1,1,184,0,0.360943," ","integrate(x^4*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{2} d x^{7} + \frac{1}{5} \, a d x^{5} + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{2} d + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d"," ",0,"1/7*a*c^2*d*x^7 + 1/5*a*d*x^5 + 1/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*c^2*d + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*d","A",0
2,1,166,0,0.359633," ","integrate(x^3*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{2} d x^{6} + \frac{1}{4} \, a d x^{4} + \frac{1}{288} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} b c^{2} d + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} b d"," ",0,"1/6*a*c^2*d*x^6 + 1/4*a*d*x^4 + 1/288*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*b*c^2*d + 1/32*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*b*d","A",0
3,1,145,0,0.441801," ","integrate(x^2*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{2} d x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{2} d + \frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d"," ",0,"1/5*a*c^2*d*x^5 + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*c^2*d + 1/3*a*d*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*d","A",0
4,1,127,0,0.529963," ","integrate(x*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a c^{2} d x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} b c^{2} d + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)}\right)} b d"," ",0,"1/4*a*c^2*d*x^4 + 1/32*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*b*c^2*d + 1/2*a*d*x^2 + 1/4*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*b*d","A",0
5,1,97,0,0.481576," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a c^{2} d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{2} d + a d x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d}{c}"," ",0,"1/3*a*c^2*d*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*c^2*d + a*d*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d/c","A",0
6,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a c^{2} d x^{2} + a d \log\left(x\right) + \int b c^{2} d x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{b d \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/2*a*c^2*d*x^2 + a*d*log(x) + integrate(b*c^2*d*x*log(c*x + sqrt(c^2*x^2 + 1)) + b*d*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
7,1,64,0,0.513038," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","a c^{2} d x + {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b c d - {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} b d - \frac{a d}{x}"," ",0,"a*c^2*d*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*c*d - (c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*b*d - a*d/x","A",0
8,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","b c^{2} d \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x} + a c^{2} d \log\left(x\right) - \frac{1}{2} \, b d {\left(\frac{\sqrt{c^{2} x^{2} + 1} c}{x} + \frac{\operatorname{arsinh}\left(c x\right)}{x^{2}}\right)} - \frac{a d}{2 \, x^{2}}"," ",0,"b*c^2*d*integrate(log(c*x + sqrt(c^2*x^2 + 1))/x, x) + a*c^2*d*log(x) - 1/2*b*d*(sqrt(c^2*x^2 + 1)*c/x + arcsinh(c*x)/x^2) - 1/2*a*d/x^2","F",0
9,1,91,0,0.339152," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","-{\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} b c^{2} d + \frac{1}{6} \, {\left({\left(c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \operatorname{arsinh}\left(c x\right)}{x^{3}}\right)} b d - \frac{a c^{2} d}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"-(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*b*c^2*d + 1/6*((c^2*arcsinh(1/(c*abs(x))) - sqrt(c^2*x^2 + 1)/x^2)*c - 2*arcsinh(c*x)/x^3)*b*d - a*c^2*d/x - 1/3*a*d/x^3","A",0
10,1,319,0,0.569895," ","integrate(x^4*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a c^{4} d^{2} x^{9} + \frac{2}{7} \, a c^{2} d^{2} x^{7} + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{5} \, a d^{2} x^{5} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2}"," ",0,"1/9*a*c^4*d^2*x^9 + 2/7*a*c^2*d^2*x^7 + 1/2835*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*b*c^4*d^2 + 1/5*a*d^2*x^5 + 2/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*c^2*d^2 + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*d^2","B",0
11,1,292,0,0.623122," ","integrate(x^3*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a c^{4} d^{2} x^{8} + \frac{1}{3} \, a c^{2} d^{2} x^{6} + \frac{1}{3072} \, {\left(384 \, x^{8} \operatorname{arsinh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{4} \, a d^{2} x^{4} + \frac{1}{144} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2}"," ",0,"1/8*a*c^4*d^2*x^8 + 1/3*a*c^2*d^2*x^6 + 1/3072*(384*x^8*arcsinh(c*x) - (48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c)*b*c^4*d^2 + 1/4*a*d^2*x^4 + 1/144*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*b*c^2*d^2 + 1/32*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*b*d^2","A",0
12,1,261,0,0.549230," ","integrate(x^2*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{4} d^{2} x^{7} + \frac{2}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{4} d^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2}"," ",0,"1/7*a*c^4*d^2*x^7 + 2/5*a*c^2*d^2*x^5 + 1/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*c^4*d^2 + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*c^2*d^2 + 1/3*a*d^2*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*d^2","A",0
13,1,234,0,0.478063," ","integrate(x*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{4} d^{2} x^{6} + \frac{1}{2} \, a c^{2} d^{2} x^{4} + \frac{1}{288} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)}\right)} b d^{2}"," ",0,"1/6*a*c^4*d^2*x^6 + 1/2*a*c^2*d^2*x^4 + 1/288*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*b*c^4*d^2 + 1/16*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*b*c^2*d^2 + 1/2*a*d^2*x^2 + 1/4*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*b*d^2","B",0
14,1,194,0,0.325310," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{4} d^{2} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{4} d^{2} + \frac{2}{3} \, a c^{2} d^{2} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{2} d^{2} + a d^{2} x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d^{2}}{c}"," ",0,"1/5*a*c^4*d^2*x^5 + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*c^4*d^2 + 2/3*a*c^2*d^2*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*c^2*d^2 + a*d^2*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^2/c","A",0
15,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a c^{4} d^{2} x^{4} + a c^{2} d^{2} x^{2} + a d^{2} \log\left(x\right) + \int b c^{4} d^{2} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, b c^{2} d^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{b d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/4*a*c^4*d^2*x^4 + a*c^2*d^2*x^2 + a*d^2*log(x) + integrate(b*c^4*d^2*x^3*log(c*x + sqrt(c^2*x^2 + 1)) + 2*b*c^2*d^2*x*log(c*x + sqrt(c^2*x^2 + 1)) + b*d^2*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
16,1,143,0,0.473852," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{4} d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{4} d^{2} + 2 \, a c^{2} d^{2} x + 2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b c d^{2} - {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} b d^{2} - \frac{a d^{2}}{x}"," ",0,"1/3*a*c^4*d^2*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*c^4*d^2 + 2*a*c^2*d^2*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*c*d^2 - (c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*b*d^2 - a*d^2/x","A",0
17,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a c^{4} d^{2} x^{2} + 2 \, a c^{2} d^{2} \log\left(x\right) - \frac{1}{2} \, b d^{2} {\left(\frac{\sqrt{c^{2} x^{2} + 1} c}{x} + \frac{\operatorname{arsinh}\left(c x\right)}{x^{2}}\right)} - \frac{a d^{2}}{2 \, x^{2}} + \int b c^{4} d^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{2 \, b c^{2} d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/2*a*c^4*d^2*x^2 + 2*a*c^2*d^2*log(x) - 1/2*b*d^2*(sqrt(c^2*x^2 + 1)*c/x + arcsinh(c*x)/x^2) - 1/2*a*d^2/x^2 + integrate(b*c^4*d^2*x*log(c*x + sqrt(c^2*x^2 + 1)) + 2*b*c^2*d^2*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
18,1,137,0,0.450486," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","a c^{4} d^{2} x + {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b c^{3} d^{2} - 2 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} b c^{2} d^{2} + \frac{1}{6} \, {\left({\left(c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \operatorname{arsinh}\left(c x\right)}{x^{3}}\right)} b d^{2} - \frac{2 \, a c^{2} d^{2}}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"a*c^4*d^2*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*c^3*d^2 - 2*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*b*c^2*d^2 + 1/6*((c^2*arcsinh(1/(c*abs(x))) - sqrt(c^2*x^2 + 1)/x^2)*c - 2*arcsinh(c*x)/x^3)*b*d^2 - 2*a*c^2*d^2/x - 1/3*a*d^2/x^3","A",0
19,1,465,0,0.487467," ","integrate(x^4*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{11} \, a c^{6} d^{3} x^{11} + \frac{1}{3} \, a c^{4} d^{3} x^{9} + \frac{3}{7} \, a c^{2} d^{3} x^{7} + \frac{1}{7623} \, {\left(693 \, x^{11} \operatorname{arsinh}\left(c x\right) - {\left(\frac{63 \, \sqrt{c^{2} x^{2} + 1} x^{10}}{c^{2}} - \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{6}} - \frac{96 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{10}} - \frac{256 \, \sqrt{c^{2} x^{2} + 1}}{c^{12}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{945} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{5} \, a d^{3} x^{5} + \frac{3}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{3}"," ",0,"1/11*a*c^6*d^3*x^11 + 1/3*a*c^4*d^3*x^9 + 3/7*a*c^2*d^3*x^7 + 1/7623*(693*x^11*arcsinh(c*x) - (63*sqrt(c^2*x^2 + 1)*x^10/c^2 - 70*sqrt(c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(c^2*x^2 + 1)*x^6/c^6 - 96*sqrt(c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(c^2*x^2 + 1)*x^2/c^10 - 256*sqrt(c^2*x^2 + 1)/c^12)*c)*b*c^6*d^3 + 1/945*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*b*c^4*d^3 + 1/5*a*d^3*x^5 + 3/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*c^2*d^3 + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*d^3","B",0
