0,0,26,0.480000," ","int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)}{c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x)","F"
189,0,0,105,0.548000," ","int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)}{\left(c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x)","F"
190,0,0,188,0.607000," ","int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)}{\left(c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x)","F"
191,0,0,566,1.644000," ","int(x^m*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x)","F"
192,0,0,352,1.419000," ","int(x^m*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x)","F"
193,0,0,212,1.339000," ","int(x^m*(c^2*d*x^2+d)^(1/2)*(a+b*arcsinh(c*x)),x)","\int x^{m} \sqrt{c^{2} d \,x^{2}+d}\, \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^(1/2)*(a+b*arcsinh(c*x)),x)","F"
194,0,0,139,0.390000," ","int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)}{\sqrt{c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x)","F"
195,0,0,238,0.534000," ","int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)}{\left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x)","F"
196,0,0,352,0.539000," ","int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)}{\left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x)","F"
197,0,0,88,0.303000," ","int(x^m*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsinh \left(a x \right)}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","F"
198,1,330,247,0.059000," ","int(x^4*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x)","\frac{d \,a^{2} \left(\frac{1}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d \,b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c^{3} x^{3} \left(c^{2} x^{2}+1\right)^{2}}{7}-\frac{3 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{35}+\frac{2 \arcsinh \left(c x \right)^{2} c x}{35}+\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{35}-\frac{2 \arcsinh \left(c x \right) c^{2} x^{2} \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{49}+\frac{62 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{1225}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{3}}{343}+\frac{37384 c x}{385875}-\frac{484 c x \left(c^{2} x^{2}+1\right)^{2}}{42875}-\frac{3358 c x \left(c^{2} x^{2}+1\right)}{385875}-\frac{4 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{35}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{105}\right)+2 d a b \left(\frac{\arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{49}-\frac{19 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1225}+\frac{76 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3675}-\frac{152 \sqrt{c^{2} x^{2}+1}}{3675}\right)}{c^{5}}"," ",0,"1/c^5*(d*a^2*(1/7*c^7*x^7+1/5*c^5*x^5)+d*b^2*(1/7*arcsinh(c*x)^2*c^3*x^3*(c^2*x^2+1)^2-3/35*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2+2/35*arcsinh(c*x)^2*c*x+1/35*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-2/49*arcsinh(c*x)*c^2*x^2*(c^2*x^2+1)^(5/2)+62/1225*arcsinh(c*x)*(c^2*x^2+1)^(5/2)+2/343*c*x*(c^2*x^2+1)^3+37384/385875*c*x-484/42875*c*x*(c^2*x^2+1)^2-3358/385875*c*x*(c^2*x^2+1)-4/35*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2/105*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d*a*b*(1/7*arcsinh(c*x)*c^7*x^7+1/5*arcsinh(c*x)*c^5*x^5-1/49*c^6*x^6*(c^2*x^2+1)^(1/2)-19/1225*c^4*x^4*(c^2*x^2+1)^(1/2)+76/3675*c^2*x^2*(c^2*x^2+1)^(1/2)-152/3675*(c^2*x^2+1)^(1/2)))","A"
199,1,267,174,0.044000," ","int(x^3*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x)","\frac{d \,a^{2} \left(\frac{1}{6} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d \,b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c^{2} x^{2} \left(c^{2} x^{2}+1\right)^{2}}{6}-\frac{\arcsinh \left(c x \right)^{2} \left(c^{2} x^{2}+1\right)^{2}}{12}-\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{18}+\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{18}+\frac{\arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{12}+\frac{\arcsinh \left(c x \right)^{2}}{24}+\frac{\left(c^{2} x^{2}+1\right)^{3}}{108}-\frac{\left(c^{2} x^{2}+1\right)^{2}}{72}-\frac{c^{2} x^{2}}{24}-\frac{1}{24}\right)+2 d a b \left(\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{6}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}-\frac{c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{36}-\frac{c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{36}+\frac{c x \sqrt{c^{2} x^{2}+1}}{24}-\frac{\arcsinh \left(c x \right)}{24}\right)}{c^{4}}"," ",0,"1/c^4*(d*a^2*(1/6*c^6*x^6+1/4*c^4*x^4)+d*b^2*(1/6*arcsinh(c*x)^2*c^2*x^2*(c^2*x^2+1)^2-1/12*arcsinh(c*x)^2*(c^2*x^2+1)^2-1/18*arcsinh(c*x)*c*x*(c^2*x^2+1)^(5/2)+1/18*arcsinh(c*x)*c*x*(c^2*x^2+1)^(3/2)+1/12*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+1/24*arcsinh(c*x)^2+1/108*(c^2*x^2+1)^3-1/72*(c^2*x^2+1)^2-1/24*c^2*x^2-1/24)+2*d*a*b*(1/6*arcsinh(c*x)*c^6*x^6+1/4*arcsinh(c*x)*c^4*x^4-1/36*c^5*x^5*(c^2*x^2+1)^(1/2)-1/36*c^3*x^3*(c^2*x^2+1)^(1/2)+1/24*c*x*(c^2*x^2+1)^(1/2)-1/24*arcsinh(c*x)))","A"
200,1,248,180,0.042000," ","int(x^2*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x)","\frac{d \,a^{2} \left(\frac{1}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d \,b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{5}-\frac{2 \arcsinh \left(c x \right)^{2} c x}{15}-\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{15}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{25}-\frac{856 c x}{3375}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{2}}{125}+\frac{22 c x \left(c^{2} x^{2}+1\right)}{3375}+\frac{4 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{15}+\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{45}\right)+2 d a b \left(\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}-\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{25}-\frac{13 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{225}+\frac{26 \sqrt{c^{2} x^{2}+1}}{225}\right)}{c^{3}}"," ",0,"1/c^3*(d*a^2*(1/5*c^5*x^5+1/3*c^3*x^3)+d*b^2*(1/5*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2-2/15*arcsinh(c*x)^2*c*x-1/15*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-2/25*arcsinh(c*x)*(c^2*x^2+1)^(5/2)-856/3375*c*x+2/125*c*x*(c^2*x^2+1)^2+22/3375*c*x*(c^2*x^2+1)+4/15*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2/45*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d*a*b*(1/5*arcsinh(c*x)*c^5*x^5+1/3*arcsinh(c*x)*c^3*x^3-1/25*c^4*x^4*(c^2*x^2+1)^(1/2)-13/225*c^2*x^2*(c^2*x^2+1)^(1/2)+26/225*(c^2*x^2+1)^(1/2)))","A"
201,1,191,119,0.038000," ","int(x*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x)","\frac{d \,a^{2} \left(\frac{1}{4} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d \,b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} \left(c^{2} x^{2}+1\right)^{2}}{4}-\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{8}-\frac{3 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{16}-\frac{3 \arcsinh \left(c x \right)^{2}}{32}+\frac{\left(c^{2} x^{2}+1\right)^{2}}{32}+\frac{3 c^{2} x^{2}}{32}+\frac{3}{32}\right)+2 d a b \left(\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}+\frac{\arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{16}-\frac{5 c x \sqrt{c^{2} x^{2}+1}}{32}+\frac{5 \arcsinh \left(c x \right)}{32}\right)}{c^{2}}"," ",0,"1/c^2*(d*a^2*(1/4*c^4*x^4+1/2*c^2*x^2)+d*b^2*(1/4*arcsinh(c*x)^2*(c^2*x^2+1)^2-1/8*arcsinh(c*x)*c*x*(c^2*x^2+1)^(3/2)-3/16*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x-3/32*arcsinh(c*x)^2+1/32*(c^2*x^2+1)^2+3/32*c^2*x^2+3/32)+2*d*a*b*(1/4*arcsinh(c*x)*c^4*x^4+1/2*arcsinh(c*x)*c^2*x^2-1/16*c^3*x^3*(c^2*x^2+1)^(1/2)-5/32*c*x*(c^2*x^2+1)^(1/2)+5/32*arcsinh(c*x)))","A"
202,1,166,109,0.049000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x)","\frac{d \,a^{2} \left(\frac{1}{3} c^{3} x^{3}+c x \right)+d \,b^{2} \left(\frac{2 \arcsinh \left(c x \right)^{2} c x}{3}+\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{3}-\frac{4 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3}+\frac{40 c x}{27}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{9}+\frac{2 c x \left(c^{2} x^{2}+1\right)}{27}\right)+2 d a b \left(\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}+\arcsinh \left(c x \right) c x -\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{9}-\frac{7 \sqrt{c^{2} x^{2}+1}}{9}\right)}{c}"," ",0,"1/c*(d*a^2*(1/3*c^3*x^3+c*x)+d*b^2*(2/3*arcsinh(c*x)^2*c*x+1/3*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-4/3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+40/27*c*x-2/9*arcsinh(c*x)*(c^2*x^2+1)^(3/2)+2/27*c*x*(c^2*x^2+1))+2*d*a*b*(1/3*arcsinh(c*x)*c^3*x^3+arcsinh(c*x)*c*x-1/9*c^2*x^2*(c^2*x^2+1)^(1/2)-7/9*(c^2*x^2+1)^(1/2)))","A"
203,1,425,179,0.168000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x,x)","\frac{d \,a^{2} c^{2} x^{2}}{2}+d \,a^{2} \ln \left(c x \right)-\frac{d \,b^{2} \arcsinh \left(c x \right)^{3}}{3}+\frac{d \,b^{2} \arcsinh \left(c x \right)^{2} c^{2} x^{2}}{2}-\frac{d \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{2}+\frac{d \,b^{2} \arcsinh \left(c x \right)^{2}}{4}+\frac{b^{2} c^{2} d \,x^{2}}{4}+\frac{d \,b^{2}}{8}+d \,b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 d \,b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-2 d \,b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)+d \,b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 d \,b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-2 d \,b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)-d a b \arcsinh \left(c x \right)^{2}+d a b \arcsinh \left(c x \right) c^{2} x^{2}-\frac{d a b c x \sqrt{c^{2} x^{2}+1}}{2}+\frac{d a b \arcsinh \left(c x \right)}{2}+2 d a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 d a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+2 d a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 d a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)"," ",0,"1/2*d*a^2*c^2*x^2+d*a^2*ln(c*x)-1/3*d*b^2*arcsinh(c*x)^3+1/2*d*b^2*arcsinh(c*x)^2*c^2*x^2-1/2*d*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+1/4*d*b^2*arcsinh(c*x)^2+1/4*b^2*c^2*d*x^2+1/8*d*b^2+d*b^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*d*b^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*d*b^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+d*b^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*d*b^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*d*b^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-d*a*b*arcsinh(c*x)^2+d*a*b*arcsinh(c*x)*c^2*x^2-1/2*d*a*b*c*x*(c^2*x^2+1)^(1/2)+1/2*d*a*b*arcsinh(c*x)+2*d*a*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*d*a*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*d*a*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*d*a*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))","B"
204,1,252,157,0.181000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x^2,x)","d \,a^{2} c^{2} x -\frac{d \,a^{2}}{x}+d \,b^{2} \arcsinh \left(c x \right)^{2} c^{2} x -2 c d \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 b^{2} c^{2} d x -\frac{d \,b^{2} \arcsinh \left(c x \right)^{2}}{x}-2 c d \,b^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)-2 b^{2} c d \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+2 c d \,b^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 b^{2} c d \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+2 d a b \arcsinh \left(c x \right) c^{2} x -\frac{2 d a b \arcsinh \left(c x \right)}{x}-2 c d a b \sqrt{c^{2} x^{2}+1}-2 c d a b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)"," ",0,"d*a^2*c^2*x-d*a^2/x+d*b^2*arcsinh(c*x)^2*c^2*x-2*c*d*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*b^2*c^2*d*x-d*b^2*arcsinh(c*x)^2/x-2*c*d*b^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*b^2*c*d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*c*d*b^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2*c*d*polylog(2,c*x+(c^2*x^2+1)^(1/2))+2*d*a*b*arcsinh(c*x)*c^2*x-2*d*a*b*arcsinh(c*x)/x-2*c*d*a*b*(c^2*x^2+1)^(1/2)-2*c*d*a*b*arctanh(1/(c^2*x^2+1)^(1/2))","A"
205,1,515,197,0.371000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x^3,x)","c^{2} d \,a^{2} \ln \left(c x \right)-\frac{d \,a^{2}}{2 x^{2}}-\frac{c^{2} d \,b^{2} \arcsinh \left(c x \right)^{3}}{3}-\frac{c d \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}+c^{2} d \,b^{2} \arcsinh \left(c x \right)-\frac{d \,b^{2} \arcsinh \left(c x \right)^{2}}{2 x^{2}}-2 c^{2} d \,b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)+c^{2} d \,b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}-1\right)+c^{2} d \,b^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+c^{2} d \,b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d \,b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-2 c^{2} d \,b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)+c^{2} d \,b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d \,b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-2 c^{2} d \,b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)-c^{2} d a b \arcsinh \left(c x \right)^{2}-\frac{c d a b \sqrt{c^{2} x^{2}+1}}{x}+c^{2} d a b -\frac{d a b \arcsinh \left(c x \right)}{x^{2}}+2 c^{2} d a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)"," ",0,"c^2*d*a^2*ln(c*x)-1/2*d*a^2/x^2-1/3*c^2*d*b^2*arcsinh(c*x)^3-c*d*b^2*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)+c^2*d*b^2*arcsinh(c*x)-1/2*d*b^2*arcsinh(c*x)^2/x^2-2*c^2*d*b^2*ln(c*x+(c^2*x^2+1)^(1/2))+c^2*d*b^2*ln(c*x+(c^2*x^2+1)^(1/2)-1)+c^2*d*b^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+c^2*d*b^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*c^2*d*b^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*c^2*d*b^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+c^2*d*b^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*c^2*d*b^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*c^2*d*b^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-c^2*d*a*b*arcsinh(c*x)^2-c*d*a*b/x*(c^2*x^2+1)^(1/2)+c^2*d*a*b-d*a*b*arcsinh(c*x)/x^2+2*c^2*d*a*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*c^2*d*a*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*c^2*d*a*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*c^2*d*a*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))","B"
206,1,278,170,0.360000," ","int((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x^4,x)","-\frac{c^{2} d \,a^{2}}{x}-\frac{d \,a^{2}}{3 x^{3}}-\frac{c^{2} d \,b^{2} \arcsinh \left(c x \right)^{2}}{x}-\frac{c d \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 x^{2}}-\frac{d \,b^{2} \arcsinh \left(c x \right)^{2}}{3 x^{3}}-\frac{b^{2} c^{2} d}{3 x}-\frac{5 c^{3} d \,b^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{3}-\frac{5 b^{2} c^{3} d \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{3}+\frac{5 c^{3} d \,b^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{3}+\frac{5 b^{2} c^{3} d \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{3}-\frac{2 c^{2} d a b \arcsinh \left(c x \right)}{x}-\frac{2 d a b \arcsinh \left(c x \right)}{3 x^{3}}-\frac{5 c^{3} d a b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{3}-\frac{c d a b \sqrt{c^{2} x^{2}+1}}{3 x^{2}}"," ",0,"-c^2*d*a^2/x-1/3*d*a^2/x^3-c^2*d*b^2*arcsinh(c*x)^2/x-1/3*c*d*b^2/x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-1/3*d*b^2/x^3*arcsinh(c*x)^2-1/3*b^2*c^2*d/x-5/3*c^3*d*b^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-5/3*b^2*c^3*d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+5/3*c^3*d*b^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+5/3*b^2*c^3*d*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*c^2*d*a*b*arcsinh(c*x)/x-2/3*d*a*b*arcsinh(c*x)/x^3-5/3*c^3*d*a*b*arctanh(1/(c^2*x^2+1)^(1/2))-1/3*c*d*a*b/x^2*(c^2*x^2+1)^(1/2)","A"
207,1,428,342,0.057000," ","int(x^4*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{9} c^{9} x^{9}+\frac{2}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{2} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c^{3} x^{3} \left(c^{2} x^{2}+1\right)^{3}}{9}-\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{3}}{21}+\frac{8 \arcsinh \left(c x \right)^{2} c x}{315}+\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{105}+\frac{4 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{315}-\frac{2 \arcsinh \left(c x \right) c^{2} x^{2} \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{81}+\frac{82 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{3969}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{4}}{729}+\frac{1493104 c x}{31255875}-\frac{836 c x \left(c^{2} x^{2}+1\right)^{3}}{250047}-\frac{33862 c x \left(c^{2} x^{2}+1\right)^{2}}{10418625}-\frac{47248 c x \left(c^{2} x^{2}+1\right)}{31255875}-\frac{16 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{315}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{525}-\frac{8 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{945}\right)+2 d^{2} a b \left(\frac{\arcsinh \left(c x \right) c^{9} x^{9}}{9}+\frac{2 \arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{81}-\frac{106 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{3969}-\frac{263 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{33075}+\frac{1052 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{99225}-\frac{2104 \sqrt{c^{2} x^{2}+1}}{99225}\right)}{c^{5}}"," ",0,"1/c^5*(d^2*a^2*(1/9*c^9*x^9+2/7*c^7*x^7+1/5*c^5*x^5)+d^2*b^2*(1/9*arcsinh(c*x)^2*c^3*x^3*(c^2*x^2+1)^3-1/21*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^3+8/315*arcsinh(c*x)^2*c*x+1/105*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2+4/315*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-2/81*arcsinh(c*x)*c^2*x^2*(c^2*x^2+1)^(7/2)+82/3969*arcsinh(c*x)*(c^2*x^2+1)^(7/2)+2/729*c*x*(c^2*x^2+1)^4+1493104/31255875*c*x-836/250047*c*x*(c^2*x^2+1)^3-33862/10418625*c*x*(c^2*x^2+1)^2-47248/31255875*c*x*(c^2*x^2+1)-16/315*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2/525*arcsinh(c*x)*(c^2*x^2+1)^(5/2)-8/945*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d^2*a*b*(1/9*arcsinh(c*x)*c^9*x^9+2/7*arcsinh(c*x)*c^7*x^7+1/5*arcsinh(c*x)*c^5*x^5-1/81*c^8*x^8*(c^2*x^2+1)^(1/2)-106/3969*c^6*x^6*(c^2*x^2+1)^(1/2)-263/33075*c^4*x^4*(c^2*x^2+1)^(1/2)+1052/99225*c^2*x^2*(c^2*x^2+1)^(1/2)-2104/99225*(c^2*x^2+1)^(1/2)))","A"
208,1,344,264,0.048000," ","int(x^3*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{8} c^{8} x^{8}+\frac{1}{3} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d^{2} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c^{2} x^{2} \left(c^{2} x^{2}+1\right)^{3}}{8}-\frac{\arcsinh \left(c x \right)^{2} \left(c^{2} x^{2}+1\right)^{3}}{24}-\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{32}+\frac{11 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{576}+\frac{55 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{2304}+\frac{55 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{1536}+\frac{55 \arcsinh \left(c x \right)^{2}}{3072}+\frac{\left(c^{2} x^{2}+1\right)^{4}}{256}-\frac{11 \left(c^{2} x^{2}+1\right)^{3}}{3456}-\frac{55 \left(c^{2} x^{2}+1\right)^{2}}{9216}-\frac{55 c^{2} x^{2}}{3072}-\frac{55}{3072}\right)+2 d^{2} a b \left(\frac{\arcsinh \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{3}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}-\frac{c^{7} x^{7} \sqrt{c^{2} x^{2}+1}}{64}-\frac{43 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{1152}-\frac{73 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{4608}+\frac{73 c x \sqrt{c^{2} x^{2}+1}}{3072}-\frac{73 \arcsinh \left(c x \right)}{3072}\right)}{c^{4}}"," ",0,"1/c^4*(d^2*a^2*(1/8*c^8*x^8+1/3*c^6*x^6+1/4*c^4*x^4)+d^2*b^2*(1/8*arcsinh(c*x)^2*c^2*x^2*(c^2*x^2+1)^3-1/24*arcsinh(c*x)^2*(c^2*x^2+1)^3-1/32*arcsinh(c*x)*c*x*(c^2*x^2+1)^(7/2)+11/576*arcsinh(c*x)*c*x*(c^2*x^2+1)^(5/2)+55/2304*arcsinh(c*x)*c*x*(c^2*x^2+1)^(3/2)+55/1536*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+55/3072*arcsinh(c*x)^2+1/256*(c^2*x^2+1)^4-11/3456*(c^2*x^2+1)^3-55/9216*(c^2*x^2+1)^2-55/3072*c^2*x^2-55/3072)+2*d^2*a*b*(1/8*arcsinh(c*x)*c^8*x^8+1/3*arcsinh(c*x)*c^6*x^6+1/4*arcsinh(c*x)*c^4*x^4-1/64*c^7*x^7*(c^2*x^2+1)^(1/2)-43/1152*c^5*x^5*(c^2*x^2+1)^(1/2)-73/4608*c^3*x^3*(c^2*x^2+1)^(1/2)+73/3072*c*x*(c^2*x^2+1)^(1/2)-73/3072*arcsinh(c*x)))","A"
209,1,346,269,0.046000," ","int(x^2*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{7} c^{7} x^{7}+\frac{2}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{2} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{3}}{7}-\frac{8 \arcsinh \left(c x \right)^{2} c x}{105}-\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{35}-\frac{4 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{105}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{49}-\frac{181456 c x}{1157625}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{3}}{343}+\frac{202 c x \left(c^{2} x^{2}+1\right)^{2}}{42875}-\frac{2528 c x \left(c^{2} x^{2}+1\right)}{1157625}+\frac{16 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{105}+\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{175}+\frac{8 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{315}\right)+2 d^{2} a b \left(\frac{\arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{2 \arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}-\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{49}-\frac{68 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1225}-\frac{409 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{11025}+\frac{818 \sqrt{c^{2} x^{2}+1}}{11025}\right)}{c^{3}}"," ",0,"1/c^3*(d^2*a^2*(1/7*c^7*x^7+2/5*c^5*x^5+1/3*c^3*x^3)+d^2*b^2*(1/7*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^3-8/105*arcsinh(c*x)^2*c*x-1/35*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2-4/105*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-2/49*arcsinh(c*x)*(c^2*x^2+1)^(7/2)-181456/1157625*c*x+2/343*c*x*(c^2*x^2+1)^3+202/42875*c*x*(c^2*x^2+1)^2-2528/1157625*c*x*(c^2*x^2+1)+16/105*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2/175*arcsinh(c*x)*(c^2*x^2+1)^(5/2)+8/315*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d^2*a*b*(1/7*arcsinh(c*x)*c^7*x^7+2/5*arcsinh(c*x)*c^5*x^5+1/3*arcsinh(c*x)*c^3*x^3-1/49*c^6*x^6*(c^2*x^2+1)^(1/2)-68/1225*c^4*x^4*(c^2*x^2+1)^(1/2)-409/11025*c^2*x^2*(c^2*x^2+1)^(1/2)+818/11025*(c^2*x^2+1)^(1/2)))","A"
210,1,268,182,0.039000," ","int(x*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{6} c^{6} x^{6}+\frac{1}{2} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d^{2} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} \left(c^{2} x^{2}+1\right)^{3}}{6}-\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{18}-\frac{5 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{72}-\frac{5 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{48}-\frac{5 \arcsinh \left(c x \right)^{2}}{96}+\frac{\left(c^{2} x^{2}+1\right)^{3}}{108}+\frac{5 \left(c^{2} x^{2}+1\right)^{2}}{288}+\frac{5 c^{2} x^{2}}{96}+\frac{5}{96}\right)+2 d^{2} a b \left(\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{6}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{2}+\frac{\arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{36}-\frac{13 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{144}-\frac{11 c x \sqrt{c^{2} x^{2}+1}}{96}+\frac{11 \arcsinh \left(c x \right)}{96}\right)}{c^{2}}"," ",0,"1/c^2*(d^2*a^2*(1/6*c^6*x^6+1/2*c^4*x^4+1/2*c^2*x^2)+d^2*b^2*(1/6*arcsinh(c*x)^2*(c^2*x^2+1)^3-1/18*arcsinh(c*x)*c*x*(c^2*x^2+1)^(5/2)-5/72*arcsinh(c*x)*c*x*(c^2*x^2+1)^(3/2)-5/48*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x-5/96*arcsinh(c*x)^2+1/108*(c^2*x^2+1)^3+5/288*(c^2*x^2+1)^2+5/96*c^2*x^2+5/96)+2*d^2*a*b*(1/6*arcsinh(c*x)*c^6*x^6+1/2*arcsinh(c*x)*c^4*x^4+1/2*arcsinh(c*x)*c^2*x^2-1/36*c^5*x^5*(c^2*x^2+1)^(1/2)-13/144*c^3*x^3*(c^2*x^2+1)^(1/2)-11/96*c*x*(c^2*x^2+1)^(1/2)+11/96*arcsinh(c*x)))","A"
211,1,264,190,0.051000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{5} c^{5} x^{5}+\frac{2}{3} c^{3} x^{3}+c x \right)+d^{2} b^{2} \left(\frac{8 \arcsinh \left(c x \right)^{2} c x}{15}+\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{5}+\frac{4 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{15}-\frac{16 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{15}+\frac{4144 c x}{3375}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{25}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{2}}{125}+\frac{272 c x \left(c^{2} x^{2}+1\right)}{3375}-\frac{8 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{45}\right)+2 d^{2} a b \left(\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{2 \arcsinh \left(c x \right) c^{3} x^{3}}{3}+\arcsinh \left(c x \right) c x -\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{25}-\frac{38 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{225}-\frac{149 \sqrt{c^{2} x^{2}+1}}{225}\right)}{c}"," ",0,"1/c*(d^2*a^2*(1/5*c^5*x^5+2/3*c^3*x^3+c*x)+d^2*b^2*(8/15*arcsinh(c*x)^2*c*x+1/5*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2+4/15*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-16/15*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+4144/3375*c*x-2/25*arcsinh(c*x)*(c^2*x^2+1)^(5/2)+2/125*c*x*(c^2*x^2+1)^2+272/3375*c*x*(c^2*x^2+1)-8/45*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d^2*a*b*(1/5*arcsinh(c*x)*c^5*x^5+2/3*arcsinh(c*x)*c^3*x^3+arcsinh(c*x)*c*x-1/25*c^4*x^4*(c^2*x^2+1)^(1/2)-38/225*c^2*x^2*(c^2*x^2+1)^(1/2)-149/225*(c^2*x^2+1)^(1/2)))","A"
212,1,586,262,0.233000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x,x)","-\frac{13 d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{16}+d^{2} a^{2} c^{2} x^{2}-d^{2} a b \arcsinh \left(c x \right)^{2}+\frac{13 d^{2} a b \arcsinh \left(c x \right)}{16}+2 d^{2} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+2 d^{2} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+d^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 d^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+d^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 d^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+\frac{d^{2} a^{2} c^{4} x^{4}}{4}+\frac{13 b^{2} c^{2} d^{2} x^{2}}{32}+\frac{b^{2} c^{4} d^{2} x^{4}}{32}+\frac{49 d^{2} b^{2}}{256}+d^{2} b^{2} \arcsinh \left(c x \right)^{2} c^{2} x^{2}+2 d^{2} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 d^{2} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+\frac{d^{2} b^{2} \arcsinh \left(c x \right)^{2} c^{4} x^{4}}{4}+\frac{13 d^{2} b^{2} \arcsinh \left(c x \right)^{2}}{32}-2 d^{2} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{2} b^{2} \arcsinh \left(c x \right)^{3}}{3}-2 d^{2} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)+d^{2} a^{2} \ln \left(c x \right)-\frac{13 d^{2} a b c x \sqrt{c^{2} x^{2}+1}}{16}+2 d^{2} a b \arcsinh \left(c x \right) c^{2} x^{2}+\frac{d^{2} a b \arcsinh \left(c x \right) c^{4} x^{4}}{2}-\frac{d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3} x^{3}}{8}-\frac{d^{2} a b \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{8}"," ",0,"d^2*a^2*c^2*x^2-d^2*a*b*arcsinh(c*x)^2+13/16*d^2*a*b*arcsinh(c*x)+2*d^2*a*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))+2*d^2*a*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+d^2*b^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*d^2*b^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))+d^2*b^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*d^2*b^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+1/4*d^2*a^2*c^4*x^4+13/32*b^2*c^2*d^2*x^2+1/32*b^2*c^4*d^2*x^4+49/256*d^2*b^2+d^2*b^2*arcsinh(c*x)^2*c^2*x^2+2*d^2*a*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*d^2*a*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+1/4*d^2*b^2*arcsinh(c*x)^2*c^4*x^4+13/32*d^2*b^2*arcsinh(c*x)^2-2*d^2*b^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-1/3*d^2*b^2*arcsinh(c*x)^3-2*d^2*b^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+d^2*a^2*ln(c*x)-13/16*d^2*a*b*c*x*(c^2*x^2+1)^(1/2)+2*d^2*a*b*arcsinh(c*x)*c^2*x^2+1/2*d^2*a*b*arcsinh(c*x)*c^4*x^4-1/8*d^2*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3*x^3-13/16*d^2*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x-1/8*d^2*a*b*c^3*x^3*(c^2*x^2+1)^(1/2)","B"
213,1,400,241,0.221000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x^2,x)","\frac{d^{2} a^{2} c^{4} x^{3}}{3}+2 d^{2} a^{2} c^{2} x -\frac{d^{2} a^{2}}{x}+\frac{32 b^{2} c^{2} d^{2} x}{9}+\frac{2 b^{2} c^{4} d^{2} x^{3}}{27}+\frac{d^{2} b^{2} \arcsinh \left(c x \right)^{2} c^{4} x^{3}}{3}+2 d^{2} b^{2} \arcsinh \left(c x \right)^{2} c^{2} x -\frac{32 c \,d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{9}-\frac{d^{2} b^{2} \arcsinh \left(c x \right)^{2}}{x}-2 c \,d^{2} b^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 c \,d^{2} b^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 b^{2} c \,d^{2} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{2 d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3} x^{2}}{9}-2 b^{2} c \,d^{2} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+\frac{2 d^{2} a b \arcsinh \left(c x \right) c^{4} x^{3}}{3}+4 d^{2} a b \arcsinh \left(c x \right) c^{2} x -\frac{2 d^{2} a b \arcsinh \left(c x \right)}{x}-\frac{2 d^{2} a b \,c^{3} x^{2} \sqrt{c^{2} x^{2}+1}}{9}-\frac{32 c \,d^{2} a b \sqrt{c^{2} x^{2}+1}}{9}-2 c \,d^{2} a b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)"," ",0,"1/3*d^2*a^2*c^4*x^3+2*d^2*a^2*c^2*x-d^2*a^2/x+32/9*b^2*c^2*d^2*x+2/27*b^2*c^4*d^2*x^3+1/3*d^2*b^2*arcsinh(c*x)^2*c^4*x^3+2*d^2*b^2*arcsinh(c*x)^2*c^2*x-32/9*c*d^2*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-d^2*b^2*arcsinh(c*x)^2/x-2*c*d^2*b^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*c*d^2*b^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2*c*d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2/9*d^2*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3*x^2-2*b^2*c*d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2/3*d^2*a*b*arcsinh(c*x)*c^4*x^3+4*d^2*a*b*arcsinh(c*x)*c^2*x-2*d^2*a*b*arcsinh(c*x)/x-2/9*d^2*a*b*c^3*x^2*(c^2*x^2+1)^(1/2)-32/9*c*d^2*a*b*(c^2*x^2+1)^(1/2)-2*c*d^2*a*b*arctanh(1/(c^2*x^2+1)^(1/2))","A"
214,1,719,285,0.482000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x^3,x)","\frac{b^{2} c^{4} d^{2} x^{2}}{4}-\frac{d^{2} a^{2}}{2 x^{2}}+2 c^{2} d^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+4 c^{2} d^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+4 c^{2} d^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-2 c^{2} d^{2} a b \arcsinh \left(c x \right)^{2}+\frac{c^{2} d^{2} a b \arcsinh \left(c x \right)}{2}-\frac{c \,d^{2} a b \sqrt{c^{2} x^{2}+1}}{x}-\frac{c^{3} d^{2} a b x \sqrt{c^{2} x^{2}+1}}{2}+c^{4} d^{2} a b \arcsinh \left(c x \right) x^{2}+\frac{d^{2} b^{2} c^{2}}{8}-\frac{c \,d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}-\frac{c^{3} d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2}+4 c^{2} d^{2} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+4 c^{2} d^{2} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+d^{2} a b \,c^{2}+\frac{c^{4} d^{2} a^{2} x^{2}}{2}-2 c^{2} d^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)+c^{2} d^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}-1\right)+c^{2} d^{2} b^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 c^{2} d^{2} a^{2} \ln \left(c x \right)-\frac{d^{2} b^{2} \arcsinh \left(c x \right)^{2}}{2 x^{2}}-4 c^{2} d^{2} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)+c^{2} d^{2} b^{2} \arcsinh \left(c x \right)+\frac{c^{2} d^{2} b^{2} \arcsinh \left(c x \right)^{2}}{4}-4 c^{2} d^{2} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{2 c^{2} d^{2} b^{2} \arcsinh \left(c x \right)^{3}}{3}+4 c^{2} d^{2} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+4 c^{2} d^{2} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{2} a b \arcsinh \left(c x \right)}{x^{2}}+\frac{c^{4} d^{2} b^{2} \arcsinh \left(c x \right)^{2} x^{2}}{2}"," ",0,"1/4*b^2*c^4*d^2*x^2-1/2*d^2*a^2/x^2+2*c^2*d^2*b^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+4*c^2*d^2*b^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))+2*c^2*d^2*b^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+4*c^2*d^2*b^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*c^2*d^2*a*b*arcsinh(c*x)^2+1/2*c^2*d^2*a*b*arcsinh(c*x)+4*c^2*d^2*a*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))+4*c^2*d^2*a*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-d^2*a*b*arcsinh(c*x)/x^2+1/2*c^4*d^2*b^2*arcsinh(c*x)^2*x^2+c^4*d^2*a*b*arcsinh(c*x)*x^2-c*d^2*b^2*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)-1/2*c^3*d^2*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-c*d^2*a*b/x*(c^2*x^2+1)^(1/2)+4*c^2*d^2*a*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+4*c^2*d^2*a*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-1/2*c^3*d^2*a*b*x*(c^2*x^2+1)^(1/2)+1/8*d^2*b^2*c^2+d^2*a*b*c^2+1/2*c^4*d^2*a^2*x^2-1/2*d^2*b^2*arcsinh(c*x)^2/x^2-2*c^2*d^2*b^2*ln(c*x+(c^2*x^2+1)^(1/2))+c^2*d^2*b^2*ln(c*x+(c^2*x^2+1)^(1/2)-1)-4*c^2*d^2*b^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+c^2*d^2*b^2*arcsinh(c*x)+c^2*d^2*b^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+1/4*c^2*d^2*b^2*arcsinh(c*x)^2-4*c^2*d^2*b^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-2/3*c^2*d^2*b^2*arcsinh(c*x)^3+2*c^2*d^2*a^2*ln(c*x)","B"
215,1,408,254,0.418000," ","int((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x^4,x)","c^{4} d^{2} a^{2} x -\frac{2 c^{2} d^{2} a^{2}}{x}-\frac{d^{2} a^{2}}{3 x^{3}}+c^{4} d^{2} b^{2} \arcsinh \left(c x \right)^{2} x -2 c^{3} d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+2 b^{2} c^{4} d^{2} x -\frac{2 c^{2} d^{2} b^{2} \arcsinh \left(c x \right)^{2}}{x}-\frac{c \,d^{2} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 x^{2}}-\frac{d^{2} b^{2} \arcsinh \left(c x \right)^{2}}{3 x^{3}}-\frac{b^{2} c^{2} d^{2}}{3 x}-\frac{11 c^{3} d^{2} b^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{3}-\frac{11 b^{2} c^{3} d^{2} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{3}+\frac{11 c^{3} d^{2} b^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{3}+\frac{11 b^{2} c^{3} d^{2} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{3}+2 c^{4} d^{2} a b \arcsinh \left(c x \right) x -\frac{4 c^{2} d^{2} a b \arcsinh \left(c x \right)}{x}-\frac{2 d^{2} a b \arcsinh \left(c x \right)}{3 x^{3}}-2 c^{3} d^{2} a b \sqrt{c^{2} x^{2}+1}-\frac{11 c^{3} d^{2} a b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{3}-\frac{c \,d^{2} a b \sqrt{c^{2} x^{2}+1}}{3 x^{2}}"," ",0,"c^4*d^2*a^2*x-2*c^2*d^2*a^2/x-1/3*d^2*a^2/x^3+c^4*d^2*b^2*arcsinh(c*x)^2*x-2*c^3*d^2*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*b^2*c^4*d^2*x-2*c^2*d^2*b^2*arcsinh(c*x)^2/x-1/3*c*d^2*b^2/x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-1/3*d^2*b^2/x^3*arcsinh(c*x)^2-1/3*b^2*c^2*d^2/x-11/3*c^3*d^2*b^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-11/3*b^2*c^3*d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+11/3*c^3*d^2*b^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+11/3*b^2*c^3*d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))+2*c^4*d^2*a*b*arcsinh(c*x)*x-4*c^2*d^2*a*b*arcsinh(c*x)/x-2/3*d^2*a*b*arcsinh(c*x)/x^3-2*c^3*d^2*a*b*(c^2*x^2+1)^(1/2)-11/3*c^3*d^2*a*b*arctanh(1/(c^2*x^2+1)^(1/2))-1/3*c*d^2*a*b/x^2*(c^2*x^2+1)^(1/2)","A"
216,1,520,413,0.099000," ","int(x^4*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{d^{3} a^{2} \left(\frac{1}{11} c^{11} x^{11}+\frac{1}{3} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{3} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c^{3} x^{3} \left(c^{2} x^{2}+1\right)^{4}}{11}-\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{4}}{33}+\frac{16 \arcsinh \left(c x \right)^{2} c x}{1155}+\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{3}}{231}+\frac{2 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{385}+\frac{8 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{1155}-\frac{5487704 c x \left(c^{2} x^{2}+1\right)^{2}}{4622396625}-\frac{16 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{3465}-\frac{606416 c x \left(c^{2} x^{2}+1\right)}{13867189875}-\frac{428 c x \left(c^{2} x^{2}+1\right)^{4}}{323433}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{1617}-\frac{4 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{1925}-\frac{148174 c x \left(c^{2} x^{2}+1\right)^{3}}{110937519}+\frac{34 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{9}{2}}}{3267}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{5}}{1331}-\frac{32 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{1155}-\frac{2 \arcsinh \left(c x \right) c^{2} x^{2} \left(c^{2} x^{2}+1\right)^{\frac{9}{2}}}{121}+\frac{382986368 c x}{13867189875}\right)+2 d^{3} a b \left(\frac{\arcsinh \left(c x \right) c^{11} x^{11}}{11}+\frac{\arcsinh \left(c x \right) c^{9} x^{9}}{3}+\frac{3 \arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsinh \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{10} x^{10} \sqrt{c^{2} x^{2}+1}}{121}-\frac{91 c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{3267}-\frac{4705 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{160083}-\frac{6311 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1334025}+\frac{25244 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{4002075}-\frac{50488 \sqrt{c^{2} x^{2}+1}}{4002075}\right)}{c^{5}}"," ",0,"1/c^5*(d^3*a^2*(1/11*c^11*x^11+1/3*c^9*x^9+3/7*c^7*x^7+1/5*c^5*x^5)+d^3*b^2*(1/11*arcsinh(c*x)^2*c^3*x^3*(c^2*x^2+1)^4-1/33*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^4+16/1155*arcsinh(c*x)^2*c*x+1/231*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^3+2/385*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2+8/1155*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-5487704/4622396625*c*x*(c^2*x^2+1)^2-16/3465*arcsinh(c*x)*(c^2*x^2+1)^(3/2)-606416/13867189875*c*x*(c^2*x^2+1)-428/323433*c*x*(c^2*x^2+1)^4-2/1617*arcsinh(c*x)*(c^2*x^2+1)^(7/2)-4/1925*arcsinh(c*x)*(c^2*x^2+1)^(5/2)-148174/110937519*c*x*(c^2*x^2+1)^3+34/3267*arcsinh(c*x)*(c^2*x^2+1)^(9/2)+2/1331*c*x*(c^2*x^2+1)^5-32/1155*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2/121*arcsinh(c*x)*c^2*x^2*(c^2*x^2+1)^(9/2)+382986368/13867189875*c*x)+2*d^3*a*b*(1/11*arcsinh(c*x)*c^11*x^11+1/3*arcsinh(c*x)*c^9*x^9+3/7*arcsinh(c*x)*c^7*x^7+1/5*arcsinh(c*x)*c^5*x^5-1/121*c^10*x^10*(c^2*x^2+1)^(1/2)-91/3267*c^8*x^8*(c^2*x^2+1)^(1/2)-4705/160083*c^6*x^6*(c^2*x^2+1)^(1/2)-6311/1334025*c^4*x^4*(c^2*x^2+1)^(1/2)+25244/4002075*c^2*x^2*(c^2*x^2+1)^(1/2)-50488/4002075*(c^2*x^2+1)^(1/2)))","A"
217,1,415,336,0.089000," ","int(x^3*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{d^{3} a^{2} \left(\frac{1}{10} c^{10} x^{10}+\frac{3}{8} c^{8} x^{8}+\frac{1}{2} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d^{3} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c^{2} x^{2} \left(c^{2} x^{2}+1\right)^{4}}{10}-\frac{\arcsinh \left(c x \right)^{2} \left(c^{2} x^{2}+1\right)^{4}}{40}-\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{9}{2}}}{50}+\frac{7 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{800}+\frac{49 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{4800}+\frac{49 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{3840}+\frac{49 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{2560}+\frac{49 \arcsinh \left(c x \right)^{2}}{5120}+\frac{\left(c^{2} x^{2}+1\right)^{5}}{500}-\frac{7 \left(c^{2} x^{2}+1\right)^{4}}{6400}-\frac{49 \left(c^{2} x^{2}+1\right)^{3}}{28800}-\frac{49 \left(c^{2} x^{2}+1\right)^{2}}{15360}-\frac{49 c^{2} x^{2}}{5120}-\frac{49}{5120}\right)+2 d^{3} a b \left(\frac{\arcsinh \left(c x \right) c^{10} x^{10}}{10}+\frac{3 \arcsinh \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{2}+\frac{\arcsinh \left(c x \right) c^{4} x^{4}}{4}-\frac{c^{9} x^{9} \sqrt{c^{2} x^{2}+1}}{100}-\frac{57 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}}{1600}-\frac{401 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{9600}-\frac{79 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{7680}+\frac{79 c x \sqrt{c^{2} x^{2}+1}}{5120}-\frac{79 \arcsinh \left(c x \right)}{5120}\right)}{c^{4}}"," ",0,"1/c^4*(d^3*a^2*(1/10*c^10*x^10+3/8*c^8*x^8+1/2*c^6*x^6+1/4*c^4*x^4)+d^3*b^2*(1/10*arcsinh(c*x)^2*c^2*x^2*(c^2*x^2+1)^4-1/40*arcsinh(c*x)^2*(c^2*x^2+1)^4-1/50*arcsinh(c*x)*c*x*(c^2*x^2+1)^(9/2)+7/800*arcsinh(c*x)*c*x*(c^2*x^2+1)^(7/2)+49/4800*arcsinh(c*x)*c*x*(c^2*x^2+1)^(5/2)+49/3840*arcsinh(c*x)*c*x*(c^2*x^2+1)^(3/2)+49/2560*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x+49/5120*arcsinh(c*x)^2+1/500*(c^2*x^2+1)^5-7/6400*(c^2*x^2+1)^4-49/28800*(c^2*x^2+1)^3-49/15360*(c^2*x^2+1)^2-49/5120*c^2*x^2-49/5120)+2*d^3*a*b*(1/10*arcsinh(c*x)*c^10*x^10+3/8*arcsinh(c*x)*c^8*x^8+1/2*arcsinh(c*x)*c^6*x^6+1/4*arcsinh(c*x)*c^4*x^4-1/100*c^9*x^9*(c^2*x^2+1)^(1/2)-57/1600*c^7*x^7*(c^2*x^2+1)^(1/2)-401/9600*c^5*x^5*(c^2*x^2+1)^(1/2)-79/7680*c^3*x^3*(c^2*x^2+1)^(1/2)+79/5120*c*x*(c^2*x^2+1)^(1/2)-79/5120*arcsinh(c*x)))","A"
218,1,438,340,0.054000," ","int(x^2*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{d^{3} a^{2} \left(\frac{1}{9} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{3} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{4}}{9}-\frac{16 \arcsinh \left(c x \right)^{2} c x}{315}-\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{3}}{63}-\frac{2 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{105}-\frac{8 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{315}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{9}{2}}}{81}-\frac{3406208 c x}{31255875}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{4}}{729}+\frac{622 c x \left(c^{2} x^{2}+1\right)^{3}}{250047}+\frac{15224 c x \left(c^{2} x^{2}+1\right)^{2}}{10418625}-\frac{115504 c x \left(c^{2} x^{2}+1\right)}{31255875}+\frac{32 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{315}+\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{441}+\frac{4 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{525}+\frac{16 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{945}\right)+2 d^{3} a b \left(\frac{\arcsinh \left(c x \right) c^{9} x^{9}}{9}+\frac{3 \arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{3 \arcsinh \left(c x \right) c^{5} x^{5}}{5}+\frac{\arcsinh \left(c x \right) c^{3} x^{3}}{3}-\frac{c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{81}-\frac{187 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{3969}-\frac{2099 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{33075}-\frac{2629 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{99225}+\frac{5258 \sqrt{c^{2} x^{2}+1}}{99225}\right)}{c^{3}}"," ",0,"1/c^3*(d^3*a^2*(1/9*c^9*x^9+3/7*c^7*x^7+3/5*c^5*x^5+1/3*c^3*x^3)+d^3*b^2*(1/9*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^4-16/315*arcsinh(c*x)^2*c*x-1/63*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^3-2/105*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2-8/315*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-2/81*arcsinh(c*x)*(c^2*x^2+1)^(9/2)-3406208/31255875*c*x+2/729*c*x*(c^2*x^2+1)^4+622/250047*c*x*(c^2*x^2+1)^3+15224/10418625*c*x*(c^2*x^2+1)^2-115504/31255875*c*x*(c^2*x^2+1)+32/315*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2/441*arcsinh(c*x)*(c^2*x^2+1)^(7/2)+4/525*arcsinh(c*x)*(c^2*x^2+1)^(5/2)+16/945*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d^3*a*b*(1/9*arcsinh(c*x)*c^9*x^9+3/7*arcsinh(c*x)*c^7*x^7+3/5*arcsinh(c*x)*c^5*x^5+1/3*arcsinh(c*x)*c^3*x^3-1/81*c^8*x^8*(c^2*x^2+1)^(1/2)-187/3969*c^6*x^6*(c^2*x^2+1)^(1/2)-2099/33075*c^4*x^4*(c^2*x^2+1)^(1/2)-2629/99225*c^2*x^2*(c^2*x^2+1)^(1/2)+5258/99225*(c^2*x^2+1)^(1/2)))","A"
219,1,339,233,0.046000," ","int(x*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{d^{3} a^{2} \left(\frac{1}{8} c^{8} x^{8}+\frac{1}{2} c^{6} x^{6}+\frac{3}{4} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d^{3} b^{2} \left(\frac{\arcsinh \left(c x \right)^{2} \left(c^{2} x^{2}+1\right)^{4}}{8}-\frac{\arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{32}-\frac{7 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{192}-\frac{35 \arcsinh \left(c x \right) c x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{768}-\frac{35 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{512}-\frac{35 \arcsinh \left(c x \right)^{2}}{1024}+\frac{\left(c^{2} x^{2}+1\right)^{4}}{256}+\frac{7 \left(c^{2} x^{2}+1\right)^{3}}{1152}+\frac{35 \left(c^{2} x^{2}+1\right)^{2}}{3072}+\frac{35 c^{2} x^{2}}{1024}+\frac{35}{1024}\right)+2 d^{3} a b \left(\frac{\arcsinh \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsinh \left(c x \right) c^{6} x^{6}}{2}+\frac{3 \arcsinh \left(c x \right) c^{4} x^{4}}{4}+\frac{\arcsinh \left(c x \right) c^{2} x^{2}}{2}-\frac{c^{7} x^{7} \sqrt{c^{2} x^{2}+1}}{64}-\frac{25 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{384}-\frac{163 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{1536}-\frac{93 c x \sqrt{c^{2} x^{2}+1}}{1024}+\frac{93 \arcsinh \left(c x \right)}{1024}\right)}{c^{2}}"," ",0,"1/c^2*(d^3*a^2*(1/8*c^8*x^8+1/2*c^6*x^6+3/4*c^4*x^4+1/2*c^2*x^2)+d^3*b^2*(1/8*arcsinh(c*x)^2*(c^2*x^2+1)^4-1/32*arcsinh(c*x)*c*x*(c^2*x^2+1)^(7/2)-7/192*arcsinh(c*x)*c*x*(c^2*x^2+1)^(5/2)-35/768*arcsinh(c*x)*c*x*(c^2*x^2+1)^(3/2)-35/512*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x-35/1024*arcsinh(c*x)^2+1/256*(c^2*x^2+1)^4+7/1152*(c^2*x^2+1)^3+35/3072*(c^2*x^2+1)^2+35/1024*c^2*x^2+35/1024)+2*d^3*a*b*(1/8*arcsinh(c*x)*c^8*x^8+1/2*arcsinh(c*x)*c^6*x^6+3/4*arcsinh(c*x)*c^4*x^4+1/2*arcsinh(c*x)*c^2*x^2-1/64*c^7*x^7*(c^2*x^2+1)^(1/2)-25/384*c^5*x^5*(c^2*x^2+1)^(1/2)-163/1536*c^3*x^3*(c^2*x^2+1)^(1/2)-93/1024*c*x*(c^2*x^2+1)^(1/2)+93/1024*arcsinh(c*x)))","A"
220,1,354,259,0.056000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{d^{3} a^{2} \left(\frac{1}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}+c^{3} x^{3}+c x \right)+d^{3} b^{2} \left(\frac{16 \arcsinh \left(c x \right)^{2} c x}{35}+\frac{\arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{3}}{7}+\frac{6 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)^{2}}{35}+\frac{8 \arcsinh \left(c x \right)^{2} c x \left(c^{2} x^{2}+1\right)}{35}-\frac{32 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{35}+\frac{413312 c x}{385875}-\frac{2 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{7}{2}}}{49}+\frac{2 c x \left(c^{2} x^{2}+1\right)^{3}}{343}+\frac{888 c x \left(c^{2} x^{2}+1\right)^{2}}{42875}+\frac{30256 c x \left(c^{2} x^{2}+1\right)}{385875}-\frac{12 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{175}-\frac{16 \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{105}\right)+2 d^{3} a b \left(\frac{\arcsinh \left(c x \right) c^{7} x^{7}}{7}+\frac{3 \arcsinh \left(c x \right) c^{5} x^{5}}{5}+\arcsinh \left(c x \right) c^{3} x^{3}+\arcsinh \left(c x \right) c x -\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{49}-\frac{117 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{1225}-\frac{757 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3675}-\frac{2161 \sqrt{c^{2} x^{2}+1}}{3675}\right)}{c}"," ",0,"1/c*(d^3*a^2*(1/7*c^7*x^7+3/5*c^5*x^5+c^3*x^3+c*x)+d^3*b^2*(16/35*arcsinh(c*x)^2*c*x+1/7*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^3+6/35*arcsinh(c*x)^2*c*x*(c^2*x^2+1)^2+8/35*arcsinh(c*x)^2*c*x*(c^2*x^2+1)-32/35*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+413312/385875*c*x-2/49*arcsinh(c*x)*(c^2*x^2+1)^(7/2)+2/343*c*x*(c^2*x^2+1)^3+888/42875*c*x*(c^2*x^2+1)^2+30256/385875*c*x*(c^2*x^2+1)-12/175*arcsinh(c*x)*(c^2*x^2+1)^(5/2)-16/105*arcsinh(c*x)*(c^2*x^2+1)^(3/2))+2*d^3*a*b*(1/7*arcsinh(c*x)*c^7*x^7+3/5*arcsinh(c*x)*c^5*x^5+arcsinh(c*x)*c^3*x^3+arcsinh(c*x)*c*x-1/49*c^6*x^6*(c^2*x^2+1)^(1/2)-117/1225*c^4*x^4*(c^2*x^2+1)^(1/2)-757/3675*c^2*x^2*(c^2*x^2+1)^(1/2)-2161/3675*(c^2*x^2+1)^(1/2)))","A"
221,1,706,334,0.301000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x,x)","\frac{d^{3} a^{2} c^{6} x^{6}}{6}+\frac{3 d^{3} a^{2} c^{4} x^{4}}{4}+\frac{3 d^{3} a^{2} c^{2} x^{2}}{2}+\frac{d^{3} b^{2} c^{6} x^{6}}{108}-d^{3} a b \arcsinh \left(c x \right)^{2}+\frac{25 d^{3} a b \arcsinh \left(c x \right)}{24}+2 d^{3} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+2 d^{3} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+2 d^{3} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+d^{3} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+d^{3} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+2 d^{3} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{3} a b \,c^{5} x^{5} \sqrt{c^{2} x^{2}+1}}{18}-\frac{11 d^{3} a b \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{36}-\frac{25 d^{3} a b c x \sqrt{c^{2} x^{2}+1}}{24}-\frac{25 d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{24}-\frac{d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5} x^{5}}{18}+\frac{d^{3} a b \arcsinh \left(c x \right) c^{6} x^{6}}{3}+\frac{3 d^{3} a b \arcsinh \left(c x \right) c^{4} x^{4}}{2}+3 d^{3} a b \arcsinh \left(c x \right) c^{2} x^{2}-\frac{11 d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3} x^{3}}{36}+\frac{25 b^{2} c^{2} d^{3} x^{2}}{48}+\frac{11 b^{2} c^{4} d^{3} x^{4}}{144}+\frac{811 d^{3} b^{2}}{3456}+\frac{25 d^{3} b^{2} \arcsinh \left(c x \right)^{2}}{48}-\frac{d^{3} b^{2} \arcsinh \left(c x \right)^{3}}{3}-2 d^{3} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)-2 d^{3} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)+d^{3} a^{2} \ln \left(c x \right)+\frac{d^{3} b^{2} \arcsinh \left(c x \right)^{2} c^{6} x^{6}}{6}+2 d^{3} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+2 d^{3} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+\frac{3 d^{3} b^{2} \arcsinh \left(c x \right)^{2} c^{4} x^{4}}{4}+\frac{3 d^{3} b^{2} \arcsinh \left(c x \right)^{2} c^{2} x^{2}}{2}"," ",0,"-d^3*a*b*arcsinh(c*x)^2+25/24*d^3*a*b*arcsinh(c*x)+2*d^3*a*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*d^3*a*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))+1/6*d^3*a^2*c^6*x^6+3/4*d^3*a^2*c^4*x^4+3/2*d^3*a^2*c^2*x^2+1/108*d^3*b^2*c^6*x^6+2*d^3*b^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+d^3*b^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+d^3*b^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*d^3*b^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-25/24*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x-1/18*d^3*a*b*c^5*x^5*(c^2*x^2+1)^(1/2)-11/36*d^3*a*b*c^3*x^3*(c^2*x^2+1)^(1/2)-25/24*d^3*a*b*c*x*(c^2*x^2+1)^(1/2)-1/18*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5*x^5+1/3*d^3*a*b*arcsinh(c*x)*c^6*x^6+3/2*d^3*a*b*arcsinh(c*x)*c^4*x^4+3*d^3*a*b*arcsinh(c*x)*c^2*x^2-11/36*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3*x^3+25/48*b^2*c^2*d^3*x^2+11/144*b^2*c^4*d^3*x^4+811/3456*d^3*b^2+1/6*d^3*b^2*arcsinh(c*x)^2*c^6*x^6+2*d^3*a*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+d^3*a^2*ln(c*x)+25/48*d^3*b^2*arcsinh(c*x)^2-1/3*d^3*b^2*arcsinh(c*x)^3-2*d^3*b^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-2*d^3*b^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+2*d^3*a*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+3/4*d^3*b^2*arcsinh(c*x)^2*c^4*x^4+3/2*d^3*b^2*arcsinh(c*x)^2*c^2*x^2","B"