20,1,429,0,0.396898," ","integrate(x^3*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{10} \, a c^{6} d^{3} x^{10} + \frac{3}{8} \, a c^{4} d^{3} x^{8} + \frac{1}{2} \, a c^{2} d^{3} x^{6} + \frac{1}{12800} \, {\left(1280 \, x^{10} \operatorname{arsinh}\left(c x\right) - {\left(\frac{128 \, \sqrt{c^{2} x^{2} + 1} x^{9}}{c^{2}} - \frac{144 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{6}} - \frac{210 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{c^{2} x^{2} + 1} x}{c^{10}} - \frac{315 \, \operatorname{arsinh}\left(c x\right)}{c^{11}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{1024} \, {\left(384 \, x^{8} \operatorname{arsinh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{4} \, a d^{3} x^{4} + \frac{1}{96} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} b d^{3}"," ",0,"1/10*a*c^6*d^3*x^10 + 3/8*a*c^4*d^3*x^8 + 1/2*a*c^2*d^3*x^6 + 1/12800*(1280*x^10*arcsinh(c*x) - (128*sqrt(c^2*x^2 + 1)*x^9/c^2 - 144*sqrt(c^2*x^2 + 1)*x^7/c^4 + 168*sqrt(c^2*x^2 + 1)*x^5/c^6 - 210*sqrt(c^2*x^2 + 1)*x^3/c^8 + 315*sqrt(c^2*x^2 + 1)*x/c^10 - 315*arcsinh(c*x)/c^11)*c)*b*c^6*d^3 + 1/1024*(384*x^8*arcsinh(c*x) - (48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c)*b*c^4*d^3 + 1/4*a*d^3*x^4 + 1/96*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*b*c^2*d^3 + 1/32*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*b*d^3","B",0
21,1,388,0,0.642211," ","integrate(x^2*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a c^{6} d^{3} x^{9} + \frac{3}{7} \, a c^{4} d^{3} x^{7} + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b c^{6} d^{3} + \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{3}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3}"," ",0,"1/9*a*c^6*d^3*x^9 + 3/7*a*c^4*d^3*x^7 + 1/2835*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*b*c^6*d^3 + 3/5*a*c^2*d^3*x^5 + 3/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*c^4*d^3 + 1/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*c^2*d^3 + 1/3*a*d^3*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*d^3","B",0
22,1,352,0,0.468777," ","integrate(x*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a c^{6} d^{3} x^{8} + \frac{1}{2} \, a c^{4} d^{3} x^{6} + \frac{1}{3072} \, {\left(384 \, x^{8} \operatorname{arsinh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c\right)} b c^{6} d^{3} + \frac{3}{4} \, a c^{2} d^{3} x^{4} + \frac{1}{96} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} b c^{4} d^{3} + \frac{3}{32} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{2} \, a d^{3} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)}\right)} b d^{3}"," ",0,"1/8*a*c^6*d^3*x^8 + 1/2*a*c^4*d^3*x^6 + 1/3072*(384*x^8*arcsinh(c*x) - (48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c)*b*c^6*d^3 + 3/4*a*c^2*d^3*x^4 + 1/96*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*b*c^4*d^3 + 3/32*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*b*c^2*d^3 + 1/2*a*d^3*x^2 + 1/4*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*b*d^3","B",0
23,1,301,0,0.554736," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{6} d^{3} x^{7} + \frac{3}{5} \, a c^{4} d^{3} x^{5} + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{4} d^{3} + a c^{2} d^{3} x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{2} d^{3} + a d^{3} x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d^{3}}{c}"," ",0,"1/7*a*c^6*d^3*x^7 + 3/5*a*c^4*d^3*x^5 + 1/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*c^6*d^3 + 1/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*c^4*d^3 + a*c^2*d^3*x^3 + 1/3*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*c^2*d^3 + a*d^3*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^3/c","B",0
24,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{6} \, a c^{6} d^{3} x^{6} + \frac{3}{4} \, a c^{4} d^{3} x^{4} + \frac{3}{2} \, a c^{2} d^{3} x^{2} + a d^{3} \log\left(x\right) + \int b c^{6} d^{3} x^{5} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3 \, b c^{4} d^{3} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3 \, b c^{2} d^{3} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{b d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/6*a*c^6*d^3*x^6 + 3/4*a*c^4*d^3*x^4 + 3/2*a*c^2*d^3*x^2 + a*d^3*log(x) + integrate(b*c^6*d^3*x^5*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b*c^4*d^3*x^3*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b*c^2*d^3*x*log(c*x + sqrt(c^2*x^2 + 1)) + b*d^3*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
25,1,231,0,0.483922," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, a c^{6} d^{3} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{6} d^{3} + a c^{4} d^{3} x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{4} d^{3} + 3 \, a c^{2} d^{3} x + 3 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b c d^{3} - {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} b d^{3} - \frac{a d^{3}}{x}"," ",0,"1/5*a*c^6*d^3*x^5 + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*c^6*d^3 + a*c^4*d^3*x^3 + 1/3*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*c^4*d^3 + 3*a*c^2*d^3*x + 3*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*c*d^3 - (c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*b*d^3 - a*d^3/x","A",0
26,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a c^{6} d^{3} x^{4} + \frac{3}{2} \, a c^{4} d^{3} x^{2} + 3 \, a c^{2} d^{3} \log\left(x\right) - \frac{1}{2} \, b d^{3} {\left(\frac{\sqrt{c^{2} x^{2} + 1} c}{x} + \frac{\operatorname{arsinh}\left(c x\right)}{x^{2}}\right)} - \frac{a d^{3}}{2 \, x^{2}} + \int b c^{6} d^{3} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3 \, b c^{4} d^{3} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{3 \, b c^{2} d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/4*a*c^6*d^3*x^4 + 3/2*a*c^4*d^3*x^2 + 3*a*c^2*d^3*log(x) - 1/2*b*d^3*(sqrt(c^2*x^2 + 1)*c/x + arcsinh(c*x)/x^2) - 1/2*a*d^3/x^2 + integrate(b*c^6*d^3*x^3*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b*c^4*d^3*x*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b*c^2*d^3*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
27,1,208,0,0.453142," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{6} d^{3} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{6} d^{3} + 3 \, a c^{4} d^{3} x + 3 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b c^{3} d^{3} - 3 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} b c^{2} d^{3} + \frac{1}{6} \, {\left({\left(c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \operatorname{arsinh}\left(c x\right)}{x^{3}}\right)} b d^{3} - \frac{3 \, a c^{2} d^{3}}{x} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"1/3*a*c^6*d^3*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*c^6*d^3 + 3*a*c^4*d^3*x + 3*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*c^3*d^3 - 3*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*b*c^2*d^3 + 1/6*((c^2*arcsinh(1/(c*abs(x))) - sqrt(c^2*x^2 + 1)/x^2)*c - 2*arcsinh(c*x)/x^3)*b*d^3 - 3*a*c^2*d^3/x - 1/3*a*d^3/x^3","A",0
28,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4} d} + \frac{3 \, \arctan\left(c x\right)}{c^{5} d}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{2} + d}\,{d x}"," ",0,"1/3*a*((c^2*x^3 - 3*x)/(c^4*d) + 3*arctan(c*x)/(c^5*d)) + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d), x)","F",0
29,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x^{2}}{c^{2} d} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d}\right)} - \frac{1}{8} \, b {\left(\frac{2 \, c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, {\left(c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) - 2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{4} d} - 8 \, \int -\frac{c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)}{2 \, {\left(c^{6} d x^{3} + c^{4} d x + {\left(c^{5} d x^{2} + c^{3} d\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)}"," ",0,"1/2*a*(x^2/(c^2*d) - log(c^2*x^2 + 1)/(c^4*d)) - 1/8*b*((2*c^2*x^2 - log(c^2*x^2 + 1)^2 - 4*(c^2*x^2 - log(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) - 2*log(c^2*x^2 + 1))/(c^4*d) - 8*integrate(-1/2*(c^2*x^2 - log(c^2*x^2 + 1))/(c^6*d*x^3 + c^4*d*x + (c^5*d*x^2 + c^3*d)*sqrt(c^2*x^2 + 1)), x))","F",0
30,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x, algorithm=""maxima"")","a {\left(\frac{x}{c^{2} d} - \frac{\arctan\left(c x\right)}{c^{3} d}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{2} + d}\,{d x}"," ",0,"a*(x/(c^2*d) - arctan(c*x)/(c^3*d)) + b*integrate(x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d), x)","F",0
31,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{\log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, \log\left(c^{2} x^{2} + 1\right) \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d} + 8 \, \int \frac{\log\left(c^{2} x^{2} + 1\right)}{2 \, {\left(c^{4} d x^{3} + c^{2} d x + {\left(c^{3} d x^{2} + c d\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)} + \frac{a \log\left(c^{2} d x^{2} + d\right)}{2 \, c^{2} d}"," ",0,"-1/8*b*((log(c^2*x^2 + 1)^2 - 4*log(c^2*x^2 + 1)*log(c*x + sqrt(c^2*x^2 + 1)))/(c^2*d) + 8*integrate(1/2*log(c^2*x^2 + 1)/(c^4*d*x^3 + c^2*d*x + (c^3*d*x^2 + c*d)*sqrt(c^2*x^2 + 1)), x)) + 1/2*a*log(c^2*d*x^2 + d)/(c^2*d)","F",0
32,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(c^2*d*x^2+d),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{2} + d}\,{d x} + \frac{a \arctan\left(c x\right)}{c d}"," ",0,"b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d), x) + a*arctan(c*x)/(c*d)","F",0