222,1,516,311,0.305000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x^2,x)","\frac{2 d^{3} a b \arcsinh \left(c x \right) c^{6} x^{5}}{5}+2 d^{3} a b \arcsinh \left(c x \right) c^{4} x^{3}+6 d^{3} a b \arcsinh \left(c x \right) c^{2} x -\frac{2 d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5} x^{4}}{25}-\frac{14 d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3} x^{2}}{25}-\frac{2 d^{3} a b \,c^{5} x^{4} \sqrt{c^{2} x^{2}+1}}{25}-\frac{14 d^{3} a b \,c^{3} x^{2} \sqrt{c^{2} x^{2}+1}}{25}+\frac{d^{3} a^{2} c^{6} x^{5}}{5}+d^{3} a^{2} c^{4} x^{3}+3 d^{3} a^{2} c^{2} x -2 b^{2} c \,d^{3} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+2 b^{2} c \,d^{3} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{3} b^{2} \arcsinh \left(c x \right)^{2}}{x}+\frac{122 b^{2} c^{2} d^{3} x}{25}+\frac{14 b^{2} c^{4} d^{3} x^{3}}{75}+\frac{2 b^{2} c^{6} d^{3} x^{5}}{125}-\frac{d^{3} a^{2}}{x}-\frac{122 c \,d^{3} a b \sqrt{c^{2} x^{2}+1}}{25}-\frac{2 d^{3} a b \arcsinh \left(c x \right)}{x}-\frac{122 c \,d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{25}+2 c \,d^{3} b^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)-2 c \,d^{3} b^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)-2 c \,d^{3} a b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{d^{3} b^{2} \arcsinh \left(c x \right)^{2} c^{6} x^{5}}{5}+d^{3} b^{2} \arcsinh \left(c x \right)^{2} c^{4} x^{3}+3 d^{3} b^{2} \arcsinh \left(c x \right)^{2} c^{2} x"," ",0,"-2*b^2*c*d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*b^2*c*d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))+2/5*d^3*a*b*arcsinh(c*x)*c^6*x^5+2*d^3*a*b*arcsinh(c*x)*c^4*x^3+6*d^3*a*b*arcsinh(c*x)*c^2*x-2/25*d^3*a*b*c^5*x^4*(c^2*x^2+1)^(1/2)-14/25*d^3*a*b*c^3*x^2*(c^2*x^2+1)^(1/2)-2/25*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5*x^4-14/25*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3*x^2+1/5*d^3*a^2*c^6*x^5+d^3*a^2*c^4*x^3+3*d^3*a^2*c^2*x-d^3*b^2*arcsinh(c*x)^2/x+122/25*b^2*c^2*d^3*x+14/75*b^2*c^4*d^3*x^3+2/125*b^2*c^6*d^3*x^5-d^3*a^2/x-2*d^3*a*b*arcsinh(c*x)/x-122/25*c*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*d^3*b^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-2*c*d^3*b^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-122/25*c*d^3*a*b*(c^2*x^2+1)^(1/2)-2*c*d^3*a*b*arctanh(1/(c^2*x^2+1)^(1/2))+1/5*d^3*b^2*arcsinh(c*x)^2*c^6*x^5+d^3*b^2*arcsinh(c*x)^2*c^4*x^3+3*d^3*b^2*arcsinh(c*x)^2*c^2*x","A"
223,1,838,357,0.800000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x^3,x)","\frac{21 b^{2} c^{4} d^{3} x^{2}}{32}+\frac{b^{2} c^{6} d^{3} x^{4}}{32}+6 c^{2} d^{3} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)+\frac{c^{6} d^{3} b^{2} \arcsinh \left(c x \right)^{2} x^{4}}{4}+\frac{3 c^{4} d^{3} b^{2} \arcsinh \left(c x \right)^{2} x^{2}}{2}+3 c^{2} d^{3} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)+3 c^{2} d^{3} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+6 c^{2} d^{3} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)-3 c^{2} d^{3} a b \arcsinh \left(c x \right)^{2}+\frac{21 c^{2} d^{3} a b \arcsinh \left(c x \right)}{16}+6 c^{2} d^{3} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{3} a b \arcsinh \left(c x \right)}{x^{2}}+6 c^{2} d^{3} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)+\frac{81 d^{3} b^{2} c^{2}}{256}-\frac{d^{3} a^{2}}{2 x^{2}}-\frac{c^{5} d^{3} a b \,x^{3} \sqrt{c^{2} x^{2}+1}}{8}-\frac{21 c^{3} d^{3} a b x \sqrt{c^{2} x^{2}+1}}{16}-\frac{c \,d^{3} a b \sqrt{c^{2} x^{2}+1}}{x}+3 c^{4} d^{3} a b \arcsinh \left(c x \right) x^{2}-\frac{c^{5} d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{8}-\frac{21 c^{3} d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{16}+6 c^{2} d^{3} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)+6 c^{2} d^{3} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{c \,d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{x}+\frac{c^{6} d^{3} a b \arcsinh \left(c x \right) x^{4}}{2}+\frac{c^{6} d^{3} a^{2} x^{4}}{4}+\frac{3 c^{4} d^{3} a^{2} x^{2}}{2}+3 c^{2} d^{3} a^{2} \ln \left(c x \right)+c^{2} d^{3} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}-1\right)+c^{2} d^{3} b^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)-2 c^{2} d^{3} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)-\frac{d^{3} b^{2} \arcsinh \left(c x \right)^{2}}{2 x^{2}}+\frac{21 c^{2} d^{3} b^{2} \arcsinh \left(c x \right)^{2}}{32}-c^{2} d^{3} b^{2} \arcsinh \left(c x \right)^{3}-6 c^{2} d^{3} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)-6 c^{2} d^{3} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)+c^{2} d^{3} b^{2} \arcsinh \left(c x \right)+d^{3} a b \,c^{2}"," ",0,"21/32*b^2*c^4*d^3*x^2+1/32*b^2*c^6*d^3*x^4+6*c^2*d^3*b^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+1/4*c^6*d^3*b^2*arcsinh(c*x)^2*x^4+3/2*c^4*d^3*b^2*arcsinh(c*x)^2*x^2+3*c^2*d^3*b^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+3*c^2*d^3*b^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+6*c^2*d^3*b^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-3*c^2*d^3*a*b*arcsinh(c*x)^2+21/16*c^2*d^3*a*b*arcsinh(c*x)+6*c^2*d^3*a*b*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-d^3*a*b*arcsinh(c*x)/x^2+6*c^2*d^3*a*b*polylog(2,c*x+(c^2*x^2+1)^(1/2))+81/256*d^3*b^2*c^2-1/2*d^3*a^2/x^2+3*c^4*d^3*a*b*arcsinh(c*x)*x^2-1/8*c^5*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-21/16*c^3*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/8*c^5*d^3*a*b*x^3*(c^2*x^2+1)^(1/2)-21/16*c^3*d^3*a*b*x*(c^2*x^2+1)^(1/2)-c*d^3*a*b/x*(c^2*x^2+1)^(1/2)+6*c^2*d^3*a*b*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+6*c^2*d^3*a*b*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-c*d^3*b^2*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)+1/2*c^6*d^3*a*b*arcsinh(c*x)*x^4+1/4*c^6*d^3*a^2*x^4+3/2*c^4*d^3*a^2*x^2-1/2*d^3*b^2*arcsinh(c*x)^2/x^2+3*c^2*d^3*a^2*ln(c*x)+21/32*c^2*d^3*b^2*arcsinh(c*x)^2-c^2*d^3*b^2*arcsinh(c*x)^3-6*c^2*d^3*b^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-6*c^2*d^3*b^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+c^2*d^3*b^2*arcsinh(c*x)+c^2*d^3*b^2*ln(c*x+(c^2*x^2+1)^(1/2)-1)+c^2*d^3*b^2*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*c^2*d^3*b^2*ln(c*x+(c^2*x^2+1)^(1/2))+d^3*a*b*c^2","B"
224,1,528,326,0.667000," ","int((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x^4,x)","-\frac{b^{2} c^{2} d^{3}}{3 x}+\frac{50 b^{2} c^{4} d^{3} x}{9}+\frac{2 b^{2} c^{6} d^{3} x^{3}}{27}+\frac{2 c^{6} d^{3} a b \arcsinh \left(c x \right) x^{3}}{3}+6 c^{4} d^{3} a b \arcsinh \left(c x \right) x -\frac{6 c^{2} d^{3} a b \arcsinh \left(c x \right)}{x}-\frac{c \,d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 x^{2}}-\frac{2 c^{5} d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{9}-\frac{d^{3} a^{2}}{3 x^{3}}-\frac{2 c^{5} d^{3} a b \,x^{2} \sqrt{c^{2} x^{2}+1}}{9}-\frac{c \,d^{3} a b \sqrt{c^{2} x^{2}+1}}{3 x^{2}}+\frac{c^{6} d^{3} a^{2} x^{3}}{3}+3 c^{4} d^{3} a^{2} x -\frac{3 c^{2} d^{3} a^{2}}{x}-\frac{17 b^{2} c^{3} d^{3} \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{3}+\frac{17 b^{2} c^{3} d^{3} \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{3}-\frac{d^{3} b^{2} \arcsinh \left(c x \right)^{2}}{3 x^{3}}-\frac{2 d^{3} a b \arcsinh \left(c x \right)}{3 x^{3}}+3 c^{4} d^{3} b^{2} \arcsinh \left(c x \right)^{2} x -\frac{3 c^{2} d^{3} b^{2} \arcsinh \left(c x \right)^{2}}{x}-\frac{17 c^{3} d^{3} a b \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{3}-\frac{50 c^{3} d^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{9}+\frac{17 c^{3} d^{3} b^{2} \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{3}-\frac{17 c^{3} d^{3} b^{2} \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{3}+\frac{c^{6} d^{3} b^{2} \arcsinh \left(c x \right)^{2} x^{3}}{3}-\frac{50 c^{3} d^{3} a b \sqrt{c^{2} x^{2}+1}}{9}"," ",0,"-17/3*b^2*c^3*d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+17/3*b^2*c^3*d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))-1/3*b^2*c^2*d^3/x+50/9*b^2*c^4*d^3*x+2/27*b^2*c^6*d^3*x^3-1/3*d^3*a^2/x^3+2/3*c^6*d^3*a*b*arcsinh(c*x)*x^3+6*c^4*d^3*a*b*arcsinh(c*x)*x-6*c^2*d^3*a*b*arcsinh(c*x)/x-2/9*c^5*d^3*a*b*x^2*(c^2*x^2+1)^(1/2)-1/3*c*d^3*a*b/x^2*(c^2*x^2+1)^(1/2)-1/3*c*d^3*b^2/x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2/9*c^5*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2-1/3*d^3*b^2/x^3*arcsinh(c*x)^2+1/3*c^6*d^3*a^2*x^3+3*c^4*d^3*a^2*x-3*c^2*d^3*a^2/x-2/3*d^3*a*b*arcsinh(c*x)/x^3+3*c^4*d^3*b^2*arcsinh(c*x)^2*x-3*c^2*d^3*b^2*arcsinh(c*x)^2/x-50/9*c^3*d^3*a*b*(c^2*x^2+1)^(1/2)-17/3*c^3*d^3*a*b*arctanh(1/(c^2*x^2+1)^(1/2))-50/9*c^3*d^3*b^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+17/3*c^3*d^3*b^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-17/3*c^3*d^3*b^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+1/3*c^6*d^3*b^2*arcsinh(c*x)^2*x^3","A"
225,0,0,300,0.341000," ","int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","\int \frac{x^{4} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","F"
226,1,380,212,0.197000," ","int(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","\frac{a^{2} x^{2}}{2 c^{2} d}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d}+\frac{b^{2} \arcsinh \left(c x \right)^{3}}{3 c^{4} d}+\frac{b^{2} \arcsinh \left(c x \right)^{2} x^{2}}{2 c^{2} d}-\frac{b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 c^{3} d}+\frac{b^{2} \arcsinh \left(c x \right)^{2}}{4 c^{4} d}+\frac{b^{2} x^{2}}{4 c^{2} d}+\frac{b^{2}}{8 c^{4} d}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}-\frac{b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}+\frac{b^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d}+\frac{a b \arcsinh \left(c x \right)^{2}}{c^{4} d}+\frac{a b \arcsinh \left(c x \right) x^{2}}{c^{2} d}-\frac{a b x \sqrt{c^{2} x^{2}+1}}{2 c^{3} d}+\frac{a b \arcsinh \left(c x \right)}{2 c^{4} d}-\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}-\frac{a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}"," ",0,"1/2/c^2*a^2/d*x^2-1/2/c^4*a^2/d*ln(c^2*x^2+1)+1/3/c^4*b^2/d*arcsinh(c*x)^3+1/2/c^2*b^2/d*arcsinh(c*x)^2*x^2-1/2/c^3*b^2/d*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x+1/4/c^4*b^2/d*arcsinh(c*x)^2+1/4*b^2*x^2/c^2/d+1/8/c^4*b^2/d-1/c^4*b^2/d*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/c^4*b^2/d*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/c^4/d+1/c^4*a*b/d*arcsinh(c*x)^2+1/c^2*a*b/d*arcsinh(c*x)*x^2-1/2/c^3*a*b/d*x*(c^2*x^2+1)^(1/2)+1/2/c^4*a*b/d*arcsinh(c*x)-2/c^4*a*b/d*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/c^4*a*b/d*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)","A"
227,0,0,233,0.154000," ","int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","\int \frac{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","F"
228,1,223,128,0.067000," ","int(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{2} d}-\frac{b^{2} \arcsinh \left(c x \right)^{3}}{3 c^{2} d}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}+\frac{b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}-\frac{b^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{2} d}-\frac{a b \arcsinh \left(c x \right)^{2}}{c^{2} d}+\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}+\frac{a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}"," ",0,"1/2/c^2*a^2/d*ln(c^2*x^2+1)-1/3/c^2*b^2/d*arcsinh(c*x)^3+1/c^2*b^2/d*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/c^2*b^2/d*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/c^2/d-1/c^2*a*b/d*arcsinh(c*x)^2+2/c^2*a*b/d*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/c^2*a*b/d*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)","A"
229,0,0,175,0.148000," ","int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{c^{2} d \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x)","F"
230,1,354,157,0.109000," ","int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d),x)","\frac{a^{2} \ln \left(c x \right)}{d}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d}+\frac{2 b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{2 b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d}+\frac{2 b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{2 b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{b^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d}+\frac{2 a b \dilog \left(\frac{1}{\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}}\right)}{d}-\frac{a b \dilog \left(\frac{1}{\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}}\right)}{2 d}"," ",0,"a^2/d*ln(c*x)-1/2*a^2/d*ln(c^2*x^2+1)+b^2/d*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*b^2/d*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*b^2/d*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+b^2/d*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2/d*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*b^2/d*polylog(3,c*x+(c^2*x^2+1)^(1/2))-b^2/d*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-b^2/d*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/d+2*a*b/d*dilog(1/(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*a*b/d*dilog(1/(c*x+(c^2*x^2+1)^(1/2))^4)","B"
231,0,0,269,0.313000," ","int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{2} \left(c^{2} d \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d),x)","F"
232,1,719,231,0.213000," ","int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d),x)","\frac{2 c^{2} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{d}+\frac{c^{2} b^{2} \arcsinh \left(c x \right)}{d}+\frac{c^{2} a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d}-\frac{c^{2} a^{2} \ln \left(c x \right)}{d}-\frac{2 c^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{d}+\frac{c^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}-1\right)}{d}+\frac{c^{2} b^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{b^{2} c^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{2 d \,x^{2}}+\frac{2 c^{2} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d}+\frac{c^{2} a b}{d}+\frac{2 c^{2} a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{c \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{d x}-\frac{2 c^{2} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{2 c^{2} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{c a b \sqrt{c^{2} x^{2}+1}}{d x}-\frac{2 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{2 c^{2} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{2 c^{2} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{a b \arcsinh \left(c x \right)}{d \,x^{2}}+\frac{c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{c^{2} a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{2 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d}-\frac{a^{2}}{2 d \,x^{2}}"," ",0,"-1/2*b^2*c^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/d-1/2*b^2/d*arcsinh(c*x)^2/x^2+1/2*c^2*a^2/d*ln(c^2*x^2+1)-c^2*a^2/d*ln(c*x)+2*c^2*b^2/d*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+2*c^2*b^2/d*polylog(3,c*x+(c^2*x^2+1)^(1/2))+c^2*b^2/d*arcsinh(c*x)-2*c^2*b^2/d*ln(c*x+(c^2*x^2+1)^(1/2))+c^2*b^2/d*ln(c*x+(c^2*x^2+1)^(1/2)-1)+c^2*b^2/d*ln(1+c*x+(c^2*x^2+1)^(1/2))+c^2*a*b/d+2*c^2*a*b/d*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-c*b^2/d*arcsinh(c*x)/x*(c^2*x^2+1)^(1/2)-c*a*b/d/x*(c^2*x^2+1)^(1/2)-2*c^2*a*b/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*c^2*a*b/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-2*c^2*b^2/d*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*c^2*a*b/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*c^2*a*b/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))-a*b/d*arcsinh(c*x)/x^2+c^2*b^2/d*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+c^2*b^2/d*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+c^2*a*b/d*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-c^2*b^2/d*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*c^2*b^2/d*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-1/2*a^2/d/x^2-c^2*b^2/d*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))","B"
233,0,0,348,0.363000," ","int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{4} \left(c^{2} d \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d),x)","F"
234,0,0,308,0.368000," ","int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","\int \frac{x^{4} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","F"
235,1,499,228,0.337000," ","int(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","\frac{a^{2}}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{4} d^{2}}-\frac{b^{2} \arcsinh \left(c x \right)^{3}}{3 c^{4} d^{2}}-\frac{b^{2} \arcsinh \left(c x \right) x}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \arcsinh \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right)^{2}}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{c^{4} d^{2}}+\frac{b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}+\frac{b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}-\frac{b^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d^{2}}-\frac{a b \arcsinh \left(c x \right)^{2}}{c^{4} d^{2}}-\frac{a b x}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{a b \,x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a b \arcsinh \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a b}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}+\frac{a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}"," ",0,"1/2/c^4*a^2/d^2/(c^2*x^2+1)+1/2/c^4*a^2/d^2*ln(c^2*x^2+1)-1/3/c^4*b^2/d^2*arcsinh(c*x)^3-1/c^3*b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)^(1/2)*x+1/c^2*b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)*x^2+1/2/c^4*b^2/d^2*arcsinh(c*x)^2/(c^2*x^2+1)+1/c^4*b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)-2/c^4*b^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2))+1/c^4*b^2/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/c^4*b^2/d^2*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/c^4*b^2/d^2*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/c^4/d^2-1/c^4*a*b/d^2*arcsinh(c*x)^2-1/c^3*a*b/d^2/(c^2*x^2+1)^(1/2)*x+1/c^2*a*b/d^2*x^2/(c^2*x^2+1)+1/c^4*a*b/d^2*arcsinh(c*x)/(c^2*x^2+1)+1/c^4*a*b/d^2/(c^2*x^2+1)+2/c^4*a*b/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/c^4*a*b/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)","B"
236,0,0,246,0.236000," ","int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","\int \frac{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","F"
237,1,222,79,0.105000," ","int(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","-\frac{a^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \arcsinh \left(c x \right)}{c^{2} d^{2}}+\frac{b^{2} \arcsinh \left(c x \right) x}{c \,d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right) x^{2}}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d^{2}}-\frac{a b \arcsinh \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a b x}{c \,d^{2} \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2/c^2*a^2/d^2/(c^2*x^2+1)+2/c^2*b^2/d^2*arcsinh(c*x)+1/c*b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)^(1/2)*x-b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)*x^2-1/2/c^2*b^2/d^2*arcsinh(c*x)^2/(c^2*x^2+1)-1/c^2*b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)-1/c^2*b^2/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/c^2*a*b/d^2/(c^2*x^2+1)*arcsinh(c*x)+1/c*a*b/d^2*x/(c^2*x^2+1)^(1/2)","B"
238,0,0,243,0.119000," ","int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x)","F"
239,1,724,228,0.192000," ","int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^2,x)","\frac{a b \,c^{2} x^{2}}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{a b c x}{d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right) c x}{d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \arcsinh \left(c x \right) c^{2} x^{2}}{d^{2} \left(c^{2} x^{2}+1\right)}+\frac{a b}{d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \arcsinh \left(c x \right)^{2}}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right)}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{a b \arcsinh \left(c x \right)}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{2}}-\frac{2 b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{a^{2}}{2 d^{2} \left(c^{2} x^{2}+1\right)}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{2}}+\frac{a^{2} \ln \left(c x \right)}{d^{2}}-\frac{2 b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}"," ",0,"-b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)^(1/2)*c*x+a*b/d^2*c^2*x^2/(c^2*x^2+1)+b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)*c^2*x^2-a*b/d^2/(c^2*x^2+1)^(1/2)*c*x+2*a*b/d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*a*b/d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))+b^2/d^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*b^2/d^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+b^2/d^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2/d^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))+1/2*b^2/d^2*arcsinh(c*x)^2/(c^2*x^2+1)+b^2/d^2*arcsinh(c*x)/(c^2*x^2+1)-b^2/d^2*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-b^2/d^2*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+a*b/d^2/(c^2*x^2+1)-a*b/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^2+a*b/d^2*arcsinh(c*x)/(c^2*x^2+1)-2*a*b/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+2*a*b/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*a*b/d^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+1/2*a^2/d^2/(c^2*x^2+1)-1/2*a^2/d^2*ln(c^2*x^2+1)+a^2/d^2*ln(c*x)-2*b^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2))+b^2/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-2*b^2/d^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))-2*b^2/d^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))","B"
240,0,0,348,0.338000," ","int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^2,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{2} \left(c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^2,x)","F"
241,1,799,292,0.233000," ","int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^2,x)","-\frac{c^{2} b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{c^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}-1\right)}{d^{2}}+\frac{c^{2} b^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{c^{2} a^{2}}{2 d^{2} \left(c^{2} x^{2}+1\right)}+\frac{c^{2} a^{2} \ln \left(c^{2} x^{2}+1\right)}{d^{2}}-\frac{2 c^{2} a^{2} \ln \left(c x \right)}{d^{2}}-\frac{b^{2} c^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{4 c^{2} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{4 c^{2} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 c^{2} a b \arcsinh \left(c x \right)}{d^{2} \left(c^{2} x^{2}+1\right)}+\frac{4 c^{2} a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{c a b}{d^{2} x \sqrt{c^{2} x^{2}+1}}-\frac{4 c^{2} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 c^{2} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{a b \arcsinh \left(c x \right)}{d^{2} x^{2} \left(c^{2} x^{2}+1\right)}-\frac{c \,b^{2} \arcsinh \left(c x \right)}{d^{2} x \sqrt{c^{2} x^{2}+1}}-\frac{a^{2}}{2 d^{2} x^{2}}-\frac{2 c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{c^{2} b^{2} \arcsinh \left(c x \right)^{2}}{d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{4 c^{2} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 c^{2} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 c^{2} a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{2 d^{2} x^{2} \left(c^{2} x^{2}+1\right)}"," ",0,"-b^2*c^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^2-c^2*b^2/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+c^2*b^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-1)+c^2*b^2/d^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+4*c^2*b^2/d^2*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+4*c^2*b^2/d^2*polylog(3,c*x+(c^2*x^2+1)^(1/2))-1/2*c^2*a^2/d^2/(c^2*x^2+1)+c^2*a^2/d^2*ln(c^2*x^2+1)-2*c^2*a^2/d^2*ln(c*x)-4*c^2*a*b/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-4*c^2*a*b/d^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-a*b/d^2*arcsinh(c*x)/x^2/(c^2*x^2+1)-c*a*b/d^2/x/(c^2*x^2+1)^(1/2)-c*b^2/d^2*arcsinh(c*x)/x/(c^2*x^2+1)^(1/2)-2*c^2*a*b/d^2*arcsinh(c*x)/(c^2*x^2+1)+4*c^2*a*b/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*a^2/d^2/x^2-2*c^2*b^2/d^2*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))-4*c^2*b^2/d^2*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-2*c^2*b^2/d^2*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))-4*c^2*b^2/d^2*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-c^2*b^2/d^2*arcsinh(c*x)^2/(c^2*x^2+1)+2*c^2*b^2/d^2*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+2*c^2*b^2/d^2*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-4*c^2*a*b/d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-4*c^2*a*b/d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))+2*c^2*a*b/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b^2/d^2*arcsinh(c*x)^2/x^2/(c^2*x^2+1)","B"
242,0,0,444,0.464000," ","int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^2,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{4} \left(c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^2,x)","F"
243,0,0,331,0.541000," ","int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","\int \frac{x^{4} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","F"
244,1,523,151,0.375000," ","int(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","-\frac{a^{2}}{2 c^{4} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{a^{2}}{4 c^{4} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 b^{2} \arcsinh \left(c x \right)}{3 c^{4} d^{3}}+\frac{2 b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{3 c \,d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{2 b^{2} \arcsinh \left(c x \right) x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2} x^{2}}{2 c^{2} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 c^{3} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{4 b^{2} \arcsinh \left(c x \right) x^{2}}{3 c^{2} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{4 c^{4} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} x^{2}}{12 c^{2} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{2 b^{2} \arcsinh \left(c x \right)}{3 c^{4} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2}}{12 c^{4} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{2 b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{4} d^{3}}-\frac{a b \arcsinh \left(c x \right)}{c^{4} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{a b \arcsinh \left(c x \right)}{2 c^{4} d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{a b x}{6 c^{3} d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{2 a b x}{3 c^{3} d^{3} \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2/c^4*a^2/d^3/(c^2*x^2+1)+1/4/c^4*a^2/d^3/(c^2*x^2+1)^2+4/3/c^4*b^2/d^3*arcsinh(c*x)+2/3/c*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-2/3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^4-1/2/c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2*x^2+1/2/c^3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-4/3/c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^2-1/4/c^4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2-1/12/c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*x^2-2/3/c^4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)-1/12/c^4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)-2/3/c^4*b^2/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/c^4*a*b/d^3/(c^2*x^2+1)*arcsinh(c*x)+1/2/c^4*a*b/d^3/(c^2*x^2+1)^2*arcsinh(c*x)-1/6/c^3*a*b/d^3/(c^2*x^2+1)^(3/2)*x+2/3/c^3*a*b/d^3*x/(c^2*x^2+1)^(1/2)","B"
245,0,0,329,0.403000," ","int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","\int \frac{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","F"
246,1,432,131,0.151000," ","int(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","-\frac{a^{2}}{4 c^{2} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{2 b^{2} \arcsinh \left(c x \right)}{3 c^{2} d^{3}}+\frac{c \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{c^{2} b^{2} \arcsinh \left(c x \right) x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 c \,d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{2 b^{2} \arcsinh \left(c x \right) x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{4 c^{2} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{b^{2} x^{2}}{12 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)}{3 c^{2} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{b^{2}}{12 c^{2} d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{2} d^{3}}-\frac{a b \arcsinh \left(c x \right)}{2 c^{2} d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{a b x}{6 c \,d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{a b x}{3 c \,d^{3} \sqrt{c^{2} x^{2}+1}}"," ",0,"-1/4/c^2*a^2/d^3/(c^2*x^2+1)^2+2/3/c^2*b^2/d^3*arcsinh(c*x)+1/3*c*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-1/3*c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^4+1/2/c*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-2/3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^2-1/4/c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2+1/12*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*x^2-1/3/c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)+1/12/c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)-1/3/c^2*b^2/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/2/c^2*a*b/d^3/(c^2*x^2+1)^2*arcsinh(c*x)+1/6/c*a*b/d^3/(c^2*x^2+1)^(3/2)*x+1/3/c*a*b/d^3*x/(c^2*x^2+1)^(1/2)","B"
247,0,0,320,0.210000," ","int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x)","F"
248,1,1129,300,0.337000," ","int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^3,x)","\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{2 a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 b^{2} \arcsinh \left(c x \right)^{2}}{4 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 b^{2} \arcsinh \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 a b}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 a b \,c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{8 a b \,c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 b^{2} \arcsinh \left(c x \right) c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right)^{2} c^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{8 b^{2} \arcsinh \left(c x \right) c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{a^{2}}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}+\frac{a^{2} \ln \left(c x \right)}{d^{3}}-\frac{a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}+\frac{a^{2}}{2 d^{3} \left(c^{2} x^{2}+1\right)}-\frac{8 b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{3 d^{3}}-\frac{b^{2}}{12 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 d^{3}}+\frac{b^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}-\frac{2 b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{2 b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 a b c x \sqrt{c^{2} x^{2}+1}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{4 a b \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{a b \arcsinh \left(c x \right) c^{2} x^{2}}{d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{4 b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3} x^{3}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{3 b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c x}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{2 a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 a b \arcsinh \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} c^{2} x^{2}}{12 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}"," ",0,"b^2/d^3*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*b^2/d^3*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-b^2/d^3*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-b^2/d^3*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+b^2/d^3*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2/d^3*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-a*b/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+2*a*b/d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*a*b/d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))+4/3*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)+3/4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2+4/3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)+4/3*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c^4*x^4+8/3*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c^2*x^2+4/3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*c^4*x^4+1/2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2*c^2*x^2+8/3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*c^2*x^2+1/2*b^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^3+1/4*a^2/d^3/(c^2*x^2+1)^2+a^2/d^3*ln(c*x)-1/2*a^2/d^3*ln(c^2*x^2+1)+1/2*a^2/d^3/(c^2*x^2+1)-8/3*b^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2))-2*b^2/d^3*polylog(3,-c*x-(c^2*x^2+1)^(1/2))-2*b^2/d^3*polylog(3,c*x+(c^2*x^2+1)^(1/2))-1/12*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)+4/3*b^2/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*c^2*x^2-3/2*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c*x*(c^2*x^2+1)^(1/2)-4/3*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*c^3*x^3*(c^2*x^2+1)^(1/2)-4/3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3*x^3-3/2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c*x-2*a*b/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+2*a*b/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))+2*a*b/d^3*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-1/12*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*c^2*x^2+3/2*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)","B"
249,0,0,428,0.489000," ","int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^3,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{2} \left(c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^3,x)","F"
250,1,1436,402,0.426000," ","int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^3,x)","-\frac{4 c^{6} a b \,x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{8 c^{4} a b \,x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{4 c^{6} b^{2} \arcsinh \left(c x \right) x^{4}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{3 c^{4} b^{2} \arcsinh \left(c x \right)^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{8 c^{4} b^{2} \arcsinh \left(c x \right) x^{2}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{6 c^{2} a b \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{6 c^{2} a b \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{9 c^{2} a b \arcsinh \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{6 c^{2} a b \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{a b \arcsinh \left(c x \right)}{d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) x^{2}}-\frac{4 c^{2} a b}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{c^{4} b^{2} x^{2}}{12 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{3 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{9 c^{2} b^{2} \arcsinh \left(c x \right)^{2}}{4 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{3 c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{6 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{4 c^{2} b^{2} \arcsinh \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) x^{2}}+\frac{3 c^{2} a b \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{6 c^{2} a b \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{6 c^{2} a b \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 c^{2} b^{2} \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{6 c^{2} b^{2} \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{a^{2}}{2 d^{3} x^{2}}-\frac{3 b^{2} c^{2} \polylog \left(3, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}+\frac{6 c^{2} b^{2} \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}+\frac{6 c^{2} b^{2} \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{c^{2} a^{2}}{4 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{c^{2} a^{2}}{d^{3} \left(c^{2} x^{2}+1\right)}+\frac{c^{2} b^{2}}{12 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{3 c^{2} a^{2} \ln \left(c x \right)}{d^{3}}+\frac{3 c^{2} a^{2} \ln \left(c^{2} x^{2}+1\right)}{2 d^{3}}+\frac{8 c^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{3 d^{3}}+\frac{c^{2} b^{2} \ln \left(c x +\sqrt{c^{2} x^{2}+1}-1\right)}{d^{3}}+\frac{c^{2} b^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{d^{3}}-\frac{7 c^{2} b^{2} \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 d^{3}}+\frac{c^{3} a b x \sqrt{c^{2} x^{2}+1}}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{4 c^{5} a b \,x^{3} \sqrt{c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{c a b \sqrt{c^{2} x^{2}+1}}{d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) x}-\frac{3 c^{4} a b \arcsinh \left(c x \right) x^{2}}{d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}-\frac{c \,b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right) x}+\frac{4 c^{5} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{3 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}+\frac{c^{3} b^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{2 d^{3} \left(c^{4} x^{4}+2 c^{2} x^{2}+1\right)}"," ",0,"-3/2*b^2*c^2*polylog(3,-(c*x+(c^2*x^2+1)^(1/2))^2)/d^3-4/3*c^6*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x^4-8/3*c^4*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x^2-4/3*c^6*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^4-3/2*c^4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2*x^2-8/3*c^4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^2-6*c^2*a*b/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-6*c^2*a*b/d^3*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))-9/2*c^2*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)+6*c^2*a*b/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-a*b/d^3/(c^4*x^4+2*c^2*x^2+1)/x^2*arcsinh(c*x)+3*c^2*b^2/d^3*arcsinh(c*x)*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-9/4*c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)^2-3*c^2*b^2/d^3*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))-6*c^2*b^2/d^3*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))+3*c^2*b^2/d^3*arcsinh(c*x)^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-4/3*c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)-4/3*c^2*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)+1/12*c^4*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*x^2-1/2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)/x^2*arcsinh(c*x)^2+3*c^2*a*b/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-6*c^2*a*b/d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-6*c^2*a*b/d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))-3*c^2*b^2/d^3*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))-6*c^2*b^2/d^3*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))-1/2*a^2/d^3/x^2-1/4*c^2*a^2/d^3/(c^2*x^2+1)^2-c^2*a^2/d^3/(c^2*x^2+1)+1/12*c^2*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)-3*c^2*a^2/d^3*ln(c*x)+3/2*c^2*a^2/d^3*ln(c^2*x^2+1)+8/3*c^2*b^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2))+6*c^2*b^2/d^3*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+6*c^2*b^2/d^3*polylog(3,c*x+(c^2*x^2+1)^(1/2))+c^2*b^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-1)+c^2*b^2/d^3*ln(1+c*x+(c^2*x^2+1)^(1/2))-7/3*c^2*b^2/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-3*c^4*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*x^2+1/2*c^3*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x*(c^2*x^2+1)^(1/2)+4/3*c^5*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)*x^3*(c^2*x^2+1)^(1/2)-c*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)/x*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-c*a*b/d^3/(c^4*x^4+2*c^2*x^2+1)/x*(c^2*x^2+1)^(1/2)+4/3*c^5*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3+1/2*c^3*b^2/d^3/(c^4*x^4+2*c^2*x^2+1)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x","B"
251,0,0,550,0.617000," ","int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^3,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{4} \left(c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^3,x)","F"
252,1,486,250,0.134000," ","int((Pi*c^2*x^2+Pi)^(5/2)*(a+b*arcsinh(c*x))^2,x)","\frac{a^{2} x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{5}{2}}}{6}+\frac{5 a^{2} \pi  x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{24}+\frac{5 a^{2} \pi^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{16}+\frac{5 a^{2} \pi^{3} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{16 \sqrt{\pi  \,c^{2}}}+\frac{b^{2} \pi^{\frac{5}{2}} c^{4} \sqrt{c^{2} x^{2}+1}\, \arcsinh \left(c x \right)^{2} x^{5}}{6}-\frac{b^{2} \pi^{\frac{5}{2}} c^{5} \arcsinh \left(c x \right) x^{6}}{18}+\frac{b^{2} \pi^{\frac{5}{2}} c^{4} x^{5} \sqrt{c^{2} x^{2}+1}}{108}+\frac{13 b^{2} \pi^{\frac{5}{2}} c^{2} \sqrt{c^{2} x^{2}+1}\, \arcsinh \left(c x \right)^{2} x^{3}}{24}-\frac{13 b^{2} \pi^{\frac{5}{2}} c^{3} \arcsinh \left(c x \right) x^{4}}{48}+\frac{97 b^{2} \pi^{\frac{5}{2}} c^{2} x^{3} \sqrt{c^{2} x^{2}+1}}{1728}+\frac{11 b^{2} \pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, x}{16}-\frac{11 b^{2} \pi^{\frac{5}{2}} c \arcsinh \left(c x \right) x^{2}}{16}+\frac{299 b^{2} \pi^{\frac{5}{2}} x \sqrt{c^{2} x^{2}+1}}{1152}+\frac{5 b^{2} \pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{3}}{48 c}-\frac{299 b^{2} \pi^{\frac{5}{2}} \arcsinh \left(c x \right)}{1152 c}+\frac{a b \,\pi^{\frac{5}{2}} c^{4} \sqrt{c^{2} x^{2}+1}\, \arcsinh \left(c x \right) x^{5}}{3}-\frac{a b \,\pi^{\frac{5}{2}} c^{5} x^{6}}{18}+\frac{13 a b \,\pi^{\frac{5}{2}} c^{2} \sqrt{c^{2} x^{2}+1}\, \arcsinh \left(c x \right) x^{3}}{12}-\frac{13 a b \,\pi^{\frac{5}{2}} c^{3} x^{4}}{48}+\frac{11 a b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{8}-\frac{11 a b \,\pi^{\frac{5}{2}} c \,x^{2}}{16}+\frac{5 a b \,\pi^{\frac{5}{2}} \arcsinh \left(c x \right)^{2}}{16 c}-\frac{17 a b \,\pi^{\frac{5}{2}}}{36 c}"," ",0,"1/6*a^2*x*(Pi*c^2*x^2+Pi)^(5/2)+5/24*a^2*Pi*x*(Pi*c^2*x^2+Pi)^(3/2)+5/16*a^2*Pi^2*x*(Pi*c^2*x^2+Pi)^(1/2)+5/16*a^2*Pi^3*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/6*b^2*Pi^(5/2)*c^4*(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*x^5-1/18*b^2*Pi^(5/2)*c^5*arcsinh(c*x)*x^6+1/108*b^2*Pi^(5/2)*c^4*x^5*(c^2*x^2+1)^(1/2)+13/24*b^2*Pi^(5/2)*c^2*(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*x^3-13/48*b^2*Pi^(5/2)*c^3*arcsinh(c*x)*x^4+97/1728*b^2*Pi^(5/2)*c^2*x^3*(c^2*x^2+1)^(1/2)+11/16*b^2*Pi^(5/2)*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x-11/16*b^2*Pi^(5/2)*c*arcsinh(c*x)*x^2+299/1152*b^2*Pi^(5/2)*x*(c^2*x^2+1)^(1/2)+5/48*b^2*Pi^(5/2)/c*arcsinh(c*x)^3-299/1152*b^2*Pi^(5/2)*arcsinh(c*x)/c+1/3*a*b*Pi^(5/2)*c^4*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^5-1/18*a*b*Pi^(5/2)*c^5*x^6+13/12*a*b*Pi^(5/2)*c^2*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^3-13/48*a*b*Pi^(5/2)*c^3*x^4+11/8*a*b*Pi^(5/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-11/16*a*b*Pi^(5/2)*c*x^2+5/16*a*b*Pi^(5/2)/c*arcsinh(c*x)^2-17/36*a*b*Pi^(5/2)/c","A"
253,1,350,174,0.118000," ","int((Pi*c^2*x^2+Pi)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\frac{a^{2} x \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}{4}+\frac{3 a^{2} \pi  x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{8}+\frac{3 a^{2} \pi^{2} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{8 \sqrt{\pi  \,c^{2}}}+\frac{b^{2} \pi^{\frac{3}{2}} c^{2} \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, x^{3}}{4}-\frac{b^{2} \pi^{\frac{3}{2}} c^{3} \arcsinh \left(c x \right) x^{4}}{8}+\frac{b^{2} \pi^{\frac{3}{2}} c^{2} x^{3} \sqrt{c^{2} x^{2}+1}}{32}+\frac{5 b^{2} \pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, x}{8}-\frac{5 b^{2} \pi^{\frac{3}{2}} c \arcsinh \left(c x \right) x^{2}}{8}+\frac{17 b^{2} \pi^{\frac{3}{2}} x \sqrt{c^{2} x^{2}+1}}{64}+\frac{b^{2} \pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{3}}{8 c}-\frac{17 b^{2} \pi^{\frac{3}{2}} \arcsinh \left(c x \right)}{64 c}+\frac{a b \,\pi^{\frac{3}{2}} c^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{3}}{2}-\frac{a b \,\pi^{\frac{3}{2}} c^{3} x^{4}}{8}+\frac{5 a b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x}{4}-\frac{5 a b \,\pi^{\frac{3}{2}} c \,x^{2}}{8}+\frac{3 a b \,\pi^{\frac{3}{2}} \arcsinh \left(c x \right)^{2}}{8 c}-\frac{a b \,\pi^{\frac{3}{2}}}{2 c}"," ",0,"1/4*a^2*x*(Pi*c^2*x^2+Pi)^(3/2)+3/8*a^2*Pi*x*(Pi*c^2*x^2+Pi)^(1/2)+3/8*a^2*Pi^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/4*b^2*Pi^(3/2)*c^2*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^3-1/8*b^2*Pi^(3/2)*c^3*arcsinh(c*x)*x^4+1/32*b^2*Pi^(3/2)*c^2*x^3*(c^2*x^2+1)^(1/2)+5/8*b^2*Pi^(3/2)*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x-5/8*b^2*Pi^(3/2)*c*arcsinh(c*x)*x^2+17/64*b^2*Pi^(3/2)*x*(c^2*x^2+1)^(1/2)+1/8*b^2*Pi^(3/2)/c*arcsinh(c*x)^3-17/64*b^2*Pi^(3/2)*arcsinh(c*x)/c+1/2*a*b*Pi^(3/2)*c^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^3-1/8*a*b*Pi^(3/2)*c^3*x^4+5/4*a*b*Pi^(3/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-5/8*a*b*Pi^(3/2)*c*x^2+3/8*a*b*Pi^(3/2)/c*arcsinh(c*x)^2-1/2*a*b*Pi^(3/2)/c","B"
254,1,213,100,0.104000," ","int((Pi*c^2*x^2+Pi)^(1/2)*(a+b*arcsinh(c*x))^2,x)","\frac{a^{2} x \sqrt{\pi  \,c^{2} x^{2}+\pi}}{2}+\frac{a^{2} \pi  \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{2 \sqrt{\pi  \,c^{2}}}+\frac{b^{2} \sqrt{\pi}\, \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, x}{2}-\frac{b^{2} \sqrt{\pi}\, c \arcsinh \left(c x \right) x^{2}}{2}+\frac{b^{2} \sqrt{\pi}\, \arcsinh \left(c x \right)^{3}}{6 c}+\frac{b^{2} x \sqrt{\pi}\, \sqrt{c^{2} x^{2}+1}}{4}-\frac{b^{2} \arcsinh \left(c x \right) \sqrt{\pi}}{4 c}+a b \sqrt{\pi}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x -\frac{a b \sqrt{\pi}\, c \,x^{2}}{2}+\frac{a b \sqrt{\pi}\, \arcsinh \left(c x \right)^{2}}{2 c}-\frac{a b \sqrt{\pi}}{2 c}"," ",0,"1/2*a^2*x*(Pi*c^2*x^2+Pi)^(1/2)+1/2*a^2*Pi*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/2*b^2*Pi^(1/2)*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x-1/2*b^2*Pi^(1/2)*c*arcsinh(c*x)*x^2+1/6*b^2*Pi^(1/2)/c*arcsinh(c*x)^3+1/4*b^2*x*Pi^(1/2)*(c^2*x^2+1)^(1/2)-1/4*b^2*arcsinh(c*x)*Pi^(1/2)/c+a*b*Pi^(1/2)*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x-1/2*a*b*Pi^(1/2)*c*x^2+1/2*a*b*Pi^(1/2)/c*arcsinh(c*x)^2-1/2*a*b*Pi^(1/2)/c","B"
255,1,72,21,0.084000," ","int((a+b*arcsinh(c*x))^2/(Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a^{2} \ln \left(\frac{\pi  x \,c^{2}}{\sqrt{\pi  \,c^{2}}}+\sqrt{\pi  \,c^{2} x^{2}+\pi}\right)}{\sqrt{\pi  \,c^{2}}}+\frac{b^{2} \arcsinh \left(c x \right)^{3}}{3 c \sqrt{\pi}}+\frac{a b \arcsinh \left(c x \right)^{2}}{c \sqrt{\pi}}"," ",0,"a^2*ln(Pi*x*c^2/(Pi*c^2)^(1/2)+(Pi*c^2*x^2+Pi)^(1/2))/(Pi*c^2)^(1/2)+1/3*b^2/c/Pi^(1/2)*arcsinh(c*x)^3+a*b*arcsinh(c*x)^2/c/Pi^(1/2)","B"
256,1,306,114,0.193000," ","int((a+b*arcsinh(c*x))^2/(Pi*c^2*x^2+Pi)^(3/2),x)","\frac{a^{2} x}{\pi  \sqrt{\pi  \,c^{2} x^{2}+\pi}}-\frac{b^{2} \arcsinh \left(c x \right)^{2} c \,x^{2}}{\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsinh \left(c x \right)^{2} x}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right)^{2}}{\pi^{\frac{3}{2}} c \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \arcsinh \left(c x \right)^{2}}{c \,\pi^{\frac{3}{2}}}-\frac{2 b^{2} \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c \,\pi^{\frac{3}{2}}}-\frac{b^{2} \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c \,\pi^{\frac{3}{2}}}+\frac{4 a b \arcsinh \left(c x \right)}{c \,\pi^{\frac{3}{2}}}-\frac{2 a b \arcsinh \left(c x \right) c \,x^{2}}{\pi^{\frac{3}{2}} \left(c^{2} x^{2}+1\right)}+\frac{2 a b \arcsinh \left(c x \right) x}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \arcsinh \left(c x \right)}{\pi^{\frac{3}{2}} c \left(c^{2} x^{2}+1\right)}-\frac{2 a b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{c \,\pi^{\frac{3}{2}}}"," ",0,"a^2/Pi*x/(Pi*c^2*x^2+Pi)^(1/2)-b^2/Pi^(3/2)*arcsinh(c*x)^2*c/(c^2*x^2+1)*x^2+b^2/Pi^(3/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)*x-b^2/Pi^(3/2)*arcsinh(c*x)^2/c/(c^2*x^2+1)+2*b^2/c/Pi^(3/2)*arcsinh(c*x)^2-2*b^2/c/Pi^(3/2)*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-b^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/c/Pi^(3/2)+4*a*b/c/Pi^(3/2)*arcsinh(c*x)-2*a*b/Pi^(3/2)*arcsinh(c*x)*c/(c^2*x^2+1)*x^2+2*a*b/Pi^(3/2)*arcsinh(c*x)/(c^2*x^2+1)^(1/2)*x-2*a*b/Pi^(3/2)*arcsinh(c*x)/c/(c^2*x^2+1)-2*a*b/c/Pi^(3/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
257,1,1730,192,0.362000," ","int((a+b*arcsinh(c*x))^2/(Pi*c^2*x^2+Pi)^(5/2),x)","-\frac{2 b^{2} \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c \,\pi^{\frac{5}{2}}}+\frac{4 b^{2} \arcsinh \left(c x \right)^{2}}{3 c \,\pi^{\frac{5}{2}}}+\frac{a^{2} x}{3 \pi  \left(\pi  \,c^{2} x^{2}+\pi \right)^{\frac{3}{2}}}+\frac{2 a^{2} x}{3 \pi^{2} \sqrt{\pi  \,c^{2} x^{2}+\pi}}+\frac{2 b^{2} c^{7} x^{8}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{10 b^{2} c^{5} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{6 b^{2} c^{3} x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{14 b^{2} c \,x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{2 b^{2} c^{5} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{b^{2} c^{4} x^{5}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{b^{2} c \,x^{2}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{5 b^{2} c^{3} x^{4}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{7 b^{2} c^{2} x^{3}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{4 a b}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{8 b^{2} \arcsinh \left(c x \right)^{2}}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 b^{2} \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 b^{2} \arcsinh \left(c x \right)^{2} x}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{34 a b \,c^{2} \arcsinh \left(c x \right) x^{3}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{40 a b \,c^{3} \arcsinh \left(c x \right) x^{4}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{44 a b c \arcsinh \left(c x \right) x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{4 a b \,c^{5} \arcsinh \left(c x \right) x^{6}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 a b \,c^{4} \arcsinh \left(c x \right) x^{5}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{16 a b c \,x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{4 b^{2} x}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{22 b^{2} c \arcsinh \left(c x \right)^{2} x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{16 a b \arcsinh \left(c x \right)}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{16 b^{2} c^{5} \arcsinh \left(c x \right) x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{20 b^{2} c^{3} \arcsinh \left(c x \right)^{2} x^{4}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 b^{2} c^{7} \arcsinh \left(c x \right) x^{8}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{2 b^{2} c^{5} \arcsinh \left(c x \right)^{2} x^{6}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{16 b^{2} c \arcsinh \left(c x \right) x^{2}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{8 b^{2} c^{3} \arcsinh \left(c x \right) x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{2 b^{2} c^{4} \arcsinh \left(c x \right)^{2} x^{5}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{4 b^{2} c^{3} \arcsinh \left(c x \right) x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}+\frac{17 b^{2} c^{2} \arcsinh \left(c x \right)^{2} x^{3}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{3 b^{2} c \arcsinh \left(c x \right) x^{2}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}-\frac{4 b^{2} c^{5} \arcsinh \left(c x \right) x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}+\frac{8 a b \arcsinh \left(c x \right) x}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{4 a b \,c^{3} x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}+\frac{4 b^{2}}{3 \pi^{\frac{5}{2}} c \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{4 a b \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c \,\pi^{\frac{5}{2}}}-\frac{4 b^{2} \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 c \,\pi^{\frac{5}{2}}}+\frac{8 a b \arcsinh \left(c x \right)}{3 c \,\pi^{\frac{5}{2}}}-\frac{3 a b c \,x^{2}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}+\frac{8 a b \,c^{3} x^{4}}{\pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{4 a b \,c^{7} x^{8}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}+\frac{16 a b \,c^{5} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)^{2}}-\frac{4 a b \,c^{5} x^{6}}{3 \pi^{\frac{5}{2}} \left(3 c^{2} x^{2}+4\right) \left(c^{2} x^{2}+1\right)}"," ",0,"-2/3*b^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)/c/Pi^(5/2)+4/3*b^2/c/Pi^(5/2)*arcsinh(c*x)^2+1/3*a^2/Pi*x/(Pi*c^2*x^2+Pi)^(3/2)+2/3*a^2/Pi^2*x/(Pi*c^2*x^2+Pi)^(1/2)-22/3*b^2/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)^2*x^2+2/3*b^2/Pi^(5/2)*c^7/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^8+10/3*b^2/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^6+6*b^2/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^4+14/3*b^2/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^2-8/3*b^2/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)^2+4/3*b^2/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)-2/3*b^2/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)*x^6-b^2/Pi^(5/2)*c^4/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*x^5+4*b^2/Pi^(5/2)/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)^2*x-b^2/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)*x^2-5/3*b^2/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)*x^4-7/3*b^2/Pi^(5/2)*c^2/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*x^3+4/3*a*b/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2+4*a*b/Pi^(5/2)*c^4/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^5+34/3*a*b/Pi^(5/2)*c^2/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x^3-40/3*a*b/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^4-44/3*a*b/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^2-4*a*b/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^6+16/3*a*b/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^2-16/3*a*b/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)-4/3*b^2/Pi^(5/2)/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*x-4*a*b/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)*x^4+16/3*b^2/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^6-20/3*b^2/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)^2*x^4+4/3*b^2/Pi^(5/2)*c^7/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^8-2*b^2/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)^2*x^6+16/3*b^2/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^2+8*b^2/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*arcsinh(c*x)*x^4+2*b^2/Pi^(5/2)*c^4/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)^2*x^5-4*b^2/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)*arcsinh(c*x)*x^4+17/3*b^2/Pi^(5/2)*c^2/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)^2*x^3-3*b^2/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)*arcsinh(c*x)*x^2-4/3*b^2/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)*arcsinh(c*x)*x^6+4/3*b^2/Pi^(5/2)/c/(3*c^2*x^2+4)/(c^2*x^2+1)^2-4/3*b^2/c/Pi^(5/2)*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+8/3*a*b/c/Pi^(5/2)*arcsinh(c*x)-4/3*a*b/c/Pi^(5/2)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+8*a*b/Pi^(5/2)/(3*c^2*x^2+4)/(c^2*x^2+1)^(3/2)*arcsinh(c*x)*x-3*a*b/Pi^(5/2)*c/(3*c^2*x^2+4)/(c^2*x^2+1)*x^2+8*a*b/Pi^(5/2)*c^3/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^4+4/3*a*b/Pi^(5/2)*c^7/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^8+16/3*a*b/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)^2*x^6-4/3*a*b/Pi^(5/2)*c^5/(3*c^2*x^2+4)/(c^2*x^2+1)*x^6","B"
258,1,1162,310,0.412000," ","int(x^3*(a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x)","a^{2} \left(\frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}-\frac{2 \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}-10 \arcsinh \left(c x \right)+2\right)}{4000 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right)}{864 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right)}{16 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right)}{16 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right)}{864 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}+10 \arcsinh \left(c x \right)+2\right)}{4000 c^{4} \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right)}{800 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{288 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{288 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right)}{800 c^{4} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a^2*(1/5*x^2*(c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(c^2*d*x^2+d)^(3/2))+b^2*(1/4000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2-10*arcsinh(c*x)+2)/c^4/(c^2*x^2+1)-1/864*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)/c^4/(c^2*x^2+1)-1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)/c^4/(c^2*x^2+1)-1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)/c^4/(c^2*x^2+1)-1/864*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)/c^4/(c^2*x^2+1)+1/4000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2+10*arcsinh(c*x)+2)/c^4/(c^2*x^2+1))+2*a*b*(1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))/c^4/(c^2*x^2+1)-1/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^4/(c^2*x^2+1)-1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^4/(c^2*x^2+1)-1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^4/(c^2*x^2+1)-1/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^4/(c^2*x^2+1)+1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))/c^4/(c^2*x^2+1))","B"
259,1,701,251,0.350000," ","int(x^2*(a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}-\frac{a^{2} x \sqrt{c^{2} d \,x^{2}+d}}{8 c^{2}}-\frac{a^{2} d \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{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{24 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right)^{2} x^{5}}{4 c^{2} x^{2}+4}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{3}}{8 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{8 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{64 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{8 c \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{5}}{32 c^{2} x^{2}+32}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{64 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{64 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) x^{4}}{8 \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{8 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{5}}{2 c^{2} x^{2}+2}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \,x^{4}}{8 \sqrt{c^{2} x^{2}+1}}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{4 \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{8 c \sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{4 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}}{64 c^{3} \sqrt{c^{2} x^{2}+1}}"," ",0,"1/4*a^2*x*(c^2*d*x^2+d)^(3/2)/c^2/d-1/8*a^2/c^2*x*(c^2*d*x^2+d)^(1/2)-1/8*a^2/c^2*d*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)-1/24*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^5+3/8*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/8*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x-1/64*b^2*(d*(c^2*x^2+1))^(1/2)/c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/8*b^2*(d*(c^2*x^2+1))^(1/2)/c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2+1/32*b^2*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*x^5+3/64*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*x^3+1/64*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/(c^2*x^2+1)*x-1/8*b^2*(d*(c^2*x^2+1))^(1/2)*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4-1/8*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^2+1/2*a*b*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/8*a*b*(d*(c^2*x^2+1))^(1/2)*c/(c^2*x^2+1)^(1/2)*x^4+3/4*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/8*a*b*(d*(c^2*x^2+1))^(1/2)/c/(c^2*x^2+1)^(1/2)*x^2+1/4*a*b*(d*(c^2*x^2+1))^(1/2)/c^2/(c^2*x^2+1)*arcsinh(c*x)*x-1/64*a*b*(d*(c^2*x^2+1))^(1/2)/c^3/(c^2*x^2+1)^(1/2)","B"
260,1,657,156,0.230000," ","int(x*(a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right)}{216 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right)}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right)}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right)}{216 c^{2} \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"1/3*a^2/c^2/d*(c^2*d*x^2+d)^(3/2)+b^2*(1/216*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)/c^2/(c^2*x^2+1)+1/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)/c^2/(c^2*x^2+1)+1/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)/c^2/(c^2*x^2+1)+1/216*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)/c^2/(c^2*x^2+1))+2*a*b*(1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^2/(c^2*x^2+1)+1/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^2/(c^2*x^2+1)+1/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^2/(c^2*x^2+1)+1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^2/(c^2*x^2+1))","B"
261,1,482,158,0.214000," ","int((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x)","\frac{x \,a^{2} \sqrt{c^{2} d \,x^{2}+d}}{2}+\frac{a^{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^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{6 \sqrt{c^{2} x^{2}+1}\, c}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right)^{2} x^{3}}{2 c^{2} x^{2}+2}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{3}}{4 c^{2} x^{2}+4}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{4 c^{2} x^{2}+4}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) x^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{2 c^{2} x^{2}+2}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{4 c \sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{3}}{c^{2} x^{2}+1}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \,x^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{2} x^{2}+1}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}}{4 c \sqrt{c^{2} x^{2}+1}}"," ",0,"1/2*x*a^2*(c^2*d*x^2+d)^(1/2)+1/2*a^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)+1/6*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^3+1/2*b^2*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*x^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*x-1/2*b^2*(d*(c^2*x^2+1))^(1/2)*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)^2*x-1/4*b^2*(d*(c^2*x^2+1))^(1/2)/c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+1/2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^2+a*b*(d*(c^2*x^2+1))^(1/2)*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/2*a*b*(d*(c^2*x^2+1))^(1/2)*c/(c^2*x^2+1)^(1/2)*x^2+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*x-1/4*a*b*(d*(c^2*x^2+1))^(1/2)/c/(c^2*x^2+1)^(1/2)","B"
262,1,823,353,0.337000," ","int((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x,x)","-\sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right) a^{2}+a^{2} \sqrt{c^{2} d \,x^{2}+d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{2} c^{2}}{c^{2} x^{2}+1}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x c}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{2}}{c^{2} x^{2}+1}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c^{2} x^{2}+1}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{c^{2} x^{2}+1}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2} c^{2}}{c^{2} x^{2}+1}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c x}{\sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{2} x^{2}+1}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}}"," ",0,"-d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)*a^2+a^2*(c^2*d*x^2+d)^(1/2)+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)^2*x^2*c^2-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*c^2*x^2+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,c*x+(c^2*x^2+1)^(1/2))+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*x^2*c^2-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*c*x+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))","B"
263,1,625,207,0.321000," ","int((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x^2,x)","-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{d x}+a^{2} c^{2} x \sqrt{c^{2} d \,x^{2}+d}+\frac{a^{2} c^{2} d \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^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} c}{3 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x \,c^{2}}{c^{2} x^{2}+1}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{x \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2}}{c^{2} x^{2}+1}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{x \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c}{\sqrt{c^{2} x^{2}+1}}"," ",0,"-a^2/d/x*(c^2*d*x^2+d)^(3/2)+a^2*c^2*x*(c^2*d*x^2+d)^(1/2)+a^2*c^2*d*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^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^3*c-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*x/(c^2*x^2+1)*c^2-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)*c-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/x/(c^2*x^2+1)+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)*x/(c^2*x^2+1)*c^2-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/x/(c^2*x^2+1)+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c","B"
264,1,870,371,0.452000," ","int((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x^3,x)","-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2 d \,x^{2}}-\frac{a^{2} \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right) c^{2}}{2}+\frac{a^{2} \sqrt{c^{2} d \,x^{2}+d}\, c^{2}}{2}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2}}{2 \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{x \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{2 x^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctanh \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{c^{2} x^{2}+1}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{x \sqrt{c^{2} x^{2}+1}}-\frac{a b \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}}{x^{2} \left(c^{2} x^{2}+1\right)}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}}"," ",0,"-1/2*a^2/d/x^2*(c^2*d*x^2+d)^(3/2)-1/2*a^2*d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)*c^2+1/2*a^2*(c^2*d*x^2+d)^(1/2)*c^2-1/2*b^2*arcsinh(c*x)^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*c^2-b^2*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)/x/(c^2*x^2+1)^(1/2)*c-1/2*b^2*arcsinh(c*x)^2*(d*(c^2*x^2+1))^(1/2)/x^2/(c^2*x^2+1)-1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,-c*x-(c^2*x^2+1)^(1/2))*c^2+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,c*x+(c^2*x^2+1)^(1/2))*c^2-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arctanh(c*x+(c^2*x^2+1)^(1/2))*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)*arcsinh(c*x)*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/x/(c^2*x^2+1)^(1/2)*c-a*b*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)/x^2/(c^2*x^2+1)+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2","B"
265,1,2557,274,0.486000," ","int((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x^4,x)","\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{9 c^{4} x^{4}+9 c^{2} x^{2}+3}-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 d \,x^{3}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} c^{5}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{2} \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right)^{2} c^{6}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right)^{2} c^{4}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{2}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4} \arcsinh \left(c x \right)^{2} c^{7}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right)^{2} c^{5}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) c^{5}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right)^{2} c^{8}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{8}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{3}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{6 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{20 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{10 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4} \arcsinh \left(c x \right) c^{7}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) c^{5}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{8}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4} c^{7}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} c^{5}}{\left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3}}{3 \left(3 c^{4} x^{4}+3 c^{2} x^{2}+1\right) \sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{3}}{3 \sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{9 c^{4} x^{4}+9 c^{2} x^{2}+3}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{9 c^{4} x^{4}+9 c^{2} x^{2}+3}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{9 c^{4} x^{4}+9 c^{2} x^{2}+3}"," ",0,"-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^3-1/3*a^2/d/x^3*(c^2*d*x^2+d)^(3/2)-3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)^2*c^6-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-10/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)^2*c^4-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-5/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)^2*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*c+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^7+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^5-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)^2*c^8-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)^2+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^3+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^3+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c^3-a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3-2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8-6*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-20/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-10/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)*c^2+2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^7+2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*c^7+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^3-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3*c^6+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x*c^4+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3*arcsinh(c*x)*c^6+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x*arcsinh(c*x)*c^4-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-5/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/x/(c^2*x^2+1)*c^2+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^3+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^3-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)*x^3*c^6+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+3*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3","B"
266,1,1766,420,0.540000," ","int(x^3*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x)","a^{2} \left(\frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}-\frac{2 \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(49 \arcsinh \left(c x \right)^{2}-14 \arcsinh \left(c x \right)+2\right) d}{43904 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}-10 \arcsinh \left(c x \right)+2\right) d}{16000 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right) d}{1152 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right) d}{128 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right) d}{128 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right) d}{1152 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}+10 \arcsinh \left(c x \right)+2\right) d}{16000 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(49 \arcsinh \left(c x \right)^{2}+14 \arcsinh \left(c x \right)+2\right) d}{43904 c^{4} \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+7 \arcsinh \left(c x \right)\right) d}{6272 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right) d}{3200 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d}{384 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d}{384 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right) d}{3200 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+7 \arcsinh \left(c x \right)\right) d}{6272 c^{4} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a^2*(1/7*x^2*(c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(c^2*d*x^2+d)^(5/2))+b^2*(1/43904*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(49*arcsinh(c*x)^2-14*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)+1/16000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2-10*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)-1/1152*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)-3/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)-3/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)-1/1152*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)+1/16000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2+10*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1)+1/43904*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(49*arcsinh(c*x)^2+14*arcsinh(c*x)+2)*d/c^4/(c^2*x^2+1))+2*a*b*(1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+7*arcsinh(c*x))*d/c^4/(c^2*x^2+1)+1/3200*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))*d/c^4/(c^2*x^2+1)-1/384*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d/c^4/(c^2*x^2+1)-3/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d/c^4/(c^2*x^2+1)-3/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d/c^4/(c^2*x^2+1)-1/384*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d/c^4/(c^2*x^2+1)+1/3200*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))*d/c^4/(c^2*x^2+1)+1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(1+7*arcsinh(c*x))*d/c^4/(c^2*x^2+1))","B"
267,1,934,351,0.486000," ","int(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right) x^{7}}{3 c^{2} x^{2}+3}+\frac{7 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{1152 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{59 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} x^{5}}{1728 \left(c^{2} x^{2}+1\right)}-\frac{7 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d x}{1152 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{7 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{1152 c^{3} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} d}{48 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{17 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)^{2} x^{3}}{48 \left(c^{2} x^{2}+1\right)}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{2}}{16 c \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{6}}{18 \sqrt{c^{2} x^{2}+1}}-\frac{7 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \,x^{4}}{48 \sqrt{c^{2} x^{2}+1}}+\frac{11 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right)^{2} x^{5}}{24 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)^{2} x}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right)^{2} x^{7}}{6 c^{2} x^{2}+6}+\frac{a^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6 c^{2} d}+\frac{11 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right) x^{5}}{12 \left(c^{2} x^{2}+1\right)}-\frac{a^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}-\frac{a^{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{65 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,x^{3}}{3456 \left(c^{2} x^{2}+1\right)}-\frac{a^{2} d x \sqrt{c^{2} d \,x^{2}+d}}{16 c^{2}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d}{16 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{17 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{3}}{24 \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} \arcsinh \left(c x \right) x^{6}}{18 \sqrt{c^{2} x^{2}+1}}-\frac{7 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \arcsinh \left(c x \right) x^{4}}{48 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{2}}{16 c \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} x^{7}}{108 c^{2} x^{2}+108}"," ",0,"7/1152*b^2*(d*(c^2*x^2+1))^(1/2)*d/c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+7/1152*a*b*(d*(c^2*x^2+1))^(1/2)*d/c^3/(c^2*x^2+1)^(1/2)+1/108*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*x^7+59/1728*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*x^5-7/1152*b^2*(d*(c^2*x^2+1))^(1/2)*d/c^2/(c^2*x^2+1)*x-1/48*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^3*d+17/48*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/8*a*b*(d*(c^2*x^2+1))^(1/2)*d/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+1/3*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7+11/12*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5+1/6*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^7+11/24*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^5+1/16*b^2*(d*(c^2*x^2+1))^(1/2)*d/c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x-1/16*a*b*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)*x^2-1/16*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^2*d+17/24*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/18*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^6-7/48*b^2*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4-1/16*b^2*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2-1/18*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^6-7/48*a*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*x^4+1/6*a^2*x*(c^2*d*x^2+d)^(5/2)/c^2/d-1/24*a^2/c^2*x*(c^2*d*x^2+d)^(3/2)-1/16*a^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)+65/3456*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*x^3-1/16*a^2/c^2*d*x*(c^2*d*x^2+d)^(1/2)","B"
268,1,1149,233,0.294000," ","int(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}-10 \arcsinh \left(c x \right)+2\right) d}{4000 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right) d}{288 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right) d}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right) d}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right) d}{288 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}+10 \arcsinh \left(c x \right)+2\right) d}{4000 c^{2} \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right) d}{800 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d}{96 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d}{96 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right) d}{800 c^{2} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"1/5*a^2/c^2/d*(c^2*d*x^2+d)^(5/2)+b^2*(1/4000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2-10*arcsinh(c*x)+2)*d/c^2/(c^2*x^2+1)+1/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)*d/c^2/(c^2*x^2+1)+1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)*d/c^2/(c^2*x^2+1)+1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)*d/c^2/(c^2*x^2+1)+1/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)*d/c^2/(c^2*x^2+1)+1/4000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2+10*arcsinh(c*x)+2)*d/c^2/(c^2*x^2+1))+2*a*b*(1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/96*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/96*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d/c^2/(c^2*x^2+1)+1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))*d/c^2/(c^2*x^2+1))","B"
269,1,709,254,0.276000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\frac{x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a^{2}}{4}+\frac{3 a^{2} d x \sqrt{c^{2} d \,x^{2}+d}}{8}+\frac{3 a^{2} d^{2} \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{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)^{2} x}{8 \left(c^{2} x^{2}+1\right)}-\frac{17 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{64 c \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right)^{2} x^{5}}{4 c^{2} x^{2}+4}+\frac{7 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right)^{2} x^{3}}{8 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} x^{5}}{32 c^{2} x^{2}+32}+\frac{19 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} x^{3}}{64 \left(c^{2} x^{2}+1\right)}+\frac{17 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d x}{64 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} d}{8 \sqrt{c^{2} x^{2}+1}\, c}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} \arcsinh \left(c x \right) x^{4}}{8 \sqrt{c^{2} x^{2}+1}}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \arcsinh \left(c x \right) x^{2}}{8 \sqrt{c^{2} x^{2}+1}}+\frac{7 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right) x^{3}}{4 \left(c^{2} x^{2}+1\right)}-\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \,x^{2}}{8 \sqrt{c^{2} x^{2}+1}}+\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x}{4 \left(c^{2} x^{2}+1\right)}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right) x^{5}}{2 c^{2} x^{2}+2}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{4}}{8 \sqrt{c^{2} x^{2}+1}}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d}{8 \sqrt{c^{2} x^{2}+1}\, c}-\frac{17 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{64 c \sqrt{c^{2} x^{2}+1}}"," ",0,"1/4*x*(c^2*d*x^2+d)^(3/2)*a^2+3/8*a^2*d*x*(c^2*d*x^2+d)^(1/2)+3/8*a^2*d^2*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+5/8*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)^2*x-17/64*b^2*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^5+7/8*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/32*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*x^5+19/64*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*x^3+17/64*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*x+1/8*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^3*d-1/8*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4-5/8*b^2*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2+7/4*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-5/8*a*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*x^2+5/4*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x+1/2*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/8*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^4+3/8*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^2*d-17/64*a*b*(d*(c^2*x^2+1))^(1/2)*d/c/(c^2*x^2+1)^(1/2)","B"
270,1,1053,491,0.374000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x,x)","-a^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)+a^{2} \sqrt{c^{2} d \,x^{2}+d}\, d -\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)}{3 \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\frac{2 a 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)}+\frac{10 a 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)}+\frac{68 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{27 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)^{2} x^{4} c^{4}}{3 c^{2} x^{2}+3}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} x^{4}}{27 \left(c^{2} x^{2}+1\right)}+\frac{70 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} x^{2}}{27 \left(c^{2} x^{2}+1\right)}+\frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{3}}{9 \sqrt{c^{2} x^{2}+1}}-\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c x}{3 \sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x^{3} c^{3}}{9 \sqrt{c^{2} x^{2}+1}}-\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right) x c}{3 \sqrt{c^{2} x^{2}+1}}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)^{2} x^{2} c^{2}}{3 \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \arcsinh \left(c x \right)^{2}}{3 \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right) d}{\sqrt{c^{2} x^{2}+1}}"," ",0,"2/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x^4*c^4-a^2*d^(3/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+a^2*(c^2*d*x^2+d)^(1/2)*d+10/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)*x^2*c^2+68/27*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)+4/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)^2-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))*d+2/27*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*c^4*x^4+70/27*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*c^2*x^2-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))*d+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d+8/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d+1/3*(c^2*d*x^2+d)^(3/2)*a^2+1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)^2*x^4*c^4-2/9*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^3*c^3-8/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x*c-2/9*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)*c^3*x^3-8/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)^(1/2)*c*x+5/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(c^2*x^2+1)*arcsinh(c*x)^2*x^2*c^2+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,-c*x-(c^2*x^2+1)^(1/2))*d-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,c*x+(c^2*x^2+1)^(1/2))*d","B"
271,1,954,372,0.361000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x^2,x)","-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{d x}+a^{2} c^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c}{4 \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} x^{2}}{2 \sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) d c}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{3} \arcsinh \left(c x \right) x^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right)^{2} x}{2 \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d c}{\sqrt{c^{2} x^{2}+1}}+\frac{3 a^{2} c^{2} d x \sqrt{c^{2} d \,x^{2}+d}}{2}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right)^{2} x^{3}}{2 c^{2} x^{2}+2}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d c}{\sqrt{c^{2} x^{2}+1}}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d c}{2 \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d}{x \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} x^{3}}{4 c^{2} x^{2}+4}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} x}{4 c^{2} x^{2}+4}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{2} \arcsinh \left(c x \right) x}{c^{2} x^{2}+1}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d \,c^{4} \arcsinh \left(c x \right) x^{3}}{c^{2} x^{2}+1}+\frac{3 a^{2} c^{2} d^{2} \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{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d c}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d}{x \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} d c}{2 \sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d c}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \arcsinh \left(c x \right)^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c \arcsinh \left(c x \right)}{4 \sqrt{c^{2} x^{2}+1}}"," ",0,"-a^2/d/x*(c^2*d*x^2+d)^(5/2)+a^2*c^2*x*(c^2*d*x^2+d)^(3/2)-a*b*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)*x+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d*c-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*d/x/(c^2*x^2+1)+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^3*d*c+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*x^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*x+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d*c-b^2*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2-1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/4*a*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)-1/2*a*b*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*x^2-2*a*b*(d*(c^2*x^2+1))^(1/2)*d*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/2*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2+1/2*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^3-1/2*b^2*(d*(c^2*x^2+1))^(1/2)*d*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d*c+3/2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d*c-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)*d/x/(c^2*x^2+1)+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d*c+3/2*a^2*c^2*d*x*(c^2*d*x^2+d)^(1/2)+a*b*(d*(c^2*x^2+1))^(1/2)*d*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^3+3/2*a^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)","B"
272,1,1131,536,0.485000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x^3,x)","\frac{a^{2} c^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{2 \sqrt{c^{2} x^{2}+1}}-\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{2 \sqrt{c^{2} x^{2}+1}}-\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} d \arcsinh \left(c x \right)}{c^{2} x^{2}+1}-\frac{a b \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{x^{2} \left(c^{2} x^{2}+1\right)}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} d \arcsinh \left(c x \right) x}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c}{x \sqrt{c^{2} x^{2}+1}}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} d \arcsinh \left(c x \right)^{2} x^{2}}{c^{2} x^{2}+1}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} d}{c^{2} x^{2}+1}-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2 d \,x^{2}}-\frac{3 a^{2} c^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2}+\frac{3 a^{2} c^{2} \sqrt{c^{2} d \,x^{2}+d}\, d}{2}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} d \arcsinh \left(c x \right) x^{2}}{c^{2} x^{2}+1}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} d x}{\sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d c}{x \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} d \arcsinh \left(c x \right)^{2}}{2 c^{2} x^{2}+2}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} d \,x^{2}}{c^{2} x^{2}+1}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctanh \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2} d}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d}{2 x^{2} \left(c^{2} x^{2}+1\right)}"," ",0,"1/2*a^2*c^2*(c^2*d*x^2+d)^(3/2)+3/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2*d-3/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2*d-3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2*d+a*b*(d*(c^2*x^2+1))^(1/2)*c^2*d/(c^2*x^2+1)*arcsinh(c*x)-a*b*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)*d/x^2/(c^2*x^2+1)+3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2*d-3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2*d+2*b^2*(d*(c^2*x^2+1))^(1/2)*c^2*d/(c^2*x^2+1)-1/2*a^2/d/x^2*(c^2*d*x^2+d)^(5/2)-3/2*a^2*c^2*d^(3/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+3/2*a^2*c^2*(c^2*d*x^2+d)^(1/2)*d+2*a*b*(d*(c^2*x^2+1))^(1/2)*c^4*d/(c^2*x^2+1)*arcsinh(c*x)*x^2+3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2*d-3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2*d-2*a*b*(d*(c^2*x^2+1))^(1/2)*c^3*d/(c^2*x^2+1)^(1/2)*x-a*b*(d*(c^2*x^2+1))^(1/2)*d/x/(c^2*x^2+1)^(1/2)*c-2*b^2*(d*(c^2*x^2+1))^(1/2)*c^3*d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x-b^2*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)*d/x/(c^2*x^2+1)^(1/2)*c+3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2*d+b^2*(d*(c^2*x^2+1))^(1/2)*c^4*d/(c^2*x^2+1)*arcsinh(c*x)^2*x^2+2*b^2*(d*(c^2*x^2+1))^(1/2)*c^4*d/(c^2*x^2+1)*x^2+1/2*b^2*(d*(c^2*x^2+1))^(1/2)*c^2*d/(c^2*x^2+1)*arcsinh(c*x)^2+3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,-c*x-(c^2*x^2+1)^(1/2))*c^2*d-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arctanh(c*x+(c^2*x^2+1)^(1/2))*c^2*d-3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,c*x+(c^2*x^2+1)^(1/2))*c^2*d-1/2*b^2*arcsinh(c*x)^2*(d*(c^2*x^2+1))^(1/2)*d/x^2/(c^2*x^2+1)","B"
273,1,2796,350,0.464000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x^4,x)","\text{Expression too large to display}"," ",0,"-2/3*a^2*c^2/d/x*(c^2*d*x^2+d)^(5/2)-4/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3*c^6+1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d*c^3+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d*c^3-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d*c^3+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^3*d*c^3-1/3*a^2/d/x^3*(c^2*d*x^2+d)^(5/2)+2/3*a^2*c^4*x*(c^2*d*x^2+d)^(3/2)+64*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^7+24*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-64*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8-104*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-146/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-28/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)*c^2-20/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-73/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)^2*c^4-4/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-14/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)^2*c^2-32*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)^2*c^8-16/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8-52*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)^2*c^6-8*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+8/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-1/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*c+12*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^5-8*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c+32*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^7-16/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-20/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-4/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-2/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d*c^3-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*d*c^3+8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d*c^3+3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+4/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^3-3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3+8*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*c^7+16/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3*c^6+4/3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x*c^4+16/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3*arcsinh(c*x)*c^6+4/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x*arcsinh(c*x)*c^4-3*a*b*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3-1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x/(c^2*x^2+1)*c^2-1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)^2+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d*c^3+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d*c^3-20/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-29/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-10/3*b^2*(d*(c^2*x^2+1))^(1/2)*d/(24*c^4*x^4+9*c^2*x^2+1)*x/(c^2*x^2+1)*c^4+a^2*c^4*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)+a^2*c^4*d*x*(c^2*d*x^2+d)^(1/2)","B"
274,1,2014,549,0.492000," ","int(x^3*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x)","a^{2} \left(\frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}-\frac{2 \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(256 c^{10} x^{10}+256 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+704 c^{8} x^{8}+576 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+688 c^{6} x^{6}+432 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+280 c^{4} x^{4}+120 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+41 c^{2} x^{2}+9 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(81 \arcsinh \left(c x \right)^{2}-18 \arcsinh \left(c x \right)+2\right) d^{2}}{373248 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(49 \arcsinh \left(c x \right)^{2}-14 \arcsinh \left(c x \right)+2\right) d^{2}}{175616 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right) d^{2}}{1728 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right) d^{2}}{1728 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(49 \arcsinh \left(c x \right)^{2}+14 \arcsinh \left(c x \right)+2\right) d^{2}}{175616 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(256 c^{10} x^{10}-256 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+704 c^{8} x^{8}-576 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+688 c^{6} x^{6}-432 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+280 c^{4} x^{4}-120 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+41 c^{2} x^{2}-9 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(81 \arcsinh \left(c x \right)^{2}+18 \arcsinh \left(c x \right)+2\right) d^{2}}{373248 c^{4} \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(256 c^{10} x^{10}+256 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+704 c^{8} x^{8}+576 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+688 c^{6} x^{6}+432 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+280 c^{4} x^{4}+120 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+41 c^{2} x^{2}+9 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+9 \arcsinh \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+7 \arcsinh \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}+1\right)}-\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+7 \arcsinh \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(256 c^{10} x^{10}-256 c^{9} x^{9} \sqrt{c^{2} x^{2}+1}+704 c^{8} x^{8}-576 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+688 c^{6} x^{6}-432 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+280 c^{4} x^{4}-120 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+41 c^{2} x^{2}-9 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+9 \arcsinh \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a^2*(1/9*x^2*(c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(c^2*d*x^2+d)^(7/2))+b^2*(1/373248*(d*(c^2*x^2+1))^(1/2)*(256*c^10*x^10+256*c^9*x^9*(c^2*x^2+1)^(1/2)+704*c^8*x^8+576*c^7*x^7*(c^2*x^2+1)^(1/2)+688*c^6*x^6+432*c^5*x^5*(c^2*x^2+1)^(1/2)+280*c^4*x^4+120*c^3*x^3*(c^2*x^2+1)^(1/2)+41*c^2*x^2+9*c*x*(c^2*x^2+1)^(1/2)+1)*(81*arcsinh(c*x)^2-18*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)+3/175616*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(49*arcsinh(c*x)^2-14*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)-1/1728*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)-3/256*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)-3/256*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)-1/1728*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)+3/175616*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(49*arcsinh(c*x)^2+14*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1)+1/373248*(d*(c^2*x^2+1))^(1/2)*(256*c^10*x^10-256*c^9*x^9*(c^2*x^2+1)^(1/2)+704*c^8*x^8-576*c^7*x^7*(c^2*x^2+1)^(1/2)+688*c^6*x^6-432*c^5*x^5*(c^2*x^2+1)^(1/2)+280*c^4*x^4-120*c^3*x^3*(c^2*x^2+1)^(1/2)+41*c^2*x^2-9*c*x*(c^2*x^2+1)^(1/2)+1)*(81*arcsinh(c*x)^2+18*arcsinh(c*x)+2)*d^2/c^4/(c^2*x^2+1))+2*a*b*(1/41472*(d*(c^2*x^2+1))^(1/2)*(256*c^10*x^10+256*c^9*x^9*(c^2*x^2+1)^(1/2)+704*c^8*x^8+576*c^7*x^7*(c^2*x^2+1)^(1/2)+688*c^6*x^6+432*c^5*x^5*(c^2*x^2+1)^(1/2)+280*c^4*x^4+120*c^3*x^3*(c^2*x^2+1)^(1/2)+41*c^2*x^2+9*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+9*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)+3/25088*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+7*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-1/576*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-3/256*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-3/256*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)-1/576*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)+3/25088*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(1+7*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1)+1/41472*(d*(c^2*x^2+1))^(1/2)*(256*c^10*x^10-256*c^9*x^9*(c^2*x^2+1)^(1/2)+704*c^8*x^8-576*c^7*x^7*(c^2*x^2+1)^(1/2)+688*c^6*x^6-432*c^5*x^5*(c^2*x^2+1)^(1/2)+280*c^4*x^4-120*c^3*x^3*(c^2*x^2+1)^(1/2)+41*c^2*x^2-9*c*x*(c^2*x^2+1)^(1/2)+1)*(1+9*arcsinh(c*x))*d^2/c^4/(c^2*x^2+1))","B"
275,1,1204,468,0.578000," ","int(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x)","-\frac{5 a^{2} d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{192 c^{2}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{8}}{32 \sqrt{c^{2} x^{2}+1}}-\frac{17 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{6}}{144 \sqrt{c^{2} x^{2}+1}}-\frac{59 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \,x^{4}}{384 \sqrt{c^{2} x^{2}+1}}-\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{2}}{128 c \sqrt{c^{2} x^{2}+1}}-\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2}}{128 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{133 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{3}}{192 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right)^{2} x^{9}}{8 c^{2} x^{2}+8}+\frac{23 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{7}}{24 \left(c^{2} x^{2}+1\right)}+\frac{127 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right) x^{5}}{96 \left(c^{2} x^{2}+1\right)}+\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x}{64 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} x^{9}}{256 c^{2} x^{2}+256}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right) x^{9}}{4 c^{2} x^{2}+4}-\frac{59 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \arcsinh \left(c x \right) x^{4}}{384 \sqrt{c^{2} x^{2}+1}}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{2}}{128 c \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} \arcsinh \left(c x \right) x^{8}}{32 \sqrt{c^{2} x^{2}+1}}-\frac{17 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} \arcsinh \left(c x \right) x^{6}}{144 \sqrt{c^{2} x^{2}+1}}+\frac{23 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right)^{2} x^{7}}{48 \left(c^{2} x^{2}+1\right)}+\frac{127 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right)^{2} x^{5}}{192 \left(c^{2} x^{2}+1\right)}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2} x}{128 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{a^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{48 c^{2}}+\frac{359 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2}}{36864 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{263 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} x^{7}}{13824 \left(c^{2} x^{2}+1\right)}+\frac{1915 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} x^{5}}{55296 \left(c^{2} x^{2}+1\right)}-\frac{359 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x}{36864 c^{2} \left(c^{2} x^{2}+1\right)}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} d^{2}}{384 \sqrt{c^{2} x^{2}+1}\, c^{3}}+\frac{133 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2} x^{3}}{384 \left(c^{2} x^{2}+1\right)}+\frac{359 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)}{36864 c^{3} \sqrt{c^{2} x^{2}+1}}+\frac{1081 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x^{3}}{110592 \left(c^{2} x^{2}+1\right)}-\frac{5 a^{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{a^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 c^{2} d}-\frac{5 a^{2} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{128 c^{2}}"," ",0,"-5/192*a^2/c^2*d*x*(c^2*d*x^2+d)^(3/2)-5/128*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^2*d^2+133/192*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-59/384*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4-5/128*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2-1/32*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^8-17/144*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^6-1/32*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^8-17/144*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^6-59/384*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*x^4-5/128*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)*x^2+1/8*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)^2*x^9+23/48*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^7+127/192*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^5+5/128*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x-1/48*a^2/c^2*x*(c^2*d*x^2+d)^(5/2)+1/4*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^9+23/24*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^7+127/96*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^5+5/64*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/c^2/(c^2*x^2+1)*arcsinh(c*x)*x+359/36864*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/c^3/(c^2*x^2+1)^(1/2)-5/384*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3*arcsinh(c*x)^3*d^2+133/384*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+359/36864*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+1/256*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*x^9+263/13824*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*x^7+1915/55296*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*x^5-359/36864*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/c^2/(c^2*x^2+1)*x+1081/110592*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*x^3-5/128*a^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)+1/8*a^2*x*(c^2*d*x^2+d)^(7/2)/c^2/d-5/128*a^2/c^2*d^2*x*(c^2*d*x^2+d)^(1/2)","B"