33,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(c^{2} x^{2} + 1\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{3} + d x}\,{d x}"," ",0,"-1/2*a*(log(c^2*x^2 + 1)/d - 2*log(x)/d) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^3 + d*x), x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{c \arctan\left(c x\right)}{d} + \frac{1}{d x}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{4} + d x^{2}}\,{d x}"," ",0,"-a*(c*arctan(c*x)/d + 1/(d*x)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^4 + d*x^2), x)","F",0
35,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} \log\left(c^{2} x^{2} + 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} - \frac{1}{d x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{5} + d x^{3}}\,{d x}"," ",0,"1/2*(c^2*log(c^2*x^2 + 1)/d - 2*c^2*log(x)/d - 1/(d*x^2))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^5 + d*x^3), x)","F",0
36,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, c^{3} \arctan\left(c x\right)}{d} + \frac{3 \, c^{2} x^{2} - 1}{d x^{3}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{6} + d x^{4}}\,{d x}"," ",0,"1/3*(3*c^3*arctan(c*x)/d + (3*c^2*x^2 - 1)/(d*x^3))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^6 + d*x^4), x)","F",0
37,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + \frac{2 \, x}{c^{4} d^{2}} - \frac{3 \, \arctan\left(c x\right)}{c^{5} d^{2}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(x/(c^6*d^2*x^2 + c^4*d^2) + 2*x/(c^4*d^2) - 3*arctan(c*x)/(c^5*d^2)) + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x)","F",0
38,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{{\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, {\left({\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) - 2}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + 8 \, \int \frac{{\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1}{2 \, {\left(c^{8} d^{2} x^{5} + 2 \, c^{6} d^{2} x^{3} + c^{4} d^{2} x + {\left(c^{7} d^{2} x^{4} + 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)} + \frac{1}{2} \, a {\left(\frac{1}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d^{2}}\right)}"," ",0,"-1/8*b*(((c^2*x^2 + 1)*log(c^2*x^2 + 1)^2 - 4*((c^2*x^2 + 1)*log(c^2*x^2 + 1) + 1)*log(c*x + sqrt(c^2*x^2 + 1)) - 2)/(c^6*d^2*x^2 + c^4*d^2) + 8*integrate(1/2*((c^2*x^2 + 1)*log(c^2*x^2 + 1) + 1)/(c^8*d^2*x^5 + 2*c^6*d^2*x^3 + c^4*d^2*x + (c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2)*sqrt(c^2*x^2 + 1)), x)) + 1/2*a*(1/(c^6*d^2*x^2 + c^4*d^2) + log(c^2*x^2 + 1)/(c^4*d^2))","F",0
39,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x}{c^{4} d^{2} x^{2} + c^{2} d^{2}} - \frac{\arctan\left(c x\right)}{c^{3} d^{2}}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a*(x/(c^4*d^2*x^2 + c^2*d^2) - arctan(c*x)/(c^3*d^2)) + b*integrate(x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x)","F",0
40,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, b {\left(\frac{2 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 1}{c^{4} d^{2} x^{2} + c^{2} d^{2}} - 4 \, \int \frac{1}{2 \, {\left(c^{6} d^{2} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{2} d^{2} x + {\left(c^{5} d^{2} x^{4} + 2 \, c^{3} d^{2} x^{2} + c d^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)} - \frac{a}{2 \, {\left(c^{4} d^{2} x^{2} + c^{2} d^{2}\right)}}"," ",0,"-1/4*b*((2*log(c*x + sqrt(c^2*x^2 + 1)) + 1)/(c^4*d^2*x^2 + c^2*d^2) - 4*integrate(1/2/(c^6*d^2*x^5 + 2*c^4*d^2*x^3 + c^2*d^2*x + (c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2)*sqrt(c^2*x^2 + 1)), x)) - 1/2*a/(c^4*d^2*x^2 + c^2*d^2)","F",0
41,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x}{c^{2} d^{2} x^{2} + d^{2}} + \frac{\arctan\left(c x\right)}{c d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(x/(c^2*d^2*x^2 + d^2) + arctan(c*x)/(c*d^2)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x)","F",0
42,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{1}{c^{2} d^{2} x^{2} + d^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{5} + 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"1/2*a*(1/(c^2*d^2*x^2 + d^2) - log(c^2*x^2 + 1)/d^2 + 2*log(x)/d^2) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^5 + 2*c^2*d^2*x^3 + d^2*x), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{3 \, c^{2} x^{2} + 2}{c^{2} d^{2} x^{3} + d^{2} x} + \frac{3 \, c \arctan\left(c x\right)}{d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{6} + 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}\,{d x}"," ",0,"-1/2*a*((3*c^2*x^2 + 2)/(c^2*d^2*x^3 + d^2*x) + 3*c*arctan(c*x)/d^2) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^6 + 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
44,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{d^{2}} - \frac{4 \, c^{2} \log\left(x\right)}{d^{2}} - \frac{2 \, c^{2} x^{2} + 1}{c^{2} d^{2} x^{4} + d^{2} x^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{7} + 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"1/2*a*(2*c^2*log(c^2*x^2 + 1)/d^2 - 4*c^2*log(x)/d^2 - (2*c^2*x^2 + 1)/(c^2*d^2*x^4 + d^2*x^2)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^7 + 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{15 \, c^{3} \arctan\left(c x\right)}{d^{2}} + \frac{15 \, c^{4} x^{4} + 10 \, c^{2} x^{2} - 2}{c^{2} d^{2} x^{5} + d^{2} x^{3}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{8} + 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}\,{d x}"," ",0,"1/6*(15*c^3*arctan(c*x)/d^2 + (15*c^4*x^4 + 10*c^2*x^2 - 2)/(c^2*d^2*x^5 + d^2*x^3))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^8 + 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
46,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{5 \, c^{2} x^{3} + 3 \, x}{c^{8} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} - \frac{3 \, \arctan\left(c x\right)}{c^{5} d^{3}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}}\,{d x}"," ",0,"-1/8*a*((5*c^2*x^3 + 3*x)/(c^8*d^3*x^4 + 2*c^6*d^3*x^2 + c^4*d^3) - 3*arctan(c*x)/(c^5*d^3)) + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3), x)","F",0
47,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, b {\left(\frac{4 \, c^{2} x^{2} + 4 \, {\left(2 \, c^{2} x^{2} + 1\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3}{c^{8} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} - 16 \, \int \frac{2 \, c^{2} x^{2} + 1}{4 \, {\left(c^{10} d^{3} x^{7} + 3 \, c^{8} d^{3} x^{5} + 3 \, c^{6} d^{3} x^{3} + c^{4} d^{3} x + {\left(c^{9} d^{3} x^{6} + 3 \, c^{7} d^{3} x^{4} + 3 \, c^{5} d^{3} x^{2} + c^{3} d^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)} - \frac{{\left(2 \, c^{2} x^{2} + 1\right)} a}{4 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}"," ",0,"-1/16*b*((4*c^2*x^2 + 4*(2*c^2*x^2 + 1)*log(c*x + sqrt(c^2*x^2 + 1)) + 3)/(c^8*d^3*x^4 + 2*c^6*d^3*x^2 + c^4*d^3) - 16*integrate(1/4*(2*c^2*x^2 + 1)/(c^10*d^3*x^7 + 3*c^8*d^3*x^5 + 3*c^6*d^3*x^3 + c^4*d^3*x + (c^9*d^3*x^6 + 3*c^7*d^3*x^4 + 3*c^5*d^3*x^2 + c^3*d^3)*sqrt(c^2*x^2 + 1)), x)) - 1/4*(2*c^2*x^2 + 1)*a/(c^8*d^3*x^4 + 2*c^6*d^3*x^2 + c^4*d^3)","F",0
48,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{c^{2} x^{3} - x}{c^{6} d^{3} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} + \frac{\arctan\left(c x\right)}{c^{3} d^{3}}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((c^2*x^3 - x)/(c^6*d^3*x^4 + 2*c^4*d^3*x^2 + c^2*d^3) + arctan(c*x)/(c^3*d^3)) + b*integrate(x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3), x)","F",0
49,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, b {\left(\frac{4 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 1}{c^{6} d^{3} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - 16 \, \int \frac{1}{4 \, {\left(c^{8} d^{3} x^{7} + 3 \, c^{6} d^{3} x^{5} + 3 \, c^{4} d^{3} x^{3} + c^{2} d^{3} x + {\left(c^{7} d^{3} x^{6} + 3 \, c^{5} d^{3} x^{4} + 3 \, c^{3} d^{3} x^{2} + c d^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)} - \frac{a}{4 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}"," ",0,"-1/16*b*((4*log(c*x + sqrt(c^2*x^2 + 1)) + 1)/(c^6*d^3*x^4 + 2*c^4*d^3*x^2 + c^2*d^3) - 16*integrate(1/4/(c^8*d^3*x^7 + 3*c^6*d^3*x^5 + 3*c^4*d^3*x^3 + c^2*d^3*x + (c^7*d^3*x^6 + 3*c^5*d^3*x^4 + 3*c^3*d^3*x^2 + c*d^3)*sqrt(c^2*x^2 + 1)), x)) - 1/4*a/(c^6*d^3*x^4 + 2*c^4*d^3*x^2 + c^2*d^3)","F",0
50,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{3 \, c^{2} x^{3} + 5 \, x}{c^{4} d^{3} x^{4} + 2 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{3 \, \arctan\left(c x\right)}{c d^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((3*c^2*x^3 + 5*x)/(c^4*d^3*x^4 + 2*c^2*d^3*x^2 + d^3) + 3*arctan(c*x)/(c*d^3)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, c^{2} x^{2} + 3}{c^{4} d^{3} x^{4} + 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{7} + 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} + d^{3} x}\,{d x}"," ",0,"1/4*a*((2*c^2*x^2 + 3)/(c^4*d^3*x^4 + 2*c^2*d^3*x^2 + d^3) - 2*log(c^2*x^2 + 1)/d^3 + 4*log(x)/d^3) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^7 + 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 + d^3*x), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{15 \, c^{4} x^{4} + 25 \, c^{2} x^{2} + 8}{c^{4} d^{3} x^{5} + 2 \, c^{2} d^{3} x^{3} + d^{3} x} + \frac{15 \, c \arctan\left(c x\right)}{d^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{8} + 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} + d^{3} x^{2}}\,{d x}"," ",0,"-1/8*a*((15*c^4*x^4 + 25*c^2*x^2 + 8)/(c^4*d^3*x^5 + 2*c^2*d^3*x^3 + d^3*x) + 15*c*arctan(c*x)/d^3) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^8 + 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 + d^3*x^2), x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{6 \, c^{4} x^{4} + 9 \, c^{2} x^{2} + 2}{c^{4} d^{3} x^{6} + 2 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} - \frac{6 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{d^{3}} + \frac{12 \, c^{2} \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{9} + 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\,{d x}"," ",0,"-1/4*a*((6*c^4*x^4 + 9*c^2*x^2 + 2)/(c^4*d^3*x^6 + 2*c^2*d^3*x^4 + d^3*x^2) - 6*c^2*log(c^2*x^2 + 1)/d^3 + 12*c^2*log(x)/d^3) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^9 + 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 + d^3*x^3), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{24} \, a {\left(\frac{105 \, c^{3} \arctan\left(c x\right)}{d^{3}} + \frac{105 \, c^{6} x^{6} + 175 \, c^{4} x^{4} + 56 \, c^{2} x^{2} - 8}{c^{4} d^{3} x^{7} + 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{10} + 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} + d^{3} x^{4}}\,{d x}"," ",0,"1/24*a*(105*c^3*arctan(c*x)/d^3 + (105*c^6*x^6 + 175*c^4*x^4 + 56*c^2*x^2 - 8)/(c^4*d^3*x^7 + 2*c^2*d^3*x^5 + d^3*x^3)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^10 + 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 + d^3*x^4), x)","F",0