276,1,1773,322,0.406000," ","int(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x)","\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(49 \arcsinh \left(c x \right)^{2}-14 \arcsinh \left(c x \right)+2\right) d^{2}}{43904 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}-10 \arcsinh \left(c x \right)+2\right) d^{2}}{3200 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right) d^{2}}{384 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right) d^{2}}{384 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}+10 \arcsinh \left(c x \right)+2\right) d^{2}}{3200 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(49 \arcsinh \left(c x \right)^{2}+14 \arcsinh \left(c x \right)+2\right) d^{2}}{43904 c^{2} \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}+64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}+112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}+56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}+7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+7 \arcsinh \left(c x \right)\right) d^{2}}{6272 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right) d^{2}}{640 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right) d^{2}}{640 c^{2} \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(64 c^{8} x^{8}-64 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+144 c^{6} x^{6}-112 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+104 c^{4} x^{4}-56 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+25 c^{2} x^{2}-7 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+7 \arcsinh \left(c x \right)\right) d^{2}}{6272 c^{2} \left(c^{2} x^{2}+1\right)}\right)"," ",0,"1/7*a^2/c^2/d*(c^2*d*x^2+d)^(7/2)+b^2*(1/43904*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(49*arcsinh(c*x)^2-14*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+1/3200*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2-10*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+1/384*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+5/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+5/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+1/384*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+1/3200*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2+10*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1)+1/43904*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(49*arcsinh(c*x)^2+14*arcsinh(c*x)+2)*d^2/c^2/(c^2*x^2+1))+2*a*b*(1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8+64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6+112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4+56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2+7*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+7*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/640*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/128*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+5/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+5/128*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/128*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/640*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1)+1/6272*(d*(c^2*x^2+1))^(1/2)*(64*c^8*x^8-64*c^7*x^7*(c^2*x^2+1)^(1/2)+144*c^6*x^6-112*c^5*x^5*(c^2*x^2+1)^(1/2)+104*c^4*x^4-56*c^3*x^3*(c^2*x^2+1)^(1/2)+25*c^2*x^2-7*c*x*(c^2*x^2+1)^(1/2)+1)*(1+7*arcsinh(c*x))*d^2/c^2/(c^2*x^2+1))","B"
277,1,966,366,0.367000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x)","\frac{5 a^{2} d x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a^{2} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{16}+\frac{5 a^{2} d^{3} \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{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right) x^{7}}{3 c^{2} x^{2}+3}+\frac{x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a^{2}}{6}+\frac{17 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{5}}{12 \left(c^{2} x^{2}+1\right)}+\frac{59 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right) x^{3}}{24 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right)^{2} x^{7}}{6 c^{2} x^{2}+6}+\frac{299 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} x}{1152 \left(c^{2} x^{2}+1\right)}+\frac{113 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} x^{5}}{1728 \left(c^{2} x^{2}+1\right)}+\frac{1091 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} x^{3}}{3456 \left(c^{2} x^{2}+1\right)}-\frac{299 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2}}{1152 c \sqrt{c^{2} x^{2}+1}}-\frac{299 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)}{1152 c \sqrt{c^{2} x^{2}+1}}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} d^{2}}{48 \sqrt{c^{2} x^{2}+1}\, c}+\frac{11 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2} x}{16 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} x^{7}}{108 c^{2} x^{2}+108}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{6}}{18 \sqrt{c^{2} x^{2}+1}}-\frac{13 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{4}}{48 \sqrt{c^{2} x^{2}+1}}-\frac{11 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \,x^{2}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{17 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right)^{2} x^{5}}{24 \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} \arcsinh \left(c x \right) x^{6}}{18 \sqrt{c^{2} x^{2}+1}}-\frac{13 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} \arcsinh \left(c x \right) x^{4}}{48 \sqrt{c^{2} x^{2}+1}}-\frac{11 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \arcsinh \left(c x \right) x^{2}}{16 \sqrt{c^{2} x^{2}+1}}+\frac{59 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right)^{2} x^{3}}{48 \left(c^{2} x^{2}+1\right)}+\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2}}{16 \sqrt{c^{2} x^{2}+1}\, c}+\frac{11 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x}{8 \left(c^{2} x^{2}+1\right)}"," ",0,"5/24*a^2*d*x*(c^2*d*x^2+d)^(3/2)+5/16*a^2*d^2*x*(c^2*d*x^2+d)^(1/2)+5/16*a^2*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/6*x*(c^2*d*x^2+d)^(5/2)*a^2+1/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^7+17/12*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^5+59/24*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x^3+299/1152*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*x-299/1152*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+1/108*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*x^7+113/1728*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*x^5+1091/3456*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*x^3+5/48*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^3*d^2+11/16*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x-299/1152*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/c/(c^2*x^2+1)^(1/2)+1/6*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)^2*x^7+17/24*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^5-1/18*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^6-13/48*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4-11/16*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2-1/18*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^6-13/48*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^4-11/16*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*x^2+59/48*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+5/16*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c*arcsinh(c*x)^2*d^2+11/8*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x","B"
278,1,1321,614,0.460000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x,x)","\frac{9394 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2}}{3375 \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2} x^{6} c^{6}}{5 c^{2} x^{2}+5}-a^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)+a^{2} \sqrt{c^{2} d \,x^{2}+d}\, d^{2}+\frac{a^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{6} c^{6}}{5 \left(c^{2} x^{2}+1\right)}+\frac{28 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{4} c^{4}}{15 \left(c^{2} x^{2}+1\right)}+\frac{68 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{2} c^{2}}{15 \left(c^{2} x^{2}+1\right)}+\frac{14 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2} x^{4} c^{4}}{15 \left(c^{2} x^{2}+1\right)}+\frac{34 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2} x^{2} c^{2}}{15 \left(c^{2} x^{2}+1\right)}+\frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a^{2}}{5}+\frac{46 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)}{15 \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} x^{6}}{125 \left(c^{2} x^{2}+1\right)}+\frac{532 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} x^{4}}{3375 \left(c^{2} x^{2}+1\right)}+\frac{9872 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} x^{2}}{3375 \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{23 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right)^{2}}{15 \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{5}}{25 \sqrt{c^{2} x^{2}+1}}-\frac{22 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{3}}{45 \sqrt{c^{2} x^{2}+1}}-\frac{46 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c x}{15 \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{46 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x c}{15 \sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{5} c^{5}}{25 \sqrt{c^{2} x^{2}+1}}-\frac{22 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} \arcsinh \left(c x \right) x^{3} c^{3}}{45 \sqrt{c^{2} x^{2}+1}}"," ",0,"-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,c*x+(c^2*x^2+1)^(1/2))*d^2+9394/3375*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)+2/5*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^6*c^6+28/15*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^4*c^4+68/15*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2*c^2-a^2*d^(5/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+a^2*(c^2*d*x^2+d)^(1/2)*d^2+1/3*a^2*d*(c^2*d*x^2+d)^(3/2)+1/5*(c^2*d*x^2+d)^(5/2)*a^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2+2/125*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*c^6*x^6+532/3375*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*c^4*x^4+9872/3375*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*c^2*x^2+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2+46/15*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,-c*x-(c^2*x^2+1)^(1/2))*d^2+23/15*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)^2-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2-46/15*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x*c-2/25*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*c^5*x^5-22/45*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*c^3*x^3-2/25*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^5*c^5-22/45*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^3*c^3-46/15*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)^(1/2)*c*x+1/5*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^6*c^6+14/15*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^4*c^4+34/15*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^2*c^2","B"
279,1,1223,490,0.446000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x^2,x)","\frac{15 a^{2} c^{2} d^{3} \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{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} x^{5}}{32 c^{2} x^{2}+32}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{4}}{8 \sqrt{c^{2} x^{2}+1}}-\frac{9 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x^{2}}{8 \sqrt{c^{2} x^{2}+1}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} \arcsinh \left(c x \right) x^{4}}{8 \sqrt{c^{2} x^{2}+1}}-\frac{9 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} \arcsinh \left(c x \right) x^{2}}{8 \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}}+\frac{11 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right)^{2} x^{3}}{8 \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}+\frac{15 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2} c}{8 \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) d^{2}}{x \left(c^{2} x^{2}+1\right)}-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{d x}+a^{2} c^{2} x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right)^{2} x^{5}}{4 c^{2} x^{2}+4}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right)^{2} x}{8 c^{2} x^{2}+8}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right) x^{5}}{2 c^{2} x^{2}+2}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right) x}{4 c^{2} x^{2}+4}+\frac{11 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{3}}{4 \left(c^{2} x^{2}+1\right)}+\frac{35 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} x^{3}}{64 \left(c^{2} x^{2}+1\right)}+\frac{33 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} x}{64 \left(c^{2} x^{2}+1\right)}-\frac{33 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c}{64 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} d^{2}}{x \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c}{\sqrt{c^{2} x^{2}+1}}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3} d^{2} c}{8 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \arcsinh \left(c x \right)^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{33 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c \arcsinh \left(c x \right)}{64 \sqrt{c^{2} x^{2}+1}}+\frac{5 a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} x \,c^{2} d}{4}+\frac{15 a^{2} c^{2} d^{2} x \sqrt{c^{2} d \,x^{2}+d}}{8}"," ",0,"15/8*a^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)-1/8*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4-9/8*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2-1/8*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^4-9/8*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x^2-2*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)^2*x^5+11/8*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/8*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)^2*x+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2*c+15/8*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d^2*c-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)*d^2/x/(c^2*x^2+1)+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d^2*c-a^2/d/x*(c^2*d*x^2+d)^(7/2)+a^2*c^2*x*(c^2*d*x^2+d)^(5/2)+1/2*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^5+11/4*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^3+1/4*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)*x+1/32*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*x^5+35/64*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*x^3+33/64*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*x-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2*d^2/x/(c^2*x^2+1)+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2*c+5/8*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^3*d^2*c-b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2-33/64*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-33/64*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c/(c^2*x^2+1)^(1/2)+5/4*a^2*(c^2*d*x^2+d)^(3/2)*x*c^2*d+15/8*a^2*c^2*d^2*x*(c^2*d*x^2+d)^(1/2)","B"
280,1,1404,664,0.571000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x^3,x)","\frac{a^{2} c^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} x^{4}}{27 \left(c^{2} x^{2}+1\right)}+\frac{124 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} x^{2}}{27 \left(c^{2} x^{2}+1\right)}+\frac{11 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right)^{2}}{6 \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2}}{2 x^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctanh \left(c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{122 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2}}{27 \left(c^{2} x^{2}+1\right)}-\frac{a^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{2 d \,x^{2}}+\frac{5 a^{2} c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6}-\frac{5 a^{2} c^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2}+\frac{5 a^{2} c^{2} \sqrt{c^{2} d \,x^{2}+d}\, d^{2}}{2}+\frac{16 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right) x^{4}}{3 \left(c^{2} x^{2}+1\right)}+\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{6} \arcsinh \left(c x \right)^{2} x^{4}}{3 c^{2} x^{2}+3}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c}{x \sqrt{c^{2} x^{2}+1}}-\frac{14 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} x}{3 \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} x^{3}}{9 \sqrt{c^{2} x^{2}+1}}+\frac{11 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{2} \arcsinh \left(c x \right)}{3 \left(c^{2} x^{2}+1\right)}-\frac{a b \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2}}{x^{2} \left(c^{2} x^{2}+1\right)}-\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{5 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{5} \arcsinh \left(c x \right) x^{3}}{9 \sqrt{c^{2} x^{2}+1}}-\frac{14 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{3} \arcsinh \left(c x \right) x}{3 \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c}{x \sqrt{c^{2} x^{2}+1}}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, d^{2} c^{4} \arcsinh \left(c x \right)^{2} x^{2}}{3 \left(c^{2} x^{2}+1\right)}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{2 \sqrt{c^{2} x^{2}+1}}-\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{\sqrt{c^{2} x^{2}+1}}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) d^{2} c^{2}}{2 \sqrt{c^{2} x^{2}+1}}"," ",0,"1/2*a^2*c^2*(c^2*d*x^2+d)^(5/2)+11/6*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)^2-1/2*b^2*arcsinh(c*x)^2*(d*(c^2*x^2+1))^(1/2)*d^2/x^2/(c^2*x^2+1)-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arctanh(c*x+(c^2*x^2+1)^(1/2))*d^2*c^2+5*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,-c*x-(c^2*x^2+1)^(1/2))*d^2*c^2-5*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(3,c*x+(c^2*x^2+1)^(1/2))*d^2*c^2+2/27*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*x^4+124/27*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*x^2+122/27*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)-1/2*a^2/d/x^2*(c^2*d*x^2+d)^(7/2)+5/6*a^2*c^2*d*(c^2*d*x^2+d)^(3/2)-5/2*a^2*c^2*d^(5/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)+5/2*a^2*c^2*(c^2*d*x^2+d)^(1/2)*d^2+16/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x^2+2/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^4+5*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2*c^2-5*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2*c^2-a*b*(d*(c^2*x^2+1))^(1/2)*d^2/x/(c^2*x^2+1)^(1/2)*c-14/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*x-2/9*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^3+11/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^2/(c^2*x^2+1)*arcsinh(c*x)-a*b*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)*d^2/x^2/(c^2*x^2+1)-5*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2*c^2+5*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2*c^2-2/9*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^3-14/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x-b^2*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)*d^2/x/(c^2*x^2+1)^(1/2)*c+5*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2*c^2+8/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x^2+1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)^2*x^4-5/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2*c^2-5*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2*c^2+5/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2*c^2","B"
281,1,3311,511,0.551000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x^4,x)","\text{output too large to display}"," ",0,"-46/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)*c^2-294*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8+70*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-406*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-380/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-4/3*a^2*c^2/d/x*(c^2*d*x^2+d)^(7/2)-7/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3*c^6-1/4*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)+5/6*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^3*d^2*c^3+14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*d^2*c^3-14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d^2*c^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*x^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*x+14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*d^2*c^3-1/4*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/3*a^2/d/x^3*(c^2*d*x^2+d)^(7/2)+4/3*a^2*c^4*x*(c^2*d*x^2+d)^(5/2)-7/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-2/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)+35*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^5-21*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5-1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c+147*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^7-147*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)^2*c^8-49/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*arcsinh(c*x)*c^8-203*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)^2*c^6-56/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*arcsinh(c*x)*c^6-21*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5+14/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3-1/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x^2/(c^2*x^2+1)^(1/2)*c+a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)*x^3+a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)*x-49/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-56/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-190/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)^2*c^4-7/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*arcsinh(c*x)*c^4-23/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x/(c^2*x^2+1)*arcsinh(c*x)^2*c^2+294*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^7+49/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3*c^6+7/3*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x*c^4+1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3-1/2*a*b*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*x^2-5*a*b*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*c^3+49/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3*arcsinh(c*x)*c^6+7/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x*arcsinh(c*x)*c^4+7/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^3-5*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3+21*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^4/(c^2*x^2+1)^(1/2)*c^7-1/2*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^5/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2+5*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^2/(c^2*x^2+1)^(1/2)*c^5-28/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*d^2*c^3+5/2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*d^2*c^3+14/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*d^2*c^3+1/2*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^6/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/2*b^2*(d*(c^2*x^2+1))^(1/2)*d^2*c^4/(c^2*x^2+1)*arcsinh(c*x)^2*x-56/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^5/(c^2*x^2+1)*c^8-71/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x^3/(c^2*x^2+1)*c^6-16/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)*x/(c^2*x^2+1)*c^4-1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x/(c^2*x^2+1)*c^2-1/3*b^2*(d*(c^2*x^2+1))^(1/2)*d^2/(63*c^4*x^4+15*c^2*x^2+1)/x^3/(c^2*x^2+1)*arcsinh(c*x)^2+14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*d^2*c^3+14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*d^2*c^3+5/2*a^2*c^4*d^2*x*(c^2*d*x^2+d)^(1/2)+5/2*a^2*c^4*d^3*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+5/3*a^2*c^4*d*x*(c^2*d*x^2+d)^(3/2)","B"
282,1,125,129,0.096000," ","int(x^4*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","\frac{16 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-8 \arcsinh \left(a x \right) x^{4} a^{4}+2 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}-24 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a x +24 \arcsinh \left(a x \right) x^{2} a^{2}+8 \arcsinh \left(a x \right)^{3}-15 \sqrt{a^{2} x^{2}+1}\, x a +15 \arcsinh \left(a x \right)}{64 a^{5}}"," ",0,"1/64*(16*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^3*x^3-8*arcsinh(a*x)*x^4*a^4+2*(a^2*x^2+1)^(1/2)*x^3*a^3-24*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a*x+24*arcsinh(a*x)*x^2*a^2+8*arcsinh(a*x)^3-15*(a^2*x^2+1)^(1/2)*x*a+15*arcsinh(a*x))/a^5","A"
283,1,113,102,0.091000," ","int(x^3*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","\frac{9 \arcsinh \left(a x \right)^{2} x^{4} a^{4}-9 \arcsinh \left(a x \right)^{2} a^{2} x^{2}-6 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}+2 x^{4} a^{4}-38 a^{2} x^{2}-18 \arcsinh \left(a x \right)^{2}+36 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x -40}{27 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/27/a^4/(a^2*x^2+1)^(1/2)*(9*arcsinh(a*x)^2*x^4*a^4-9*arcsinh(a*x)^2*a^2*x^2-6*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3+2*x^4*a^4-38*a^2*x^2-18*arcsinh(a*x)^2+36*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x-40)","A"
284,1,69,73,0.082000," ","int(x^2*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","-\frac{-6 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a x +6 \arcsinh \left(a x \right) x^{2} a^{2}+2 \arcsinh \left(a x \right)^{3}-3 \sqrt{a^{2} x^{2}+1}\, x a +3 \arcsinh \left(a x \right)}{12 a^{3}}"," ",0,"-1/12*(-6*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a*x+6*arcsinh(a*x)*x^2*a^2+2*arcsinh(a*x)^3-3*(a^2*x^2+1)^(1/2)*x*a+3*arcsinh(a*x))/a^3","A"
285,1,64,48,0.075000," ","int(x*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{2} a^{2} x^{2}+\arcsinh \left(a x \right)^{2}-2 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +2 a^{2} x^{2}+2}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/a^2/(a^2*x^2+1)^(1/2)*(arcsinh(a*x)^2*a^2*x^2+arcsinh(a*x)^2-2*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+2*a^2*x^2+2)","A"
286,1,12,11,0.005000," ","int(arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{3}}{3 a}"," ",0,"1/3*arcsinh(a*x)^3/a","A"
287,1,144,115,0.089000," ","int(arcsinh(a*x)^2/x/(a^2*x^2+1)^(1/2),x)","-\arcsinh \left(a x \right)^{2} \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)-2 \arcsinh \left(a x \right) \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)+2 \polylog \left(3, -a x -\sqrt{a^{2} x^{2}+1}\right)+\arcsinh \left(a x \right)^{2} \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)+2 \arcsinh \left(a x \right) \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)-2 \polylog \left(3, a x +\sqrt{a^{2} x^{2}+1}\right)"," ",0,"-arcsinh(a*x)^2*ln(1+a*x+(a^2*x^2+1)^(1/2))-2*arcsinh(a*x)*polylog(2,-a*x-(a^2*x^2+1)^(1/2))+2*polylog(3,-a*x-(a^2*x^2+1)^(1/2))+arcsinh(a*x)^2*ln(1-a*x-(a^2*x^2+1)^(1/2))+2*arcsinh(a*x)*polylog(2,a*x+(a^2*x^2+1)^(1/2))-2*polylog(3,a*x+(a^2*x^2+1)^(1/2))","A"
288,1,132,82,0.148000," ","int(arcsinh(a*x)^2/x^2/(a^2*x^2+1)^(1/2),x)","\frac{\left(a x -\sqrt{a^{2} x^{2}+1}\right) \arcsinh \left(a x \right)^{2}}{x}-2 a \arcsinh \left(a x \right)^{2}+2 a \arcsinh \left(a x \right) \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)+2 a \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)+2 a \arcsinh \left(a x \right) \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)+2 a \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)"," ",0,"(a*x-(a^2*x^2+1)^(1/2))/x*arcsinh(a*x)^2-2*a*arcsinh(a*x)^2+2*a*arcsinh(a*x)*ln(1+a*x+(a^2*x^2+1)^(1/2))+2*a*polylog(2,-a*x-(a^2*x^2+1)^(1/2))+2*a*arcsinh(a*x)*ln(1-a*x-(a^2*x^2+1)^(1/2))+2*a*polylog(2,a*x+(a^2*x^2+1)^(1/2))","A"
289,1,233,176,0.224000," ","int(arcsinh(a*x)^2/x^3/(a^2*x^2+1)^(1/2),x)","-\frac{\arcsinh \left(a x \right) \left(\arcsinh \left(a x \right) x^{2} a^{2}+2 \sqrt{a^{2} x^{2}+1}\, x a +\arcsinh \left(a x \right)\right)}{2 \sqrt{a^{2} x^{2}+1}\, x^{2}}+\frac{a^{2} \arcsinh \left(a x \right)^{2} \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)}{2}+a^{2} \arcsinh \left(a x \right) \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)-a^{2} \polylog \left(3, -a x -\sqrt{a^{2} x^{2}+1}\right)-\frac{a^{2} \arcsinh \left(a x \right)^{2} \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-a^{2} \arcsinh \left(a x \right) \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)+a^{2} \polylog \left(3, a x +\sqrt{a^{2} x^{2}+1}\right)-2 a^{2} \arctanh \left(a x +\sqrt{a^{2} x^{2}+1}\right)"," ",0,"-1/2/(a^2*x^2+1)^(1/2)/x^2*arcsinh(a*x)*(arcsinh(a*x)*x^2*a^2+2*(a^2*x^2+1)^(1/2)*x*a+arcsinh(a*x))+1/2*a^2*arcsinh(a*x)^2*ln(1+a*x+(a^2*x^2+1)^(1/2))+a^2*arcsinh(a*x)*polylog(2,-a*x-(a^2*x^2+1)^(1/2))-a^2*polylog(3,-a*x-(a^2*x^2+1)^(1/2))-1/2*a^2*arcsinh(a*x)^2*ln(1-a*x-(a^2*x^2+1)^(1/2))-a^2*arcsinh(a*x)*polylog(2,a*x+(a^2*x^2+1)^(1/2))+a^2*polylog(3,a*x+(a^2*x^2+1)^(1/2))-2*a^2*arctanh(a*x+(a^2*x^2+1)^(1/2))","A"
290,1,1227,335,0.496000," ","int(x^5*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","a^{2} \left(\frac{x^{4} \sqrt{c^{2} d \,x^{2}+d}}{5 c^{2} d}-\frac{4 \left(\frac{x^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)}{5 c^{2}}\right)+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}-10 \arcsinh \left(c x \right)+2\right)}{4000 c^{6} d \left(c^{2} x^{2}+1\right)}-\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right)}{864 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right)}{16 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right)}{16 c^{6} d \left(c^{2} x^{2}+1\right)}-\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right)}{864 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(25 \arcsinh \left(c x \right)^{2}+10 \arcsinh \left(c x \right)+2\right)}{4000 c^{6} d \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}+16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}+20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}+5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+5 \arcsinh \left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}+1\right)}-\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}+1\right)}-\frac{5 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{288 c^{6} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(16 c^{6} x^{6}-16 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+28 c^{4} x^{4}-20 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+13 c^{2} x^{2}-5 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+5 \arcsinh \left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a^2*(1/5*x^4/c^2/d*(c^2*d*x^2+d)^(1/2)-4/5/c^2*(1/3*x^2/c^2/d*(c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(c^2*d*x^2+d)^(1/2)))+b^2*(1/4000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2-10*arcsinh(c*x)+2)/c^6/d/(c^2*x^2+1)-5/864*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)/c^6/d/(c^2*x^2+1)+5/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)/c^6/d/(c^2*x^2+1)+5/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)/c^6/d/(c^2*x^2+1)-5/864*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)/c^6/d/(c^2*x^2+1)+1/4000*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(25*arcsinh(c*x)^2+10*arcsinh(c*x)+2)/c^6/d/(c^2*x^2+1))+2*a*b*(1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6+16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4+20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2+5*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+5*arcsinh(c*x))/c^6/d/(c^2*x^2+1)-5/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^6/d/(c^2*x^2+1)+5/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^6/d/(c^2*x^2+1)+5/16*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^6/d/(c^2*x^2+1)-5/288*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^6/d/(c^2*x^2+1)+1/800*(d*(c^2*x^2+1))^(1/2)*(16*c^6*x^6-16*c^5*x^5*(c^2*x^2+1)^(1/2)+28*c^4*x^4-20*c^3*x^3*(c^2*x^2+1)^(1/2)+13*c^2*x^2-5*c*x*(c^2*x^2+1)^(1/2)+1)*(1+5*arcsinh(c*x))/c^6/d/(c^2*x^2+1))","B"
291,1,760,283,0.536000," ","int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} x^{3} \sqrt{c^{2} d \,x^{2}+d}}{4 c^{2} d}-\frac{3 a^{2} x \sqrt{c^{2} d \,x^{2}+d}}{8 c^{4} d}+\frac{3 a^{2} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{8 c^{4} \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{8 \sqrt{c^{2} x^{2}+1}\, c^{5} d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5}}{32 d \left(c^{2} x^{2}+1\right)}-\frac{13 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{64 c^{2} d \left(c^{2} x^{2}+1\right)}-\frac{15 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{64 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{4}}{8 c d \sqrt{c^{2} x^{2}+1}}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{8 c^{3} d \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{5}}{4 d \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{3}}{8 c^{2} d \left(c^{2} x^{2}+1\right)}-\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{8 c^{4} d \left(c^{2} x^{2}+1\right)}+\frac{15 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{64 c^{5} d \sqrt{c^{2} x^{2}+1}}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{8 \sqrt{c^{2} x^{2}+1}\, c^{5} d}+\frac{15 a b \sqrt{d \left(c^{2} x^{2}+1\right)}}{64 c^{5} d \sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{5}}{2 d \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4}}{8 c d \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{4 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{8 c^{3} d \sqrt{c^{2} x^{2}+1}}-\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{4 c^{4} d \left(c^{2} x^{2}+1\right)}"," ",0,"1/4*a^2*x^3/c^2/d*(c^2*d*x^2+d)^(1/2)-3/8*a^2/c^4*x/d*(c^2*d*x^2+d)^(1/2)+3/8*a^2/c^4*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/8*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d*arcsinh(c*x)^3+1/32*b^2*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*x^5-13/64*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*x^3-15/64*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d/(c^2*x^2+1)*x-1/8*b^2*(d*(c^2*x^2+1))^(1/2)/c/d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^4+3/8*b^2*(d*(c^2*x^2+1))^(1/2)/c^3/d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2+1/4*b^2*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)^2*x^5-1/8*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*arcsinh(c*x)^2*x^3-3/8*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d/(c^2*x^2+1)*arcsinh(c*x)^2*x+15/64*b^2*(d*(c^2*x^2+1))^(1/2)/c^5/d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+3/8*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d*arcsinh(c*x)^2+15/64*a*b*(d*(c^2*x^2+1))^(1/2)/c^5/d/(c^2*x^2+1)^(1/2)+1/2*a*b*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)*x^5-1/8*a*b*(d*(c^2*x^2+1))^(1/2)/c/d/(c^2*x^2+1)^(1/2)*x^4-1/4*a*b*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x^3+3/8*a*b*(d*(c^2*x^2+1))^(1/2)/c^3/d/(c^2*x^2+1)^(1/2)*x^2-3/4*a*b*(d*(c^2*x^2+1))^(1/2)/c^4/d/(c^2*x^2+1)*arcsinh(c*x)*x","B"
292,1,706,231,0.375000," ","int(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","a^{2} \left(\frac{x^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}-6 \arcsinh \left(c x \right)+2\right)}{216 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right)}{8 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right)}{8 c^{4} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(9 \arcsinh \left(c x \right)^{2}+6 \arcsinh \left(c x \right)+2\right)}{216 c^{4} d \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}+4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}+3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+3 \arcsinh \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}+1\right)}-\frac{3 \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(4 c^{4} x^{4}-4 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+5 c^{2} x^{2}-3 c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+3 \arcsinh \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a^2*(1/3*x^2/c^2/d*(c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(c^2*d*x^2+d)^(1/2))+b^2*(1/216*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2-6*arcsinh(c*x)+2)/c^4/d/(c^2*x^2+1)-3/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)/c^4/d/(c^2*x^2+1)-3/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)/c^4/d/(c^2*x^2+1)+1/216*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(9*arcsinh(c*x)^2+6*arcsinh(c*x)+2)/c^4/d/(c^2*x^2+1))+2*a*b*(1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4+4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2+3*c*x*(c^2*x^2+1)^(1/2)+1)*(-1+3*arcsinh(c*x))/c^4/d/(c^2*x^2+1)-3/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^4/d/(c^2*x^2+1)-3/8*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^4/d/(c^2*x^2+1)+1/72*(d*(c^2*x^2+1))^(1/2)*(4*c^4*x^4-4*c^3*x^3*(c^2*x^2+1)^(1/2)+5*c^2*x^2-3*c*x*(c^2*x^2+1)^(1/2)+1)*(1+3*arcsinh(c*x))/c^4/d/(c^2*x^2+1))","B"
293,1,530,178,0.399000," ","int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} x \sqrt{c^{2} d \,x^{2}+d}}{2 c^{2} d}-\frac{a^{2} \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{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{6 \sqrt{c^{2} x^{2}+1}\, c^{3} d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{4 d \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{4 c^{2} d \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{2 c d \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{4 c^{3} d \sqrt{c^{2} x^{2}+1}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{3}}{2 d \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{2 c^{2} d \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c^{3} d}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{d \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{2 c d \sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{2} d \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}}{4 c^{3} d \sqrt{c^{2} x^{2}+1}}"," ",0,"1/2*a^2*x/c^2/d*(c^2*d*x^2+d)^(1/2)-1/2*a^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)-1/6*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d*arcsinh(c*x)^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*x^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*x-1/2*b^2*(d*(c^2*x^2+1))^(1/2)/c/d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2-1/4*b^2*(d*(c^2*x^2+1))^(1/2)/c^3/d/(c^2*x^2+1)^(1/2)*arcsinh(c*x)+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*arcsinh(c*x)^2*x-1/2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d*arcsinh(c*x)^2+a*b*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/2*a*b*(d*(c^2*x^2+1))^(1/2)/c/d/(c^2*x^2+1)^(1/2)*x^2+a*b*(d*(c^2*x^2+1))^(1/2)/c^2/d/(c^2*x^2+1)*arcsinh(c*x)*x-1/4*a*b*(d*(c^2*x^2+1))^(1/2)/c^3/d/(c^2*x^2+1)^(1/2)","B"
294,1,296,126,0.186000," ","int(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} \sqrt{c^{2} d \,x^{2}+d}}{c^{2} d}+b^{2} \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}-2 \arcsinh \left(c x \right)+2\right)}{2 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(\arcsinh \left(c x \right)^{2}+2 \arcsinh \left(c x \right)+2\right)}{2 c^{2} d \left(c^{2} x^{2}+1\right)}\right)+2 a b \left(\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+c x \sqrt{c^{2} x^{2}+1}+1\right) \left(-1+\arcsinh \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}+1\right)}+\frac{\sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}-c x \sqrt{c^{2} x^{2}+1}+1\right) \left(1+\arcsinh \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}+1\right)}\right)"," ",0,"a^2/c^2/d*(c^2*d*x^2+d)^(1/2)+b^2*(1/2*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2-2*arcsinh(c*x)+2)/c^2/d/(c^2*x^2+1)+1/2*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(arcsinh(c*x)^2+2*arcsinh(c*x)+2)/c^2/d/(c^2*x^2+1))+2*a*b*(1/2*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2+c*x*(c^2*x^2+1)^(1/2)+1)*(-1+arcsinh(c*x))/c^2/d/(c^2*x^2+1)+1/2*(d*(c^2*x^2+1))^(1/2)*(c^2*x^2-c*x*(c^2*x^2+1)^(1/2)+1)*(1+arcsinh(c*x))/c^2/d/(c^2*x^2+1))","B"
295,1,120,41,0.068000," ","int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","\frac{a^{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{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{3 \sqrt{c^{2} x^{2}+1}\, c d}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{\sqrt{c^{2} x^{2}+1}\, c d}"," ",0,"a^2*ln(x*c^2*d/(c^2*d)^(1/2)+(c^2*d*x^2+d)^(1/2))/(c^2*d)^(1/2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d*arcsinh(c*x)^3+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d*arcsinh(c*x)^2","B"
296,1,564,250,0.296000," ","int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{\sqrt{d}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right)}{\sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-a^2/d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(3,-c*x-(c^2*x^2+1)^(1/2))+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(3,c*x+(c^2*x^2+1)^(1/2))+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))","B"
297,1,526,171,0.311000," ","int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{c^{2} d \,x^{2}+d}}{d x}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x \,c^{2}}{\left(c^{2} x^{2}+1\right) d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{\left(c^{2} x^{2}+1\right) d x}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}+1\right) d}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(c^{2} x^{2}+1\right) d x}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c}{\sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-a^2/d/x*(c^2*d*x^2+d)^(1/2)-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)/d*x*c^2-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/d*c-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)/d/x+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*c-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d*x*c^2-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d/x+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c","B"
298,1,901,373,0.482000," ","int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{c^{2} d \,x^{2}+d}}{2 d \,x^{2}}+\frac{a^{2} c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{c^{2} d \,x^{2}+d}}{x}\right)}{2 \sqrt{d}}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2}}{2 d \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{x d \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \arcsinh \left(c x \right)^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{2 x^{2} d \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{2 \sqrt{c^{2} x^{2}+1}\, d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(3, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arctanh \left(c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{d \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c}{x d \sqrt{c^{2} x^{2}+1}}-\frac{a b \arcsinh \left(c x \right) \sqrt{d \left(c^{2} x^{2}+1\right)}}{x^{2} d \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{2}}{\sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-1/2*a^2/d/x^2*(c^2*d*x^2+d)^(1/2)+1/2*a^2*c^2/d^(1/2)*ln((2*d+2*d^(1/2)*(c^2*d*x^2+d)^(1/2))/x)-1/2*b^2*arcsinh(c*x)^2*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*c^2-b^2*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)/x/d/(c^2*x^2+1)^(1/2)*c-1/2*b^2*arcsinh(c*x)^2*(d*(c^2*x^2+1))^(1/2)/x^2/d/(c^2*x^2+1)+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)^2*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(3,-c*x-(c^2*x^2+1)^(1/2))*c^2-1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)^2*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(3,c*x+(c^2*x^2+1)^(1/2))*c^2-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arctanh(c*x+(c^2*x^2+1)^(1/2))*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/d/(c^2*x^2+1)*arcsinh(c*x)*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/x/d/(c^2*x^2+1)^(1/2)*c-a*b*arcsinh(c*x)*(d*(c^2*x^2+1))^(1/2)/x^2/d/(c^2*x^2+1)-a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^2-a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^2+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^2+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^2","B"
299,1,2147,281,0.487000," ","int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^(1/2),x)","-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 a^{2} c^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 d x}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d x}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d \,x^{3}}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d \,x^{2}}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, c^{5}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{a^{2} \sqrt{c^{2} d \,x^{2}+d}}{3 d \,x^{3}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \sqrt{c^{2} x^{2}+1}\, c^{5}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d \,x^{2}}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d x}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d \,x^{3}}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right)^{2} c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{2}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d x}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{8}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right)^{2} c^{6}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{\left(3 c^{4} x^{4}+2 c^{2} x^{2}-1\right) d}+\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d}"," ",0,"-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*c^4+2/3*a^2*c^2/d/x*(c^2*d*x^2+d)^(1/2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x*c^2+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x^3*arcsinh(c*x)^2+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^5*c^8-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*c^6-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^3-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^3-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*c^3*(c^2*x^2+1)^(1/2)+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)^2*c^3-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*arcsinh(c*x)*(c^2*x^2+1)*c^6-2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^2*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^5+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*arcsinh(c*x)*(c^2*x^2+1)*c^4+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c-4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*(c^2*x^2+1)*c^6+4*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*arcsinh(c*x)*c^6+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*(c^2*x^2+1)*c^4+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*arcsinh(c*x)*c^4+4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x*arcsinh(c*x)*c^2+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x^2*c*(c^2*x^2+1)^(1/2)-1/3*a^2/d/x^3*(c^2*d*x^2+d)^(1/2)+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x^3*arcsinh(c*x)-4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c^3-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^3+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^2*(c^2*x^2+1)^(1/2)*c^5+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*arcsinh(c*x)^2*c^4-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*arcsinh(c*x)*c^4-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d/x*arcsinh(c*x)^2*c^2+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^5*arcsinh(c*x)*c^8+2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*arcsinh(c*x)^2*c^6-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*(c^2*x^2+1)*c^6-4*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*arcsinh(c*x)*c^6-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^3+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^3-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3+8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d*arcsinh(c*x)*c^3+4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^5*c^8+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x^3*c^6-2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*x*c^4-a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^4*x^4+2*c^2*x^2-1)/d*c^3*(c^2*x^2+1)^(1/2)","B"
300,1,933,486,0.515000," ","int(x^5*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x^{4}}{3 c^{2} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{4 a^{2} x^{2}}{3 c^{4} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{8 a^{2}}{3 c^{6} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{4}}{27 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{92 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{27 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{9 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{3 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{2 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}+\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}+\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}-\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 c^{6} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{94 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{27 c^{6} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{4}}{3 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{2}}{3 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{16 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 c^{6} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{4}}{3 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{9 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{3 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{10 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{3 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{6} d^{2}}"," ",0,"1/3*a^2*x^4/c^2/d/(c^2*d*x^2+d)^(1/2)-4/3*a^2/c^4*x^2/d/(c^2*d*x^2+d)^(1/2)-8/3*a^2/c^6/d/(c^2*d*x^2+d)^(1/2)+2/27*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*x^4-92/27*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*x^2+2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*arcsinh(c*x)*ln(1-I*(c*x+(c^2*x^2+1)^(1/2)))-2/9*b^2*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^3+10/3*b^2*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x-2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*arcsinh(c*x)*ln(1+I*(c*x+(c^2*x^2+1)^(1/2)))+2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*dilog(1-I*(c*x+(c^2*x^2+1)^(1/2)))-2*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-I)-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/c^6/d^2/(c^2*x^2+1)*arcsinh(c*x)^2-94/27*b^2*(d*(c^2*x^2+1))^(1/2)/c^6/d^2/(c^2*x^2+1)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^4-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^2-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/c^6/d^2/(c^2*x^2+1)*arcsinh(c*x)-2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*dilog(1+I*(c*x+(c^2*x^2+1)^(1/2)))+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^4-2/9*a*b*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*x^3-8/3*a*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2+10/3*a*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*x+2*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^2*ln(c*x+(c^2*x^2+1)^(1/2)+I)","A"
301,1,816,378,0.543000," ","int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x^{3}}{2 c^{2} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{3 a^{2} x}{2 c^{4} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{3 a^{2} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{2 c^{4} d \sqrt{c^{2} d}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{3}}{2 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{2 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{4 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{2 \sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3}}{4 c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{4 c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{2 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{2 \sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{3}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{2 c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{3 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}}{4 c^{5} d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{5} d^{2}}"," ",0,"1/2*a^2*x^3/c^2/d/(c^2*d*x^2+d)^(1/2)+3/2*a^2/c^4*x/d/(c^2*d*x^2+d)^(1/2)-3/2*a^2/c^4/d*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^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/2*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^3+3/2*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x+b^2*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2-1/4*b^2*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^2*arcsinh(c*x)^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*x^3+1/4*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*x-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-1/2*b^2*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x^2-3/2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^2*arcsinh(c*x)^2+a*b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^3-1/2*a*b*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*x^2+3*a*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)*x+2*a*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)-1/4*a*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^2/(c^2*x^2+1)^(1/2)-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
302,1,703,376,0.402000," ","int(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x^{2}}{c^{2} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{2 a^{2}}{d \,c^{4} \sqrt{c^{2} d \,x^{2}+d}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}+\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}-\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}+\frac{2 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}-\frac{2 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{4} d^{2}}"," ",0,"a^2*x^2/c^2/d/(c^2*d*x^2+d)^(1/2)+2*a^2/d/c^4/(c^2*d*x^2+d)^(1/2)+b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)^2*x^2-2*b^2*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x+2*b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*x^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)+2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*arcsinh(c*x)*ln(1+I*(c*x+(c^2*x^2+1)^(1/2)))-2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*dilog(1-I*(c*x+(c^2*x^2+1)^(1/2)))-2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*arcsinh(c*x)*ln(1-I*(c*x+(c^2*x^2+1)^(1/2)))+2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*dilog(1+I*(c*x+(c^2*x^2+1)^(1/2)))+2*a*b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)*x^2-2*a*b*(d*(c^2*x^2+1))^(1/2)/c^3/d^2/(c^2*x^2+1)^(1/2)*x+4*a*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^2/(c^2*x^2+1)*arcsinh(c*x)+2*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-I)-2*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^2*ln(c*x+(c^2*x^2+1)^(1/2)+I)","A"
303,1,478,231,0.409000," ","int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x}{c^{2} d \sqrt{c^{2} d \,x^{2}+d}}+\frac{a^{2} \ln \left(\frac{x \,c^{2} d}{\sqrt{c^{2} d}}+\sqrt{c^{2} d \,x^{2}+d}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{3}}{3 \sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c^{3} d^{2} \sqrt{c^{2} x^{2}+1}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c^{3} d^{2}}"," ",0,"-a^2*x/c^2/d/(c^2*d*x^2+d)^(1/2)+a^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)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*arcsinh(c*x)^3-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/c^2/d^2/(c^2*x^2+1)*x-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/c^3/d^2/(c^2*x^2+1)^(1/2)+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*arcsinh(c*x)^2-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*arcsinh(c*x)-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/c^2/d^2/(c^2*x^2+1)*x+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^3/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","B"
304,1,446,197,0.217000," ","int(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2}}{c^{2} d \sqrt{c^{2} d \,x^{2}+d}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}+\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}-\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}+\frac{2 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}+1\right)}+\frac{2 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}-\frac{2 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{\sqrt{c^{2} x^{2}+1}\, c^{2} d^{2}}"," ",0,"-a^2/c^2/d/(c^2*d*x^2+d)^(1/2)-b^2*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)^2-2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*arcsinh(c*x)*ln(1+I*(c*x+(c^2*x^2+1)^(1/2)))+2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*arcsinh(c*x)*ln(1-I*(c*x+(c^2*x^2+1)^(1/2)))-2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*dilog(1+I*(c*x+(c^2*x^2+1)^(1/2)))+2*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*dilog(1-I*(c*x+(c^2*x^2+1)^(1/2)))-2*a*b*(d*(c^2*x^2+1))^(1/2)/c^2/d^2/(c^2*x^2+1)*arcsinh(c*x)+2*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2)+I)-2*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^2*ln(c*x+(c^2*x^2+1)^(1/2)-I)","B"
305,1,343,183,0.183000," ","int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x}{d \sqrt{c^{2} d \,x^{2}+d}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{d^{2} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c \,d^{2} \sqrt{c^{2} x^{2}+1}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c \,d^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c \,d^{2}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\sqrt{c^{2} x^{2}+1}\, c \,d^{2}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{d^{2} \left(c^{2} x^{2}+1\right)}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{c^{2} x^{2}+1}\, c \,d^{2}}"," ",0,"a^2*x/d/(c^2*d*x^2+d)^(1/2)+b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/d^2/(c^2*x^2+1)*x+b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/c/d^2/(c^2*x^2+1)^(1/2)-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^2*arcsinh(c*x)+2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/d^2/(c^2*x^2+1)*x-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)","A"
306,0,0,448,0.401000," ","int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(3/2),x)","F"
307,1,660,317,0.308000," ","int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2}}{d x \sqrt{c^{2} d \,x^{2}+d}}-\frac{2 a^{2} c^{2} x}{d \sqrt{c^{2} d \,x^{2}+d}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x \,c^{2}}{\left(c^{2} x^{2}+1\right) d^{2}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{\left(c^{2} x^{2}+1\right) d^{2} x}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}+1\right) d^{2}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{\left(c^{2} x^{2}+1\right) d^{2} x}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{4}-1\right) c}{\sqrt{c^{2} x^{2}+1}\, d^{2}}"," ",0,"-a^2/d/x/(c^2*d*x^2+d)^(1/2)-2*a^2*c^2/d*x/(c^2*d*x^2+d)^(1/2)-2*b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)/d^2*x*c^2-2*b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)^(1/2)/d^2*c-b^2*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)^2/(c^2*x^2+1)/d^2/x+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c+b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c+2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c-4*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*c-4*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d^2*x*c^2-2*a*b*(d*(c^2*x^2+1))^(1/2)*arcsinh(c*x)/(c^2*x^2+1)/d^2/x+2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*ln((c*x+(c^2*x^2+1)^(1/2))^4-1)*c","B"
308,0,0,593,0.543000," ","int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{3} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(3/2),x)","F"
309,1,2609,438,0.503000," ","int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^(3/2),x)","\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x}+\frac{4 a^{2} c^{2}}{3 d x \sqrt{c^{2} d \,x^{2}+d}}-\frac{a^{2}}{3 d \,x^{3} \sqrt{c^{2} d \,x^{2}+d}}-\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, c x +\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{16 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c^{3}}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{128 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{5}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} c^{5} \sqrt{c^{2} x^{2}+1}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right)^{2} c^{4}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} c^{2}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x}+\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-c x -\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+c x +\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{32 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x^{3}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c^{3}}{\sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{64 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} \arcsinh \left(c x \right) c^{10}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{32 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) c^{8}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{64 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right)^{2} c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \sqrt{c^{2} x^{2}+1}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x^{2}}-\frac{64 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \left(c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{32 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{128 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{16 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) c^{4}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{16 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{3}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) c^{2}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x}-\frac{64 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2} \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, c^{5}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x^{2}}-\frac{64 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{32 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{32 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} c^{10}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{40 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{7 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2} x^{3}}-\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -c x -\sqrt{c^{2} x^{2}+1}\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}+\frac{8 a^{2} c^{4} x}{3 d \sqrt{c^{2} d \,x^{2}+d}}+\frac{64 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{7} c^{10}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{32 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} c^{8}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} c^{6}}{\left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x \,c^{4}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right) c^{3}}{\sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{10 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 \sqrt{c^{2} x^{2}+1}\, d^{2}}-\frac{32 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{5} \left(c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}-\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{3} \left(c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{4} x^{4}+7 c^{2} x^{2}-1\right) d^{2}}"," ",0,"1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x*c^2+4/3*a^2*c^2/d/x/(c^2*d*x^2+d)^(1/2)-1/3*a^2/d/x^3/(c^2*d*x^2+d)^(1/2)-128/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^2*c^5*(c^2*x^2+1)^(1/2)+8*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*arcsinh(c*x)^2*c^4-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*arcsinh(c*x)*c^4+128/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*arcsinh(c*x)*c^6+8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*(c^2*x^2+1)*c^4+16*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*arcsinh(c*x)*c^4+16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-8*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x*arcsinh(c*x)*c^2+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x^2*c*(c^2*x^2+1)^(1/2)-64/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*(c^2*x^2+1)*c^8-32/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*(c^2*x^2+1)*c^6-64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^2*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^5+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*arcsinh(c*x)*(c^2*x^2+1)*c^4+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c-64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*arcsinh(c*x)*(c^2*x^2+1)*c^8-32/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*arcsinh(c*x)*(c^2*x^2+1)*c^6+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x^3*arcsinh(c*x)^2-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*c^3*(c^2*x^2+1)^(1/2)-10/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^3-10/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^3+16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)^2*c^3-b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)*c^3+32/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^7*c^10+40/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*c^8-7/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*c^4+8/3*a^2*c^4/d*x/(c^2*d*x^2+d)^(1/2)-4*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x*arcsinh(c*x)^2*c^2+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^3-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-10/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^3-10/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^3+32/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*c^3+64/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^7*c^10+32*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*c^8+8*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*c^6-8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x*c^4-8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*c^3*(c^2*x^2+1)^(1/2)+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2/x^3*arcsinh(c*x)-2*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c^3-10/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c^3-2*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/d^2*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c^3+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^7*arcsinh(c*x)*c^10-32/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*(c^2*x^2+1)*c^8+32*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^5*arcsinh(c*x)*c^8+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*arcsinh(c*x)^2*c^6-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*(c^2*x^2+1)*c^6+8*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^4*x^4+7*c^2*x^2-1)/d^2*x^3*arcsinh(c*x)*c^6","B"
310,1,1040,475,0.497000," ","int(x^5*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{6}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{c^{6} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{a^{2} x^{4}}{c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 a^{2} x^{2}}{c^{4} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{c^{5} d^{3} \sqrt{c^{2} x^{2}+1}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{3 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{5}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{c^{5} d^{3} \sqrt{c^{2} x^{2}+1}}+\frac{8 a^{2}}{3 c^{6} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{3 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{5}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{c^{6} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{10 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{6}}+\frac{11 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}-\frac{11 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{11 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}-\frac{11 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}+\frac{11 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}-\frac{11 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{6} d^{3}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{c^{6} d^{3} \left(c^{2} x^{2}+1\right)}+\frac{5 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{6}}"," ",0,"1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^6+2*b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^3/(c^2*x^2+1)*x^2+b^2*(d*(c^2*x^2+1))^(1/2)/c^6/d^3/(c^2*x^2+1)*arcsinh(c*x)^2+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*x^2+5/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^6*arcsinh(c*x)^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/c^6/d^3/(c^2*x^2+1)+a^2*x^4/c^2/d/(c^2*d*x^2+d)^(3/2)+4*a^2/c^4*x^2/d/(c^2*d*x^2+d)^(3/2)-2*b^2*(d*(c^2*x^2+1))^(1/2)/c^5/d^3/(c^2*x^2+1)^(1/2)*arcsinh(c*x)*x+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c^5*arcsinh(c*x)*x+b^2*(d*(c^2*x^2+1))^(1/2)/c^4/d^3/(c^2*x^2+1)*arcsinh(c*x)^2*x^2+2*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*arcsinh(c*x)^2*x^2+11/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*dilog(1+I*(c*x+(c^2*x^2+1)^(1/2)))-11/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*dilog(1-I*(c*x+(c^2*x^2+1)^(1/2)))-2*a*b*(d*(c^2*x^2+1))^(1/2)/c^5/d^3/(c^2*x^2+1)^(1/2)*x+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c^5*x+2*a*b*(d*(c^2*x^2+1))^(1/2)/c^6/d^3/(c^2*x^2+1)*arcsinh(c*x)+10/3*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^6*arcsinh(c*x)+8/3*a^2/c^6/d/(c^2*d*x^2+d)^(3/2)+11/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*arcsinh(c*x)*ln(1+I*(c*x+(c^2*x^2+1)^(1/2)))-11/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*arcsinh(c*x)*ln(1-I*(c*x+(c^2*x^2+1)^(1/2)))+2*a*b*(d*(c^2*x^2+1))^(1/2)/c^4/d^3/(c^2*x^2+1)*arcsinh(c*x)*x^2+4*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*arcsinh(c*x)*x^2+11/3*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-I)-11/3*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^6/d^3*ln(c*x+(c^2*x^2+1)^(1/2)+I)","B"
311,1,3705,370,0.555000," ","int(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"64*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^6+28/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*(c^2*x^2+1)*x^3-362/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*arcsinh(c*x)*x^3+13*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*x^2*(c^2*x^2+1)^(1/2)+4*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*(c^2*x^2+1)*x-32*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*arcsinh(c*x)*x+128/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+440/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2-4*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*arcsinh(c*x)*x+8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*arcsinh(c*x)*(c^2*x^2+1)*x^5-4*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*x+16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*(c^2*x^2+1)^(1/2)+8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*arcsinh(c*x)^2-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*arcsinh(c*x)-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*x^7+16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*(c^2*x^2+1)*x^5-152*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*arcsinh(c*x)*x^5-40/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*x^3+16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-32*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*arcsinh(c*x)^2*x^7-1/3*a^2*x^3/c^2/d/(c^2*d*x^2+d)^(3/2)+168*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4+13*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2+4*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*arcsinh(c*x)*(c^2*x^2+1)*x+32*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^6+84*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^4+8*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4+28/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*arcsinh(c*x)*(c^2*x^2+1)*x^3+220/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^2-64*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*arcsinh(c*x)*x^7+8*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*(c^2*x^2+1)^(1/2)*x^4-16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*arcsinh(c*x)*x^7+8*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c/d^3*(c^2*x^2+1)^(1/2)*x^6+21*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c/d^3*(c^2*x^2+1)^(1/2)*x^4-181/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*arcsinh(c*x)^2*x^3-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*(c^2*x^2+1)*x^3-40/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*arcsinh(c*x)*x^3+55/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^3/d^3*x^2*(c^2*x^2+1)^(1/2)-16*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*arcsinh(c*x)^2*x-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*(c^2*x^2+1)*x+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)-a^2/c^4/d^2*x/(c^2*d*x^2+d)^(1/2)+a^2/c^4/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*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*x^5-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*arcsinh(c*x)^2+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)-76*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*arcsinh(c*x)^2*x^5-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*(c^2*x^2+1)*x^5-44/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*arcsinh(c*x)*x^5-20/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)*c^2/d^3*x^7-43/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^2/d^3*x^3-4*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^4/d^3*x+16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/c^5/d^3*(c^2*x^2+1)^(1/2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^5/d^3*arcsinh(c*x)^3-44/3*a*b*(d*(c^2*x^2+1))^(1/2)/(24*c^8*x^8+87*c^6*x^6+118*c^4*x^4+71*c^2*x^2+16)/d^3*x^5","B"
312,1,705,294,0.390000," ","int(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","-\frac{a^{2} x^{2}}{c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a^{2}}{3 d \,c^{4} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{3 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{3}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{5 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}-\frac{5 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}+\frac{5 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}-\frac{5 i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}-\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{3 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c^{3}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{4}}+\frac{5 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}-\frac{5 i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{4} d^{3}}"," ",0,"-a^2*x^2/c^2/d/(c^2*d*x^2+d)^(3/2)-2/3*a^2/d/c^4/(c^2*d*x^2+d)^(3/2)-b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*arcsinh(c*x)^2*x^2-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c^3*arcsinh(c*x)*x-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*x^2-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*arcsinh(c*x)^2-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4+5/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*dilog(1-I*(c*x+(c^2*x^2+1)^(1/2)))-5/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*arcsinh(c*x)*ln(1+I*(c*x+(c^2*x^2+1)^(1/2)))+5/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*arcsinh(c*x)*ln(1-I*(c*x+(c^2*x^2+1)^(1/2)))-5/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*dilog(1+I*(c*x+(c^2*x^2+1)^(1/2)))-2*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*arcsinh(c*x)*x^2-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c^3*x-4/3*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^4*arcsinh(c*x)+5/3*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*ln(c*x+(c^2*x^2+1)^(1/2)+I)-5/3*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^4/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-I)","B"
313,1,3112,292,0.465000," ","int(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*(c^2*x^2+1)^(1/2)-1/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c^3/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*arcsinh(c*x)^2*x^3+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*(c^2*x^2+1)*x^3+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*arcsinh(c*x)*x^3+2/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c^3/d^3*arcsinh(c*x)^2+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*x^3+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*x^7+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*x^5+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*arcsinh(c*x)*x^7-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^3/d^3*(c^2*x^2+1)^(1/2)*x^6+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*arcsinh(c*x)^2*x^5+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*(c^2*x^2+1)*x^5+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*arcsinh(c*x)*x^5-2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*(c^2*x^2+1)^(1/2)*x^4-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*x^2*(c^2*x^2+1)^(1/2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^2/d^3*(c^2*x^2+1)*x-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+4/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c^3/d^3*arcsinh(c*x)+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*x^7+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*x^5-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*(c^2*x^2+1)*x^3+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*arcsinh(c*x)*x^3-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*(c^2*x^2+1)^(1/2)-2/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c^3/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*x^3-2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^6-4*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4-8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2+2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*arcsinh(c*x)*x^5-a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*(c^2*x^2+1)^(1/2)*x^4-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^2-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2+2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*arcsinh(c*x)*x^7-1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*(c^2*x^2+1)*x^5-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^2/d^3*arcsinh(c*x)*(c^2*x^2+1)*x^5-2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^4-b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^3/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^6-a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c/d^3*x^2*(c^2*x^2+1)^(1/2)-2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-1/3*a^2/c^2*x/d/(c^2*d*x^2+d)^(3/2)+1/3*a^2/c^2/d^2*x/(c^2*d*x^2+d)^(1/2)-2/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c^3/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)/d^3*arcsinh(c*x)*(c^2*x^2+1)*x^3+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^8*x^8+9*c^6*x^6+10*c^4*x^4+5*c^2*x^2+1)*c^4/d^3*arcsinh(c*x)^2*x^7","B"
314,1,591,261,0.254000," ","int(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","-\frac{a^{2}}{3 c^{2} d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{3 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2}}-\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}-\frac{i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}+\frac{i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}-\frac{i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1+i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}+\frac{i b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \dilog \left(1-i \left(c x +\sqrt{c^{2} x^{2}+1}\right)\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{3 d^{3} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} c}-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}+1\right)^{2} c^{2}}+\frac{i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}+i\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}-\frac{i a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(c x +\sqrt{c^{2} x^{2}+1}-i\right)}{3 \sqrt{c^{2} x^{2}+1}\, c^{2} d^{3}}"," ",0,"-1/3*a^2/c^2/d/(c^2*d*x^2+d)^(3/2)+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c*arcsinh(c*x)*x+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2*x^2-1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*arcsinh(c*x)^2+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2-1/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*arcsinh(c*x)*ln(1+I*(c*x+(c^2*x^2+1)^(1/2)))+1/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*arcsinh(c*x)*ln(1-I*(c*x+(c^2*x^2+1)^(1/2)))-1/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*dilog(1+I*(c*x+(c^2*x^2+1)^(1/2)))+1/3*I*b^2*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*dilog(1-I*(c*x+(c^2*x^2+1)^(1/2)))+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^(3/2)/c*x-2/3*a*b*(d*(c^2*x^2+1))^(1/2)/d^3/(c^2*x^2+1)^2/c^2*arcsinh(c*x)+1/3*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2)+I)-1/3*I*a*b*(d*(c^2*x^2+1))^(1/2)/(c^2*x^2+1)^(1/2)/c^2/d^3*ln(c*x+(c^2*x^2+1)^(1/2)-I)","B"
315,1,2729,274,0.246000," ","int((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","-\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{6} x^{7}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{3 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} x^{5}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{13 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}+\frac{a^{2} x}{3 d \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{2 a^{2} x}{3 d^{2} \sqrt{c^{2} d \,x^{2}+d}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{28 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \arcsinh \left(c x \right) x^{5}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{10 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{14 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}\, x^{2}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, x^{2}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{10 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \left(c^{2} x^{2}+1\right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \,x^{2} \sqrt{c^{2} x^{2}+1}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{34 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \left(c^{2} x^{2}+1\right) x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{16 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2}}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}-\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{6} \arcsinh \left(c x \right) x^{7}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \arcsinh \left(c x \right)^{2} x^{5}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{14 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \arcsinh \left(c x \right) x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}+\frac{8 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{17 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right)^{2} x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \left(c^{2} x^{2}+1\right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{7 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c \,x^{2} \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} \left(c^{2} x^{2}+1\right) x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{6} x^{7}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{14 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{4} x^{5}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{16 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{2 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \left(c^{2} x^{2}+1\right) x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}+\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}-\frac{4 a b \sqrt{d \left(c^{2} x^{2}+1\right)}\, \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}-\frac{16 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{2} \arcsinh \left(c x \right) x^{3}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{8 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right)^{2} \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}+\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}}{3 \left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) c \,d^{3}}+\frac{2 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \left(c^{2} x^{2}+1\right) x}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}-\frac{4 b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, \arcsinh \left(c x \right) \ln \left(1+\left(c x +\sqrt{c^{2} x^{2}+1}\right)^{2}\right)}{3 \sqrt{c^{2} x^{2}+1}\, c \,d^{3}}+\frac{b^{2} \sqrt{d \left(c^{2} x^{2}+1\right)}\, c^{3} \sqrt{c^{2} x^{2}+1}\, x^{4}}{\left(3 c^{6} x^{6}+10 c^{4} x^{4}+11 c^{2} x^{2}+4\right) d^{3}}"," ",0,"-2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*x-2/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)+4*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*arcsinh(c*x)^2*x+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*(c^2*x^2+1)*x-2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*arcsinh(c*x)*x+4/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c/d^3*arcsinh(c*x)^2-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^6/d^3*x^7-3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*x^5-13/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*x^3+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*(c^2*x^2+1)^(1/2)+1/3*a^2*x/d/(c^2*d*x^2+d)^(3/2)+2/3*a^2/d^2*x/(c^2*d*x^2+d)^(1/2)-28/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2-4*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^3/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^4+10/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*(c^2*x^2+1)*x^3+34/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*arcsinh(c*x)*x^3+a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*x^2*(c^2*x^2+1)^(1/2)-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)-2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^3/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^4+10/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*arcsinh(c*x)*(c^2*x^2+1)*x^3-14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*x^2+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*x^2+4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*(c^2*x^2+1)*x^5+4*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*arcsinh(c*x)*x^5+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*arcsinh(c*x)*(c^2*x^2+1)*x^5-2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*x+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*(c^2*x^2+1)*x^3-16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*arcsinh(c*x)*x^3+7/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c/d^3*x^2*(c^2*x^2+1)^(1/2)-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)+4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*arcsinh(c*x)*(c^2*x^2+1)*x-4/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)-4/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^6/d^3*arcsinh(c*x)*x^7+2*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*arcsinh(c*x)^2*x^5+2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*(c^2*x^2+1)*x^5-14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*arcsinh(c*x)*x^5+8/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c/d^3*arcsinh(c*x)-4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^6/d^3*x^7-14/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^4/d^3*x^5-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*x^3+2*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*(c^2*x^2+1)*x+8*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/d^3*arcsinh(c*x)*x+4/3*a*b*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)/c/d^3*(c^2*x^2+1)^(1/2)-4/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/c/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)+b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^3/d^3*(c^2*x^2+1)^(1/2)*x^4+17/3*b^2*(d*(c^2*x^2+1))^(1/2)/(3*c^6*x^6+10*c^4*x^4+11*c^2*x^2+4)*c^2/d^3*arcsinh(c*x)^2*x^3","B"
316,0,0,534,0.395000," ","int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(5/2),x)","F"
317,1,3517,411,0.421000," ","int((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-40*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*c^8-160/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*c^6-29*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*c^4-16/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)^2*c+2*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c+5/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)*c+2*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c-5*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*c^2-9*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3/x*arcsinh(c*x)^2-3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*c*(c^2*x^2+1)^(1/2)-32/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^9*c^10-a^2/d/x/(c^2*d*x^2+d)^(3/2)+128/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^4*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^5+272/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3+64/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*(c^2*x^2+1)*c^8+160/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*(c^2*x^2+1)*c^6-128/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*arcsinh(c*x)*c^6+40*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*(c^2*x^2+1)*c^4-112*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*arcsinh(c*x)*c^4-8/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*c^3*(c^2*x^2+1)^(1/2)+8*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*(c^2*x^2+1)*c^2-88*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*arcsinh(c*x)*c^2+48*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*(c^2*x^2+1)*arcsinh(c*x)*c^8+160/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*(c^2*x^2+1)*arcsinh(c*x)*c^6+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^4*(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^5+40*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*(c^2*x^2+1)*arcsinh(c*x)*c^4+136/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c^3-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c^3+8*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*(c^2*x^2+1)*arcsinh(c*x)*c^2-4/3*a^2*c^2*x/d/(c^2*d*x^2+d)^(3/2)+80/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*(c^2*x^2+1)*c^4-56*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*arcsinh(c*x)^2*c^4-48*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*arcsinh(c*x)*c^4-280/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*arcsinh(c*x)*c^6-64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*arcsinh(c*x)^2*c^6-32/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*c-64/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^9*c^10-224/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*c^8+24*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*(c^2*x^2+1)^(1/2)*arcsinh(c*x)^2*c-280/3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*c^6-48*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^3*c^4-8*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*c^2-3*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*c*(c^2*x^2+1)^(1/2)-18*a*b*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3/x*arcsinh(c*x)+10/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c+2*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*ln((c*x+(c^2*x^2+1)^(1/2))^2-1)*c-3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*(c^2*x^2+1)^(1/2)*arcsinh(c*x)*c+88/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^5*(c^2*x^2+1)*c^6-17/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^2*c^3*(c^2*x^2+1)^(1/2)+8*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*(c^2*x^2+1)*c^2-44*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*arcsinh(c*x)^2*c^2-8*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x*arcsinh(c*x)*c^2+2*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c+2*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c+10/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c-8/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^4*c^5*(c^2*x^2+1)^(1/2)-64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^9*arcsinh(c*x)*c^10+32/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*(c^2*x^2+1)*c^8-224/3*b^2*(d*(c^2*x^2+1))^(1/2)/(8*c^6*x^6+25*c^4*x^4+26*c^2*x^2+9)/d^3*x^7*arcsinh(c*x)*c^8-8/3*a^2*c^2/d^2*x/(c^2*d*x^2+d)^(1/2)","B"
318,0,0,687,0.622000," ","int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{x^{3} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(5/2),x)","F"
319,1,4955,484,0.532000," ","int((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-16/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*polylog(2,-c*x-(c^2*x^2+1)^(1/2))*c^3+2*a^2*c^2/d/x/(c^2*d*x^2+d)^(3/2)-256/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*(c^2*x^2+1)*c^12-640/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*(c^2*x^2+1)*c^10+128*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*arcsinh(c*x)*c^10-1/3*a^2/d/x^3/(c^2*d*x^2+d)^(3/2)+8*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^6*(c^2*x^2+1)^(1/2)*c^9+160*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*arcsinh(c*x)^2*c^8-256*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^4*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^7-352/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5-128*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^6*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^9+32/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)^2*c^3-16/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*polylog(2,c*x+(c^2*x^2+1)^(1/2))*c^3+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^11*c^14+224/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*c^12+88*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*c^10+100/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*c^8-14/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*c^6-3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*c^4+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x*c^2+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x^3*arcsinh(c*x)^2-8/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*polylog(2,-(c*x+(c^2*x^2+1)^(1/2))^2)*c^3-2/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*c^3*(c^2*x^2+1)^(1/2)-80/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*arcsinh(c*x)*(c^2*x^2+1)*c^6-176/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^5-4*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^5+16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*arcsinh(c*x)*(c^2*x^2+1)*c^4+1/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x^2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c-64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*(c^2*x^2+1)*c^12+896/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*arcsinh(c*x)*c^12+32/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-160*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*(c^2*x^2+1)*c^8+320*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*arcsinh(c*x)*c^8-80/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*(c^2*x^2+1)*c^6+688/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*arcsinh(c*x)*c^6-4*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*c^5*(c^2*x^2+1)^(1/2)+24*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*arcsinh(c*x)*c^4+16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*(c^2*x^2+1)*c^4-12*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x*arcsinh(c*x)*c^2+1/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x^2*c*(c^2*x^2+1)^(1/2)-64*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^6*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^9-160*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*arcsinh(c*x)*(c^2*x^2+1)*c^8-128*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^4*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^7-640/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*arcsinh(c*x)*(c^2*x^2+1)*c^10-256/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*arcsinh(c*x)*(c^2*x^2+1)*c^12-32/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*(c^2*x^2+1)*c^6+64/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*arcsinh(c*x)*c^6+22/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^2*c^5*(c^2*x^2+1)^(1/2)+12*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*arcsinh(c*x)^2*c^4+64*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*arcsinh(c*x)^2*c^10-160/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*(c^2*x^2+1)*c^10+1120/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*arcsinh(c*x)*c^10+560/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*c^8+16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*arcsinh(c*x)^2*(c^2*x^2+1)^(1/2)*c^3-4*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^3-16/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*ln(1+c*x+(c^2*x^2+1)^(1/2))*c^3+2/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x^3*arcsinh(c*x)-128/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*(c^2*x^2+1)*c^8+560/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^5*arcsinh(c*x)*c^8+16*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^4*c^7*(c^2*x^2+1)^(1/2)+344/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*arcsinh(c*x)^2*c^6+8/3*a^2*c^4*x/d/(c^2*d*x^2+d)^(3/2)+16/3*a^2*c^4/d^2*x/(c^2*d*x^2+d)^(1/2)-16/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*ln((c*x+(c^2*x^2+1)^(1/2))^4-1)*c^3+64/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^3*c^6-16/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*ln(1+(c*x+(c^2*x^2+1)^(1/2))^2)*c^3+256/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^11*arcsinh(c*x)*c^14+64/3*a*b/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*c^3-16/3*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*arcsinh(c*x)*c^4-6*b^2*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3/x*arcsinh(c*x)^2*c^2-16/3*b^2/(c^2*x^2+1)^(1/2)*(d*(c^2*x^2+1))^(1/2)/d^3*arcsinh(c*x)*ln(1-c*x-(c^2*x^2+1)^(1/2))*c^3+256/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^11*c^14+896/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^9*c^12+1120/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x^7*c^10-16/3*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*x*c^4-4*a*b*(d*(c^2*x^2+1))^(1/2)/(12*c^8*x^8+36*c^6*x^6+35*c^4*x^4+10*c^2*x^2-1)/d^3*c^3*(c^2*x^2+1)^(1/2)","B"
320,1,570,334,0.253000," ","int(arcsinh(a*x)^2/(a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}-8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+20 x^{3} a^{3}-16 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+15 a x -8 \sqrt{a^{2} x^{2}+1}\right) \left(-64 \arcsinh \left(a x \right) x^{8} a^{8}-64 \sqrt{a^{2} x^{2}+1}\, \arcsinh \left(a x \right) x^{7} a^{7}-32 x^{8} a^{8}-32 \sqrt{a^{2} x^{2}+1}\, x^{7} a^{7}-280 \arcsinh \left(a x \right) x^{6} a^{6}-248 \sqrt{a^{2} x^{2}+1}\, \arcsinh \left(a x \right) x^{5} a^{5}-142 x^{6} a^{6}-126 \sqrt{a^{2} x^{2}+1}\, x^{5} a^{5}+80 \arcsinh \left(a x \right)^{2} x^{4} a^{4}-456 \arcsinh \left(a x \right) x^{4} a^{4}-340 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-265 x^{4} a^{4}-156 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+190 \arcsinh \left(a x \right)^{2} a^{2} x^{2}-328 \arcsinh \left(a x \right) x^{2} a^{2}-165 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x -235 a^{2} x^{2}-62 \sqrt{a^{2} x^{2}+1}\, x a +128 \arcsinh \left(a x \right)^{2}-88 \arcsinh \left(a x \right)-80\right)}{30 \left(40 a^{10} x^{10}+215 x^{8} a^{8}+469 x^{6} a^{6}+517 x^{4} a^{4}+287 a^{2} x^{2}+64\right) a \,c^{4}}+\frac{16 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{2}}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}-\frac{16 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right) \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}-\frac{8 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \polylog \left(2, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}"," ",0,"1/30*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5-8*(a^2*x^2+1)^(1/2)*x^4*a^4+20*x^3*a^3-16*(a^2*x^2+1)^(1/2)*x^2*a^2+15*a*x-8*(a^2*x^2+1)^(1/2))*(-64*arcsinh(a*x)*x^8*a^8-64*(a^2*x^2+1)^(1/2)*arcsinh(a*x)*x^7*a^7-32*x^8*a^8-32*(a^2*x^2+1)^(1/2)*x^7*a^7-280*arcsinh(a*x)*x^6*a^6-248*(a^2*x^2+1)^(1/2)*arcsinh(a*x)*x^5*a^5-142*x^6*a^6-126*(a^2*x^2+1)^(1/2)*x^5*a^5+80*arcsinh(a*x)^2*x^4*a^4-456*arcsinh(a*x)*x^4*a^4-340*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3-265*x^4*a^4-156*(a^2*x^2+1)^(1/2)*x^3*a^3+190*arcsinh(a*x)^2*a^2*x^2-328*arcsinh(a*x)*x^2*a^2-165*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x-235*a^2*x^2-62*(a^2*x^2+1)^(1/2)*x*a+128*arcsinh(a*x)^2-88*arcsinh(a*x)-80)/(40*a^10*x^10+215*a^8*x^8+469*a^6*x^6+517*a^4*x^4+287*a^2*x^2+64)/a/c^4+16/15/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)/a/c^4*arcsinh(a*x)^2-16/15/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)/a/c^4*arcsinh(a*x)*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)-8/15/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)/a/c^4*polylog(2,-(a*x+(a^2*x^2+1)^(1/2))^2)","A"
321,0,0,873,1.868000," ","int(x^m*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x)","F"
322,0,0,451,1.424000," ","int(x^m*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\int x^{m} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x)","F"
323,0,0,182,1.219000," ","int(x^m*(c^2*d*x^2+d)^(1/2)*(a+b*arcsinh(c*x))^2,x)","\int x^{m} \sqrt{c^{2} d \,x^{2}+d}\, \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(c^2*d*x^2+d)^(1/2)*(a+b*arcsinh(c*x))^2,x)","F"
324,0,0,28,0.352000," ","int(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x)","F"
325,0,0,28,0.614000," ","int(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x)","F"
326,0,0,28,0.569000," ","int(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","\int \frac{x^{m} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x)","F"
327,0,0,23,0.280000," ","int(x^m*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsinh \left(a x \right)^{2}}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x)","F"
328,1,270,311,0.114000," ","int((a^2*c*x^2+c)^3*arcsinh(a*x)^3,x)","\frac{c^{3} \left(1929375 \arcsinh \left(a x \right)^{3} a^{7} x^{7}-826875 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{6} x^{6}+8103375 \arcsinh \left(a x \right)^{3} a^{5} x^{5}+236250 \arcsinh \left(a x \right) a^{7} x^{7}-3869775 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{4} x^{4}-33750 a^{6} x^{6} \sqrt{a^{2} x^{2}+1}+13505625 \arcsinh \left(a x \right)^{3} a^{3} x^{3}+1547910 \arcsinh \left(a x \right) a^{5} x^{5}-8345925 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{2} x^{2}-269082 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+13505625 \arcsinh \left(a x \right)^{3} a x +5563950 \arcsinh \left(a x \right) a^{3} x^{3}-23825025 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}-1495874 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+47650050 a x \arcsinh \left(a x \right)-44658302 \sqrt{a^{2} x^{2}+1}\right)}{13505625 a}"," ",0,"1/13505625/a*c^3*(1929375*arcsinh(a*x)^3*a^7*x^7-826875*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^6*x^6+8103375*arcsinh(a*x)^3*a^5*x^5+236250*arcsinh(a*x)*a^7*x^7-3869775*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^4*x^4-33750*a^6*x^6*(a^2*x^2+1)^(1/2)+13505625*arcsinh(a*x)^3*a^3*x^3+1547910*arcsinh(a*x)*a^5*x^5-8345925*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^2*x^2-269082*(a^2*x^2+1)^(1/2)*x^4*a^4+13505625*arcsinh(a*x)^3*a*x+5563950*arcsinh(a*x)*a^3*x^3-23825025*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)-1495874*(a^2*x^2+1)^(1/2)*x^2*a^2+47650050*a*x*arcsinh(a*x)-44658302*(a^2*x^2+1)^(1/2))","A"