55,1,134,0,0.409638," ","integrate(x^3*(a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, b {\left(\frac{3 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{2}}{\pi c^{2}} - \frac{2 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}}{\pi c^{4}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{15} \, a {\left(\frac{3 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{2}}{\pi c^{2}} - \frac{2 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}}{\pi c^{4}}\right)} - \frac{{\left(9 \, \sqrt{\pi} c^{4} x^{5} + 5 \, \sqrt{\pi} c^{2} x^{3} - 30 \, \sqrt{\pi} x\right)} b}{225 \, c^{3}}"," ",0,"1/15*b*(3*(pi + pi*c^2*x^2)^(3/2)*x^2/(pi*c^2) - 2*(pi + pi*c^2*x^2)^(3/2)/(pi*c^4))*arcsinh(c*x) + 1/15*a*(3*(pi + pi*c^2*x^2)^(3/2)*x^2/(pi*c^2) - 2*(pi + pi*c^2*x^2)^(3/2)/(pi*c^4)) - 1/225*(9*sqrt(pi)*c^4*x^5 + 5*sqrt(pi)*c^2*x^3 - 30*sqrt(pi)*x)*b/c^3","A",0
56,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
57,1,73,0,0.502440," ","integrate(x*(a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} b \operatorname{arsinh}\left(c x\right)}{3 \, \pi c^{2}} - \frac{{\left(\pi^{\frac{3}{2}} c^{2} x^{3} + 3 \, \pi^{\frac{3}{2}} x\right)} b}{9 \, \pi c} + \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} a}{3 \, \pi c^{2}}"," ",0,"1/3*(pi + pi*c^2*x^2)^(3/2)*b*arcsinh(c*x)/(pi*c^2) - 1/9*(pi^(3/2)*c^2*x^3 + 3*pi^(3/2)*x)*b/(pi*c) + 1/3*(pi + pi*c^2*x^2)^(3/2)*a/(pi*c^2)","A",0
58,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
59,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{\pi} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \sqrt{\pi + \pi c^{2} x^{2}}\right)} a + b \int \frac{\sqrt{\pi + \pi c^{2} x^{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-(sqrt(pi)*arcsinh(1/(c*abs(x))) - sqrt(pi + pi*c^2*x^2))*a + b*integrate(sqrt(pi + pi*c^2*x^2)*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2)/x^2,x, algorithm=""maxima"")","{\left(\sqrt{\pi} c \operatorname{arsinh}\left(c x\right) - \frac{\sqrt{\pi + \pi c^{2} x^{2}}}{x}\right)} a + b \int \frac{\sqrt{\pi + \pi c^{2} x^{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{2}}\,{d x}"," ",0,"(sqrt(pi)*c*arcsinh(c*x) - sqrt(pi + pi*c^2*x^2)/x)*a + b*integrate(sqrt(pi + pi*c^2*x^2)*log(c*x + sqrt(c^2*x^2 + 1))/x^2, x)","F",0
61,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\sqrt{\pi} c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \sqrt{\pi + \pi c^{2} x^{2}} c^{2} + \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}}{\pi x^{2}}\right)} a + b \int \frac{\sqrt{\pi + \pi c^{2} x^{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(sqrt(pi)*c^2*arcsinh(1/(c*abs(x))) - sqrt(pi + pi*c^2*x^2)*c^2 + (pi + pi*c^2*x^2)^(3/2)/(pi*x^2))*a + b*integrate(sqrt(pi + pi*c^2*x^2)*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
62,1,133,0,0.603545," ","integrate((a+b*arcsinh(c*x))*(pi*c^2*x^2+pi)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{{\left(\pi^{\frac{3}{2}} \left(-1\right)^{2 \, \pi + 2 \, \pi c^{2} x^{2}} c^{2} \log\left(2 \, \pi c^{2} + \frac{2 \, \pi}{x^{2}}\right) - \pi^{\frac{3}{2}} c^{2} \log\left(x^{2} + \frac{1}{c^{2}}\right) + \frac{\pi \sqrt{\pi + \pi c^{4} x^{4} + 2 \, \pi c^{2} x^{2}}}{x^{2}}\right)} b c}{6 \, \pi} - \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} b \operatorname{arsinh}\left(c x\right)}{3 \, \pi x^{3}} - \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} a}{3 \, \pi x^{3}}"," ",0,"-1/6*(pi^(3/2)*(-1)^(2*pi + 2*pi*c^2*x^2)*c^2*log(2*pi*c^2 + 2*pi/x^2) - pi^(3/2)*c^2*log(x^2 + 1/c^2) + pi*sqrt(pi + pi*c^4*x^4 + 2*pi*c^2*x^2)/x^2)*b*c/pi - 1/3*(pi + pi*c^2*x^2)^(3/2)*b*arcsinh(c*x)/(pi*x^3) - 1/3*(pi + pi*c^2*x^2)^(3/2)*a/(pi*x^3)","B",0
63,1,145,0,0.491458," ","integrate(x^3*(pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{5 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} x^{2}}{\pi c^{2}} - \frac{2 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}{\pi c^{4}}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{35} \, {\left(\frac{5 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} x^{2}}{\pi c^{2}} - \frac{2 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}{\pi c^{4}}\right)} a - \frac{{\left(75 \, \pi^{\frac{3}{2}} c^{6} x^{7} + 168 \, \pi^{\frac{3}{2}} c^{4} x^{5} + 35 \, \pi^{\frac{3}{2}} c^{2} x^{3} - 210 \, \pi^{\frac{3}{2}} x\right)} b}{3675 \, c^{3}}"," ",0,"1/35*(5*(pi + pi*c^2*x^2)^(5/2)*x^2/(pi*c^2) - 2*(pi + pi*c^2*x^2)^(5/2)/(pi*c^4))*b*arcsinh(c*x) + 1/35*(5*(pi + pi*c^2*x^2)^(5/2)*x^2/(pi*c^2) - 2*(pi + pi*c^2*x^2)^(5/2)/(pi*c^4))*a - 1/3675*(75*pi^(3/2)*c^6*x^7 + 168*pi^(3/2)*c^4*x^5 + 35*pi^(3/2)*c^2*x^3 - 210*pi^(3/2)*x)*b/c^3","A",0
64,-2,0,0,0.000000," ","integrate(x^2*(pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
65,1,85,0,0.381099," ","integrate(x*(pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} b \operatorname{arsinh}\left(c x\right)}{5 \, \pi c^{2}} + \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} a}{5 \, \pi c^{2}} - \frac{{\left(3 \, \pi^{\frac{5}{2}} c^{4} x^{5} + 10 \, \pi^{\frac{5}{2}} c^{2} x^{3} + 15 \, \pi^{\frac{5}{2}} x\right)} b}{75 \, \pi c}"," ",0,"1/5*(pi + pi*c^2*x^2)^(5/2)*b*arcsinh(c*x)/(pi*c^2) + 1/5*(pi + pi*c^2*x^2)^(5/2)*a/(pi*c^2) - 1/75*(3*pi^(5/2)*c^4*x^5 + 10*pi^(5/2)*c^2*x^3 + 15*pi^(5/2)*x)*b/(pi*c)","A",0
66,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
67,0,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, \pi^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 3 \, \pi \sqrt{\pi + \pi c^{2} x^{2}} - {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}\right)} a + b \int \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-1/3*(3*pi^(3/2)*arcsinh(1/(c*abs(x))) - 3*pi*sqrt(pi + pi*c^2*x^2) - (pi + pi*c^2*x^2)^(3/2))*a + b*integrate((pi + pi*c^2*x^2)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
68,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
69,0,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \pi^{\frac{3}{2}} c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 3 \, \pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2} - {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2} + \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}{\pi x^{2}}\right)} a + b \int \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(3*pi^(3/2)*c^2*arcsinh(1/(c*abs(x))) - 3*pi*sqrt(pi + pi*c^2*x^2)*c^2 - (pi + pi*c^2*x^2)^(3/2)*c^2 + (pi + pi*c^2*x^2)^(5/2)/(pi*x^2))*a + b*integrate((pi + pi*c^2*x^2)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
70,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
71,1,156,0,0.518815," ","integrate(x^3*(pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{63} \, {\left(\frac{7 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}} x^{2}}{\pi c^{2}} - \frac{2 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}}}{\pi c^{4}}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{63} \, {\left(\frac{7 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}} x^{2}}{\pi c^{2}} - \frac{2 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}}}{\pi c^{4}}\right)} a - \frac{{\left(49 \, \pi^{\frac{5}{2}} c^{8} x^{9} + 171 \, \pi^{\frac{5}{2}} c^{6} x^{7} + 189 \, \pi^{\frac{5}{2}} c^{4} x^{5} + 21 \, \pi^{\frac{5}{2}} c^{2} x^{3} - 126 \, \pi^{\frac{5}{2}} x\right)} b}{3969 \, c^{3}}"," ",0,"1/63*(7*(pi + pi*c^2*x^2)^(7/2)*x^2/(pi*c^2) - 2*(pi + pi*c^2*x^2)^(7/2)/(pi*c^4))*b*arcsinh(c*x) + 1/63*(7*(pi + pi*c^2*x^2)^(7/2)*x^2/(pi*c^2) - 2*(pi + pi*c^2*x^2)^(7/2)/(pi*c^4))*a - 1/3969*(49*pi^(5/2)*c^8*x^9 + 171*pi^(5/2)*c^6*x^7 + 189*pi^(5/2)*c^4*x^5 + 21*pi^(5/2)*c^2*x^3 - 126*pi^(5/2)*x)*b/c^3","A",0
72,-2,0,0,0.000000," ","integrate(x^2*(pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
73,1,96,0,0.367415," ","integrate(x*(pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}} b \operatorname{arsinh}\left(c x\right)}{7 \, \pi c^{2}} + \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}} a}{7 \, \pi c^{2}} - \frac{{\left(5 \, \pi^{\frac{7}{2}} c^{6} x^{7} + 21 \, \pi^{\frac{7}{2}} c^{4} x^{5} + 35 \, \pi^{\frac{7}{2}} c^{2} x^{3} + 35 \, \pi^{\frac{7}{2}} x\right)} b}{245 \, \pi c}"," ",0,"1/7*(pi + pi*c^2*x^2)^(7/2)*b*arcsinh(c*x)/(pi*c^2) + 1/7*(pi + pi*c^2*x^2)^(7/2)*a/(pi*c^2) - 1/245*(5*pi^(7/2)*c^6*x^7 + 21*pi^(7/2)*c^4*x^5 + 35*pi^(7/2)*c^2*x^3 + 35*pi^(7/2)*x)*b/(pi*c)","A",0
74,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
75,0,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(15 \, \pi^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 15 \, \pi^{2} \sqrt{\pi + \pi c^{2} x^{2}} - 5 \, \pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} - 3 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}\right)} a + b \int \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-1/15*(15*pi^(5/2)*arcsinh(1/(c*abs(x))) - 15*pi^2*sqrt(pi + pi*c^2*x^2) - 5*pi*(pi + pi*c^2*x^2)^(3/2) - 3*(pi + pi*c^2*x^2)^(5/2))*a + b*integrate((pi + pi*c^2*x^2)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
76,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