329,1,200,229,0.063000," ","int((a^2*c*x^2+c)^2*arcsinh(a*x)^3,x)","\frac{c^{2} \left(3375 \arcsinh \left(a x \right)^{3} a^{5} x^{5}-2025 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{4} x^{4}+11250 \arcsinh \left(a x \right)^{3} a^{3} x^{3}+810 \arcsinh \left(a x \right) a^{5} x^{5}-8550 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{2} x^{2}-162 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+16875 \arcsinh \left(a x \right)^{3} a x +5700 \arcsinh \left(a x \right) a^{3} x^{3}-33525 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}-1684 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+67050 a x \arcsinh \left(a x \right)-63682 \sqrt{a^{2} x^{2}+1}\right)}{16875 a}"," ",0,"1/16875/a*c^2*(3375*arcsinh(a*x)^3*a^5*x^5-2025*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^4*x^4+11250*arcsinh(a*x)^3*a^3*x^3+810*arcsinh(a*x)*a^5*x^5-8550*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^2*x^2-162*(a^2*x^2+1)^(1/2)*x^4*a^4+16875*arcsinh(a*x)^3*a*x+5700*arcsinh(a*x)*a^3*x^3-33525*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)-1684*(a^2*x^2+1)^(1/2)*x^2*a^2+67050*a*x*arcsinh(a*x)-63682*(a^2*x^2+1)^(1/2))","A"
330,1,128,131,0.055000," ","int((a^2*c*x^2+c)*arcsinh(a*x)^3,x)","\frac{c \left(9 \arcsinh \left(a x \right)^{3} a^{3} x^{3}-9 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{2} x^{2}+27 \arcsinh \left(a x \right)^{3} a x +6 \arcsinh \left(a x \right) a^{3} x^{3}-63 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}-2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+126 a x \arcsinh \left(a x \right)-122 \sqrt{a^{2} x^{2}+1}\right)}{27 a}"," ",0,"1/27/a*c*(9*arcsinh(a*x)^3*a^3*x^3-9*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^2*x^2+27*arcsinh(a*x)^3*a*x+6*arcsinh(a*x)*a^3*x^3-63*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)-2*(a^2*x^2+1)^(1/2)*x^2*a^2+126*a*x*arcsinh(a*x)-122*(a^2*x^2+1)^(1/2))","A"
331,0,0,225,0.086000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c),x)","\int \frac{\arcsinh \left(a x \right)^{3}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(arcsinh(a*x)^3/(a^2*c*x^2+c),x)","F"
332,0,0,358,0.209000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c)^2,x)","\int \frac{\arcsinh \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(arcsinh(a*x)^3/(a^2*c*x^2+c)^2,x)","F"
333,0,0,447,0.343000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c)^3,x)","\int \frac{\arcsinh \left(a x \right)^{3}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(arcsinh(a*x)^3/(a^2*c*x^2+c)^3,x)","F"
334,1,802,437,0.255000," ","int((a^2*c*x^2+c)^(5/2)*arcsinh(a*x)^3,x)","\frac{5 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{4} c^{2}}{64 \sqrt{a^{2} x^{2}+1}\, a}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(32 x^{7} a^{7}+32 a^{6} x^{6} \sqrt{a^{2} x^{2}+1}+64 x^{5} a^{5}+48 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+38 x^{3} a^{3}+18 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+6 a x +\sqrt{a^{2} x^{2}+1}\right) \left(36 \arcsinh \left(a x \right)^{3}-18 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)-1\right) c^{2}}{13824 a \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}+8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+12 x^{3} a^{3}+8 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+4 a x +\sqrt{a^{2} x^{2}+1}\right) \left(32 \arcsinh \left(a x \right)^{3}-24 \arcsinh \left(a x \right)^{2}+12 \arcsinh \left(a x \right)-3\right) c^{2}}{4096 a \left(a^{2} x^{2}+1\right)}+\frac{15 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}+2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+2 a x +\sqrt{a^{2} x^{2}+1}\right) \left(4 \arcsinh \left(a x \right)^{3}-6 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)-3\right) c^{2}}{512 a \left(a^{2} x^{2}+1\right)}+\frac{15 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}-2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+2 a x -\sqrt{a^{2} x^{2}+1}\right) \left(4 \arcsinh \left(a x \right)^{3}+6 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)+3\right) c^{2}}{512 a \left(a^{2} x^{2}+1\right)}+\frac{3 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}-8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+12 x^{3} a^{3}-8 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+4 a x -\sqrt{a^{2} x^{2}+1}\right) \left(32 \arcsinh \left(a x \right)^{3}+24 \arcsinh \left(a x \right)^{2}+12 \arcsinh \left(a x \right)+3\right) c^{2}}{4096 a \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(32 x^{7} a^{7}-32 a^{6} x^{6} \sqrt{a^{2} x^{2}+1}+64 x^{5} a^{5}-48 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+38 x^{3} a^{3}-18 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+6 a x -\sqrt{a^{2} x^{2}+1}\right) \left(36 \arcsinh \left(a x \right)^{3}+18 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)+1\right) c^{2}}{13824 a \left(a^{2} x^{2}+1\right)}"," ",0,"5/64*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a*arcsinh(a*x)^4*c^2+1/13824*(c*(a^2*x^2+1))^(1/2)*(32*x^7*a^7+32*a^6*x^6*(a^2*x^2+1)^(1/2)+64*x^5*a^5+48*(a^2*x^2+1)^(1/2)*x^4*a^4+38*x^3*a^3+18*(a^2*x^2+1)^(1/2)*x^2*a^2+6*a*x+(a^2*x^2+1)^(1/2))*(36*arcsinh(a*x)^3-18*arcsinh(a*x)^2+6*arcsinh(a*x)-1)*c^2/a/(a^2*x^2+1)+3/4096*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5+8*(a^2*x^2+1)^(1/2)*x^4*a^4+12*x^3*a^3+8*(a^2*x^2+1)^(1/2)*x^2*a^2+4*a*x+(a^2*x^2+1)^(1/2))*(32*arcsinh(a*x)^3-24*arcsinh(a*x)^2+12*arcsinh(a*x)-3)*c^2/a/(a^2*x^2+1)+15/512*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3+2*(a^2*x^2+1)^(1/2)*x^2*a^2+2*a*x+(a^2*x^2+1)^(1/2))*(4*arcsinh(a*x)^3-6*arcsinh(a*x)^2+6*arcsinh(a*x)-3)*c^2/a/(a^2*x^2+1)+15/512*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3-2*(a^2*x^2+1)^(1/2)*x^2*a^2+2*a*x-(a^2*x^2+1)^(1/2))*(4*arcsinh(a*x)^3+6*arcsinh(a*x)^2+6*arcsinh(a*x)+3)*c^2/a/(a^2*x^2+1)+3/4096*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5-8*(a^2*x^2+1)^(1/2)*x^4*a^4+12*x^3*a^3-8*(a^2*x^2+1)^(1/2)*x^2*a^2+4*a*x-(a^2*x^2+1)^(1/2))*(32*arcsinh(a*x)^3+24*arcsinh(a*x)^2+12*arcsinh(a*x)+3)*c^2/a/(a^2*x^2+1)+1/13824*(c*(a^2*x^2+1))^(1/2)*(32*x^7*a^7-32*a^6*x^6*(a^2*x^2+1)^(1/2)+64*x^5*a^5-48*(a^2*x^2+1)^(1/2)*x^4*a^4+38*x^3*a^3-18*(a^2*x^2+1)^(1/2)*x^2*a^2+6*a*x-(a^2*x^2+1)^(1/2))*(36*arcsinh(a*x)^3+18*arcsinh(a*x)^2+6*arcsinh(a*x)+1)*c^2/a/(a^2*x^2+1)","A"
335,1,484,296,0.195000," ","int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^3,x)","\frac{3 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{4} c}{32 \sqrt{a^{2} x^{2}+1}\, a}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}+8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+12 x^{3} a^{3}+8 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+4 a x +\sqrt{a^{2} x^{2}+1}\right) \left(32 \arcsinh \left(a x \right)^{3}-24 \arcsinh \left(a x \right)^{2}+12 \arcsinh \left(a x \right)-3\right) c}{2048 a \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}+2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+2 a x +\sqrt{a^{2} x^{2}+1}\right) \left(4 \arcsinh \left(a x \right)^{3}-6 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)-3\right) c}{32 a \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}-2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+2 a x -\sqrt{a^{2} x^{2}+1}\right) \left(4 \arcsinh \left(a x \right)^{3}+6 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)+3\right) c}{32 a \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}-8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+12 x^{3} a^{3}-8 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+4 a x -\sqrt{a^{2} x^{2}+1}\right) \left(32 \arcsinh \left(a x \right)^{3}+24 \arcsinh \left(a x \right)^{2}+12 \arcsinh \left(a x \right)+3\right) c}{2048 a \left(a^{2} x^{2}+1\right)}"," ",0,"3/32*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a*arcsinh(a*x)^4*c+1/2048*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5+8*(a^2*x^2+1)^(1/2)*x^4*a^4+12*x^3*a^3+8*(a^2*x^2+1)^(1/2)*x^2*a^2+4*a*x+(a^2*x^2+1)^(1/2))*(32*arcsinh(a*x)^3-24*arcsinh(a*x)^2+12*arcsinh(a*x)-3)*c/a/(a^2*x^2+1)+1/32*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3+2*(a^2*x^2+1)^(1/2)*x^2*a^2+2*a*x+(a^2*x^2+1)^(1/2))*(4*arcsinh(a*x)^3-6*arcsinh(a*x)^2+6*arcsinh(a*x)-3)*c/a/(a^2*x^2+1)+1/32*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3-2*(a^2*x^2+1)^(1/2)*x^2*a^2+2*a*x-(a^2*x^2+1)^(1/2))*(4*arcsinh(a*x)^3+6*arcsinh(a*x)^2+6*arcsinh(a*x)+3)*c/a/(a^2*x^2+1)+1/2048*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5-8*(a^2*x^2+1)^(1/2)*x^4*a^4+12*x^3*a^3-8*(a^2*x^2+1)^(1/2)*x^2*a^2+4*a*x-(a^2*x^2+1)^(1/2))*(32*arcsinh(a*x)^3+24*arcsinh(a*x)^2+12*arcsinh(a*x)+3)*c/a/(a^2*x^2+1)","A"
336,1,231,173,0.164000," ","int(arcsinh(a*x)^3*(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{4}}{8 \sqrt{a^{2} x^{2}+1}\, a}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}+2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+2 a x +\sqrt{a^{2} x^{2}+1}\right) \left(4 \arcsinh \left(a x \right)^{3}-6 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)-3\right)}{32 a \left(a^{2} x^{2}+1\right)}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}-2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+2 a x -\sqrt{a^{2} x^{2}+1}\right) \left(4 \arcsinh \left(a x \right)^{3}+6 \arcsinh \left(a x \right)^{2}+6 \arcsinh \left(a x \right)+3\right)}{32 a \left(a^{2} x^{2}+1\right)}"," ",0,"1/8*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a*arcsinh(a*x)^4+1/32*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3+2*(a^2*x^2+1)^(1/2)*x^2*a^2+2*a*x+(a^2*x^2+1)^(1/2))*(4*arcsinh(a*x)^3-6*arcsinh(a*x)^2+6*arcsinh(a*x)-3)/a/(a^2*x^2+1)+1/32*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3-2*(a^2*x^2+1)^(1/2)*x^2*a^2+2*a*x-(a^2*x^2+1)^(1/2))*(4*arcsinh(a*x)^3+6*arcsinh(a*x)^2+6*arcsinh(a*x)+3)/a/(a^2*x^2+1)","A"
337,1,39,34,0.043000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{4}}{4 \sqrt{a^{2} x^{2}+1}\, a c}"," ",0,"1/4*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c*arcsinh(a*x)^4","A"
338,1,262,225,0.187000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(a x -\sqrt{a^{2} x^{2}+1}\right) \arcsinh \left(a x \right)^{3}}{a \,c^{2} \left(a^{2} x^{2}+1\right)}+\frac{2 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{3}}{\sqrt{a^{2} x^{2}+1}\, a \,c^{2}}-\frac{3 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{2} \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{2}}-\frac{3 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right) \polylog \left(2, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{2}}+\frac{3 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \polylog \left(3, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{2 \sqrt{a^{2} x^{2}+1}\, a \,c^{2}}"," ",0,"(c*(a^2*x^2+1))^(1/2)*(a*x-(a^2*x^2+1)^(1/2))*arcsinh(a*x)^3/a/c^2/(a^2*x^2+1)+2*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^2*arcsinh(a*x)^3-3*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^2*arcsinh(a*x)^2*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)-3*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^2*arcsinh(a*x)*polylog(2,-(a*x+(a^2*x^2+1)^(1/2))^2)+3/2*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^2*polylog(3,-(a*x+(a^2*x^2+1)^(1/2))^2)","A"
339,1,550,350,0.273000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(2 x^{3} a^{3}-2 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+3 a x -2 \sqrt{a^{2} x^{2}+1}\right) \arcsinh \left(a x \right) \left(-6 \arcsinh \left(a x \right) x^{4} a^{4}-6 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-6 x^{4} a^{4}-6 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}+6 \arcsinh \left(a x \right)^{2} a^{2} x^{2}-12 \arcsinh \left(a x \right) x^{2} a^{2}-9 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x -18 a^{2} x^{2}-6 \sqrt{a^{2} x^{2}+1}\, x a +8 \arcsinh \left(a x \right)^{2}-6 \arcsinh \left(a x \right)-12\right)}{6 \left(3 x^{6} a^{6}+10 x^{4} a^{4}+11 a^{2} x^{2}+4\right) a \,c^{3}}-\frac{2 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(a x +\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{3}}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{3}}+\frac{4 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{3}}{3 \sqrt{a^{2} x^{2}+1}\, a \,c^{3}}-\frac{2 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{2} \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{3}}-\frac{2 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right) \polylog \left(2, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{3}}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \polylog \left(3, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{3}}"," ",0,"1/6*(c*(a^2*x^2+1))^(1/2)*(2*x^3*a^3-2*(a^2*x^2+1)^(1/2)*x^2*a^2+3*a*x-2*(a^2*x^2+1)^(1/2))*arcsinh(a*x)*(-6*arcsinh(a*x)*x^4*a^4-6*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3-6*x^4*a^4-6*(a^2*x^2+1)^(1/2)*x^3*a^3+6*arcsinh(a*x)^2*a^2*x^2-12*arcsinh(a*x)*x^2*a^2-9*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x-18*a^2*x^2-6*(a^2*x^2+1)^(1/2)*x*a+8*arcsinh(a*x)^2-6*arcsinh(a*x)-12)/(3*a^6*x^6+10*a^4*x^4+11*a^2*x^2+4)/a/c^3-2*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^3*ln(a*x+(a^2*x^2+1)^(1/2))+(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^3*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)+4/3*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^3*arcsinh(a*x)^3-2*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^3*arcsinh(a*x)^2*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)-2*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^3*arcsinh(a*x)*polylog(2,-(a*x+(a^2*x^2+1)^(1/2))^2)+(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^3*polylog(3,-(a*x+(a^2*x^2+1)^(1/2))^2)","A"
340,1,888,476,0.349000," ","int(arcsinh(a*x)^3/(a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(8 x^{5} a^{5}-8 \sqrt{a^{2} x^{2}+1}\, x^{4} a^{4}+20 x^{3} a^{3}-16 \sqrt{a^{2} x^{2}+1}\, x^{2} a^{2}+15 a x -8 \sqrt{a^{2} x^{2}+1}\right) \left(24-1020 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-495 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a x -936 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-372 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +24 x^{8} a^{8}+96 x^{6} a^{6}+144 x^{4} a^{4}-192 \sqrt{a^{2} x^{2}+1}\, \arcsinh \left(a x \right) x^{7} a^{7}-756 \sqrt{a^{2} x^{2}+1}\, \arcsinh \left(a x \right) x^{5} a^{5}+96 a^{2} x^{2}-480 \arcsinh \left(a x \right)-264 \arcsinh \left(a x \right)^{2}+380 \arcsinh \left(a x \right)^{3} x^{2} a^{2}-192 \arcsinh \left(a x \right)^{2} x^{8} a^{8}-840 \arcsinh \left(a x \right)^{2} x^{6} a^{6}+160 \arcsinh \left(a x \right)^{3} x^{4} a^{4}+256 \arcsinh \left(a x \right)^{3}-1368 \arcsinh \left(a x \right)^{2} x^{4} a^{4}-984 \arcsinh \left(a x \right)^{2} a^{2} x^{2}-192 \arcsinh \left(a x \right) x^{8} a^{8}-852 \arcsinh \left(a x \right) x^{6} a^{6}-192 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, x^{7} a^{7}-744 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, x^{5} a^{5}+24 \sqrt{a^{2} x^{2}+1}\, x^{7} a^{7}+84 \sqrt{a^{2} x^{2}+1}\, x^{5} a^{5}+105 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}-1590 \arcsinh \left(a x \right) x^{4} a^{4}-1410 \arcsinh \left(a x \right) x^{2} a^{2}+45 \sqrt{a^{2} x^{2}+1}\, x a \right)}{60 \left(40 a^{10} x^{10}+215 x^{8} a^{8}+469 x^{6} a^{6}+517 x^{4} a^{4}+287 a^{2} x^{2}+64\right) a \,c^{4}}-\frac{2 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(a x +\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{4}}+\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{\sqrt{a^{2} x^{2}+1}\, a \,c^{4}}+\frac{16 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{3}}{15 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}-\frac{8 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right)^{2} \ln \left(1+\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{5 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}-\frac{8 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \arcsinh \left(a x \right) \polylog \left(2, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{5 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}+\frac{4 \sqrt{c \left(a^{2} x^{2}+1\right)}\, \polylog \left(3, -\left(a x +\sqrt{a^{2} x^{2}+1}\right)^{2}\right)}{5 \sqrt{a^{2} x^{2}+1}\, a \,c^{4}}"," ",0,"1/60*(c*(a^2*x^2+1))^(1/2)*(8*x^5*a^5-8*(a^2*x^2+1)^(1/2)*x^4*a^4+20*x^3*a^3-16*(a^2*x^2+1)^(1/2)*x^2*a^2+15*a*x-8*(a^2*x^2+1)^(1/2))*(24-1020*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^3*x^3-495*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a*x-936*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3-372*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+24*x^8*a^8+96*x^6*a^6+144*x^4*a^4-192*(a^2*x^2+1)^(1/2)*arcsinh(a*x)*x^7*a^7-756*(a^2*x^2+1)^(1/2)*arcsinh(a*x)*x^5*a^5-480*arcsinh(a*x)+96*a^2*x^2-192*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*x^7*a^7-744*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*x^5*a^5+256*arcsinh(a*x)^3-264*arcsinh(a*x)^2-1368*arcsinh(a*x)^2*x^4*a^4-984*arcsinh(a*x)^2*a^2*x^2-192*arcsinh(a*x)*x^8*a^8-852*arcsinh(a*x)*x^6*a^6+24*(a^2*x^2+1)^(1/2)*x^7*a^7+84*(a^2*x^2+1)^(1/2)*x^5*a^5-1590*arcsinh(a*x)*x^4*a^4+105*(a^2*x^2+1)^(1/2)*x^3*a^3-1410*arcsinh(a*x)*x^2*a^2+45*(a^2*x^2+1)^(1/2)*x*a+380*arcsinh(a*x)^3*x^2*a^2-192*arcsinh(a*x)^2*x^8*a^8-840*arcsinh(a*x)^2*x^6*a^6+160*arcsinh(a*x)^3*x^4*a^4)/(40*a^10*x^10+215*a^8*x^8+469*a^6*x^6+517*a^4*x^4+287*a^2*x^2+64)/a/c^4-2*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*ln(a*x+(a^2*x^2+1)^(1/2))+(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)+16/15*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*arcsinh(a*x)^3-8/5*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*arcsinh(a*x)^2*ln(1+(a*x+(a^2*x^2+1)^(1/2))^2)-8/5*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*arcsinh(a*x)*polylog(2,-(a*x+(a^2*x^2+1)^(1/2))^2)+4/5*(c*(a^2*x^2+1))^(1/2)/(a^2*x^2+1)^(1/2)/a/c^4*polylog(3,-(a*x+(a^2*x^2+1)^(1/2))^2)","A"
341,0,0,23,0.270000," ","int(x^m*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsinh \left(a x \right)^{3}}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","F"
342,1,156,159,0.120000," ","int(x^4*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","\frac{32 \arcsinh \left(a x \right)^{3} \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-24 \arcsinh \left(a x \right)^{2} x^{4} a^{4}+12 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}-3 x^{4} a^{4}-48 \arcsinh \left(a x \right)^{3} \sqrt{a^{2} x^{2}+1}\, a x +72 \arcsinh \left(a x \right)^{2} a^{2} x^{2}+12 \arcsinh \left(a x \right)^{4}-90 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +45 a^{2} x^{2}+45 \arcsinh \left(a x \right)^{2}+45}{128 a^{5}}"," ",0,"1/128*(32*arcsinh(a*x)^3*(a^2*x^2+1)^(1/2)*a^3*x^3-24*arcsinh(a*x)^2*x^4*a^4+12*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a^3*x^3-3*x^4*a^4-48*arcsinh(a*x)^3*(a^2*x^2+1)^(1/2)*a*x+72*arcsinh(a*x)^2*a^2*x^2+12*arcsinh(a*x)^4-90*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+45*a^2*x^2+45*arcsinh(a*x)^2+45)/a^5","A"
343,1,164,131,0.098000," ","int(x^3*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","\frac{9 \arcsinh \left(a x \right)^{3} x^{4} a^{4}-9 \arcsinh \left(a x \right)^{3} x^{2} a^{2}-9 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a^{3} x^{3}+6 \arcsinh \left(a x \right) x^{4} a^{4}-114 \arcsinh \left(a x \right) x^{2} a^{2}-2 \sqrt{a^{2} x^{2}+1}\, x^{3} a^{3}-18 \arcsinh \left(a x \right)^{3}+54 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a x -120 \arcsinh \left(a x \right)+120 \sqrt{a^{2} x^{2}+1}\, x a}{27 a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/27/a^4/(a^2*x^2+1)^(1/2)*(9*arcsinh(a*x)^3*x^4*a^4-9*arcsinh(a*x)^3*x^2*a^2-9*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a^3*x^3+6*arcsinh(a*x)*x^4*a^4-114*arcsinh(a*x)*x^2*a^2-2*(a^2*x^2+1)^(1/2)*x^3*a^3-18*arcsinh(a*x)^3+54*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a*x-120*arcsinh(a*x)+120*(a^2*x^2+1)^(1/2)*x*a)","A"
344,1,84,89,0.088000," ","int(x^2*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","-\frac{-4 \arcsinh \left(a x \right)^{3} \sqrt{a^{2} x^{2}+1}\, a x +6 \arcsinh \left(a x \right)^{2} a^{2} x^{2}+\arcsinh \left(a x \right)^{4}-6 \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}\, a x +3 a^{2} x^{2}+3 \arcsinh \left(a x \right)^{2}+3}{8 a^{3}}"," ",0,"-1/8*(-4*arcsinh(a*x)^3*(a^2*x^2+1)^(1/2)*a*x+6*arcsinh(a*x)^2*a^2*x^2+arcsinh(a*x)^4-6*arcsinh(a*x)*(a^2*x^2+1)^(1/2)*a*x+3*a^2*x^2+3*arcsinh(a*x)^2+3)/a^3","A"
345,1,90,60,0.080000," ","int(x*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{3} x^{2} a^{2}+\arcsinh \left(a x \right)^{3}-3 \arcsinh \left(a x \right)^{2} \sqrt{a^{2} x^{2}+1}\, a x +6 \arcsinh \left(a x \right) x^{2} a^{2}+6 \arcsinh \left(a x \right)-6 \sqrt{a^{2} x^{2}+1}\, x a}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"1/a^2/(a^2*x^2+1)^(1/2)*(arcsinh(a*x)^3*x^2*a^2+arcsinh(a*x)^3-3*arcsinh(a*x)^2*(a^2*x^2+1)^(1/2)*a*x+6*arcsinh(a*x)*x^2*a^2+6*arcsinh(a*x)-6*(a^2*x^2+1)^(1/2)*x*a)","A"
346,1,12,11,0.005000," ","int(arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{4}}{4 a}"," ",0,"1/4*arcsinh(a*x)^4/a","A"
347,1,197,168,0.097000," ","int(arcsinh(a*x)^3/x/(a^2*x^2+1)^(1/2),x)","-\arcsinh \left(a x \right)^{3} \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)-3 \arcsinh \left(a x \right)^{2} \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)+6 \arcsinh \left(a x \right) \polylog \left(3, -a x -\sqrt{a^{2} x^{2}+1}\right)-6 \polylog \left(4, -a x -\sqrt{a^{2} x^{2}+1}\right)+\arcsinh \left(a x \right)^{3} \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)+3 \arcsinh \left(a x \right)^{2} \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)-6 \arcsinh \left(a x \right) \polylog \left(3, a x +\sqrt{a^{2} x^{2}+1}\right)+6 \polylog \left(4, a x +\sqrt{a^{2} x^{2}+1}\right)"," ",0,"-arcsinh(a*x)^3*ln(1+a*x+(a^2*x^2+1)^(1/2))-3*arcsinh(a*x)^2*polylog(2,-a*x-(a^2*x^2+1)^(1/2))+6*arcsinh(a*x)*polylog(3,-a*x-(a^2*x^2+1)^(1/2))-6*polylog(4,-a*x-(a^2*x^2+1)^(1/2))+arcsinh(a*x)^3*ln(1-a*x-(a^2*x^2+1)^(1/2))+3*arcsinh(a*x)^2*polylog(2,a*x+(a^2*x^2+1)^(1/2))-6*arcsinh(a*x)*polylog(3,a*x+(a^2*x^2+1)^(1/2))+6*polylog(4,a*x+(a^2*x^2+1)^(1/2))","A"
348,1,187,111,0.178000," ","int(arcsinh(a*x)^3/x^2/(a^2*x^2+1)^(1/2),x)","\frac{\left(a x -\sqrt{a^{2} x^{2}+1}\right) \arcsinh \left(a x \right)^{3}}{x}-2 a \arcsinh \left(a x \right)^{3}+3 a \arcsinh \left(a x \right)^{2} \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)+6 a \arcsinh \left(a x \right) \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)-6 a \polylog \left(3, -a x -\sqrt{a^{2} x^{2}+1}\right)+3 a \arcsinh \left(a x \right)^{2} \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)+6 a \arcsinh \left(a x \right) \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)-6 a \polylog \left(3, a x +\sqrt{a^{2} x^{2}+1}\right)"," ",0,"(a*x-(a^2*x^2+1)^(1/2))/x*arcsinh(a*x)^3-2*a*arcsinh(a*x)^3+3*a*arcsinh(a*x)^2*ln(1+a*x+(a^2*x^2+1)^(1/2))+6*a*arcsinh(a*x)*polylog(2,-a*x-(a^2*x^2+1)^(1/2))-6*a*polylog(3,-a*x-(a^2*x^2+1)^(1/2))+3*a*arcsinh(a*x)^2*ln(1-a*x-(a^2*x^2+1)^(1/2))+6*a*arcsinh(a*x)*polylog(2,a*x+(a^2*x^2+1)^(1/2))-6*a*polylog(3,a*x+(a^2*x^2+1)^(1/2))","A"
349,1,377,294,0.265000," ","int(arcsinh(a*x)^3/x^3/(a^2*x^2+1)^(1/2),x)","-\frac{\arcsinh \left(a x \right)^{2} \left(\arcsinh \left(a x \right) x^{2} a^{2}+3 \sqrt{a^{2} x^{2}+1}\, x a +\arcsinh \left(a x \right)\right)}{2 \sqrt{a^{2} x^{2}+1}\, x^{2}}+\frac{a^{2} \arcsinh \left(a x \right)^{3} \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)}{2}+\frac{3 a^{2} \arcsinh \left(a x \right)^{2} \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-3 a^{2} \arcsinh \left(a x \right) \polylog \left(3, -a x -\sqrt{a^{2} x^{2}+1}\right)+3 a^{2} \polylog \left(4, -a x -\sqrt{a^{2} x^{2}+1}\right)-\frac{a^{2} \arcsinh \left(a x \right)^{3} \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)}{2}-\frac{3 a^{2} \arcsinh \left(a x \right)^{2} \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)}{2}+3 a^{2} \arcsinh \left(a x \right) \polylog \left(3, a x +\sqrt{a^{2} x^{2}+1}\right)-3 a^{2} \polylog \left(4, a x +\sqrt{a^{2} x^{2}+1}\right)-3 a^{2} \arcsinh \left(a x \right) \ln \left(1+a x +\sqrt{a^{2} x^{2}+1}\right)-3 a^{2} \polylog \left(2, -a x -\sqrt{a^{2} x^{2}+1}\right)+3 a^{2} \arcsinh \left(a x \right) \ln \left(1-a x -\sqrt{a^{2} x^{2}+1}\right)+3 a^{2} \polylog \left(2, a x +\sqrt{a^{2} x^{2}+1}\right)"," ",0,"-1/2/(a^2*x^2+1)^(1/2)/x^2*arcsinh(a*x)^2*(arcsinh(a*x)*x^2*a^2+3*(a^2*x^2+1)^(1/2)*x*a+arcsinh(a*x))+1/2*a^2*arcsinh(a*x)^3*ln(1+a*x+(a^2*x^2+1)^(1/2))+3/2*a^2*arcsinh(a*x)^2*polylog(2,-a*x-(a^2*x^2+1)^(1/2))-3*a^2*arcsinh(a*x)*polylog(3,-a*x-(a^2*x^2+1)^(1/2))+3*a^2*polylog(4,-a*x-(a^2*x^2+1)^(1/2))-1/2*a^2*arcsinh(a*x)^3*ln(1-a*x-(a^2*x^2+1)^(1/2))-3/2*a^2*arcsinh(a*x)^2*polylog(2,a*x+(a^2*x^2+1)^(1/2))+3*a^2*arcsinh(a*x)*polylog(3,a*x+(a^2*x^2+1)^(1/2))-3*a^2*polylog(4,a*x+(a^2*x^2+1)^(1/2))-3*a^2*arcsinh(a*x)*ln(1+a*x+(a^2*x^2+1)^(1/2))-3*a^2*polylog(2,-a*x-(a^2*x^2+1)^(1/2))+3*a^2*arcsinh(a*x)*ln(1-a*x-(a^2*x^2+1)^(1/2))+3*a^2*polylog(2,a*x+(a^2*x^2+1)^(1/2))","A"
350,1,42,59,0.080000," ","int((a^2*c*x^2+c)^3/arcsinh(a*x),x)","\frac{c^{3} \left(35 \Chi \left(\arcsinh \left(a x \right)\right)+21 \Chi \left(3 \arcsinh \left(a x \right)\right)+7 \Chi \left(5 \arcsinh \left(a x \right)\right)+\Chi \left(7 \arcsinh \left(a x \right)\right)\right)}{64 a}"," ",0,"1/64/a*c^3*(35*Chi(arcsinh(a*x))+21*Chi(3*arcsinh(a*x))+7*Chi(5*arcsinh(a*x))+Chi(7*arcsinh(a*x)))","A"
351,1,33,44,0.042000," ","int((a^2*c*x^2+c)^2/arcsinh(a*x),x)","\frac{c^{2} \left(10 \Chi \left(\arcsinh \left(a x \right)\right)+5 \Chi \left(3 \arcsinh \left(a x \right)\right)+\Chi \left(5 \arcsinh \left(a x \right)\right)\right)}{16 a}"," ",0,"1/16/a*c^2*(10*Chi(arcsinh(a*x))+5*Chi(3*arcsinh(a*x))+Chi(5*arcsinh(a*x)))","A"
352,1,22,25,0.041000," ","int((a^2*c*x^2+c)/arcsinh(a*x),x)","\frac{c \left(3 \Chi \left(\arcsinh \left(a x \right)\right)+\Chi \left(3 \arcsinh \left(a x \right)\right)\right)}{4 a}"," ",0,"1/4/a*c*(3*Chi(arcsinh(a*x))+Chi(3*arcsinh(a*x)))","A"
353,0,0,21,0.086000," ","int(1/(a^2*c*x^2+c)/arcsinh(a*x),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right) \arcsinh \left(a x \right)}\, dx"," ",0,"int(1/(a^2*c*x^2+c)/arcsinh(a*x),x)","F"
354,0,0,21,0.202000," ","int(1/(a^2*c*x^2+c)^2/arcsinh(a*x),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{2} \arcsinh \left(a x \right)}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^2/arcsinh(a*x),x)","F"
355,1,199,192,0.514000," ","int(x^4*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","\frac{\ln \left(a +b \arcsinh \left(c x \right)\right)}{16 b \,c^{5}}-\frac{{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{64 c^{5} b}+\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{32 c^{5} b}+\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{64 c^{5} b}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{64 c^{5} b}+\frac{{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{32 c^{5} b}-\frac{{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right)}{64 c^{5} b}"," ",0,"1/16*ln(a+b*arcsinh(c*x))/b/c^5-1/64/c^5/b*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)+1/32/c^5/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/64/c^5/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/64/c^5/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)+1/32/c^5/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)-1/64/c^5/b*exp(-6*a/b)*Ei(1,-6*arcsinh(c*x)-6*a/b)","A"
356,1,178,171,0.353000," ","int(x^3*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","\frac{{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{4} b}-\frac{{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{4} b}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{16 c^{4} b}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{16 c^{4} b}+\frac{{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{32 c^{4} b}-\frac{{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{32 c^{4} b}"," ",0,"1/32/c^4/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-1/32/c^4/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/16/c^4/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+1/16/c^4/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+1/32/c^4/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-1/32/c^4/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)","A"
357,1,79,76,0.206000," ","int(x^2*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","-\frac{\ln \left(a +b \arcsinh \left(c x \right)\right)}{8 b \,c^{3}}-\frac{{\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{{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{16 c^{3} b}"," ",0,"-1/8*ln(a+b*arcsinh(c*x))/b/c^3-1/16/c^3/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)-1/16/c^3/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)","A"
358,1,118,113,0.196000," ","int(x*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","\frac{{\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)}{8 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{8 c^{2} b}-\frac{{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{8 c^{2} b}"," ",0,"1/8/c^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+1/8/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/8/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)-1/8/c^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)","A"
359,1,79,76,0.154000," ","int((c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","\frac{\ln \left(a +b \arcsinh \left(c x \right)\right)}{2 b c}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{4 c b}-\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{4 c b}"," ",0,"1/2*ln(a+b*arcsinh(c*x))/b/c-1/4/c/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)","A"
360,0,0,75,0.279000," ","int((c^2*x^2+1)^(1/2)/x/(a+b*arcsinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x/(a+b*arcsinh(c*x)),x)","F"
361,0,0,42,0.290000," ","int((c^2*x^2+1)^(1/2)/x^2/(a+b*arcsinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x^2/(a+b*arcsinh(c*x)),x)","F"
362,0,0,27,0.631000," ","int((c^2*x^2+1)^(1/2)/x^3/(a+b*arcsinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x^{3} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x^3/(a+b*arcsinh(c*x)),x)","F"
363,0,0,27,0.722000," ","int((c^2*x^2+1)^(1/2)/x^4/(a+b*arcsinh(c*x)),x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x^{4} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x^4/(a+b*arcsinh(c*x)),x)","F"
364,1,238,229,0.449000," ","int(x^3*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\frac{{\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{128 c^{4} b}+\frac{{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{128 c^{4} b}-\frac{3 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{128 c^{4} b}-\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{128 c^{4} b}+\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{128 c^{4} b}+\frac{3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{128 c^{4} b}-\frac{{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{128 c^{4} b}-\frac{{\mathrm e}^{-\frac{7 a}{b}} \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right)}{128 c^{4} b}"," ",0,"1/128/c^4/b*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)+1/128/c^4/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-3/128/c^4/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-3/128/c^4/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+3/128/c^4/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+3/128/c^4/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-1/128/c^4/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)-1/128/c^4/b*exp(-7*a/b)*Ei(1,-7*arcsinh(c*x)-7*a/b)","A"
365,1,199,192,0.422000," ","int(x^2*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","-\frac{\ln \left(a +b \arcsinh \left(c x \right)\right)}{16 b \,c^{3}}-\frac{{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{64 c^{3} b}-\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{32 c^{3} b}+\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{64 c^{3} b}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{64 c^{3} b}-\frac{{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{32 c^{3} b}-\frac{{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right)}{64 c^{3} b}"," ",0,"-1/16*ln(a+b*arcsinh(c*x))/b/c^3-1/64/c^3/b*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)-1/32/c^3/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/64/c^3/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/64/c^3/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)-1/32/c^3/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)-1/64/c^3/b*exp(-6*a/b)*Ei(1,-6*arcsinh(c*x)-6*a/b)","A"
366,1,178,171,0.278000," ","int(x*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\frac{{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{2} b}+\frac{3 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{2} b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{16 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{16 c^{2} b}-\frac{3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{32 c^{2} b}-\frac{{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{32 c^{2} b}"," ",0,"1/32/c^2/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)+3/32/c^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+1/16/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/16/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)-3/32/c^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-1/32/c^2/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)","A"
367,1,139,134,0.313000," ","int((c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\frac{3 \ln \left(a +b \arcsinh \left(c x \right)\right)}{8 b c}-\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{16 c b}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{4 c b}-\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{4 c b}-\frac{{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{16 c b}"," ",0,"3/8*ln(a+b*arcsinh(c*x))/b/c-1/16/c/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)-1/4/c/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)-1/16/c/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)","A"
368,0,0,128,0.372000," ","int((c^2*x^2+1)^(3/2)/x/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x/(a+b*arcsinh(c*x)),x)","F"
369,0,0,97,0.310000," ","int((c^2*x^2+1)^(3/2)/x^2/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x^2/(a+b*arcsinh(c*x)),x)","F"
370,0,0,27,0.829000," ","int((c^2*x^2+1)^(3/2)/x^3/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{3} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x^3/(a+b*arcsinh(c*x)),x)","F"
371,0,0,27,0.589000," ","int((c^2*x^2+1)^(3/2)/x^4/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{4} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x^4/(a+b*arcsinh(c*x)),x)","F"
372,1,238,229,0.536000," ","int(x^3*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x)","\frac{{\mathrm e}^{\frac{9 a}{b}} \Ei \left(1, 9 \arcsinh \left(c x \right)+\frac{9 a}{b}\right)}{512 c^{4} b}+\frac{3 \,{\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{512 c^{4} b}-\frac{{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{64 c^{4} b}-\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{256 c^{4} b}+\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{256 c^{4} b}+\frac{{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{64 c^{4} b}-\frac{3 \,{\mathrm e}^{-\frac{7 a}{b}} \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right)}{512 c^{4} b}-\frac{{\mathrm e}^{-\frac{9 a}{b}} \Ei \left(1, -9 \arcsinh \left(c x \right)-\frac{9 a}{b}\right)}{512 c^{4} b}"," ",0,"1/512/c^4/b*exp(9*a/b)*Ei(1,9*arcsinh(c*x)+9*a/b)+3/512/c^4/b*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)-1/64/c^4/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-3/256/c^4/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+3/256/c^4/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+1/64/c^4/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-3/512/c^4/b*exp(-7*a/b)*Ei(1,-7*arcsinh(c*x)-7*a/b)-1/512/c^4/b*exp(-9*a/b)*Ei(1,-9*arcsinh(c*x)-9*a/b)","A"
373,1,259,250,0.604000," ","int(x^2*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x)","-\frac{5 \ln \left(a +b \arcsinh \left(c x \right)\right)}{128 b \,c^{3}}-\frac{{\mathrm e}^{\frac{8 a}{b}} \Ei \left(1, 8 \arcsinh \left(c x \right)+\frac{8 a}{b}\right)}{256 c^{3} b}-\frac{{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{64 c^{3} b}-\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{64 c^{3} b}+\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{64 c^{3} b}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{64 c^{3} b}-\frac{{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{64 c^{3} b}-\frac{{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right)}{64 c^{3} b}-\frac{{\mathrm e}^{-\frac{8 a}{b}} \Ei \left(1, -8 \arcsinh \left(c x \right)-\frac{8 a}{b}\right)}{256 c^{3} b}"," ",0,"-5/128*ln(a+b*arcsinh(c*x))/b/c^3-1/256/c^3/b*exp(8*a/b)*Ei(1,8*arcsinh(c*x)+8*a/b)-1/64/c^3/b*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)-1/64/c^3/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/64/c^3/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/64/c^3/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)-1/64/c^3/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)-1/64/c^3/b*exp(-6*a/b)*Ei(1,-6*arcsinh(c*x)-6*a/b)-1/256/c^3/b*exp(-8*a/b)*Ei(1,-8*arcsinh(c*x)-8*a/b)","A"
374,1,238,229,0.423000," ","int(x*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x)","\frac{{\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{128 c^{2} b}+\frac{5 \,{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{128 c^{2} b}+\frac{9 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{128 c^{2} b}+\frac{5 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{128 c^{2} b}-\frac{5 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{128 c^{2} b}-\frac{9 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{128 c^{2} b}-\frac{5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{128 c^{2} b}-\frac{{\mathrm e}^{-\frac{7 a}{b}} \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right)}{128 c^{2} b}"," ",0,"1/128/c^2/b*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)+5/128/c^2/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)+9/128/c^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+5/128/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-5/128/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)-9/128/c^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-5/128/c^2/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)-1/128/c^2/b*exp(-7*a/b)*Ei(1,-7*arcsinh(c*x)-7*a/b)","A"
375,1,199,192,0.509000," ","int((c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x)","\frac{5 \ln \left(a +b \arcsinh \left(c x \right)\right)}{16 b c}-\frac{{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{64 c b}-\frac{3 \,{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{32 c b}-\frac{15 \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{64 c b}-\frac{15 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{64 c b}-\frac{3 \,{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{32 c b}-\frac{{\mathrm e}^{-\frac{6 a}{b}} \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right)}{64 c b}"," ",0,"5/16*ln(a+b*arcsinh(c*x))/b/c-1/64/c/b*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)-3/32/c/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)-15/64/c/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-15/64/c/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)-3/32/c/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)-1/64/c/b*exp(-6*a/b)*Ei(1,-6*arcsinh(c*x)-6*a/b)","A"
376,0,0,180,0.461000," ","int((c^2*x^2+1)^(5/2)/x/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x/(a+b*arcsinh(c*x)),x)","F"
377,0,0,150,0.375000," ","int((c^2*x^2+1)^(5/2)/x^2/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x^2/(a+b*arcsinh(c*x)),x)","F"
378,0,0,27,0.954000," ","int((c^2*x^2+1)^(5/2)/x^3/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x^3/(a+b*arcsinh(c*x)),x)","F"
379,0,0,27,0.689000," ","int((c^2*x^2+1)^(5/2)/x^4/(a+b*arcsinh(c*x)),x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{4} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x^4/(a+b*arcsinh(c*x)),x)","F"
380,1,36,35,0.108000," ","int(x^4/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","-\frac{\Chi \left(2 \arcsinh \left(a x \right)\right)}{2 a^{5}}+\frac{\Chi \left(4 \arcsinh \left(a x \right)\right)}{8 a^{5}}+\frac{3 \ln \left(\arcsinh \left(a x \right)\right)}{8 a^{5}}"," ",0,"-1/2*Chi(2*arcsinh(a*x))/a^5+1/8*Chi(4*arcsinh(a*x))/a^5+3/8*ln(arcsinh(a*x))/a^5","A"
381,1,23,23,0.095000," ","int(x^3/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","-\frac{3 \Shi \left(\arcsinh \left(a x \right)\right)-\Shi \left(3 \arcsinh \left(a x \right)\right)}{4 a^{4}}"," ",0,"-1/4*(3*Shi(arcsinh(a*x))-Shi(3*arcsinh(a*x)))/a^4","A"
382,1,24,23,0.077000," ","int(x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\Chi \left(2 \arcsinh \left(a x \right)\right)}{2 a^{3}}-\frac{\ln \left(\arcsinh \left(a x \right)\right)}{2 a^{3}}"," ",0,"1/2*Chi(2*arcsinh(a*x))/a^3-1/2*ln(arcsinh(a*x))/a^3","A"
383,1,24,23,0.002000," ","int(x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\Chi \left(2 \arcsinh \left(a x \right)\right)}{2 a^{3}}-\frac{\ln \left(\arcsinh \left(a x \right)\right)}{2 a^{3}}"," ",0,"1/2*Chi(2*arcsinh(a*x))/a^3-1/2*ln(arcsinh(a*x))/a^3","A"
384,1,10,9,0.062000," ","int(x/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\Shi \left(\arcsinh \left(a x \right)\right)}{a^{2}}"," ",0,"Shi(arcsinh(a*x))/a^2","A"
385,1,10,9,0.006000," ","int(1/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\ln \left(\arcsinh \left(a x \right)\right)}{a}"," ",0,"ln(arcsinh(a*x))/a","A"
386,0,0,23,0.115000," ","int(1/x/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\int \frac{1}{x \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","F"
387,0,0,23,0.210000," ","int(1/x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \arcsinh \left(a x \right) \sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x)","F"
388,1,178,171,0.329000," ","int(x^5/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\frac{{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{6} b}-\frac{5 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{6} b}+\frac{5 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{16 c^{6} b}-\frac{5 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{16 c^{6} b}+\frac{5 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{32 c^{6} b}-\frac{{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{32 c^{6} b}"," ",0,"1/32/c^6/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-5/32/c^6/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+5/16/c^6/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-5/16/c^6/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+5/32/c^6/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-1/32/c^6/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)","A"
389,1,139,134,0.395000," ","int(x^4/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\frac{3 \ln \left(a +b \arcsinh \left(c x \right)\right)}{8 b \,c^{5}}-\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{16 c^{5} b}+\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{4 c^{5} b}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{4 c^{5} b}-\frac{{\mathrm e}^{-\frac{4 a}{b}} \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right)}{16 c^{5} b}"," ",0,"3/8*ln(a+b*arcsinh(c*x))/b/c^5-1/16/c^5/b*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/4/c^5/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/4/c^5/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)-1/16/c^5/b*exp(-4*a/b)*Ei(1,-4*arcsinh(c*x)-4*a/b)","A"
390,1,118,113,0.227000," ","int(x^3/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\frac{{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{8 c^{4} b}-\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{8 c^{4} b}+\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{8 c^{4} b}-\frac{{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{8 c^{4} b}"," ",0,"1/8/c^4/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-3/8/c^4/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+3/8/c^4/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)-1/8/c^4/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)","A"
391,1,79,76,0.196000," ","int(x^2/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","-\frac{\ln \left(a +b \arcsinh \left(c x \right)\right)}{2 b \,c^{3}}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{4 c^{3} b}-\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right)}{4 c^{3} b}"," ",0,"-1/2*ln(a+b*arcsinh(c*x))/b/c^3-1/4/c^3/b*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c^3/b*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)","A"
392,1,58,54,0.077000," ","int(x/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{2 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{2 c^{2} b}"," ",0,"1/2/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/2/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)","A"
393,1,17,16,0.006000," ","int(1/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\frac{\ln \left(a +b \arcsinh \left(c x \right)\right)}{b c}"," ",0,"ln(a+b*arcsinh(c*x))/b/c","A"
394,0,0,27,0.089000," ","int(1/x/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\int \frac{1}{x \left(a +b \arcsinh \left(c x \right)\right) \sqrt{c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","F"
395,0,0,27,0.173000," ","int(1/x^2/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \left(a +b \arcsinh \left(c x \right)\right) \sqrt{c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x)","F"
396,0,0,27,0.313000," ","int(x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x^{2}}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
397,0,0,25,0.217000," ","int(x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
398,0,0,24,0.141000," ","int(1/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
399,0,0,27,0.497000," ","int(1/x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
400,0,0,27,0.263000," ","int(1/x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{x^{2} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
401,-2,0,27,180.000000," ","int(x^m*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x^{m} \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int(x^m*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x)","F"
402,-2,0,27,180.000000," ","int(x^m*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x^{m} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int(x^m*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
403,-2,0,27,180.000000," ","int(x^m*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x^{m} \sqrt{c^{2} x^{2}+1}}{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int(x^m*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","F"
404,0,0,27,0.156000," ","int(x^m/(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x^{m}}{\sqrt{c^{2} x^{2}+1}\, \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(x^m/(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x)","F"
405,0,0,27,0.498000," ","int(x^m/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{x^{m}}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(x^m/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
406,1,106,84,0.127000," ","int((a^2*c*x^2+c)^3/arcsinh(a*x)^2,x)","\frac{c^{3} \left(35 \Shi \left(5 \arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)+7 \Shi \left(7 \arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)+35 \Shi \left(\arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)+63 \Shi \left(3 \arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)-35 \sqrt{a^{2} x^{2}+1}-\cosh \left(7 \arcsinh \left(a x \right)\right)-21 \cosh \left(3 \arcsinh \left(a x \right)\right)-7 \cosh \left(5 \arcsinh \left(a x \right)\right)\right)}{64 a \arcsinh \left(a x \right)}"," ",0,"1/64/a*c^3*(35*Shi(5*arcsinh(a*x))*arcsinh(a*x)+7*Shi(7*arcsinh(a*x))*arcsinh(a*x)+35*Shi(arcsinh(a*x))*arcsinh(a*x)+63*Shi(3*arcsinh(a*x))*arcsinh(a*x)-35*(a^2*x^2+1)^(1/2)-cosh(7*arcsinh(a*x))-21*cosh(3*arcsinh(a*x))-7*cosh(5*arcsinh(a*x)))/arcsinh(a*x)","A"
407,1,84,69,0.072000," ","int((a^2*c*x^2+c)^2/arcsinh(a*x)^2,x)","\frac{c^{2} \left(10 \Shi \left(\arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)+15 \Shi \left(3 \arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)+5 \Shi \left(5 \arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)-10 \sqrt{a^{2} x^{2}+1}-5 \cosh \left(3 \arcsinh \left(a x \right)\right)-\cosh \left(5 \arcsinh \left(a x \right)\right)\right)}{16 a \arcsinh \left(a x \right)}"," ",0,"1/16/a*c^2*(10*Shi(arcsinh(a*x))*arcsinh(a*x)+15*Shi(3*arcsinh(a*x))*arcsinh(a*x)+5*Shi(5*arcsinh(a*x))*arcsinh(a*x)-10*(a^2*x^2+1)^(1/2)-5*cosh(3*arcsinh(a*x))-cosh(5*arcsinh(a*x)))/arcsinh(a*x)","A"
408,1,60,48,0.064000," ","int((a^2*c*x^2+c)/arcsinh(a*x)^2,x)","\frac{c \left(3 \Shi \left(\arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)+3 \Shi \left(3 \arcsinh \left(a x \right)\right) \arcsinh \left(a x \right)-3 \sqrt{a^{2} x^{2}+1}-\cosh \left(3 \arcsinh \left(a x \right)\right)\right)}{4 a \arcsinh \left(a x \right)}"," ",0,"1/4/a*c*(3*Shi(arcsinh(a*x))*arcsinh(a*x)+3*Shi(3*arcsinh(a*x))*arcsinh(a*x)-3*(a^2*x^2+1)^(1/2)-cosh(3*arcsinh(a*x)))/arcsinh(a*x)","A"
409,0,0,53,0.096000," ","int(1/(a^2*c*x^2+c)/arcsinh(a*x)^2,x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right) \arcsinh \left(a x \right)^{2}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)/arcsinh(a*x)^2,x)","F"
410,0,0,53,0.225000," ","int(1/(a^2*c*x^2+c)^2/arcsinh(a*x)^2,x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{2} \arcsinh \left(a x \right)^{2}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^2/arcsinh(a*x)^2,x)","F"
411,1,633,201,0.501000," ","int(x^3*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{16 c^{5} x^{5}-16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+20 c^{3} x^{3}-12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+5 c x -\sqrt{c^{2} x^{2}+1}}{32 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \,{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{4} b^{2}}+\frac{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}}{32 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{4} b^{2}}+\frac{c x -\sqrt{c^{2} x^{2}+1}}{16 c^{4} 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)}{16 c^{4} b^{2}}+\frac{\arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a +x b c +\sqrt{c^{2} x^{2}+1}\, b}{16 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}+\frac{4 x^{3} b \,c^{3}+4 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b +3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a +3 x b c +\sqrt{c^{2} x^{2}+1}\, b}{32 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{16 x^{5} b \,c^{5}+16 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+20 x^{3} b \,c^{3}+12 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+5 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) a +5 x b c +\sqrt{c^{2} x^{2}+1}\, b}{32 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/32*(16*c^5*x^5-16*c^4*x^4*(c^2*x^2+1)^(1/2)+20*c^3*x^3-12*c^2*x^2*(c^2*x^2+1)^(1/2)+5*c*x-(c^2*x^2+1)^(1/2))/c^4/b/(a+b*arcsinh(c*x))-5/32/c^4/b^2*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)+1/32*(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))/c^4/b/(a+b*arcsinh(c*x))+3/32/c^4/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+1/16*(c*x-(c^2*x^2+1)^(1/2))/c^4/b/(a+b*arcsinh(c*x))+1/16/c^4/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+1/16/c^4/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))+1/32/c^4/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/32/c^4/b^2*(16*x^5*b*c^5+16*(c^2*x^2+1)^(1/2)*x^4*b*c^4+20*x^3*b*c^3+12*(c^2*x^2+1)^(1/2)*x^2*b*c^2+5*arcsinh(c*x)*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*b+5*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*a+5*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
412,1,248,89,0.278000," ","int(x^2*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","\frac{1}{8 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{8 c^{4} x^{4}-8 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+8 c^{2} x^{2}-4 c x \sqrt{c^{2} x^{2}+1}+1}{16 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{4 c^{3} b^{2}}-\frac{8 x^{4} b \,c^{4}+8 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+8 x^{2} b \,c^{2}+4 b c \sqrt{c^{2} x^{2}+1}\, x +4 \arcsinh \left(c x \right) \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b}{16 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"1/8/c^3/(a+b*arcsinh(c*x))/b-1/16*(8*c^4*x^4-8*c^3*x^3*(c^2*x^2+1)^(1/2)+8*c^2*x^2-4*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+1/4/c^3/b^2*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)-1/16/c^3/b^2*(8*x^4*b*c^4+8*(c^2*x^2+1)^(1/2)*x^3*b*c^3+8*x^2*b*c^2+4*b*c*(c^2*x^2+1)^(1/2)*x+4*arcsinh(c*x)*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
413,1,364,141,0.271000," ","int(x*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{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}}{8 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 \,{\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{c x -\sqrt{c^{2} x^{2}+1}}{8 c^{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)}{8 c^{2} b^{2}}-\frac{\arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a +x b c +\sqrt{c^{2} x^{2}+1}\, b}{8 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{4 x^{3} b \,c^{3}+4 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b +3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a +3 x b c +\sqrt{c^{2} x^{2}+1}\, b}{8 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-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))/c^2/b/(a+b*arcsinh(c*x))-3/8/c^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/8*(c*x-(c^2*x^2+1)^(1/2))/c^2/b/(a+b*arcsinh(c*x))-1/8/c^2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/8/c^2/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/8/c^2/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
414,1,192,85,0.264000," ","int((c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{1}{2 b c \left(a +b \arcsinh \left(c x \right)\right)}-\frac{2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1}{4 c \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\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{2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b}{4 c \,b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/2/b/c/(a+b*arcsinh(c*x))-1/4*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c/(a+b*arcsinh(c*x))/b+1/2/c/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
415,0,0,102,0.413000," ","int((c^2*x^2+1)^(1/2)/x/(a+b*arcsinh(c*x))^2,x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x/(a+b*arcsinh(c*x))^2,x)","F"
416,0,0,55,0.350000," ","int((c^2*x^2+1)^(1/2)/x^2/(a+b*arcsinh(c*x))^2,x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x^2/(a+b*arcsinh(c*x))^2,x)","F"
417,0,0,27,0.752000," ","int((c^2*x^2+1)^(1/2)/x^3/(a+b*arcsinh(c*x))^2,x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x^{3} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x^3/(a+b*arcsinh(c*x))^2,x)","F"
418,0,0,27,0.848000," ","int((c^2*x^2+1)^(1/2)/x^4/(a+b*arcsinh(c*x))^2,x)","\int \frac{\sqrt{c^{2} x^{2}+1}}{x^{4} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(1/2)/x^4/(a+b*arcsinh(c*x))^2,x)","F"
419,1,958,261,0.588000," ","int(x^3*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{64 c^{7} x^{7}-64 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}+112 c^{5} x^{5}-80 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+56 c^{3} x^{3}-24 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+7 c x -\sqrt{c^{2} x^{2}+1}}{128 c^{4} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{7 \,{\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{128 c^{4} b^{2}}-\frac{16 c^{5} x^{5}-16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+20 c^{3} x^{3}-12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+5 c x -\sqrt{c^{2} x^{2}+1}}{128 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \,{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{128 c^{4} b^{2}}+\frac{\frac{3 c^{3} x^{3}}{32}-\frac{3 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{32}+\frac{9 c x}{128}-\frac{3 \sqrt{c^{2} x^{2}+1}}{128}}{c^{4} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{9 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{128 c^{4} b^{2}}+\frac{\frac{3 c x}{128}-\frac{3 \sqrt{c^{2} x^{2}+1}}{128}}{c^{4} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{128 c^{4} b^{2}}+\frac{\frac{3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b}{128}+\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a}{128}+\frac{3 x b c}{128}+\frac{3 \sqrt{c^{2} x^{2}+1}\, b}{128}}{c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}+\frac{\frac{3 x^{3} b \,c^{3}}{32}+\frac{3 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}}{32}+\frac{9 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b}{128}+\frac{9 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a}{128}+\frac{9 x b c}{128}+\frac{3 \sqrt{c^{2} x^{2}+1}\, b}{128}}{c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{16 x^{5} b \,c^{5}+16 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+20 x^{3} b \,c^{3}+12 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+5 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) a +5 x b c +\sqrt{c^{2} x^{2}+1}\, b}{128 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{64 x^{7} b \,c^{7}+64 \sqrt{c^{2} x^{2}+1}\, x^{6} b \,c^{6}+112 x^{5} b \,c^{5}+80 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+56 x^{3} b \,c^{3}+24 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+7 \arcsinh \left(c x \right) \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} b +7 \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} a +7 x b c +\sqrt{c^{2} x^{2}+1}\, b}{128 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/128*(64*c^7*x^7-64*c^6*x^6*(c^2*x^2+1)^(1/2)+112*c^5*x^5-80*c^4*x^4*(c^2*x^2+1)^(1/2)+56*c^3*x^3-24*c^2*x^2*(c^2*x^2+1)^(1/2)+7*c*x-(c^2*x^2+1)^(1/2))/c^4/(a+b*arcsinh(c*x))/b-7/128/c^4/b^2*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)-1/128*(16*c^5*x^5-16*c^4*x^4*(c^2*x^2+1)^(1/2)+20*c^3*x^3-12*c^2*x^2*(c^2*x^2+1)^(1/2)+5*c*x-(c^2*x^2+1)^(1/2))/c^4/b/(a+b*arcsinh(c*x))-5/128/c^4/b^2*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)+3/128*(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))/c^4/b/(a+b*arcsinh(c*x))+9/128/c^4/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+3/128*(c*x-(c^2*x^2+1)^(1/2))/c^4/b/(a+b*arcsinh(c*x))+3/128/c^4/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+3/128/c^4/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))+3/128/c^4/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/128/c^4/b^2*(16*x^5*b*c^5+16*(c^2*x^2+1)^(1/2)*x^4*b*c^4+20*x^3*b*c^3+12*(c^2*x^2+1)^(1/2)*x^2*b*c^2+5*arcsinh(c*x)*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*b+5*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*a+5*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/128/c^4/b^2*(64*x^7*b*c^7+64*(c^2*x^2+1)^(1/2)*x^6*b*c^6+112*x^5*b*c^5+80*(c^2*x^2+1)^(1/2)*x^4*b*c^4+56*x^3*b*c^3+24*(c^2*x^2+1)^(1/2)*x^2*b*c^2+7*arcsinh(c*x)*Ei(1,-7*arcsinh(c*x)-7*a/b)*exp(-7*a/b)*b+7*Ei(1,-7*arcsinh(c*x)-7*a/b)*exp(-7*a/b)*a+7*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
420,1,704,207,0.597000," ","int(x^2*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\frac{1}{16 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{32 c^{6} x^{6}-32 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+48 c^{4} x^{4}-32 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+18 c^{2} x^{2}-6 c x \sqrt{c^{2} x^{2}+1}+1}{64 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{3 \,{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{32 c^{3} b^{2}}-\frac{8 c^{4} x^{4}-8 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+8 c^{2} x^{2}-4 c x \sqrt{c^{2} x^{2}+1}+1}{32 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{8 c^{3} b^{2}}+\frac{2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1}{64 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{32 c^{3} b^{2}}+\frac{2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b}{64 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{8 x^{4} b \,c^{4}+8 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+8 x^{2} b \,c^{2}+4 b c \sqrt{c^{2} x^{2}+1}\, x +4 \arcsinh \left(c x \right) \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b}{32 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{32 x^{6} b \,c^{6}+32 \sqrt{c^{2} x^{2}+1}\, x^{5} b \,c^{5}+48 x^{4} b \,c^{4}+32 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+18 x^{2} b \,c^{2}+6 b c \sqrt{c^{2} x^{2}+1}\, x +6 \arcsinh \left(c x \right) \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{-\frac{6 a}{b}} b +6 \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{-\frac{6 a}{b}} a +b}{64 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"1/16/c^3/(a+b*arcsinh(c*x))/b-1/64*(32*c^6*x^6-32*c^5*x^5*(c^2*x^2+1)^(1/2)+48*c^4*x^4-32*c^3*x^3*(c^2*x^2+1)^(1/2)+18*c^2*x^2-6*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+3/32/c^3/b^2*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)-1/32*(8*c^4*x^4-8*c^3*x^3*(c^2*x^2+1)^(1/2)+8*c^2*x^2-4*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+1/8/c^3/b^2*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/64*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b-1/32/c^3/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/64/c^3/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))-1/32/c^3/b^2*(8*x^4*b*c^4+8*(c^2*x^2+1)^(1/2)*x^3*b*c^3+8*x^2*b*c^2+4*b*c*(c^2*x^2+1)^(1/2)*x+4*arcsinh(c*x)*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/(a+b*arcsinh(c*x))-1/64/c^3/b^2*(32*x^6*b*c^6+32*(c^2*x^2+1)^(1/2)*x^5*b*c^5+48*x^4*b*c^4+32*(c^2*x^2+1)^(1/2)*x^3*b*c^3+18*x^2*b*c^2+6*b*c*(c^2*x^2+1)^(1/2)*x+6*arcsinh(c*x)*Ei(1,-6*arcsinh(c*x)-6*a/b)*exp(-6*a/b)*b+6*Ei(1,-6*arcsinh(c*x)-6*a/b)*exp(-6*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
421,1,633,201,0.404000," ","int(x*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{16 c^{5} x^{5}-16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+20 c^{3} x^{3}-12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+5 c x -\sqrt{c^{2} x^{2}+1}}{32 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \,{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{2} b^{2}}-\frac{3 \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)}{32 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{9 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{2} b^{2}}-\frac{c x -\sqrt{c^{2} x^{2}+1}}{16 c^{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)}{16 c^{2} b^{2}}-\frac{\arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a +x b c +\sqrt{c^{2} x^{2}+1}\, b}{16 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 \left(4 x^{3} b \,c^{3}+4 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b +3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a +3 x b c +\sqrt{c^{2} x^{2}+1}\, b \right)}{32 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{16 x^{5} b \,c^{5}+16 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+20 x^{3} b \,c^{3}+12 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+5 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) a +5 x b c +\sqrt{c^{2} x^{2}+1}\, b}{32 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/32*(16*c^5*x^5-16*c^4*x^4*(c^2*x^2+1)^(1/2)+20*c^3*x^3-12*c^2*x^2*(c^2*x^2+1)^(1/2)+5*c*x-(c^2*x^2+1)^(1/2))/c^2/b/(a+b*arcsinh(c*x))-5/32/c^2/b^2*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-3/32*(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))/c^2/b/(a+b*arcsinh(c*x))-9/32/c^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/16*(c*x-(c^2*x^2+1)^(1/2))/c^2/b/(a+b*arcsinh(c*x))-1/16/c^2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/16/c^2/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-3/32/c^2/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/32/c^2/b^2*(16*x^5*b*c^5+16*(c^2*x^2+1)^(1/2)*x^4*b*c^4+20*x^3*b*c^3+12*(c^2*x^2+1)^(1/2)*x^2*b*c^2+5*arcsinh(c*x)*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*b+5*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*a+5*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
422,1,420,145,0.408000," ","int((c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{3}{8 b c \left(a +b \arcsinh \left(c x \right)\right)}-\frac{8 c^{4} x^{4}-8 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+8 c^{2} x^{2}-4 c x \sqrt{c^{2} x^{2}+1}+1}{16 c \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{4 c \,b^{2}}-\frac{2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1}{4 c \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\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{2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b}{4 c \,b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{8 x^{4} b \,c^{4}+8 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+8 x^{2} b \,c^{2}+4 b c \sqrt{c^{2} x^{2}+1}\, x +4 \arcsinh \left(c x \right) \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b}{16 c \,b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-3/8/b/c/(a+b*arcsinh(c*x))-1/16*(8*c^4*x^4-8*c^3*x^3*(c^2*x^2+1)^(1/2)+8*c^2*x^2-4*c*x*(c^2*x^2+1)^(1/2)+1)/c/(a+b*arcsinh(c*x))/b+1/4/c/b^2*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)-1/4*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c/(a+b*arcsinh(c*x))/b+1/2/c/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))-1/16/c/b^2*(8*x^4*b*c^4+8*(c^2*x^2+1)^(1/2)*x^3*b*c^3+8*x^2*b*c^2+4*b*c*(c^2*x^2+1)^(1/2)*x+4*arcsinh(c*x)*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
423,0,0,166,0.457000," ","int((c^2*x^2+1)^(3/2)/x/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x/(a+b*arcsinh(c*x))^2,x)","F"
424,0,0,97,0.510000," ","int((c^2*x^2+1)^(3/2)/x^2/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x^2/(a+b*arcsinh(c*x))^2,x)","F"
425,0,0,27,1.287000," ","int((c^2*x^2+1)^(3/2)/x^3/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{3} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x^3/(a+b*arcsinh(c*x))^2,x)","F"
426,0,0,66,0.773000," ","int((c^2*x^2+1)^(3/2)/x^4/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{4} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(3/2)/x^4/(a+b*arcsinh(c*x))^2,x)","F"
427,1,1070,261,0.739000," ","int(x^3*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{256 c^{9} x^{9}-256 c^{8} x^{8} \sqrt{c^{2} x^{2}+1}+576 c^{7} x^{7}-448 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}+432 c^{5} x^{5}-240 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+120 c^{3} x^{3}-40 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+9 c x -\sqrt{c^{2} x^{2}+1}}{512 c^{4} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{9 \,{\mathrm e}^{\frac{9 a}{b}} \Ei \left(1, 9 \arcsinh \left(c x \right)+\frac{9 a}{b}\right)}{512 c^{4} b^{2}}-\frac{3 \left(64 c^{7} x^{7}-64 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}+112 c^{5} x^{5}-80 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+56 c^{3} x^{3}-24 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+7 c x -\sqrt{c^{2} x^{2}+1}\right)}{512 c^{4} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{21 \,{\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{512 c^{4} b^{2}}+\frac{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}}{64 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{64 c^{4} b^{2}}+\frac{\frac{3 c x}{256}-\frac{3 \sqrt{c^{2} x^{2}+1}}{256}}{c^{4} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{256 c^{4} b^{2}}+\frac{\frac{3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b}{256}+\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a}{256}+\frac{3 x b c}{256}+\frac{3 \sqrt{c^{2} x^{2}+1}\, b}{256}}{c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}+\frac{4 x^{3} b \,c^{3}+4 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b +3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a +3 x b c +\sqrt{c^{2} x^{2}+1}\, b}{64 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 \left(64 x^{7} b \,c^{7}+64 \sqrt{c^{2} x^{2}+1}\, x^{6} b \,c^{6}+112 x^{5} b \,c^{5}+80 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+56 x^{3} b \,c^{3}+24 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+7 \arcsinh \left(c x \right) \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} b +7 \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} a +7 x b c +\sqrt{c^{2} x^{2}+1}\, b \right)}{512 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{256 x^{9} b \,c^{9}+256 \sqrt{c^{2} x^{2}+1}\, x^{8} b \,c^{8}+576 x^{7} b \,c^{7}+448 \sqrt{c^{2} x^{2}+1}\, x^{6} b \,c^{6}+432 x^{5} b \,c^{5}+240 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+120 x^{3} b \,c^{3}+40 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+9 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{9 a}{b}} \Ei \left(1, -9 \arcsinh \left(c x \right)-\frac{9 a}{b}\right) b +9 \,{\mathrm e}^{-\frac{9 a}{b}} \Ei \left(1, -9 \arcsinh \left(c x \right)-\frac{9 a}{b}\right) a +9 x b c +\sqrt{c^{2} x^{2}+1}\, b}{512 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/512*(256*c^9*x^9-256*c^8*x^8*(c^2*x^2+1)^(1/2)+576*c^7*x^7-448*c^6*x^6*(c^2*x^2+1)^(1/2)+432*c^5*x^5-240*c^4*x^4*(c^2*x^2+1)^(1/2)+120*c^3*x^3-40*c^2*x^2*(c^2*x^2+1)^(1/2)+9*c*x-(c^2*x^2+1)^(1/2))/c^4/(a+b*arcsinh(c*x))/b-9/512/c^4/b^2*exp(9*a/b)*Ei(1,9*arcsinh(c*x)+9*a/b)-3/512*(64*c^7*x^7-64*c^6*x^6*(c^2*x^2+1)^(1/2)+112*c^5*x^5-80*c^4*x^4*(c^2*x^2+1)^(1/2)+56*c^3*x^3-24*c^2*x^2*(c^2*x^2+1)^(1/2)+7*c*x-(c^2*x^2+1)^(1/2))/c^4/(a+b*arcsinh(c*x))/b-21/512/c^4/b^2*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)+1/64*(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))/c^4/b/(a+b*arcsinh(c*x))+3/64/c^4/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+3/256*(c*x-(c^2*x^2+1)^(1/2))/c^4/b/(a+b*arcsinh(c*x))+3/256/c^4/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+3/256/c^4/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))+1/64/c^4/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-3/512/c^4/b^2*(64*x^7*b*c^7+64*(c^2*x^2+1)^(1/2)*x^6*b*c^6+112*x^5*b*c^5+80*(c^2*x^2+1)^(1/2)*x^4*b*c^4+56*x^3*b*c^3+24*(c^2*x^2+1)^(1/2)*x^2*b*c^2+7*arcsinh(c*x)*Ei(1,-7*arcsinh(c*x)-7*a/b)*exp(-7*a/b)*b+7*Ei(1,-7*arcsinh(c*x)-7*a/b)*exp(-7*a/b)*a+7*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/512/c^4/b^2*(256*x^9*b*c^9+256*(c^2*x^2+1)^(1/2)*x^8*b*c^8+576*x^7*b*c^7+448*(c^2*x^2+1)^(1/2)*x^6*b*c^6+432*x^5*b*c^5+240*(c^2*x^2+1)^(1/2)*x^4*b*c^4+120*x^3*b*c^3+40*(c^2*x^2+1)^(1/2)*x^2*b*c^2+9*arcsinh(c*x)*exp(-9*a/b)*Ei(1,-9*arcsinh(c*x)-9*a/b)*b+9*exp(-9*a/b)*Ei(1,-9*arcsinh(c*x)-9*a/b)*a+9*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
428,1,1044,265,0.886000," ","int(x^2*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\frac{5}{128 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{128 c^{8} x^{8}-128 c^{7} x^{7} \sqrt{c^{2} x^{2}+1}+256 c^{6} x^{6}-192 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+160 c^{4} x^{4}-80 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+32 c^{2} x^{2}-8 c x \sqrt{c^{2} x^{2}+1}+1}{256 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{8 a}{b}} \Ei \left(1, 8 \arcsinh \left(c x \right)+\frac{8 a}{b}\right)}{32 c^{3} b^{2}}-\frac{32 c^{6} x^{6}-32 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+48 c^{4} x^{4}-32 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+18 c^{2} x^{2}-6 c x \sqrt{c^{2} x^{2}+1}+1}{64 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{3 \,{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{32 c^{3} b^{2}}-\frac{8 c^{4} x^{4}-8 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+8 c^{2} x^{2}-4 c x \sqrt{c^{2} x^{2}+1}+1}{64 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{16 c^{3} b^{2}}+\frac{2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1}{64 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{32 c^{3} b^{2}}+\frac{2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b}{64 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{8 x^{4} b \,c^{4}+8 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+8 x^{2} b \,c^{2}+4 b c \sqrt{c^{2} x^{2}+1}\, x +4 \arcsinh \left(c x \right) \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b}{64 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{32 x^{6} b \,c^{6}+32 \sqrt{c^{2} x^{2}+1}\, x^{5} b \,c^{5}+48 x^{4} b \,c^{4}+32 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+18 x^{2} b \,c^{2}+6 b c \sqrt{c^{2} x^{2}+1}\, x +6 \arcsinh \left(c x \right) \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{-\frac{6 a}{b}} b +6 \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{-\frac{6 a}{b}} a +b}{64 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{128 x^{8} b \,c^{8}+128 \sqrt{c^{2} x^{2}+1}\, x^{7} b \,c^{7}+256 x^{6} b \,c^{6}+192 \sqrt{c^{2} x^{2}+1}\, x^{5} b \,c^{5}+160 x^{4} b \,c^{4}+80 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+32 x^{2} b \,c^{2}+8 \arcsinh \left(c x \right) \Ei \left(1, -8 \arcsinh \left(c x \right)-\frac{8 a}{b}\right) {\mathrm e}^{-\frac{8 a}{b}} b +8 b c \sqrt{c^{2} x^{2}+1}\, x +8 \Ei \left(1, -8 \arcsinh \left(c x \right)-\frac{8 a}{b}\right) {\mathrm e}^{-\frac{8 a}{b}} a +b}{256 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"5/128/c^3/(a+b*arcsinh(c*x))/b-1/256*(128*c^8*x^8-128*c^7*x^7*(c^2*x^2+1)^(1/2)+256*c^6*x^6-192*c^5*x^5*(c^2*x^2+1)^(1/2)+160*c^4*x^4-80*c^3*x^3*(c^2*x^2+1)^(1/2)+32*c^2*x^2-8*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+1/32/c^3/b^2*exp(8*a/b)*Ei(1,8*arcsinh(c*x)+8*a/b)-1/64*(32*c^6*x^6-32*c^5*x^5*(c^2*x^2+1)^(1/2)+48*c^4*x^4-32*c^3*x^3*(c^2*x^2+1)^(1/2)+18*c^2*x^2-6*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+3/32/c^3/b^2*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)-1/64*(8*c^4*x^4-8*c^3*x^3*(c^2*x^2+1)^(1/2)+8*c^2*x^2-4*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+1/16/c^3/b^2*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/64*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b-1/32/c^3/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/64/c^3/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))-1/64/c^3/b^2*(8*x^4*b*c^4+8*(c^2*x^2+1)^(1/2)*x^3*b*c^3+8*x^2*b*c^2+4*b*c*(c^2*x^2+1)^(1/2)*x+4*arcsinh(c*x)*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/(a+b*arcsinh(c*x))-1/64/c^3/b^2*(32*x^6*b*c^6+32*(c^2*x^2+1)^(1/2)*x^5*b*c^5+48*x^4*b*c^4+32*(c^2*x^2+1)^(1/2)*x^3*b*c^3+18*x^2*b*c^2+6*b*c*(c^2*x^2+1)^(1/2)*x+6*arcsinh(c*x)*Ei(1,-6*arcsinh(c*x)-6*a/b)*exp(-6*a/b)*b+6*Ei(1,-6*arcsinh(c*x)-6*a/b)*exp(-6*a/b)*a+b)/(a+b*arcsinh(c*x))-1/256/c^3/b^2*(128*x^8*b*c^8+128*(c^2*x^2+1)^(1/2)*x^7*b*c^7+256*x^6*b*c^6+192*(c^2*x^2+1)^(1/2)*x^5*b*c^5+160*x^4*b*c^4+80*(c^2*x^2+1)^(1/2)*x^3*b*c^3+32*x^2*b*c^2+8*arcsinh(c*x)*Ei(1,-8*arcsinh(c*x)-8*a/b)*exp(-8*a/b)*b+8*b*c*(c^2*x^2+1)^(1/2)*x+8*Ei(1,-8*arcsinh(c*x)-8*a/b)*exp(-8*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
429,1,958,259,0.615000," ","int(x*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{64 c^{7} x^{7}-64 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}+112 c^{5} x^{5}-80 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+56 c^{3} x^{3}-24 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+7 c x -\sqrt{c^{2} x^{2}+1}}{128 c^{2} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{7 \,{\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{128 c^{2} b^{2}}-\frac{5 \left(16 c^{5} x^{5}-16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+20 c^{3} x^{3}-12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+5 c x -\sqrt{c^{2} x^{2}+1}\right)}{128 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{25 \,{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{128 c^{2} b^{2}}-\frac{9 \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)}{128 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{27 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{128 c^{2} b^{2}}-\frac{5 \left(c x -\sqrt{c^{2} x^{2}+1}\right)}{128 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{128 c^{2} b^{2}}-\frac{5 \left(\arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a +x b c +\sqrt{c^{2} x^{2}+1}\, b \right)}{128 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{9 \left(4 x^{3} b \,c^{3}+4 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b +3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a +3 x b c +\sqrt{c^{2} x^{2}+1}\, b \right)}{128 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \left(16 x^{5} b \,c^{5}+16 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+20 x^{3} b \,c^{3}+12 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+5 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) a +5 x b c +\sqrt{c^{2} x^{2}+1}\, b \right)}{128 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{64 x^{7} b \,c^{7}+64 \sqrt{c^{2} x^{2}+1}\, x^{6} b \,c^{6}+112 x^{5} b \,c^{5}+80 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+56 x^{3} b \,c^{3}+24 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+7 \arcsinh \left(c x \right) \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} b +7 \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right) {\mathrm e}^{-\frac{7 a}{b}} a +7 x b c +\sqrt{c^{2} x^{2}+1}\, b}{128 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/128*(64*c^7*x^7-64*c^6*x^6*(c^2*x^2+1)^(1/2)+112*c^5*x^5-80*c^4*x^4*(c^2*x^2+1)^(1/2)+56*c^3*x^3-24*c^2*x^2*(c^2*x^2+1)^(1/2)+7*c*x-(c^2*x^2+1)^(1/2))/c^2/(a+b*arcsinh(c*x))/b-7/128/c^2/b^2*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)-5/128*(16*c^5*x^5-16*c^4*x^4*(c^2*x^2+1)^(1/2)+20*c^3*x^3-12*c^2*x^2*(c^2*x^2+1)^(1/2)+5*c*x-(c^2*x^2+1)^(1/2))/c^2/b/(a+b*arcsinh(c*x))-25/128/c^2/b^2*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-9/128*(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))/c^2/b/(a+b*arcsinh(c*x))-27/128/c^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-5/128*(c*x-(c^2*x^2+1)^(1/2))/c^2/b/(a+b*arcsinh(c*x))-5/128/c^2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-5/128/c^2/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-9/128/c^2/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-5/128/c^2/b^2*(16*x^5*b*c^5+16*(c^2*x^2+1)^(1/2)*x^4*b*c^4+20*x^3*b*c^3+12*(c^2*x^2+1)^(1/2)*x^2*b*c^2+5*arcsinh(c*x)*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*b+5*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*a+5*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/128/c^2/b^2*(64*x^7*b*c^7+64*(c^2*x^2+1)^(1/2)*x^6*b*c^6+112*x^5*b*c^5+80*(c^2*x^2+1)^(1/2)*x^4*b*c^4+56*x^3*b*c^3+24*(c^2*x^2+1)^(1/2)*x^2*b*c^2+7*arcsinh(c*x)*Ei(1,-7*arcsinh(c*x)-7*a/b)*exp(-7*a/b)*b+7*Ei(1,-7*arcsinh(c*x)-7*a/b)*exp(-7*a/b)*a+7*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
430,1,704,204,0.713000," ","int((c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","-\frac{5}{16 b c \left(a +b \arcsinh \left(c x \right)\right)}-\frac{32 c^{6} x^{6}-32 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+48 c^{4} x^{4}-32 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+18 c^{2} x^{2}-6 c x \sqrt{c^{2} x^{2}+1}+1}{64 c \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{3 \,{\mathrm e}^{\frac{6 a}{b}} \Ei \left(1, 6 \arcsinh \left(c x \right)+\frac{6 a}{b}\right)}{32 c \,b^{2}}-\frac{3 \left(8 c^{4} x^{4}-8 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+8 c^{2} x^{2}-4 c x \sqrt{c^{2} x^{2}+1}+1\right)}{32 c \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{3 \,{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{8 c \,b^{2}}-\frac{15 \left(2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1\right)}{64 c \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{15 \,{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{32 c \,b^{2}}-\frac{15 \left(2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b \right)}{64 c \,b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 \left(8 x^{4} b \,c^{4}+8 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+8 x^{2} b \,c^{2}+4 b c \sqrt{c^{2} x^{2}+1}\, x +4 \arcsinh \left(c x \right) \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b \right)}{32 c \,b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{32 x^{6} b \,c^{6}+32 \sqrt{c^{2} x^{2}+1}\, x^{5} b \,c^{5}+48 x^{4} b \,c^{4}+32 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+18 x^{2} b \,c^{2}+6 b c \sqrt{c^{2} x^{2}+1}\, x +6 \arcsinh \left(c x \right) \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{-\frac{6 a}{b}} b +6 \Ei \left(1, -6 \arcsinh \left(c x \right)-\frac{6 a}{b}\right) {\mathrm e}^{-\frac{6 a}{b}} a +b}{64 c \,b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-5/16/b/c/(a+b*arcsinh(c*x))-1/64*(32*c^6*x^6-32*c^5*x^5*(c^2*x^2+1)^(1/2)+48*c^4*x^4-32*c^3*x^3*(c^2*x^2+1)^(1/2)+18*c^2*x^2-6*c*x*(c^2*x^2+1)^(1/2)+1)/c/(a+b*arcsinh(c*x))/b+3/32/c/b^2*exp(6*a/b)*Ei(1,6*arcsinh(c*x)+6*a/b)-3/32*(8*c^4*x^4-8*c^3*x^3*(c^2*x^2+1)^(1/2)+8*c^2*x^2-4*c*x*(c^2*x^2+1)^(1/2)+1)/c/(a+b*arcsinh(c*x))/b+3/8/c/b^2*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)-15/64*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c/(a+b*arcsinh(c*x))/b+15/32/c/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-15/64/c/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))-3/32/c/b^2*(8*x^4*b*c^4+8*(c^2*x^2+1)^(1/2)*x^3*b*c^3+8*x^2*b*c^2+4*b*c*(c^2*x^2+1)^(1/2)*x+4*arcsinh(c*x)*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/(a+b*arcsinh(c*x))-1/64/c/b^2*(32*x^6*b*c^6+32*(c^2*x^2+1)^(1/2)*x^5*b*c^5+48*x^4*b*c^4+32*(c^2*x^2+1)^(1/2)*x^3*b*c^3+18*x^2*b*c^2+6*b*c*(c^2*x^2+1)^(1/2)*x+6*arcsinh(c*x)*Ei(1,-6*arcsinh(c*x)-6*a/b)*exp(-6*a/b)*b+6*Ei(1,-6*arcsinh(c*x)-6*a/b)*exp(-6*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
431,0,0,220,0.617000," ","int((c^2*x^2+1)^(5/2)/x/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x/(a+b*arcsinh(c*x))^2,x)","F"
432,0,0,101,0.495000," ","int((c^2*x^2+1)^(5/2)/x^2/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x^2/(a+b*arcsinh(c*x))^2,x)","F"
433,0,0,27,1.433000," ","int((c^2*x^2+1)^(5/2)/x^3/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x^3/(a+b*arcsinh(c*x))^2,x)","F"
434,0,0,27,1.240000," ","int((c^2*x^2+1)^(5/2)/x^4/(a+b*arcsinh(c*x))^2,x)","\int \frac{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{4} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((c^2*x^2+1)^(5/2)/x^4/(a+b*arcsinh(c*x))^2,x)","F"
435,1,633,192,0.425000," ","int(x^5/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","-\frac{16 c^{5} x^{5}-16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+20 c^{3} x^{3}-12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+5 c x -\sqrt{c^{2} x^{2}+1}}{32 c^{6} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \,{\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{6} b^{2}}+\frac{\frac{5 c^{3} x^{3}}{8}-\frac{5 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{8}+\frac{15 c x}{32}-\frac{5 \sqrt{c^{2} x^{2}+1}}{32}}{c^{6} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{15 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{6} b^{2}}-\frac{5 \left(c x -\sqrt{c^{2} x^{2}+1}\right)}{16 c^{6} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{16 c^{6} b^{2}}-\frac{5 \left(\arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a +x b c +\sqrt{c^{2} x^{2}+1}\, b \right)}{16 c^{6} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}+\frac{\frac{5 x^{3} b \,c^{3}}{8}+\frac{5 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}}{8}+\frac{15 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b}{32}+\frac{15 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a}{32}+\frac{15 x b c}{32}+\frac{5 \sqrt{c^{2} x^{2}+1}\, b}{32}}{c^{6} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{16 x^{5} b \,c^{5}+16 \sqrt{c^{2} x^{2}+1}\, x^{4} b \,c^{4}+20 x^{3} b \,c^{3}+12 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+5 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) b +5 \,{\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) a +5 x b c +\sqrt{c^{2} x^{2}+1}\, b}{32 c^{6} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/32*(16*c^5*x^5-16*c^4*x^4*(c^2*x^2+1)^(1/2)+20*c^3*x^3-12*c^2*x^2*(c^2*x^2+1)^(1/2)+5*c*x-(c^2*x^2+1)^(1/2))/c^6/b/(a+b*arcsinh(c*x))-5/32/c^6/b^2*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)+5/32*(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))/c^6/b/(a+b*arcsinh(c*x))+15/32/c^6/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-5/16*(c*x-(c^2*x^2+1)^(1/2))/c^6/b/(a+b*arcsinh(c*x))-5/16/c^6/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-5/16/c^6/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))+5/32/c^6/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/32/c^6/b^2*(16*x^5*b*c^5+16*(c^2*x^2+1)^(1/2)*x^4*b*c^4+20*x^3*b*c^3+12*(c^2*x^2+1)^(1/2)*x^2*b*c^2+5*arcsinh(c*x)*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*b+5*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*a+5*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
436,1,420,137,0.474000," ","int(x^4/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","-\frac{3}{8 c^{5} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{8 c^{4} x^{4}-8 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+8 c^{2} x^{2}-4 c x \sqrt{c^{2} x^{2}+1}+1}{16 c^{5} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{4 a}{b}} \Ei \left(1, 4 \arcsinh \left(c x \right)+\frac{4 a}{b}\right)}{4 c^{5} b^{2}}+\frac{2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1}{4 c^{5} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{2 c^{5} b^{2}}+\frac{2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b}{4 c^{5} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{8 x^{4} b \,c^{4}+8 \sqrt{c^{2} x^{2}+1}\, x^{3} b \,c^{3}+8 x^{2} b \,c^{2}+4 b c \sqrt{c^{2} x^{2}+1}\, x +4 \arcsinh \left(c x \right) \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} b +4 \Ei \left(1, -4 \arcsinh \left(c x \right)-\frac{4 a}{b}\right) {\mathrm e}^{-\frac{4 a}{b}} a +b}{16 c^{5} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-3/8/c^5/(a+b*arcsinh(c*x))/b-1/16*(8*c^4*x^4-8*c^3*x^3*(c^2*x^2+1)^(1/2)+8*c^2*x^2-4*c*x*(c^2*x^2+1)^(1/2)+1)/c^5/(a+b*arcsinh(c*x))/b+1/4/c^5/b^2*exp(4*a/b)*Ei(1,4*arcsinh(c*x)+4*a/b)+1/4*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c^5/(a+b*arcsinh(c*x))/b-1/2/c^5/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)+1/4/c^5/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))-1/16/c^5/b^2*(8*x^4*b*c^4+8*(c^2*x^2+1)^(1/2)*x^3*b*c^3+8*x^2*b*c^2+4*b*c*(c^2*x^2+1)^(1/2)*x+4*arcsinh(c*x)*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*b+4*Ei(1,-4*arcsinh(c*x)-4*a/b)*exp(-4*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
437,1,364,134,0.290000," ","int(x^3/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","-\frac{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}}{8 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{8 c^{4} b^{2}}+\frac{\frac{3 c x}{8}-\frac{3 \sqrt{c^{2} x^{2}+1}}{8}}{c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{8 c^{4} b^{2}}+\frac{\frac{3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b}{8}+\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a}{8}+\frac{3 x b c}{8}+\frac{3 \sqrt{c^{2} x^{2}+1}\, b}{8}}{c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{4 x^{3} b \,c^{3}+4 \sqrt{c^{2} x^{2}+1}\, x^{2} b \,c^{2}+3 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) b +3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) a +3 x b c +\sqrt{c^{2} x^{2}+1}\, b}{8 c^{4} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-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))/c^4/b/(a+b*arcsinh(c*x))-3/8/c^4/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)+3/8*(c*x-(c^2*x^2+1)^(1/2))/c^4/b/(a+b*arcsinh(c*x))+3/8/c^4/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+3/8/c^4/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))-1/8/c^4/b^2*(4*x^3*b*c^3+4*(c^2*x^2+1)^(1/2)*x^2*b*c^2+3*arcsinh(c*x)*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*b+3*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*a+3*x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
438,1,192,79,0.221000," ","int(x^2/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","\frac{1}{2 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}-\frac{2 c^{2} x^{2}-2 c x \sqrt{c^{2} x^{2}+1}+1}{4 c^{3} \left(a +b \arcsinh \left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, 2 \arcsinh \left(c x \right)+\frac{2 a}{b}\right)}{2 c^{3} b^{2}}-\frac{2 x^{2} b \,c^{2}+2 b c \sqrt{c^{2} x^{2}+1}\, x +2 \arcsinh \left(c x \right) {\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) b +2 \,{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \arcsinh \left(c x \right)-\frac{2 a}{b}\right) a +b}{4 c^{3} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"1/2/c^3/(a+b*arcsinh(c*x))/b-1/4*(2*c^2*x^2-2*c*x*(c^2*x^2+1)^(1/2)+1)/c^3/(a+b*arcsinh(c*x))/b+1/2/c^3/b^2*exp(2*a/b)*Ei(1,2*arcsinh(c*x)+2*a/b)-1/4/c^3/b^2*(2*x^2*b*c^2+2*b*c*(c^2*x^2+1)^(1/2)*x+2*arcsinh(c*x)*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*b+2*exp(-2*a/b)*Ei(1,-2*arcsinh(c*x)-2*a/b)*a+b)/(a+b*arcsinh(c*x))","B"
439,1,151,73,0.084000," ","int(x/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","-\frac{c x -\sqrt{c^{2} x^{2}+1}}{2 c^{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 c^{2} b^{2}}-\frac{\arcsinh \left(c x \right) {\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) b +{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) a +x b c +\sqrt{c^{2} x^{2}+1}\, b}{2 c^{2} b^{2} \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/2*(c*x-(c^2*x^2+1)^(1/2))/c^2/b/(a+b*arcsinh(c*x))-1/2/c^2/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/2/c^2/b^2*(arcsinh(c*x)*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*b+exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*a+x*b*c+(c^2*x^2+1)^(1/2)*b)/(a+b*arcsinh(c*x))","B"
440,1,19,18,0.007000," ","int(1/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","-\frac{1}{b c \left(a +b \arcsinh \left(c x \right)\right)}"," ",0,"-1/b/c/(a+b*arcsinh(c*x))","A"
441,0,0,46,0.152000," ","int(1/x/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","\int \frac{1}{x \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","F"
442,0,0,46,0.126000," ","int(1/x^2/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x)","F"
443,0,0,27,0.702000," ","int(x^3/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{3}}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^3/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
444,0,0,66,0.358000," ","int(x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{2}}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
445,0,0,25,0.251000," ","int(x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
446,0,0,61,0.144000," ","int(1/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
447,0,0,27,0.553000," ","int(1/x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{x \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
448,0,0,27,0.321000," ","int(1/x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{x^{2} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
449,0,0,27,1.000000," ","int(x^3/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{3}}{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^3/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
450,0,0,27,0.826000," ","int(x^2/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{2}}{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^2/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
451,0,0,25,0.495000," ","int(x/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x}{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
452,0,0,61,0.252000," ","int(1/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
453,0,0,27,1.015000," ","int(1/x/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{x \left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
454,0,0,27,1.190000," ","int(1/x^2/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{x^{2} \left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
455,-2,0,27,180.000000," ","int(x^m*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{m} \left(c^{2} x^{2}+1\right)^{\frac{5}{2}}}{\left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
456,-2,0,27,180.000000," ","int(x^m*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{m} \left(c^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
457,-2,0,27,180.000000," ","int(x^m*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{m} \sqrt{c^{2} x^{2}+1}}{\left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","F"
458,0,0,48,0.201000," ","int(x^m/(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{m}}{\sqrt{c^{2} x^{2}+1}\, \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m/(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x)","F"
459,0,0,27,0.533000," ","int(x^m/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{m}}{\left(c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
460,0,0,27,0.720000," ","int(x^m/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{x^{m}}{\left(c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"
461,1,12,11,0.013000," ","int(1/arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x)","-\frac{1}{2 a \arcsinh \left(a x \right)^{2}}"," ",0,"-1/2/a/arcsinh(a*x)^2","A"
462,-2,0,198,180.000000," ","int(x^3*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{x^{3} \left(c^{2} d \,x^{2}+d \right)}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","F"
463,-2,0,266,180.000000," ","int(x^2*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{x^{2} \left(c^{2} d \,x^{2}+d \right)}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","F"
464,-2,0,186,180.000000," ","int(x*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{x \left(c^{2} d \,x^{2}+d \right)}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","F"
465,-2,0,181,180.000000," ","int((c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{c^{2} d \,x^{2}+d}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","F"
466,-2,0,146,180.000000," ","int((c^2*d*x^2+d)/x/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{c^{2} d \,x^{2}+d}{x \left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c^2*d*x^2+d)/x/(a+b*arcsinh(c*x))^(3/2),x)","F"
467,-2,0,372,180.000000," ","int(x^3*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{x^{3} \left(c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","F"
468,-2,0,366,180.000000," ","int(x^2*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{x^{2} \left(c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","F"
469,-2,0,282,180.000000," ","int(x*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{x \left(c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","F"
470,-2,0,277,180.000000," ","int((c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{\left(c^{2} d \,x^{2}+d \right)^{2}}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","F"
471,-2,0,224,180.000000," ","int((c^2*d*x^2+d)^2/x/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{\left(c^{2} d \,x^{2}+d \right)^{2}}{x \left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c^2*d*x^2+d)^2/x/(a+b*arcsinh(c*x))^(3/2),x)","F"
472,0,0,253,0.388000," ","int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(1/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arcsinh \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(1/2),x)","F"
473,0,0,146,0.355000," ","int((a^2*c*x^2+c)^(1/2)*arcsinh(a*x)^(1/2),x)","\int \sqrt{a^{2} c \,x^{2}+c}\, \sqrt{\arcsinh \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)*arcsinh(a*x)^(1/2),x)","F"
474,1,36,34,0.057000," ","int(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{2 \arcsinh \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} x^{2}+1}}{3 a \sqrt{c \left(a^{2} x^{2}+1\right)}}"," ",0,"2/3*arcsinh(a*x)^(3/2)/a/(c*(a^2*x^2+1))^(1/2)*(a^2*x^2+1)^(1/2)","A"
475,0,0,74,0.419000," ","int(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\sqrt{\arcsinh \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","F"
476,0,0,149,0.467000," ","int(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","\int \frac{\sqrt{\arcsinh \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x)","F"
477,0,0,359,0.320000," ","int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(3/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsinh \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(3/2),x)","F"
478,0,0,215,0.344000," ","int(arcsinh(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","\int \arcsinh \left(a x \right)^{\frac{3}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(arcsinh(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x)","F"
479,1,36,34,0.056000," ","int(arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{2 \arcsinh \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} x^{2}+1}}{5 a \sqrt{c \left(a^{2} x^{2}+1\right)}}"," ",0,"2/5*arcsinh(a*x)^(5/2)/a/(c*(a^2*x^2+1))^(1/2)*(a^2*x^2+1)^(1/2)","A"
480,0,0,74,0.383000," ","int(arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arcsinh \left(a x \right)^{\frac{3}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","F"
481,0,0,412,0.317000," ","int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(5/2),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsinh \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(5/2),x)","F"
482,0,0,236,0.338000," ","int(arcsinh(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","\int \arcsinh \left(a x \right)^{\frac{5}{2}} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(arcsinh(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x)","F"
483,1,36,34,0.055000," ","int(arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{2 \arcsinh \left(a x \right)^{\frac{7}{2}} \sqrt{a^{2} x^{2}+1}}{7 a \sqrt{c \left(a^{2} x^{2}+1\right)}}"," ",0,"2/7*arcsinh(a*x)^(7/2)/a/(c*(a^2*x^2+1))^(1/2)*(a^2*x^2+1)^(1/2)","A"
484,0,0,74,0.378000," ","int(arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","\int \frac{\arcsinh \left(a x \right)^{\frac{5}{2}}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","F"
485,0,0,243,0.375000," ","int((a^2+x^2)^(3/2)*arcsinh(x/a)^(1/2),x)","\int \left(a^{2}+x^{2}\right)^{\frac{3}{2}} \sqrt{\arcsinh \left(\frac{x}{a}\right)}\, dx"," ",0,"int((a^2+x^2)^(3/2)*arcsinh(x/a)^(1/2),x)","F"
486,0,0,136,0.361000," ","int((a^2+x^2)^(1/2)*arcsinh(x/a)^(1/2),x)","\int \sqrt{a^{2}+x^{2}}\, \sqrt{\arcsinh \left(\frac{x}{a}\right)}\, dx"," ",0,"int((a^2+x^2)^(1/2)*arcsinh(x/a)^(1/2),x)","F"
487,1,34,31,0.065000," ","int(arcsinh(x/a)^(1/2)/(a^2+x^2)^(1/2),x)","\frac{2 \arcsinh \left(\frac{x}{a}\right)^{\frac{3}{2}} a \sqrt{\frac{a^{2}+x^{2}}{a^{2}}}}{3 \sqrt{a^{2}+x^{2}}}"," ",0,"2/3*arcsinh(x/a)^(3/2)*a/(a^2+x^2)^(1/2)*((a^2+x^2)/a^2)^(1/2)","A"
488,0,0,71,0.460000," ","int(arcsinh(x/a)^(1/2)/(a^2+x^2)^(3/2),x)","\int \frac{\sqrt{\arcsinh \left(\frac{x}{a}\right)}}{\left(a^{2}+x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsinh(x/a)^(1/2)/(a^2+x^2)^(3/2),x)","F"
489,0,0,143,0.452000," ","int(arcsinh(x/a)^(1/2)/(a^2+x^2)^(5/2),x)","\int \frac{\sqrt{\arcsinh \left(\frac{x}{a}\right)}}{\left(a^{2}+x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(arcsinh(x/a)^(1/2)/(a^2+x^2)^(5/2),x)","F"
490,0,0,343,0.316000," ","int((a^2+x^2)^(3/2)*arcsinh(x/a)^(3/2),x)","\int \left(a^{2}+x^{2}\right)^{\frac{3}{2}} \arcsinh \left(\frac{x}{a}\right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2+x^2)^(3/2)*arcsinh(x/a)^(3/2),x)","F"
491,0,0,203,0.346000," ","int(arcsinh(x/a)^(3/2)*(a^2+x^2)^(1/2),x)","\int \arcsinh \left(\frac{x}{a}\right)^{\frac{3}{2}} \sqrt{a^{2}+x^{2}}\, dx"," ",0,"int(arcsinh(x/a)^(3/2)*(a^2+x^2)^(1/2),x)","F"
492,1,34,31,0.057000," ","int(arcsinh(x/a)^(3/2)/(a^2+x^2)^(1/2),x)","\frac{2 \arcsinh \left(\frac{x}{a}\right)^{\frac{5}{2}} a \sqrt{\frac{a^{2}+x^{2}}{a^{2}}}}{5 \sqrt{a^{2}+x^{2}}}"," ",0,"2/5*arcsinh(x/a)^(5/2)*a/(a^2+x^2)^(1/2)*((a^2+x^2)/a^2)^(1/2)","A"
493,0,0,71,0.372000," ","int(arcsinh(x/a)^(3/2)/(a^2+x^2)^(3/2),x)","\int \frac{\arcsinh \left(\frac{x}{a}\right)^{\frac{3}{2}}}{\left(a^{2}+x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsinh(x/a)^(3/2)/(a^2+x^2)^(3/2),x)","F"
494,0,0,21,0.163000," ","int(x/(x^2+1)^(1/2)/arcsinh(x)^(1/2),x)","\int \frac{x}{\sqrt{x^{2}+1}\, \sqrt{\arcsinh \left(x \right)}}\, dx"," ",0,"int(x/(x^2+1)^(1/2)/arcsinh(x)^(1/2),x)","F"
495,0,0,316,0.338000," ","int((a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\sqrt{\arcsinh \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(1/2),x)","F"
496,0,0,210,0.333000," ","int((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(1/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\sqrt{\arcsinh \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(1/2),x)","F"
497,0,0,124,0.365000," ","int((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(1/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\sqrt{\arcsinh \left(a x \right)}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(1/2),x)","F"
498,1,36,34,0.056000," ","int(1/(a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(1/2),x)","\frac{2 \sqrt{\arcsinh \left(a x \right)}\, \sqrt{a^{2} x^{2}+1}}{a \sqrt{c \left(a^{2} x^{2}+1\right)}}"," ",0,"2*arcsinh(a*x)^(1/2)/a/(c*(a^2*x^2+1))^(1/2)*(a^2*x^2+1)^(1/2)","A"
499,0,0,21,0.390000," ","int(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(1/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arcsinh \left(a x \right)}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(1/2),x)","F"
500,0,0,21,0.456000," ","int(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(1/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arcsinh \left(a x \right)}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(1/2),x)","F"
501,0,0,313,0.315000," ","int((a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arcsinh \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(3/2),x)","F"
502,0,0,209,0.321000," ","int((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(3/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arcsinh \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(3/2),x)","F"
503,0,0,125,0.349000," ","int((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(3/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arcsinh \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(3/2),x)","F"
504,1,36,34,0.056000," ","int(1/arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","-\frac{2 \sqrt{a^{2} x^{2}+1}}{\sqrt{\arcsinh \left(a x \right)}\, a \sqrt{c \left(a^{2} x^{2}+1\right)}}"," ",0,"-2/arcsinh(a*x)^(1/2)/a/(c*(a^2*x^2+1))^(1/2)*(a^2*x^2+1)^(1/2)","A"
505,0,0,85,0.388000," ","int(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(3/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsinh \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(3/2),x)","F"
506,0,0,85,0.459000," ","int(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(3/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arcsinh \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(3/2),x)","F"
507,0,0,240,0.325000," ","int((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(5/2),x)","\int \frac{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arcsinh \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(5/2),x)","F"
508,0,0,146,0.346000," ","int((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(5/2),x)","\int \frac{\sqrt{a^{2} c \,x^{2}+c}}{\arcsinh \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(5/2),x)","F"
509,1,36,34,0.059000," ","int(1/arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","-\frac{2 \sqrt{a^{2} x^{2}+1}}{3 \arcsinh \left(a x \right)^{\frac{3}{2}} a \sqrt{c \left(a^{2} x^{2}+1\right)}}"," ",0,"-2/3/arcsinh(a*x)^(3/2)/a/(c*(a^2*x^2+1))^(1/2)*(a^2*x^2+1)^(1/2)","A"
510,0,0,85,0.401000," ","int(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(5/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsinh \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(5/2),x)","F"