77,0,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(15 \, \pi^{\frac{5}{2}} c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 15 \, \pi^{2} \sqrt{\pi + \pi c^{2} x^{2}} c^{2} - 5 \, \pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} c^{2} + \frac{3 \, {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{7}{2}}}{\pi x^{2}}\right)} a + b \int \frac{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/6*(15*pi^(5/2)*c^2*arcsinh(1/(c*abs(x))) - 15*pi^2*sqrt(pi + pi*c^2*x^2)*c^2 - 5*pi*(pi + pi*c^2*x^2)^(3/2)*c^2 - 3*(pi + pi*c^2*x^2)^(5/2)*c^2 + 3*(pi + pi*c^2*x^2)^(7/2)/(pi*x^2))*a + b*integrate((pi + pi*c^2*x^2)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
78,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
79,1,28,0,0.612736," ","integrate(arcsinh(x)*(x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{2} + \frac{1}{2} \, {\left(\sqrt{x^{2} + 1} x + \operatorname{arsinh}\left(x\right)\right)} \operatorname{arsinh}\left(x\right) - \frac{1}{4} \, \operatorname{arsinh}\left(x\right)^{2}"," ",0,"-1/4*x^2 + 1/2*(sqrt(x^2 + 1)*x + arcsinh(x))*arcsinh(x) - 1/4*arcsinh(x)^2","A",0
80,1,174,0,0.441659," ","integrate(x^5*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, \sqrt{\pi + \pi c^{2} x^{2}} x^{4}}{\pi c^{2}} - \frac{4 \, \sqrt{\pi + \pi c^{2} x^{2}} x^{2}}{\pi c^{4}} + \frac{8 \, \sqrt{\pi + \pi c^{2} x^{2}}}{\pi c^{6}}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{15} \, {\left(\frac{3 \, \sqrt{\pi + \pi c^{2} x^{2}} x^{4}}{\pi c^{2}} - \frac{4 \, \sqrt{\pi + \pi c^{2} x^{2}} x^{2}}{\pi c^{4}} + \frac{8 \, \sqrt{\pi + \pi c^{2} x^{2}}}{\pi c^{6}}\right)} a - \frac{{\left(9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x\right)} b}{225 \, \sqrt{\pi} c^{5}}"," ",0,"1/15*(3*sqrt(pi + pi*c^2*x^2)*x^4/(pi*c^2) - 4*sqrt(pi + pi*c^2*x^2)*x^2/(pi*c^4) + 8*sqrt(pi + pi*c^2*x^2)/(pi*c^6))*b*arcsinh(c*x) + 1/15*(3*sqrt(pi + pi*c^2*x^2)*x^4/(pi*c^2) - 4*sqrt(pi + pi*c^2*x^2)*x^2/(pi*c^4) + 8*sqrt(pi + pi*c^2*x^2)/(pi*c^6))*a - 1/225*(9*c^4*x^5 - 20*c^2*x^3 + 120*x)*b/(sqrt(pi)*c^5)","A",0
81,-2,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
82,1,117,0,0.382943," ","integrate(x^3*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, b {\left(\frac{\sqrt{\pi + \pi c^{2} x^{2}} x^{2}}{\pi c^{2}} - \frac{2 \, \sqrt{\pi + \pi c^{2} x^{2}}}{\pi c^{4}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{\sqrt{\pi + \pi c^{2} x^{2}} x^{2}}{\pi c^{2}} - \frac{2 \, \sqrt{\pi + \pi c^{2} x^{2}}}{\pi c^{4}}\right)} - \frac{{\left(c^{2} x^{3} - 6 \, x\right)} b}{9 \, \sqrt{\pi} c^{3}}"," ",0,"1/3*b*(sqrt(pi + pi*c^2*x^2)*x^2/(pi*c^2) - 2*sqrt(pi + pi*c^2*x^2)/(pi*c^4))*arcsinh(c*x) + 1/3*a*(sqrt(pi + pi*c^2*x^2)*x^2/(pi*c^2) - 2*sqrt(pi + pi*c^2*x^2)/(pi*c^4)) - 1/9*(c^2*x^3 - 6*x)*b/(sqrt(pi)*c^3)","A",0
83,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
84,1,55,0,0.505754," ","integrate(x*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","-\frac{b x}{\sqrt{\pi} c} + \frac{\sqrt{\pi + \pi c^{2} x^{2}} b \operatorname{arsinh}\left(c x\right)}{\pi c^{2}} + \frac{\sqrt{\pi + \pi c^{2} x^{2}} a}{\pi c^{2}}"," ",0,"-b*x/(sqrt(pi)*c) + sqrt(pi + pi*c^2*x^2)*b*arcsinh(c*x)/(pi*c^2) + sqrt(pi + pi*c^2*x^2)*a/(pi*c^2)","A",0
85,1,28,0,0.499860," ","integrate((a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{b \operatorname{arsinh}\left(c x\right)^{2}}{2 \, \sqrt{\pi} c} + \frac{a \operatorname{arsinh}\left(c x\right)}{\sqrt{\pi} c}"," ",0,"1/2*b*arcsinh(c*x)^2/(sqrt(pi)*c) + a*arcsinh(c*x)/(sqrt(pi)*c)","A",0
86,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{\pi + \pi c^{2} x^{2}} x}\,{d x} - \frac{a \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\sqrt{\pi}}"," ",0,"b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(pi + pi*c^2*x^2)*x), x) - a*arcsinh(1/(c*abs(x)))/sqrt(pi)","F",0
87,1,101,0,0.461625," ","integrate((a+b*arcsinh(c*x))/x^2/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\sqrt{\pi} \left(-1\right)^{2 \, \pi + 2 \, \pi c^{2} x^{2}} \log\left(2 \, \pi c^{2} + \frac{2 \, \pi}{x^{2}}\right) - \sqrt{\pi} \log\left(x^{2} + \frac{1}{c^{2}}\right)\right)} b c}{2 \, \pi} - \frac{\sqrt{\pi + \pi c^{2} x^{2}} b \operatorname{arsinh}\left(c x\right)}{\pi x} - \frac{\sqrt{\pi + \pi c^{2} x^{2}} a}{\pi x}"," ",0,"-1/2*(sqrt(pi)*(-1)^(2*pi + 2*pi*c^2*x^2)*log(2*pi*c^2 + 2*pi/x^2) - sqrt(pi)*log(x^2 + 1/c^2))*b*c/pi - sqrt(pi + pi*c^2*x^2)*b*arcsinh(c*x)/(pi*x) - sqrt(pi + pi*c^2*x^2)*a/(pi*x)","B",0
88,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\sqrt{\pi}} - \frac{\sqrt{\pi + \pi c^{2} x^{2}}}{\pi x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{\pi + \pi c^{2} x^{2}} x^{3}}\,{d x}"," ",0,"1/2*(c^2*arcsinh(1/(c*abs(x)))/sqrt(pi) - sqrt(pi + pi*c^2*x^2)/(pi*x^2))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(pi + pi*c^2*x^2)*x^3), x)","F",0
89,1,121,0,0.452586," ","integrate((a+b*arcsinh(c*x))/x^4/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{4 \, c^{2} \log\left(x\right)}{\sqrt{\pi}} + \frac{1}{\sqrt{\pi} x^{2}}\right)} b c + \frac{1}{3} \, b {\left(\frac{2 \, \sqrt{\pi + \pi c^{2} x^{2}} c^{2}}{\pi x} - \frac{\sqrt{\pi + \pi c^{2} x^{2}}}{\pi x^{3}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{2 \, \sqrt{\pi + \pi c^{2} x^{2}} c^{2}}{\pi x} - \frac{\sqrt{\pi + \pi c^{2} x^{2}}}{\pi x^{3}}\right)}"," ",0,"-1/6*(4*c^2*log(x)/sqrt(pi) + 1/(sqrt(pi)*x^2))*b*c + 1/3*b*(2*sqrt(pi + pi*c^2*x^2)*c^2/(pi*x) - sqrt(pi + pi*c^2*x^2)/(pi*x^3))*arcsinh(c*x) + 1/3*a*(2*sqrt(pi + pi*c^2*x^2)*c^2/(pi*x) - sqrt(pi + pi*c^2*x^2)/(pi*x^3))","A",0
90,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{x^{4}}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2}} - \frac{4 \, x^{2}}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{4}} - \frac{8}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{6}}\right)} + \frac{1}{3} \, b {\left(\frac{{\left(\sqrt{\pi} c^{4} x^{4} - 4 \, \sqrt{\pi} c^{2} x^{2} - 8 \, \sqrt{\pi}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\pi^{2} \sqrt{c^{2} x^{2} + 1} c^{6}} - \frac{\frac{1}{3} \, \sqrt{\pi} \sqrt{c^{2} x^{2} + 1} c^{2} x^{2} + 8 \, \sqrt{\pi} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{14}{3} \, \sqrt{\pi} \sqrt{c^{2} x^{2} + 1}}{\pi^{2} c^{6}} + 3 \, \int \frac{\sqrt{\pi} c^{4} x^{4} - 4 \, \sqrt{\pi} c^{2} x^{2} - 8 \, \sqrt{\pi}}{3 \, {\left(\pi^{2} c^{9} x^{4} + \pi^{2} c^{7} x^{2} + {\left(\pi^{2} c^{8} x^{3} + \pi^{2} c^{6} x\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)}"," ",0,"1/3*a*(x^4/(pi*sqrt(pi + pi*c^2*x^2)*c^2) - 4*x^2/(pi*sqrt(pi + pi*c^2*x^2)*c^4) - 8/(pi*sqrt(pi + pi*c^2*x^2)*c^6)) + 1/3*b*((sqrt(pi)*c^4*x^4 - 4*sqrt(pi)*c^2*x^2 - 8*sqrt(pi))*log(c*x + sqrt(c^2*x^2 + 1))/(pi^2*sqrt(c^2*x^2 + 1)*c^6) - integrate((sqrt(pi)*c^4*x^4 - 4*sqrt(pi)*c^2*x^2 - 8*sqrt(pi))/(sqrt(c^2*x^2 + 1)*x), x)/(pi^2*c^6) + 3*integrate(1/3*(sqrt(pi)*c^4*x^4 - 4*sqrt(pi)*c^2*x^2 - 8*sqrt(pi))/(pi^2*c^9*x^4 + pi^2*c^7*x^2 + (pi^2*c^8*x^3 + pi^2*c^6*x)*sqrt(c^2*x^2 + 1)), x))","F",0
91,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x^{3}}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2}} + \frac{3 \, x}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{4}} - \frac{3 \, \operatorname{arsinh}\left(c x\right)}{\pi^{\frac{3}{2}} c^{5}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*a*(x^3/(pi*sqrt(pi + pi*c^2*x^2)*c^2) + 3*x/(pi*sqrt(pi + pi*c^2*x^2)*c^4) - 3*arcsinh(c*x)/(pi^(3/2)*c^5)) + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(pi + pi*c^2*x^2)^(3/2), x)","F",0
92,1,119,0,0.592974," ","integrate(x^3*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","-b c {\left(\frac{x}{\pi^{\frac{3}{2}} c^{4}} + \frac{\arctan\left(c x\right)}{\pi^{\frac{3}{2}} c^{5}}\right)} + b {\left(\frac{x^{2}}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2}} + \frac{2}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{4}}\right)} \operatorname{arsinh}\left(c x\right) + a {\left(\frac{x^{2}}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2}} + \frac{2}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{4}}\right)}"," ",0,"-b*c*(x/(pi^(3/2)*c^4) + arctan(c*x)/(pi^(3/2)*c^5)) + b*(x^2/(pi*sqrt(pi + pi*c^2*x^2)*c^2) + 2/(pi*sqrt(pi + pi*c^2*x^2)*c^4))*arcsinh(c*x) + a*(x^2/(pi*sqrt(pi + pi*c^2*x^2)*c^2) + 2/(pi*sqrt(pi + pi*c^2*x^2)*c^4))","A",0
93,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{x}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{\pi^{\frac{3}{2}} c^{3}}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-a*(x/(pi*sqrt(pi + pi*c^2*x^2)*c^2) - arcsinh(c*x)/(pi^(3/2)*c^3)) + b*integrate(x^2*log(c*x + sqrt(c^2*x^2 + 1))/(pi + pi*c^2*x^2)^(3/2), x)","F",0
94,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","b {\left(\frac{-\operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\pi^{\frac{3}{2}} c^{2}} - \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\pi^{\frac{3}{2}} \sqrt{c^{2} x^{2} + 1} c^{2}} - \int \frac{1}{\pi^{\frac{3}{2}} c^{5} x^{4} + \pi^{\frac{3}{2}} c^{3} x^{2} + {\left(\pi^{\frac{3}{2}} c^{4} x^{3} + \pi^{\frac{3}{2}} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} - \frac{a}{\pi \sqrt{\pi + \pi c^{2} x^{2}} c^{2}}"," ",0,"b*(integrate(1/(sqrt(c^2*x^2 + 1)*x), x)/(pi^(3/2)*c^2) - log(c*x + sqrt(c^2*x^2 + 1))/(pi^(3/2)*sqrt(c^2*x^2 + 1)*c^2) - integrate(1/(pi^(3/2)*c^5*x^4 + pi^(3/2)*c^3*x^2 + (pi^(3/2)*c^4*x^3 + pi^(3/2)*c^2*x)*sqrt(c^2*x^2 + 1)), x)) - a/(pi*sqrt(pi + pi*c^2*x^2)*c^2)","F",0
95,1,58,0,0.552280," ","integrate((a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","\frac{b x \operatorname{arsinh}\left(c x\right)}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{a x}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} - \frac{b \log\left(x^{2} + \frac{1}{c^{2}}\right)}{2 \, \pi^{\frac{3}{2}} c}"," ",0,"b*x*arcsinh(c*x)/(pi*sqrt(pi + pi*c^2*x^2)) + a*x/(pi*sqrt(pi + pi*c^2*x^2)) - 1/2*b*log(x^2 + 1/c^2)/(pi^(3/2)*c)","A",0
96,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\pi^{\frac{3}{2}}} - \frac{1}{\pi \sqrt{\pi + \pi c^{2} x^{2}}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-a*(arcsinh(1/(c*abs(x)))/pi^(3/2) - 1/(pi*sqrt(pi + pi*c^2*x^2))) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((pi + pi*c^2*x^2)^(3/2)*x), x)","F",0
97,1,119,0,0.555110," ","integrate((a+b*arcsinh(c*x))/x^2/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, b c {\left(\frac{\log\left(c^{2} x^{2} + 1\right)}{\pi^{\frac{3}{2}}} + \frac{2 \, \log\left(x\right)}{\pi^{\frac{3}{2}}}\right)} - {\left(\frac{2 \, c^{2} x}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{1}{\pi \sqrt{\pi + \pi c^{2} x^{2}} x}\right)} b \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, c^{2} x}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{1}{\pi \sqrt{\pi + \pi c^{2} x^{2}} x}\right)} a"," ",0,"1/2*b*c*(log(c^2*x^2 + 1)/pi^(3/2) + 2*log(x)/pi^(3/2)) - (2*c^2*x/(pi*sqrt(pi + pi*c^2*x^2)) + 1/(pi*sqrt(pi + pi*c^2*x^2)*x))*b*arcsinh(c*x) - (2*c^2*x/(pi*sqrt(pi + pi*c^2*x^2)) + 1/(pi*sqrt(pi + pi*c^2*x^2)*x))*a","A",0
98,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\pi^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} - \frac{1}{\pi \sqrt{\pi + \pi c^{2} x^{2}} x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"1/2*(3*c^2*arcsinh(1/(c*abs(x)))/pi^(3/2) - 3*c^2/(pi*sqrt(pi + pi*c^2*x^2)) - 1/(pi*sqrt(pi + pi*c^2*x^2)*x^2))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((pi + pi*c^2*x^2)^(3/2)*x^3), x)","F",0
99,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^4/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{4 \, c^{2}}{\pi \sqrt{\pi + \pi c^{2} x^{2}} x} - \frac{1}{\pi \sqrt{\pi + \pi c^{2} x^{2}} x^{3}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"1/3*(8*c^4*x/(pi*sqrt(pi + pi*c^2*x^2)) + 4*c^2/(pi*sqrt(pi + pi*c^2*x^2)*x) - 1/(pi*sqrt(pi + pi*c^2*x^2)*x^3))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((pi + pi*c^2*x^2)^(3/2)*x^4), x)","F",0
100,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{3 \, x^{5}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} + \frac{5 \, x {\left(\frac{3 \, x^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} + \frac{2}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{4}}\right)}}{c^{2}} + \frac{5 \, x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}} c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{\pi^{\frac{5}{2}} c^{7}}\right)} + b \int \frac{x^{6} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/6*a*(3*x^5/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) + 5*x*(3*x^2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) + 2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^4))/c^2 + 5*x/(pi^2*sqrt(pi + pi*c^2*x^2)*c^6) - 15*arcsinh(c*x)/(pi^(5/2)*c^7)) + b*integrate(x^6*log(c*x + sqrt(c^2*x^2 + 1))/(pi + pi*c^2*x^2)^(5/2), x)","F",0
101,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, b {\left(\frac{{\left(3 \, \sqrt{\pi} c^{4} x^{4} + 12 \, \sqrt{\pi} c^{2} x^{2} + 8 \, \sqrt{\pi}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi^{3} c^{8} x^{2} + \pi^{3} c^{6}\right)} \sqrt{c^{2} x^{2} + 1}} + 3 \, \int \frac{3 \, \sqrt{\pi} c^{4} x^{4} + 12 \, \sqrt{\pi} c^{2} x^{2} + 8 \, \sqrt{\pi}}{3 \, {\left(\pi^{3} c^{11} x^{6} + 2 \, \pi^{3} c^{9} x^{4} + \pi^{3} c^{7} x^{2} + {\left(\pi^{3} c^{10} x^{5} + 2 \, \pi^{3} c^{8} x^{3} + \pi^{3} c^{6} x\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x} - 3 \, \int \frac{3 \, \sqrt{\pi} c^{4} x^{4} + 12 \, \sqrt{\pi} c^{2} x^{2} + 8 \, \sqrt{\pi}}{3 \, {\left(\pi^{3} c^{8} x^{3} + \pi^{3} c^{6} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} + \frac{1}{3} \, a {\left(\frac{3 \, x^{4}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} + \frac{12 \, x^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{4}} + \frac{8}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{6}}\right)}"," ",0,"1/3*b*((3*sqrt(pi)*c^4*x^4 + 12*sqrt(pi)*c^2*x^2 + 8*sqrt(pi))*log(c*x + sqrt(c^2*x^2 + 1))/((pi^3*c^8*x^2 + pi^3*c^6)*sqrt(c^2*x^2 + 1)) + 3*integrate(1/3*(3*sqrt(pi)*c^4*x^4 + 12*sqrt(pi)*c^2*x^2 + 8*sqrt(pi))/(pi^3*c^11*x^6 + 2*pi^3*c^9*x^4 + pi^3*c^7*x^2 + (pi^3*c^10*x^5 + 2*pi^3*c^8*x^3 + pi^3*c^6*x)*sqrt(c^2*x^2 + 1)), x) - 3*integrate(1/3*(3*sqrt(pi)*c^4*x^4 + 12*sqrt(pi)*c^2*x^2 + 8*sqrt(pi))/((pi^3*c^8*x^3 + pi^3*c^6*x)*sqrt(c^2*x^2 + 1)), x)) + 1/3*a*(3*x^4/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) + 12*x^2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^4) + 8/(pi*(pi + pi*c^2*x^2)^(3/2)*c^6))","F",0
102,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} + \frac{2}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{4}}\right)} + \frac{x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}} c^{4}} - \frac{3 \, \operatorname{arsinh}\left(c x\right)}{\pi^{\frac{5}{2}} c^{5}}\right)} a + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*(x*(3*x^2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) + 2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^4)) + x/(pi^2*sqrt(pi + pi*c^2*x^2)*c^4) - 3*arcsinh(c*x)/(pi^(5/2)*c^5))*a + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(pi + pi*c^2*x^2)^(5/2), x)","F",0
103,1,138,0,0.608693," ","integrate(x^3*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, b c {\left(\frac{x}{\pi^{\frac{5}{2}} c^{6} x^{2} + \pi^{\frac{5}{2}} c^{4}} - \frac{5 \, \arctan\left(c x\right)}{\pi^{\frac{5}{2}} c^{5}}\right)} - \frac{1}{3} \, b {\left(\frac{3 \, x^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} + \frac{2}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{3 \, x^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} + \frac{2}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{4}}\right)}"," ",0,"-1/6*b*c*(x/(pi^(5/2)*c^6*x^2 + pi^(5/2)*c^4) - 5*arctan(c*x)/(pi^(5/2)*c^5)) - 1/3*b*(3*x^2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) + 2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^4))*arcsinh(c*x) - 1/3*a*(3*x^2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) + 2/(pi*(pi + pi*c^2*x^2)^(3/2)*c^4))","A",0
104,1,137,0,0.526934," ","integrate(x^2*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, b c {\left(\frac{1}{\pi^{\frac{5}{2}} c^{6} x^{2} + \pi^{\frac{5}{2}} c^{4}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{\pi^{\frac{5}{2}} c^{4}}\right)} - \frac{1}{3} \, b {\left(\frac{x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} - \frac{x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}} c^{2}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}} - \frac{x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}} c^{2}}\right)}"," ",0,"-1/6*b*c*(1/(pi^(5/2)*c^6*x^2 + pi^(5/2)*c^4) + log(c^2*x^2 + 1)/(pi^(5/2)*c^4)) - 1/3*b*(x/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) - x/(pi^2*sqrt(pi + pi*c^2*x^2)*c^2))*arcsinh(c*x) - 1/3*a*(x/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2) - x/(pi^2*sqrt(pi + pi*c^2*x^2)*c^2))","B",0
105,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","b \int \frac{x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}\,{d x} - \frac{a}{3 \, \pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} c^{2}}"," ",0,"b*integrate(x*log(c*x + sqrt(c^2*x^2 + 1))/(pi + pi*c^2*x^2)^(5/2), x) - 1/3*a/(pi*(pi + pi*c^2*x^2)^(3/2)*c^2)","F",0
106,1,126,0,0.487592," ","integrate((a+b*arcsinh(c*x))/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{1}{\pi^{\frac{5}{2}} c^{4} x^{2} + \pi^{\frac{5}{2}} c^{2}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{\pi^{\frac{5}{2}} c^{2}}\right)} + \frac{1}{3} \, b {\left(\frac{x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}}\right)}"," ",0,"1/6*b*c*(1/(pi^(5/2)*c^4*x^2 + pi^(5/2)*c^2) - 2*log(c^2*x^2 + 1)/(pi^(5/2)*c^2)) + 1/3*b*(x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 2*x/(pi^2*sqrt(pi + pi*c^2*x^2)))*arcsinh(c*x) + 1/3*a*(x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 2*x/(pi^2*sqrt(pi + pi*c^2*x^2)))","A",0
107,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\pi^{\frac{5}{2}}} - \frac{1}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} - \frac{3}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"-1/3*a*(3*arcsinh(1/(c*abs(x)))/pi^(5/2) - 1/(pi*(pi + pi*c^2*x^2)^(3/2)) - 3/(pi^2*sqrt(pi + pi*c^2*x^2))) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((pi + pi*c^2*x^2)^(5/2)*x), x)","F",0
108,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^2/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{4 \, c^{2} x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{8 \, c^{2} x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{3}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"-1/3*a*(4*c^2*x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 8*c^2*x/(pi^2*sqrt(pi + pi*c^2*x^2)) + 3/(pi*(pi + pi*c^2*x^2)^(3/2)*x)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((pi + pi*c^2*x^2)^(5/2)*x^2), x)","F",0
109,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{15 \, c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\pi^{\frac{5}{2}}} - \frac{5 \, c^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} - \frac{15 \, c^{2}}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}} - \frac{3}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"1/6*a*(15*c^2*arcsinh(1/(c*abs(x)))/pi^(5/2) - 5*c^2/(pi*(pi + pi*c^2*x^2)^(3/2)) - 15*c^2/(pi^2*sqrt(pi + pi*c^2*x^2)) - 3/(pi*(pi + pi*c^2*x^2)^(3/2)*x^2)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((pi + pi*c^2*x^2)^(5/2)*x^3), x)","F",0