511,0,0,85,0.457000," ","int(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(5/2),x)","\int \frac{1}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arcsinh \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(5/2),x)","F"
512,-2,0,227,180.000000," ","int(x^2*(a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x)","\int x^{2} \left(a +b \arcsinh \left(c x \right)\right)^{n} \sqrt{c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x)","F"
513,0,0,336,0.179000," ","int(x*(a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x)","\int x \left(a +b \arcsinh \left(c x \right)\right)^{n} \sqrt{c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x)","F"
514,0,0,223,0.217000," ","int((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x)","\int \left(a +b \arcsinh \left(c x \right)\right)^{n} \sqrt{c^{2} d \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x)","F"
515,0,0,187,0.273000," ","int((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{n} \sqrt{c^{2} d \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2)/x,x)","F"
516,0,0,77,0.269000," ","int((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{n} \sqrt{c^{2} d \,x^{2}+d}}{x^{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2)/x^2,x)","F"
517,-2,0,592,180.000000," ","int(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x)","\int x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x)","F"
518,0,0,513,0.151000," ","int(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x)","\int x \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x)","F"
519,0,0,406,0.178000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x)","\int \left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}\, dx"," ",0,"int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x)","F"
520,0,0,368,0.234000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n/x,x)","\int \frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n/x,x)","F"
521,0,0,258,0.262000," ","int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n/x^2,x)","\int \frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n/x^2,x)","F"
522,-2,0,790,180.000000," ","int(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x)","\int x^{2} \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x)","F"
523,0,0,706,0.152000," ","int(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x)","\int x \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x)","F"
524,0,0,608,0.177000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x)","\int \left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}\, dx"," ",0,"int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x)","F"
525,0,0,714,0.230000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n/x,x)","\int \frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n/x,x)","F"
526,0,0,438,0.260000," ","int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n/x^2,x)","\int \frac{\left(c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n/x^2,x)","F"
527,0,0,23,0.162000," ","int(x^m*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsinh \left(a x \right)^{n}}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","F"
528,-2,0,105,180.000000," ","int(x^3*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","\int \frac{x^{3} \arcsinh \left(a x \right)^{n}}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x^3*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","F"
529,-2,0,78,180.000000," ","int(x^2*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \arcsinh \left(a x \right)^{n}}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x^2*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","F"
530,0,0,45,0.129000," ","int(x*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","\int \frac{x \arcsinh \left(a x \right)^{n}}{\sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(x*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","F"
531,1,18,17,0.006000," ","int(arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x)","\frac{\arcsinh \left(a x \right)^{1+n}}{a \left(1+n \right)}"," ",0,"arcsinh(a*x)^(1+n)/a/(1+n)","A"
532,0,0,23,0.148000," ","int(arcsinh(a*x)^n/x/(a^2*x^2+1)^(1/2),x)","\int \frac{\arcsinh \left(a x \right)^{n}}{x \sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(arcsinh(a*x)^n/x/(a^2*x^2+1)^(1/2),x)","F"
533,0,0,23,0.234000," ","int(arcsinh(a*x)^n/x^2/(a^2*x^2+1)^(1/2),x)","\int \frac{\arcsinh \left(a x \right)^{n}}{x^{2} \sqrt{a^{2} x^{2}+1}}\, dx"," ",0,"int(arcsinh(a*x)^n/x^2/(a^2*x^2+1)^(1/2),x)","F"
534,0,0,339,0.401000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2),x)","\int \left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right) \sqrt{-i c f x +f}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2),x)","F"
535,0,0,245,0.285000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2),x)","\int \left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right) \sqrt{-i c f x +f}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2),x)","F"
536,0,0,119,0.285000," ","int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)*(f-I*c*f*x)^(1/2),x)","\int \left(a +b \arcsinh \left(c x \right)\right) \sqrt{i c d x +d}\, \sqrt{-i c f x +f}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)*(f-I*c*f*x)^(1/2),x)","F"
537,0,0,132,0.365000," ","int((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{-i c f x +f}}{\sqrt{i c d x +d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(1/2),x)","F"
538,0,0,154,0.336000," ","int((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{-i c f x +f}}{\left(i c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(3/2),x)","F"
539,0,0,154,0.311000," ","int((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{-i c f x +f}}{\left(i c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(5/2),x)","F"
540,0,0,371,0.276000," ","int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x)","\int \left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x)","F"
541,0,0,201,0.315000," ","int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x)","\int \left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x)","F"
542,0,0,245,0.278000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2),x)","\int \left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right) \sqrt{i c d x +d}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2),x)","F"
543,0,0,222,0.327000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\sqrt{i c d x +d}}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2),x)","F"
544,0,0,241,0.330000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(i c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x)","F"
545,0,0,305,0.351000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(i c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x)","F"
546,0,0,280,0.293000," ","int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x)","\int \left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x)","F"
547,0,0,371,0.299000," ","int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x)","\int \left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x)","F"
548,0,0,339,0.295000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2),x)","\int \left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right) \sqrt{i c d x +d}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2),x)","F"
549,0,0,313,0.337000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\sqrt{i c d x +d}}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2),x)","F"
550,0,0,432,0.328000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(i c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x)","F"
551,0,0,395,0.332000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(i c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x)","F"
552,0,0,313,0.349000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\sqrt{-i c f x +f}}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(1/2),x)","F"
553,0,0,222,0.343000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\sqrt{-i c f x +f}}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(1/2),x)","F"
554,0,0,132,0.340000," ","int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{i c d x +d}}{\sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","F"
555,0,0,49,0.308000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\sqrt{i c d x +d}\, \sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","F"
556,0,0,95,0.339000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(i c d x +d \right)^{\frac{3}{2}} \sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(1/2),x)","F"
557,0,0,244,0.334000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(i c d x +d \right)^{\frac{5}{2}} \sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(1/2),x)","F"
558,0,0,431,0.333000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x)","F"
559,0,0,240,0.333000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x)","F"
560,0,0,153,0.333000," ","int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{i c d x +d}}{\left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(3/2),x)","F"
561,0,0,96,0.337000," ","int((a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2)/(d+I*c*d*x)^(1/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(-i c f x +f \right)^{\frac{3}{2}} \sqrt{i c d x +d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2)/(d+I*c*d*x)^(1/2),x)","F"
562,0,0,87,0.323000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(3/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(3/2),x)","F"
563,0,0,232,0.332000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(3/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(3/2),x)","F"
564,0,0,393,0.366000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x)","F"
565,0,0,303,0.353000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}{\left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x)","F"
566,0,0,152,0.337000," ","int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{i c d x +d}}{\left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(5/2),x)","F"
567,0,0,243,0.336000," ","int((a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2)/(d+I*c*d*x)^(1/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(-i c f x +f \right)^{\frac{5}{2}} \sqrt{i c d x +d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2)/(d+I*c*d*x)^(1/2),x)","F"
568,0,0,232,0.332000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(5/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(5/2),x)","F"
569,0,0,167,0.339000," ","int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(5/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(5/2),x)","F"
570,0,0,559,0.294000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2),x)","\int \left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{-i c f x +f}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2),x)","F"
571,0,0,413,0.296000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2),x)","\int \left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{-i c f x +f}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2),x)","F"
572,0,0,198,0.294000," ","int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)*(f-I*c*f*x)^(1/2),x)","\int \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{i c d x +d}\, \sqrt{-i c f x +f}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)*(f-I*c*f*x)^(1/2),x)","F"
573,0,0,217,0.339000," ","int((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{-i c f x +f}}{\sqrt{i c d x +d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(1/2),x)","F"
574,0,0,515,0.282000," ","int((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{-i c f x +f}}{\left(i c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(3/2),x)","F"
575,0,0,436,0.347000," ","int((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{-i c f x +f}}{\left(i c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(5/2),x)","F"
576,0,0,633,0.295000," ","int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\int \left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x)","F"
577,0,0,324,0.295000," ","int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x)","\int \left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x)","F"
578,0,0,413,0.300000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2),x)","\int \left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{i c d x +d}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2),x)","F"
579,0,0,367,0.351000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{i c d x +d}}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2),x)","F"
580,0,0,693,0.319000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x)","F"
581,0,0,488,0.280000," ","int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x)","F"
582,0,0,450,0.301000," ","int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x)","\int \left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x)","F"
583,0,0,633,0.305000," ","int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x)","\int \left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x)","F"
584,0,0,559,0.301000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2),x)","\int \left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{i c d x +d}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2),x)","F"
585,0,0,511,0.346000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{i c d x +d}}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2),x)","F"
586,0,0,875,0.276000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x)","F"
587,0,0,666,0.278000," ","int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x)","\int \frac{\left(-i c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x)","F"
588,0,0,511,0.354000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{-i c f x +f}}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(1/2),x)","F"
589,0,0,367,0.352000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{-i c f x +f}}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(1/2),x)","F"
590,0,0,217,0.356000," ","int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{i c d x +d}}{\sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","F"
591,0,0,49,0.338000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{i c d x +d}\, \sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x)","F"
592,0,0,445,0.366000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{3}{2}} \sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(1/2),x)","F"
593,0,0,833,0.352000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{5}{2}} \sqrt{-i c f x +f}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(1/2),x)","F"
594,0,0,875,0.295000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x)","F"
595,0,0,693,0.287000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x)","F"
596,0,0,515,0.301000," ","int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{i c d x +d}}{\left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(3/2),x)","F"
597,0,0,445,0.362000," ","int((a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2)/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(-i c f x +f \right)^{\frac{3}{2}} \sqrt{i c d x +d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2)/(d+I*c*d*x)^(1/2),x)","F"
598,0,0,212,0.344000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(3/2),x)","F"
599,0,0,662,0.347000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(3/2),x)","F"
600,0,0,670,0.287000," ","int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x)","F"
601,0,0,492,0.291000," ","int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(i c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x)","F"
602,0,0,440,0.351000," ","int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{i c d x +d}}{\left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(5/2),x)","F"
603,0,0,833,0.346000," ","int((a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2)/(d+I*c*d*x)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(-i c f x +f \right)^{\frac{5}{2}} \sqrt{i c d x +d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2)/(d+I*c*d*x)^(1/2),x)","F"
604,0,0,662,0.355000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{3}{2}} \left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(5/2),x)","F"
605,0,0,340,0.350000," ","int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(i c d x +d \right)^{\frac{5}{2}} \left(-i c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(5/2),x)","F"
606,1,451,284,0.020000," ","int((e*x^2+d)^4*(a+b*arcsinh(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{4} c^{9} x^{9}+\frac{4}{7} c^{9} d \,e^{3} x^{7}+\frac{6}{5} c^{9} d^{2} e^{2} x^{5}+\frac{4}{3} c^{9} d^{3} e \,x^{3}+c^{9} d^{4} x \right)}{c^{8}}+\frac{b \left(\frac{\arcsinh \left(c x \right) e^{4} c^{9} x^{9}}{9}+\frac{4 \arcsinh \left(c x \right) c^{9} d \,e^{3} x^{7}}{7}+\frac{6 \arcsinh \left(c x \right) c^{9} d^{2} e^{2} x^{5}}{5}+\frac{4 \arcsinh \left(c x \right) c^{9} d^{3} e \,x^{3}}{3}+\arcsinh \left(c x \right) c^{9} d^{4} x -\frac{e^{4} \left(\frac{c^{8} x^{8} \sqrt{c^{2} x^{2}+1}}{9}-\frac{8 c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{63}+\frac{16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{105}-\frac{64 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{315}+\frac{128 \sqrt{c^{2} x^{2}+1}}{315}\right)}{9}-\frac{4 c^{2} d \,e^{3} \left(\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{35}+\frac{8 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{c^{2} x^{2}+1}}{35}\right)}{7}-\frac{6 c^{4} d^{2} e^{2} \left(\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{15}+\frac{8 \sqrt{c^{2} x^{2}+1}}{15}\right)}{5}-\frac{4 c^{6} d^{3} e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)}{3}-c^{8} d^{4} \sqrt{c^{2} x^{2}+1}\right)}{c^{8}}}{c}"," ",0,"1/c*(a/c^8*(1/9*e^4*c^9*x^9+4/7*c^9*d*e^3*x^7+6/5*c^9*d^2*e^2*x^5+4/3*c^9*d^3*e*x^3+c^9*d^4*x)+b/c^8*(1/9*arcsinh(c*x)*e^4*c^9*x^9+4/7*arcsinh(c*x)*c^9*d*e^3*x^7+6/5*arcsinh(c*x)*c^9*d^2*e^2*x^5+4/3*arcsinh(c*x)*c^9*d^3*e*x^3+arcsinh(c*x)*c^9*d^4*x-1/9*e^4*(1/9*c^8*x^8*(c^2*x^2+1)^(1/2)-8/63*c^6*x^6*(c^2*x^2+1)^(1/2)+16/105*c^4*x^4*(c^2*x^2+1)^(1/2)-64/315*c^2*x^2*(c^2*x^2+1)^(1/2)+128/315*(c^2*x^2+1)^(1/2))-4/7*c^2*d*e^3*(1/7*c^6*x^6*(c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(c^2*x^2+1)^(1/2)+8/35*c^2*x^2*(c^2*x^2+1)^(1/2)-16/35*(c^2*x^2+1)^(1/2))-6/5*c^4*d^2*e^2*(1/5*c^4*x^4*(c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(c^2*x^2+1)^(1/2)+8/15*(c^2*x^2+1)^(1/2))-4/3*c^6*d^3*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-c^8*d^4*(c^2*x^2+1)^(1/2)))","A"
607,1,316,201,0.006000," ","int((e*x^2+d)^3*(a+b*arcsinh(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{3} c^{7} x^{7}+\frac{3}{5} c^{7} d \,e^{2} x^{5}+c^{7} d^{2} e \,x^{3}+x \,c^{7} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\arcsinh \left(c x \right) e^{3} c^{7} x^{7}}{7}+\frac{3 \arcsinh \left(c x \right) c^{7} d \,e^{2} x^{5}}{5}+\arcsinh \left(c x \right) c^{7} d^{2} e \,x^{3}+\arcsinh \left(c x \right) c^{7} x \,d^{3}-\frac{e^{3} \left(\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{35}+\frac{8 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{c^{2} x^{2}+1}}{35}\right)}{7}-\frac{3 c^{2} d \,e^{2} \left(\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{15}+\frac{8 \sqrt{c^{2} x^{2}+1}}{15}\right)}{5}-c^{4} d^{2} e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)-d^{3} c^{6} \sqrt{c^{2} x^{2}+1}\right)}{c^{6}}}{c}"," ",0,"1/c*(a/c^6*(1/7*e^3*c^7*x^7+3/5*c^7*d*e^2*x^5+c^7*d^2*e*x^3+x*c^7*d^3)+b/c^6*(1/7*arcsinh(c*x)*e^3*c^7*x^7+3/5*arcsinh(c*x)*c^7*d*e^2*x^5+arcsinh(c*x)*c^7*d^2*e*x^3+arcsinh(c*x)*c^7*x*d^3-1/7*e^3*(1/7*c^6*x^6*(c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(c^2*x^2+1)^(1/2)+8/35*c^2*x^2*(c^2*x^2+1)^(1/2)-16/35*(c^2*x^2+1)^(1/2))-3/5*c^2*d*e^2*(1/5*c^4*x^4*(c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(c^2*x^2+1)^(1/2)+8/15*(c^2*x^2+1)^(1/2))-c^4*d^2*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-d^3*c^6*(c^2*x^2+1)^(1/2)))","A"
608,1,204,131,0.005000," ","int((e*x^2+d)^2*(a+b*arcsinh(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} d e \,x^{3}+x \,c^{5} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\arcsinh \left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \arcsinh \left(c x \right) c^{5} d e \,x^{3}}{3}+\arcsinh \left(c x \right) c^{5} x \,d^{2}-\frac{e^{2} \left(\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{15}+\frac{8 \sqrt{c^{2} x^{2}+1}}{15}\right)}{5}-\frac{2 c^{2} d e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)}{3}-d^{2} c^{4} \sqrt{c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*d*e*x^3+x*c^5*d^2)+b/c^4*(1/5*arcsinh(c*x)*e^2*c^5*x^5+2/3*arcsinh(c*x)*c^5*d*e*x^3+arcsinh(c*x)*c^5*x*d^2-1/5*e^2*(1/5*c^4*x^4*(c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(c^2*x^2+1)^(1/2)+8/15*(c^2*x^2+1)^(1/2))-2/3*c^2*d*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-d^2*c^4*(c^2*x^2+1)^(1/2)))","A"
609,1,109,71,0.005000," ","int((e*x^2+d)*(a+b*arcsinh(c*x)),x)","\frac{\frac{a \left(\frac{1}{3} c^{3} x^{3} e +c^{3} d x \right)}{c^{2}}+\frac{b \left(\frac{\arcsinh \left(c x \right) c^{3} x^{3} e}{3}+\arcsinh \left(c x \right) c^{3} d x -\frac{e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)}{3}-c^{2} d \sqrt{c^{2} x^{2}+1}\right)}{c^{2}}}{c}"," ",0,"1/c*(a/c^2*(1/3*c^3*x^3*e+c^3*d*x)+b/c^2*(1/3*arcsinh(c*x)*c^3*x^3*e+arcsinh(c*x)*c^3*d*x-1/3*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-c^2*d*(c^2*x^2+1)^(1/2)))","A"
610,1,31,28,0.007000," ","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"
611,1,224,461,0.666000," ","int((a+b*arcsinh(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\arcsinh \left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d -e \right)}\right)}{2}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\arcsinh \left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d -e}\right)}{2}"," ",0,"a/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/2*c*b*sum(1/_R1/(_R1^2*e+2*c^2*d-e)*(arcsinh(c*x)*ln((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d-2*e)*_Z^2+e))+1/2*c*b*sum(_R1/(_R1^2*e+2*c^2*d-e)*(arcsinh(c*x)*ln((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d-2*e)*_Z^2+e))","C"
612,1,1745,642,1.165000," ","int((a+b*arcsinh(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{c^{2} b \arcsinh \left(c x \right) x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\arcsinh \left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e +2 c^{2} d -e \right)}\right)}{4 d}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(\arcsinh \left(c x \right) \ln \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -c x -\sqrt{c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e +2 c^{2} d -e}\right)}{4 d}+\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right) d}{\left(c^{2} d -e \right) e^{3}}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right) \sqrt{d \,c^{2} \left(c^{2} d -e \right)}}{\left(c^{2} d -e \right) e^{3}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right)}{\left(c^{2} d -e \right) e^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right) \sqrt{d \,c^{2} \left(c^{2} d -e \right)}}{2 d \left(c^{2} d -e \right) e^{2}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right)}{e^{3}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right) \sqrt{d \,c^{2} \left(c^{2} d -e \right)}}{d \,e^{3}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctanh \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(-2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}+e \right) e}}\right)}{2 d \,e^{2}}+\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right) d}{\left(c^{2} d -e \right) e^{3}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right) \sqrt{d \,c^{2} \left(c^{2} d -e \right)}}{\left(c^{2} d -e \right) e^{3}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right)}{\left(c^{2} d -e \right) e^{2}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right) \sqrt{d \,c^{2} \left(c^{2} d -e \right)}}{2 d \left(c^{2} d -e \right) e^{2}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right)}{e^{3}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right) \sqrt{d \,c^{2} \left(c^{2} d -e \right)}}{d \,e^{3}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}\, \arctan \left(\frac{\left(c x +\sqrt{c^{2} x^{2}+1}\right) e}{\sqrt{\left(2 c^{2} d +2 \sqrt{d \,c^{2} \left(c^{2} d -e \right)}-e \right) e}}\right)}{2 d \,e^{2}}"," ",0,"1/2*c^2*a*x/d/(c^2*e*x^2+c^2*d)+1/2*a/d/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+1/2*c^2*b*arcsinh(c*x)*x/d/(c^2*e*x^2+c^2*d)+1/4*c*b/d*sum(1/_R1/(_R1^2*e+2*c^2*d-e)*(arcsinh(c*x)*ln((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d-2*e)*_Z^2+e))+1/4*c*b/d*sum(_R1/(_R1^2*e+2*c^2*d-e)*(arcsinh(c*x)*ln((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-c*x-(c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(4*c^2*d-2*e)*_Z^2+e))+c^5*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))*d/(c^2*d-e)/e^3+c^3*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))/(c^2*d-e)/e^3*(d*c^2*(c^2*d-e))^(1/2)-c^3*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))/(c^2*d-e)/e^2-1/2*c*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))/d/(c^2*d-e)/e^2*(d*c^2*(c^2*d-e))^(1/2)-c^3*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))/e^3-c*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))/d/e^3*(d*c^2*(c^2*d-e))^(1/2)+1/2*c*b*(-(2*c^2*d-2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctanh((c*x+(c^2*x^2+1)^(1/2))*e/((-2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)+e)*e)^(1/2))/d/e^2+c^5*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))*d/(c^2*d-e)/e^3-c^3*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))/(c^2*d-e)/e^3*(d*c^2*(c^2*d-e))^(1/2)-c^3*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))/(c^2*d-e)/e^2+1/2*c*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))/d/(c^2*d-e)/e^2*(d*c^2*(c^2*d-e))^(1/2)-c^3*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))/e^3+c*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))/d/e^3*(d*c^2*(c^2*d-e))^(1/2)+1/2*c*b*((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2)*arctan((c*x+(c^2*x^2+1)^(1/2))*e/((2*c^2*d+2*(d*c^2*(c^2*d-e))^(1/2)-e)*e)^(1/2))/d/e^2","C"
613,1,1166,499,0.162000," ","int((e*x^2+d)^3*(a+b*arcsinh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{7} e^{3} c^{7} x^{7}+\frac{3}{5} c^{7} d \,e^{2} x^{5}+c^{7} d^{2} e \,x^{3}+x \,c^{7} d^{3}\right)}{c^{6}}+\frac{b^{2} \left(d^{3} c^{6} \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^{4} d^{2} e \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}-3 c^{4} d^{2} e \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{d \,e^{2} c^{2} \left(675 \arcsinh \left(c x \right)^{2} c^{5} x^{5}-270 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4} x^{4}+2250 \arcsinh \left(c x \right)^{2} c^{3} x^{3}+54 c^{5} x^{5}-1140 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2} x^{2}+3375 \arcsinh \left(c x \right)^{2} c x +380 c^{3} x^{3}-4470 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+4470 c x \right)}{1125}-\frac{2 d \,e^{2} c^{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}+3 d \,e^{2} c^{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(55125 \arcsinh \left(c x \right)^{2} c^{7} x^{7}-15750 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{6} x^{6}+231525 \arcsinh \left(c x \right)^{2} c^{5} x^{5}+2250 c^{7} x^{7}-73710 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4} x^{4}+385875 \arcsinh \left(c x \right)^{2} c^{3} x^{3}+14742 c^{5} x^{5}-158970 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2} x^{2}+385875 \arcsinh \left(c x \right)^{2} c x +52990 c^{3} x^{3}-453810 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+453810 c x \right)}{385875}-\frac{e^{3} \left(675 \arcsinh \left(c x \right)^{2} c^{5} x^{5}-270 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4} x^{4}+2250 \arcsinh \left(c x \right)^{2} c^{3} x^{3}+54 c^{5} x^{5}-1140 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2} x^{2}+3375 \arcsinh \left(c x \right)^{2} c x +380 c^{3} x^{3}-4470 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+4470 c x \right)}{1125}+\frac{e^{3} \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}-e^{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)\right)}{c^{6}}+\frac{2 a b \left(\frac{\arcsinh \left(c x \right) e^{3} c^{7} x^{7}}{7}+\frac{3 \arcsinh \left(c x \right) c^{7} d \,e^{2} x^{5}}{5}+\arcsinh \left(c x \right) c^{7} d^{2} e \,x^{3}+\arcsinh \left(c x \right) c^{7} x \,d^{3}-\frac{e^{3} \left(\frac{c^{6} x^{6} \sqrt{c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{35}+\frac{8 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{c^{2} x^{2}+1}}{35}\right)}{7}-\frac{3 c^{2} d \,e^{2} \left(\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{15}+\frac{8 \sqrt{c^{2} x^{2}+1}}{15}\right)}{5}-c^{4} d^{2} e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)-d^{3} c^{6} \sqrt{c^{2} x^{2}+1}\right)}{c^{6}}}{c}"," ",0,"1/c*(a^2/c^6*(1/7*e^3*c^7*x^7+3/5*c^7*d*e^2*x^5+c^7*d^2*e*x^3+x*c^7*d^3)+b^2/c^6*(d^3*c^6*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+1/9*c^4*d^2*e*(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)-3*c^4*d^2*e*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+1/1125*d*e^2*c^2*(675*arcsinh(c*x)^2*c^5*x^5-270*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4*x^4+2250*arcsinh(c*x)^2*c^3*x^3+54*c^5*x^5-1140*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2*x^2+3375*arcsinh(c*x)^2*c*x+380*c^3*x^3-4470*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+4470*c*x)-2/9*d*e^2*c^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)+3*d*e^2*c^2*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+1/385875*e^3*(55125*arcsinh(c*x)^2*c^7*x^7-15750*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^6*x^6+231525*arcsinh(c*x)^2*c^5*x^5+2250*c^7*x^7-73710*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4*x^4+385875*arcsinh(c*x)^2*c^3*x^3+14742*c^5*x^5-158970*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2*x^2+385875*arcsinh(c*x)^2*c*x+52990*c^3*x^3-453810*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+453810*c*x)-1/1125*e^3*(675*arcsinh(c*x)^2*c^5*x^5-270*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4*x^4+2250*arcsinh(c*x)^2*c^3*x^3+54*c^5*x^5-1140*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2*x^2+3375*arcsinh(c*x)^2*c*x+380*c^3*x^3-4470*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+4470*c*x)+1/9*e^3*(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^3*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x))+2*a*b/c^6*(1/7*arcsinh(c*x)*e^3*c^7*x^7+3/5*arcsinh(c*x)*c^7*d*e^2*x^5+arcsinh(c*x)*c^7*d^2*e*x^3+arcsinh(c*x)*c^7*x*d^3-1/7*e^3*(1/7*c^6*x^6*(c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(c^2*x^2+1)^(1/2)+8/35*c^2*x^2*(c^2*x^2+1)^(1/2)-16/35*(c^2*x^2+1)^(1/2))-3/5*c^2*d*e^2*(1/5*c^4*x^4*(c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(c^2*x^2+1)^(1/2)+8/15*(c^2*x^2+1)^(1/2))-c^4*d^2*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-d^3*c^6*(c^2*x^2+1)^(1/2)))","B"
614,1,620,293,0.105000," ","int((e*x^2+d)^2*(a+b*arcsinh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} d e \,x^{3}+x \,c^{5} d^{2}\right)}{c^{4}}+\frac{b^{2} \left(d^{2} c^{4} \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{2 c^{2} d e \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}-2 c^{2} d e \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^{2} \left(675 \arcsinh \left(c x \right)^{2} c^{5} x^{5}-270 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{4} x^{4}+2250 \arcsinh \left(c x \right)^{2} c^{3} x^{3}+54 c^{5} x^{5}-1140 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}\, c^{2} x^{2}+3375 \arcsinh \left(c x \right)^{2} c x +380 c^{3} x^{3}-4470 \arcsinh \left(c x \right) \sqrt{c^{2} x^{2}+1}+4470 c x \right)}{3375}-\frac{2 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^{4}}+\frac{2 a b \left(\frac{\arcsinh \left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \arcsinh \left(c x \right) c^{5} d e \,x^{3}}{3}+\arcsinh \left(c x \right) c^{5} x \,d^{2}-\frac{e^{2} \left(\frac{c^{4} x^{4} \sqrt{c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{15}+\frac{8 \sqrt{c^{2} x^{2}+1}}{15}\right)}{5}-\frac{2 c^{2} d e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)}{3}-d^{2} c^{4} \sqrt{c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a^2/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*d*e*x^3+x*c^5*d^2)+b^2/c^4*(d^2*c^4*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+2/27*c^2*d*e*(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)-2*c^2*d*e*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+1/3375*e^2*(675*arcsinh(c*x)^2*c^5*x^5-270*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^4*x^4+2250*arcsinh(c*x)^2*c^3*x^3+54*c^5*x^5-1140*arcsinh(c*x)*(c^2*x^2+1)^(1/2)*c^2*x^2+3375*arcsinh(c*x)^2*c*x+380*c^3*x^3-4470*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+4470*c*x)-2/27*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^4*(1/5*arcsinh(c*x)*e^2*c^5*x^5+2/3*arcsinh(c*x)*c^5*d*e*x^3+arcsinh(c*x)*c^5*x*d^2-1/5*e^2*(1/5*c^4*x^4*(c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(c^2*x^2+1)^(1/2)+8/15*(c^2*x^2+1)^(1/2))-2/3*c^2*d*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-d^2*c^4*(c^2*x^2+1)^(1/2)))","B"
615,1,271,137,0.089000," ","int((e*x^2+d)*(a+b*arcsinh(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{3} c^{3} x^{3} e +c^{3} d x \right)}{c^{2}}+\frac{b^{2} \left(c^{2} 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)+\frac{e \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 \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{\arcsinh \left(c x \right) c^{3} x^{3} e}{3}+\arcsinh \left(c x \right) c^{3} d x -\frac{e \left(\frac{c^{2} x^{2} \sqrt{c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{c^{2} x^{2}+1}}{3}\right)}{3}-c^{2} d \sqrt{c^{2} x^{2}+1}\right)}{c^{2}}}{c}"," ",0,"1/c*(a^2/c^2*(1/3*c^3*x^3*e+c^3*d*x)+b^2/c^2*(c^2*d*(arcsinh(c*x)^2*c*x-2*arcsinh(c*x)*(c^2*x^2+1)^(1/2)+2*c*x)+1/27*e*(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*(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*arcsinh(c*x)*c^3*x^3*e+arcsinh(c*x)*c^3*d*x-1/3*e*(1/3*c^2*x^2*(c^2*x^2+1)^(1/2)-2/3*(c^2*x^2+1)^(1/2))-c^2*d*(c^2*x^2+1)^(1/2)))","A"
616,1,72,44,0.050000," ","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"
617,0,0,719,0.409000," ","int((a+b*arcsinh(c*x))^2/(e*x^2+d),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(e*x^2+d),x)","F"
618,1,654,634,0.474000," ","int((e*x^2+d)^3/(a+b*arcsinh(c*x)),x)","\frac{-\frac{e^{3} {\mathrm e}^{-\frac{7 a}{b}} \Ei \left(1, -7 \arcsinh \left(c x \right)-\frac{7 a}{b}\right)}{128 c^{6} b}-\frac{e^{3} {\mathrm e}^{\frac{7 a}{b}} \Ei \left(1, 7 \arcsinh \left(c x \right)+\frac{7 a}{b}\right)}{128 c^{6} 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 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) d^{2} e}{8 c^{2} b}-\frac{3 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) d \,e^{2}}{16 c^{4} b}+\frac{5 \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) e^{3}}{128 c^{6} 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 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) d^{2} e}{8 c^{2} b}-\frac{3 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) d \,e^{2}}{16 c^{4} b}+\frac{5 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) e^{3}}{128 c^{6} b}-\frac{3 e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right) d^{2}}{8 c^{2} b}+\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right) d}{32 c^{4} b}-\frac{9 e^{3} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{128 c^{6} b}-\frac{3 e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) d^{2}}{8 c^{2} b}+\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) d}{32 c^{4} b}-\frac{9 e^{3} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{128 c^{6} b}-\frac{3 e^{2} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right) d}{32 c^{4} b}+\frac{5 e^{3} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{128 c^{6} b}-\frac{3 e^{2} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right) d}{32 c^{4} b}+\frac{5 e^{3} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{128 c^{6} b}}{c}"," ",0,"1/c*(-1/128/c^6*e^3/b*exp(-7*a/b)*Ei(1,-7*arcsinh(c*x)-7*a/b)-1/128/c^6*e^3/b*exp(7*a/b)*Ei(1,7*arcsinh(c*x)+7*a/b)-1/2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d^3+3/8/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d^2*e-3/16/c^4/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d*e^2+5/128/c^6/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*e^3-1/2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d^3+3/8/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d^2*e-3/16/c^4/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d*e^2+5/128/c^6/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*e^3-3/8/c^2*e/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)*d^2+9/32/c^4*e^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)*d-9/128/c^6*e^3/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-3/8/c^2*e/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*d^2+9/32/c^4*e^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*d-9/128/c^6*e^3/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-3/32/c^4*e^2/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)*d+5/128/c^6*e^3/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-3/32/c^4*e^2/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)*d+5/128/c^6*e^3/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b))","A"
619,1,380,368,0.292000," ","int((e*x^2+d)^2/(a+b*arcsinh(c*x)),x)","\frac{-\frac{e^{2} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{32 c^{4} b}-\frac{e^{2} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{4} 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) d e}{4 c^{2} b}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) e^{2}}{16 c^{4} 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) d e}{4 c^{2} b}-\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right) e^{2}}{16 c^{4} b}-\frac{e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right) d}{4 c^{2} b}+\frac{3 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{4} b}-\frac{e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) d}{4 c^{2} b}+\frac{3 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{32 c^{4} b}}{c}"," ",0,"1/c*(-1/32/c^4*e^2/b*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*a/b)-1/32/c^4*e^2/b*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-1/2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d^2+1/4/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*d*e-1/16/c^4/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+1/4/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d*e-1/16/c^4/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*e^2-1/4/c^2*e/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)*d+3/32/c^4*e^2/b*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/4/c^2*e/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*d+3/32/c^4*e^2/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b))","A"
620,1,178,172,0.201000," ","int((e*x^2+d)/(a+b*arcsinh(c*x)),x)","\frac{-\frac{e \,{\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 \,{\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 b}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right) e}{8 c^{2} b}-\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) e}{8 c^{2} b}}{c}"," ",0,"1/c*(-1/8/c^2*e/b*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)-1/8/c^2*e/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+1/8/c^2/b*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)*e-1/2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*d+1/8/c^2/b*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)*e)","A"
621,1,56,54,0.033000," ","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"
622,0,0,22,0.270000," ","int(1/(e*x^2+d)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsinh(c*x)),x)","F"
623,0,0,22,0.500000," ","int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x)),x)","F"
624,1,1036,469,0.398000," ","int((e*x^2+d)^2/(a+b*arcsinh(c*x))^2,x)","\frac{\frac{\left(16 c^{5} x^{5}-16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+20 c^{3} x^{3}-12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+5 c x -\sqrt{c^{2} x^{2}+1}\right) e^{2}}{32 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{5 e^{2} {\mathrm e}^{\frac{5 a}{b}} \Ei \left(1, 5 \arcsinh \left(c x \right)+\frac{5 a}{b}\right)}{32 c^{4} b^{2}}-\frac{e^{2} \left(16 c^{5} x^{5}+20 c^{3} x^{3}+16 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+5 c x +12 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+\sqrt{c^{2} x^{2}+1}\right)}{32 b \,c^{4} \left(a +b \arcsinh \left(c x \right)\right)}-\frac{5 e^{2} {\mathrm e}^{-\frac{5 a}{b}} \Ei \left(1, -5 \arcsinh \left(c x \right)-\frac{5 a}{b}\right)}{32 b^{2} c^{4}}+\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) d e}{4 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{d e \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{4 c^{2} b^{2}}+\frac{\left(c x -\sqrt{c^{2} x^{2}+1}\right) e^{2}}{16 c^{4} 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)}{16 c^{4} 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{d e \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{4 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{d e \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{4 c^{2} b^{2}}-\frac{e^{2} \left(c x +\sqrt{c^{2} x^{2}+1}\right)}{16 c^{4} 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)}{16 c^{4} b^{2}}+\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) d e}{4 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 \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}}{32 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 e \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right) d}{4 c^{2} b^{2}}-\frac{9 e^{2} {\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, 3 \arcsinh \left(c x \right)+\frac{3 a}{b}\right)}{32 c^{4} b^{2}}-\frac{e \left(4 c^{3} x^{3}+3 c x +4 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+\sqrt{c^{2} x^{2}+1}\right) d}{4 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 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)}{32 c^{4} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{3 e \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right) d}{4 c^{2} b^{2}}+\frac{9 e^{2} {\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \arcsinh \left(c x \right)-\frac{3 a}{b}\right)}{32 c^{4} b^{2}}}{c}"," ",0,"1/c*(1/32*(16*c^5*x^5-16*c^4*x^4*(c^2*x^2+1)^(1/2)+20*c^3*x^3-12*c^2*x^2*(c^2*x^2+1)^(1/2)+5*c*x-(c^2*x^2+1)^(1/2))*e^2/c^4/b/(a+b*arcsinh(c*x))+5/32*e^2/c^4/b^2*exp(5*a/b)*Ei(1,5*arcsinh(c*x)+5*a/b)-1/32/b*e^2/c^4*(16*c^5*x^5+20*c^3*x^3+16*c^4*x^4*(c^2*x^2+1)^(1/2)+5*c*x+12*c^2*x^2*(c^2*x^2+1)^(1/2)+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-5/32/b^2*e^2/c^4*exp(-5*a/b)*Ei(1,-5*arcsinh(c*x)-5*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)-1/4*(c*x-(c^2*x^2+1)^(1/2))*d*e/c^2/b/(a+b*arcsinh(c*x))-1/4/c^2*d*e/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)+1/16*(c*x-(c^2*x^2+1)^(1/2))*e^2/c^4/b/(a+b*arcsinh(c*x))+1/16/c^4*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)+1/4/c^2/b*d*e*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))+1/4/c^2/b^2*d*e*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)-1/16/c^4/b*e^2*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))-1/16/c^4/b^2*e^2*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b)+1/4*(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))*d*e/c^2/b/(a+b*arcsinh(c*x))-3/32*(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^4/b/(a+b*arcsinh(c*x))+3/4*e/c^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)*d-9/32*e^2/c^4/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/4/c^2*e/b*(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))*d+3/32/c^4*e^2/b*(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))-3/4/c^2*e/b^2*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b)*d+9/32/c^4*e^2/b^2*exp(-3*a/b)*Ei(1,-3*arcsinh(c*x)-3*a/b))","B"
625,1,438,235,0.250000," ","int((e*x^2+d)/(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}{8 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}+\frac{3 e \,{\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 \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 \,{\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 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(c x -\sqrt{c^{2} x^{2}+1}\right) e}{8 c^{2} b \left(a +b \arcsinh \left(c x \right)\right)}-\frac{e \,{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \arcsinh \left(c x \right)+\frac{a}{b}\right)}{8 c^{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{e \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 \,{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\arcsinh \left(c x \right)-\frac{a}{b}\right)}{8 c^{2} b^{2}}}{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/c^2/b/(a+b*arcsinh(c*x))+3/8*e/c^2/b^2*exp(3*a/b)*Ei(1,3*arcsinh(c*x)+3*a/b)-1/8/b*e/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/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/b/(a+b*arcsinh(c*x))+1/2*d/b^2*exp(a/b)*Ei(1,arcsinh(c*x)+a/b)-1/8*(c*x-(c^2*x^2+1)^(1/2))*e/c^2/b/(a+b*arcsinh(c*x))-1/8/c^2*e/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)+1/8/c^2/b*e*(c*x+(c^2*x^2+1)^(1/2))/(a+b*arcsinh(c*x))+1/8/c^2/b^2*e*exp(-a/b)*Ei(1,-arcsinh(c*x)-a/b))","A"
626,1,118,83,0.047000," ","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"
627,0,0,22,0.268000," ","int(1/(e*x^2+d)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsinh(c*x))^2,x)","F"
628,0,0,22,0.556000," ","int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^2,x)","F"
629,-2,0,521,180.000000," ","int((e*x^2+d)^2*(a+b*arcsinh(c*x))^(1/2),x)","\int \left(e \,x^{2}+d \right)^{2} \sqrt{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int((e*x^2+d)^2*(a+b*arcsinh(c*x))^(1/2),x)","F"
630,-2,0,248,180.000000," ","int((e*x^2+d)*(a+b*arcsinh(c*x))^(1/2),x)","\int \left(e \,x^{2}+d \right) \sqrt{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int((e*x^2+d)*(a+b*arcsinh(c*x))^(1/2),x)","F"
631,0,0,79,0.060000," ","int((a+b*arcsinh(c*x))^(1/2),x)","\int \sqrt{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int((a+b*arcsinh(c*x))^(1/2),x)","F"
632,0,0,22,0.401000," ","int((a+b*arcsinh(c*x))^(1/2)/(e*x^2+d),x)","\int \frac{\sqrt{a +b \arcsinh \left(c x \right)}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^(1/2)/(e*x^2+d),x)","F"
633,0,0,22,0.934000," ","int((a+b*arcsinh(c*x))^(1/2)/(e*x^2+d)^2,x)","\int \frac{\sqrt{a +b \arcsinh \left(c x \right)}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^(1/2)/(e*x^2+d)^2,x)","F"
634,-2,0,335,180.000000," ","int((e*x^2+d)*(a+b*arcsinh(c*x))^(3/2),x)","\int \left(e \,x^{2}+d \right) \left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((e*x^2+d)*(a+b*arcsinh(c*x))^(3/2),x)","F"
635,0,0,106,0.066000," ","int((a+b*arcsinh(c*x))^(3/2),x)","\int \left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^(3/2),x)","F"
636,0,0,22,0.394000," ","int((a+b*arcsinh(c*x))^(3/2)/(e*x^2+d),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^(3/2)/(e*x^2+d),x)","F"
637,0,0,22,0.947000," ","int((a+b*arcsinh(c*x))^(3/2)/(e*x^2+d)^2,x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^(3/2)/(e*x^2+d)^2,x)","F"
638,-2,0,471,180.000000," ","int((e*x^2+d)^2/(a+b*arcsinh(c*x))^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right)^{2}}{\sqrt{a +b \arcsinh \left(c x \right)}}\, dx"," ",0,"int((e*x^2+d)^2/(a+b*arcsinh(c*x))^(1/2),x)","F"
639,-2,0,219,180.000000," ","int((e*x^2+d)/(a+b*arcsinh(c*x))^(1/2),x)","\int \frac{e \,x^{2}+d}{\sqrt{a +b \arcsinh \left(c x \right)}}\, dx"," ",0,"int((e*x^2+d)/(a+b*arcsinh(c*x))^(1/2),x)","F"
640,0,0,67,0.062000," ","int(1/(a+b*arcsinh(c*x))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsinh \left(c x \right)}}\, dx"," ",0,"int(1/(a+b*arcsinh(c*x))^(1/2),x)","F"
641,0,0,22,0.397000," ","int(1/(e*x^2+d)/(a+b*arcsinh(c*x))^(1/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \sqrt{a +b \arcsinh \left(c x \right)}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsinh(c*x))^(1/2),x)","F"
642,0,0,22,0.907000," ","int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^(1/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \sqrt{a +b \arcsinh \left(c x \right)}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^(1/2),x)","F"
643,-2,0,281,180.000000," ","int((e*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{e \,x^{2}+d}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","F"
644,0,0,95,0.059000," ","int(1/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsinh(c*x))^(3/2),x)","F"
645,0,0,22,0.393000," ","int(1/(e*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x)","F"
646,0,0,22,0.923000," ","int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \arcsinh \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x)","F"
647,0,0,20,0.464000," ","int((a+b*arcsinh(c*x))*(e*x^2+d)^(1/2),x)","\int \left(a +b \arcsinh \left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))*(e*x^2+d)^(1/2),x)","F"
648,0,0,20,0.437000," ","int((a+b*arcsinh(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(e*x^2+d)^(1/2),x)","F"
649,0,0,60,0.349000," ","int((a+b*arcsinh(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(e*x^2+d)^(3/2),x)","F"
650,0,0,122,0.378000," ","int((a+b*arcsinh(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(e*x^2+d)^(5/2),x)","F"
651,0,0,193,0.381000," ","int((a+b*arcsinh(c*x))/(e*x^2+d)^(7/2),x)","\int \frac{a +b \arcsinh \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))/(e*x^2+d)^(7/2),x)","F"
652,0,0,22,0.265000," ","int((a+b*arcsinh(c*x))^2*(e*x^2+d)^(1/2),x)","\int \left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2*(e*x^2+d)^(1/2),x)","F"
653,0,0,22,0.320000," ","int((a+b*arcsinh(c*x))^2/(e*x^2+d)^(1/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(e*x^2+d)^(1/2),x)","F"
654,0,0,22,0.284000," ","int((a+b*arcsinh(c*x))^2/(e*x^2+d)^(3/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(e*x^2+d)^(3/2),x)","F"
655,0,0,22,0.290000," ","int((a+b*arcsinh(c*x))^2/(e*x^2+d)^(5/2),x)","\int \frac{\left(a +b \arcsinh \left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsinh(c*x))^2/(e*x^2+d)^(5/2),x)","F"
656,0,0,22,0.217000," ","int((e*x^2+d)^(1/2)/(a+b*arcsinh(c*x)),x)","\int \frac{\sqrt{e \,x^{2}+d}}{a +b \arcsinh \left(c x \right)}\, dx"," ",0,"int((e*x^2+d)^(1/2)/(a+b*arcsinh(c*x)),x)","F"
657,0,0,22,0.254000," ","int(1/(a+b*arcsinh(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(c x \right)\right) \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(1/(a+b*arcsinh(c*x))/(e*x^2+d)^(1/2),x)","F"
658,0,0,22,0.234000," ","int(1/(e*x^2+d)^(3/2)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(3/2)/(a+b*arcsinh(c*x)),x)","F"
659,0,0,22,0.249000," ","int(1/(e*x^2+d)^(5/2)/(a+b*arcsinh(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(5/2)/(a+b*arcsinh(c*x)),x)","F"
660,0,0,22,0.232000," ","int((e*x^2+d)^(1/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{\sqrt{e \,x^{2}+d}}{\left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int((e*x^2+d)^(1/2)/(a+b*arcsinh(c*x))^2,x)","F"
661,0,0,22,0.260000," ","int(1/(a+b*arcsinh(c*x))^2/(e*x^2+d)^(1/2),x)","\int \frac{1}{\left(a +b \arcsinh \left(c x \right)\right)^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(1/(a+b*arcsinh(c*x))^2/(e*x^2+d)^(1/2),x)","F"
662,0,0,22,0.244000," ","int(1/(e*x^2+d)^(3/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(3/2)/(a+b*arcsinh(c*x))^2,x)","F"
663,0,0,22,0.256000," ","int(1/(e*x^2+d)^(5/2)/(a+b*arcsinh(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsinh \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(5/2)/(a+b*arcsinh(c*x))^2,x)","F"