110,1,236,0,0.520949," ","integrate((a+b*arcsinh(c*x))/x^4/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, b c {\left(\frac{8 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{\pi^{\frac{5}{2}}} + \frac{16 \, c^{2} \log\left(x\right)}{\pi^{\frac{5}{2}}} + \frac{1}{\pi^{\frac{5}{2}} c^{2} x^{4} + \pi^{\frac{5}{2}} x^{2}}\right)} + \frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{16 \, c^{4} x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{6 \, c^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x} - \frac{1}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{3}}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{16 \, c^{4} x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{6 \, c^{2}}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x} - \frac{1}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}} x^{3}}\right)} a"," ",0,"-1/6*b*c*(8*c^2*log(c^2*x^2 + 1)/pi^(5/2) + 16*c^2*log(x)/pi^(5/2) + 1/(pi^(5/2)*c^2*x^4 + pi^(5/2)*x^2)) + 1/3*(8*c^4*x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 16*c^4*x/(pi^2*sqrt(pi + pi*c^2*x^2)) + 6*c^2/(pi*(pi + pi*c^2*x^2)^(3/2)*x) - 1/(pi*(pi + pi*c^2*x^2)^(3/2)*x^3))*b*arcsinh(c*x) + 1/3*(8*c^4*x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 16*c^4*x/(pi^2*sqrt(pi + pi*c^2*x^2)) + 6*c^2/(pi*(pi + pi*c^2*x^2)^(3/2)*x) - 1/(pi*(pi + pi*c^2*x^2)^(3/2)*x^3))*a","A",0
111,1,143,0,0.410711," ","integrate(arcsinh(a*x)/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{1}{60} \, a {\left(\frac{3}{{\left(a^{6} c^{\frac{5}{2}} x^{4} + 2 \, a^{4} c^{\frac{5}{2}} x^{2} + a^{2} c^{\frac{5}{2}}\right)} c} + \frac{8}{{\left(a^{4} c^{\frac{3}{2}} x^{2} + a^{2} c^{\frac{3}{2}}\right)} c^{2}} - \frac{16 \, \log\left(x^{2} + \frac{1}{a^{2}}\right)}{a^{2} c^{\frac{7}{2}}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{a^{2} c x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"1/60*a*(3/((a^6*c^(5/2)*x^4 + 2*a^4*c^(5/2)*x^2 + a^2*c^(5/2))*c) + 8/((a^4*c^(3/2)*x^2 + a^2*c^(3/2))*c^2) - 16*log(x^2 + 1/a^2)/(a^2*c^(7/2))) + 1/15*(8*x/(sqrt(a^2*c*x^2 + c)*c^3) + 4*x/((a^2*c*x^2 + c)^(3/2)*c^2) + 3*x/((a^2*c*x^2 + c)^(5/2)*c))*arcsinh(a*x)","A",0
112,1,83,0,0.367099," ","integrate(x^4*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{x^{4}}{a^{2}} - \frac{3 \, x^{2}}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)^{2}}{a^{6}}\right)} a + \frac{1}{8} \, {\left(\frac{2 \, \sqrt{a^{2} x^{2} + 1} x^{3}}{a^{2}} - \frac{3 \, \sqrt{a^{2} x^{2} + 1} x}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a^{5}}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"-1/16*(x^4/a^2 - 3*x^2/a^4 + 3*arcsinh(a*x)^2/a^6)*a + 1/8*(2*sqrt(a^2*x^2 + 1)*x^3/a^2 - 3*sqrt(a^2*x^2 + 1)*x/a^4 + 3*arcsinh(a*x)/a^5)*arcsinh(a*x)","A",0
113,1,59,0,0.322682," ","integrate(x^3*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{9} \, a {\left(\frac{x^{3}}{a^{2}} - \frac{6 \, x}{a^{4}}\right)} + \frac{1}{3} \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x^{2}}{a^{2}} - \frac{2 \, \sqrt{a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"-1/9*a*(x^3/a^2 - 6*x/a^4) + 1/3*(sqrt(a^2*x^2 + 1)*x^2/a^2 - 2*sqrt(a^2*x^2 + 1)/a^4)*arcsinh(a*x)","A",0
114,1,55,0,0.325683," ","integrate(x^2*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{x^{2}}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)^{2}}{a^{4}}\right)} + \frac{1}{2} \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"-1/4*a*(x^2/a^2 - arcsinh(a*x)^2/a^4) + 1/2*(sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)*arcsinh(a*x)","A",0
115,1,26,0,0.355556," ","integrate(x*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}{a^{2}}"," ",0,"-x/a + sqrt(a^2*x^2 + 1)*arcsinh(a*x)/a^2","A",0
116,1,11,0,0.348427," ","integrate(arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)^{2}}{2 \, a}"," ",0,"1/2*arcsinh(a*x)^2/a","A",0
117,0,0,0,0.000000," ","integrate(arcsinh(a*x)/x/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsinh(a*x)/(sqrt(a^2*x^2 + 1)*x), x)","F",0
118,1,25,0,0.341450," ","integrate(arcsinh(a*x)/x^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","a \log\left(x\right) - \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}{x}"," ",0,"a*log(x) - sqrt(a^2*x^2 + 1)*arcsinh(a*x)/x","A",0
119,0,0,0,0.000000," ","integrate(arcsinh(a*x)/x^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsinh(a*x)/(sqrt(a^2*x^2 + 1)*x^3), x)","F",0
120,1,134,0,0.404638," ","integrate(x^3*(a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, b {\left(\frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{15} \, a {\left(\frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} - \frac{{\left(9 \, c^{4} \sqrt{d} x^{5} + 5 \, c^{2} \sqrt{d} x^{3} - 30 \, \sqrt{d} x\right)} b}{225 \, c^{3}}"," ",0,"1/15*b*(3*(c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(3/2)/(c^4*d))*arcsinh(c*x) + 1/15*a*(3*(c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(3/2)/(c^4*d)) - 1/225*(9*c^4*sqrt(d)*x^5 + 5*c^2*sqrt(d)*x^3 - 30*sqrt(d)*x)*b/c^3","A",0
121,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
122,1,73,0,0.432860," ","integrate(x*(a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b \operatorname{arsinh}\left(c x\right)}{3 \, c^{2} d} - \frac{{\left(c^{2} d^{\frac{3}{2}} x^{3} + 3 \, d^{\frac{3}{2}} x\right)} b}{9 \, c d} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, c^{2} d}"," ",0,"1/3*(c^2*d*x^2 + d)^(3/2)*b*arcsinh(c*x)/(c^2*d) - 1/9*(c^2*d^(3/2)*x^3 + 3*d^(3/2)*x)*b/(c*d) + 1/3*(c^2*d*x^2 + d)^(3/2)*a/(c^2*d)","A",0
123,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
124,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \sqrt{c^{2} d x^{2} + d}\right)} a + b \int \frac{\sqrt{c^{2} d x^{2} + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*arcsinh(1/(c*abs(x))) - sqrt(c^2*d*x^2 + d))*a + b*integrate(sqrt(c^2*d*x^2 + d)*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","{\left(c \sqrt{d} \operatorname{arsinh}\left(c x\right) - \frac{\sqrt{c^{2} d x^{2} + d}}{x}\right)} a + b \int \frac{\sqrt{c^{2} d x^{2} + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{2}}\,{d x}"," ",0,"(c*sqrt(d)*arcsinh(c*x) - sqrt(c^2*d*x^2 + d)/x)*a + b*integrate(sqrt(c^2*d*x^2 + d)*log(c*x + sqrt(c^2*x^2 + 1))/x^2, x)","F",0
126,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \sqrt{c^{2} d x^{2} + d} c^{2} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a + b \int \frac{\sqrt{c^{2} d x^{2} + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(c^2*sqrt(d)*arcsinh(1/(c*abs(x))) - sqrt(c^2*d*x^2 + d)*c^2 + (c^2*d*x^2 + d)^(3/2)/(d*x^2))*a + b*integrate(sqrt(c^2*d*x^2 + d)*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
127,1,133,0,0.532685," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{{\left(\left(-1\right)^{2 \, c^{2} d x^{2} + 2 \, d} c^{2} d^{\frac{3}{2}} \log\left(2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) - c^{2} d^{\frac{3}{2}} \log\left(x^{2} + \frac{1}{c^{2}}\right) + \frac{\sqrt{c^{4} d x^{4} + 2 \, c^{2} d x^{2} + d} d}{x^{2}}\right)} b c}{6 \, d} - \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b \operatorname{arsinh}\left(c x\right)}{3 \, d x^{3}} - \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, d x^{3}}"," ",0,"-1/6*((-1)^(2*c^2*d*x^2 + 2*d)*c^2*d^(3/2)*log(2*c^2*d + 2*d/x^2) - c^2*d^(3/2)*log(x^2 + 1/c^2) + sqrt(c^4*d*x^4 + 2*c^2*d*x^2 + d)*d/x^2)*b*c/d - 1/3*(c^2*d*x^2 + d)^(3/2)*b*arcsinh(c*x)/(d*x^3) - 1/3*(c^2*d*x^2 + d)^(3/2)*a/(d*x^3)","A",0
128,1,145,0,0.394928," ","integrate(x^3*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{35} \, {\left(\frac{5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a - \frac{{\left(75 \, c^{6} d^{\frac{3}{2}} x^{7} + 168 \, c^{4} d^{\frac{3}{2}} x^{5} + 35 \, c^{2} d^{\frac{3}{2}} x^{3} - 210 \, d^{\frac{3}{2}} x\right)} b}{3675 \, c^{3}}"," ",0,"1/35*(5*(c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(5/2)/(c^4*d))*b*arcsinh(c*x) + 1/35*(5*(c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(5/2)/(c^4*d))*a - 1/3675*(75*c^6*d^(3/2)*x^7 + 168*c^4*d^(3/2)*x^5 + 35*c^2*d^(3/2)*x^3 - 210*d^(3/2)*x)*b/c^3","A",0
129,-2,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
130,1,85,0,0.442007," ","integrate(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b \operatorname{arsinh}\left(c x\right)}{5 \, c^{2} d} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, c^{2} d} - \frac{{\left(3 \, c^{4} d^{\frac{5}{2}} x^{5} + 10 \, c^{2} d^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} x\right)} b}{75 \, c d}"," ",0,"1/5*(c^2*d*x^2 + d)^(5/2)*b*arcsinh(c*x)/(c^2*d) + 1/5*(c^2*d*x^2 + d)^(5/2)*a/(c^2*d) - 1/75*(3*c^4*d^(5/2)*x^5 + 10*c^2*d^(5/2)*x^3 + 15*d^(5/2)*x)*b/(c*d)","A",0
131,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
132,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{c^{2} d x^{2} + d} d\right)} a + b \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-1/3*(3*d^(3/2)*arcsinh(1/(c*abs(x))) - (c^2*d*x^2 + d)^(3/2) - 3*sqrt(c^2*d*x^2 + d)*d)*a + b*integrate((c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
133,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
134,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, c^{2} d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, \sqrt{c^{2} d x^{2} + d} c^{2} d + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a + b \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(3*c^2*d^(3/2)*arcsinh(1/(c*abs(x))) - (c^2*d*x^2 + d)^(3/2)*c^2 - 3*sqrt(c^2*d*x^2 + d)*c^2*d + (c^2*d*x^2 + d)^(5/2)/(d*x^2))*a + b*integrate((c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
135,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
136,1,156,0,0.443654," ","integrate(x^3*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{63} \, {\left(\frac{7 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{63} \, {\left(\frac{7 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a - \frac{{\left(49 \, c^{8} d^{\frac{5}{2}} x^{9} + 171 \, c^{6} d^{\frac{5}{2}} x^{7} + 189 \, c^{4} d^{\frac{5}{2}} x^{5} + 21 \, c^{2} d^{\frac{5}{2}} x^{3} - 126 \, d^{\frac{5}{2}} x\right)} b}{3969 \, c^{3}}"," ",0,"1/63*(7*(c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(7/2)/(c^4*d))*b*arcsinh(c*x) + 1/63*(7*(c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(7/2)/(c^4*d))*a - 1/3969*(49*c^8*d^(5/2)*x^9 + 171*c^6*d^(5/2)*x^7 + 189*c^4*d^(5/2)*x^5 + 21*c^2*d^(5/2)*x^3 - 126*d^(5/2)*x)*b/c^3","A",0
137,-2,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
138,1,96,0,0.371095," ","integrate(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b \operatorname{arsinh}\left(c x\right)}{7 \, c^{2} d} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a}{7 \, c^{2} d} - \frac{{\left(5 \, c^{6} d^{\frac{7}{2}} x^{7} + 21 \, c^{4} d^{\frac{7}{2}} x^{5} + 35 \, c^{2} d^{\frac{7}{2}} x^{3} + 35 \, d^{\frac{7}{2}} x\right)} b}{245 \, c d}"," ",0,"1/7*(c^2*d*x^2 + d)^(7/2)*b*arcsinh(c*x)/(c^2*d) + 1/7*(c^2*d*x^2 + d)^(7/2)*a/(c^2*d) - 1/245*(5*c^6*d^(7/2)*x^7 + 21*c^4*d^(7/2)*x^5 + 35*c^2*d^(7/2)*x^3 + 35*d^(7/2)*x)*b/(c*d)","A",0
139,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
140,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(15 \, d^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d - 15 \, \sqrt{c^{2} d x^{2} + d} d^{2}\right)} a + b \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-1/15*(15*d^(5/2)*arcsinh(1/(c*abs(x))) - 3*(c^2*d*x^2 + d)^(5/2) - 5*(c^2*d*x^2 + d)^(3/2)*d - 15*sqrt(c^2*d*x^2 + d)*d^2)*a + b*integrate((c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
141,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
142,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(15 \, c^{2} d^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2} - 5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d - 15 \, \sqrt{c^{2} d x^{2} + d} c^{2} d^{2} + \frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{2}}\right)} a + b \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/6*(15*c^2*d^(5/2)*arcsinh(1/(c*abs(x))) - 3*(c^2*d*x^2 + d)^(5/2)*c^2 - 5*(c^2*d*x^2 + d)^(3/2)*c^2*d - 15*sqrt(c^2*d*x^2 + d)*c^2*d^2 + 3*(c^2*d*x^2 + d)^(7/2)/(d*x^2))*a + b*integrate((c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
143,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
144,1,28,0,0.471544," ","integrate(arcsinh(x)*(x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{2} + \frac{1}{2} \, {\left(\sqrt{x^{2} + 1} x + \operatorname{arsinh}\left(x\right)\right)} \operatorname{arsinh}\left(x\right) - \frac{1}{4} \, \operatorname{arsinh}\left(x\right)^{2}"," ",0,"-1/4*x^2 + 1/2*(sqrt(x^2 + 1)*x + arcsinh(x))*arcsinh(x) - 1/4*arcsinh(x)^2","A",0
145,1,174,0,0.378647," ","integrate(x^5*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, \sqrt{c^{2} d x^{2} + d} x^{4}}{c^{2} d} - \frac{4 \, \sqrt{c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{c^{2} d x^{2} + d}}{c^{6} d}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{15} \, {\left(\frac{3 \, \sqrt{c^{2} d x^{2} + d} x^{4}}{c^{2} d} - \frac{4 \, \sqrt{c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{c^{2} d x^{2} + d}}{c^{6} d}\right)} a - \frac{{\left(9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x\right)} b}{225 \, c^{5} \sqrt{d}}"," ",0,"1/15*(3*sqrt(c^2*d*x^2 + d)*x^4/(c^2*d) - 4*sqrt(c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(c^2*d*x^2 + d)/(c^6*d))*b*arcsinh(c*x) + 1/15*(3*sqrt(c^2*d*x^2 + d)*x^4/(c^2*d) - 4*sqrt(c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(c^2*d*x^2 + d)/(c^6*d))*a - 1/225*(9*c^4*x^5 - 20*c^2*x^3 + 120*x)*b/(c^5*sqrt(d))","A",0
146,-2,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
147,1,117,0,0.360945," ","integrate(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, b {\left(\frac{\sqrt{c^{2} d x^{2} + d} x^{2}}{c^{2} d} - \frac{2 \, \sqrt{c^{2} d x^{2} + d}}{c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{\sqrt{c^{2} d x^{2} + d} x^{2}}{c^{2} d} - \frac{2 \, \sqrt{c^{2} d x^{2} + d}}{c^{4} d}\right)} - \frac{{\left(c^{2} x^{3} - 6 \, x\right)} b}{9 \, c^{3} \sqrt{d}}"," ",0,"1/3*b*(sqrt(c^2*d*x^2 + d)*x^2/(c^2*d) - 2*sqrt(c^2*d*x^2 + d)/(c^4*d))*arcsinh(c*x) + 1/3*a*(sqrt(c^2*d*x^2 + d)*x^2/(c^2*d) - 2*sqrt(c^2*d*x^2 + d)/(c^4*d)) - 1/9*(c^2*x^3 - 6*x)*b/(c^3*sqrt(d))","A",0
148,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
149,1,55,0,0.410441," ","integrate(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{b x}{c \sqrt{d}} + \frac{\sqrt{c^{2} d x^{2} + d} b \operatorname{arsinh}\left(c x\right)}{c^{2} d} + \frac{\sqrt{c^{2} d x^{2} + d} a}{c^{2} d}"," ",0,"-b*x/(c*sqrt(d)) + sqrt(c^2*d*x^2 + d)*b*arcsinh(c*x)/(c^2*d) + sqrt(c^2*d*x^2 + d)*a/(c^2*d)","A",0
150,1,28,0,0.378617," ","integrate((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b \operatorname{arsinh}\left(c x\right)^{2}}{2 \, c \sqrt{d}} + \frac{a \operatorname{arsinh}\left(c x\right)}{c \sqrt{d}}"," ",0,"1/2*b*arcsinh(c*x)^2/(c*sqrt(d)) + a*arcsinh(c*x)/(c*sqrt(d))","A",0
151,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{c^{2} d x^{2} + d} x}\,{d x} - \frac{a \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\sqrt{d}}"," ",0,"b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(c^2*d*x^2 + d)*x), x) - a*arcsinh(1/(c*abs(x)))/sqrt(d)","F",0
152,1,101,0,0.343639," ","integrate((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\left(-1\right)^{2 \, c^{2} d x^{2} + 2 \, d} \sqrt{d} \log\left(2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) - \sqrt{d} \log\left(x^{2} + \frac{1}{c^{2}}\right)\right)} b c}{2 \, d} - \frac{\sqrt{c^{2} d x^{2} + d} b \operatorname{arsinh}\left(c x\right)}{d x} - \frac{\sqrt{c^{2} d x^{2} + d} a}{d x}"," ",0,"-1/2*((-1)^(2*c^2*d*x^2 + 2*d)*sqrt(d)*log(2*c^2*d + 2*d/x^2) - sqrt(d)*log(x^2 + 1/c^2))*b*c/d - sqrt(c^2*d*x^2 + d)*b*arcsinh(c*x)/(d*x) - sqrt(c^2*d*x^2 + d)*a/(d*x)","A",0
153,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\sqrt{d}} - \frac{\sqrt{c^{2} d x^{2} + d}}{d x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{c^{2} d x^{2} + d} x^{3}}\,{d x}"," ",0,"1/2*(c^2*arcsinh(1/(c*abs(x)))/sqrt(d) - sqrt(c^2*d*x^2 + d)/(d*x^2))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(c^2*d*x^2 + d)*x^3), x)","F",0
154,1,121,0,0.354258," ","integrate((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{4 \, c^{2} \log\left(x\right)}{\sqrt{d}} + \frac{1}{\sqrt{d} x^{2}}\right)} b c + \frac{1}{3} \, b {\left(\frac{2 \, \sqrt{c^{2} d x^{2} + d} c^{2}}{d x} - \frac{\sqrt{c^{2} d x^{2} + d}}{d x^{3}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{2 \, \sqrt{c^{2} d x^{2} + d} c^{2}}{d x} - \frac{\sqrt{c^{2} d x^{2} + d}}{d x^{3}}\right)}"," ",0,"-1/6*(4*c^2*log(x)/sqrt(d) + 1/(sqrt(d)*x^2))*b*c + 1/3*b*(2*sqrt(c^2*d*x^2 + d)*c^2/(d*x) - sqrt(c^2*d*x^2 + d)/(d*x^3))*arcsinh(c*x) + 1/3*a*(2*sqrt(c^2*d*x^2 + d)*c^2/(d*x) - sqrt(c^2*d*x^2 + d)/(d*x^3))","A",0
155,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{x^{4}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} - \frac{4 \, x^{2}}{\sqrt{c^{2} d x^{2} + d} c^{4} d} - \frac{8}{\sqrt{c^{2} d x^{2} + d} c^{6} d}\right)} + \frac{1}{3} \, b {\left(\frac{{\left(c^{4} \sqrt{d} x^{4} - 4 \, c^{2} \sqrt{d} x^{2} - 8 \, \sqrt{d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{c^{2} x^{2} + 1} c^{6} d^{2}} - \frac{\frac{1}{3} \, \sqrt{c^{2} x^{2} + 1} c^{2} \sqrt{d} x^{2} + 8 \, \sqrt{d} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{14}{3} \, \sqrt{c^{2} x^{2} + 1} \sqrt{d}}{c^{6} d^{2}} + 3 \, \int \frac{c^{4} \sqrt{d} x^{4} - 4 \, c^{2} \sqrt{d} x^{2} - 8 \, \sqrt{d}}{3 \, {\left(c^{9} d^{2} x^{4} + c^{7} d^{2} x^{2} + {\left(c^{8} d^{2} x^{3} + c^{6} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}\right)}"," ",0,"1/3*a*(x^4/(sqrt(c^2*d*x^2 + d)*c^2*d) - 4*x^2/(sqrt(c^2*d*x^2 + d)*c^4*d) - 8/(sqrt(c^2*d*x^2 + d)*c^6*d)) + 1/3*b*((c^4*sqrt(d)*x^4 - 4*c^2*sqrt(d)*x^2 - 8*sqrt(d))*log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(c^2*x^2 + 1)*c^6*d^2) - integrate((c^4*sqrt(d)*x^4 - 4*c^2*sqrt(d)*x^2 - 8*sqrt(d))/(sqrt(c^2*x^2 + 1)*x), x)/(c^6*d^2) + 3*integrate(1/3*(c^4*sqrt(d)*x^4 - 4*c^2*sqrt(d)*x^2 - 8*sqrt(d))/(c^9*d^2*x^4 + c^7*d^2*x^2 + (c^8*d^2*x^3 + c^6*d^2*x)*sqrt(c^2*x^2 + 1)), x))","F",0
156,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x^{3}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \frac{3 \, x}{\sqrt{c^{2} d x^{2} + d} c^{4} d} - \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*a*(x^3/(sqrt(c^2*d*x^2 + d)*c^2*d) + 3*x/(sqrt(c^2*d*x^2 + d)*c^4*d) - 3*arcsinh(c*x)/(c^5*d^(3/2))) + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(3/2), x)","F",0
157,1,119,0,0.487088," ","integrate(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-b c {\left(\frac{x}{c^{4} d^{\frac{3}{2}}} + \frac{\arctan\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + b {\left(\frac{x^{2}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \frac{2}{\sqrt{c^{2} d x^{2} + d} c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) + a {\left(\frac{x^{2}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \frac{2}{\sqrt{c^{2} d x^{2} + d} c^{4} d}\right)}"," ",0,"-b*c*(x/(c^4*d^(3/2)) + arctan(c*x)/(c^5*d^(3/2))) + b*(x^2/(sqrt(c^2*d*x^2 + d)*c^2*d) + 2/(sqrt(c^2*d*x^2 + d)*c^4*d))*arcsinh(c*x) + a*(x^2/(sqrt(c^2*d*x^2 + d)*c^2*d) + 2/(sqrt(c^2*d*x^2 + d)*c^4*d))","A",0
158,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{x}{\sqrt{c^{2} d x^{2} + d} c^{2} d} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-a*(x/(sqrt(c^2*d*x^2 + d)*c^2*d) - arcsinh(c*x)/(c^3*d^(3/2))) + b*integrate(x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(3/2), x)","F",0
159,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","b {\left(\frac{-\operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{c^{2} d^{\frac{3}{2}}} - \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{c^{2} x^{2} + 1} c^{2} d^{\frac{3}{2}}} - \int \frac{1}{c^{5} d^{\frac{3}{2}} x^{4} + c^{3} d^{\frac{3}{2}} x^{2} + {\left(c^{4} d^{\frac{3}{2}} x^{3} + c^{2} d^{\frac{3}{2}} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} - \frac{a}{\sqrt{c^{2} d x^{2} + d} c^{2} d}"," ",0,"b*(integrate(1/(sqrt(c^2*x^2 + 1)*x), x)/(c^2*d^(3/2)) - log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(c^2*x^2 + 1)*c^2*d^(3/2)) - integrate(1/(c^5*d^(3/2)*x^4 + c^3*d^(3/2)*x^2 + (c^4*d^(3/2)*x^3 + c^2*d^(3/2)*x)*sqrt(c^2*x^2 + 1)), x)) - a/(sqrt(c^2*d*x^2 + d)*c^2*d)","F",0
160,1,58,0,0.346642," ","integrate((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{b x \operatorname{arsinh}\left(c x\right)}{\sqrt{c^{2} d x^{2} + d} d} + \frac{a x}{\sqrt{c^{2} d x^{2} + d} d} - \frac{b \log\left(x^{2} + \frac{1}{c^{2}}\right)}{2 \, c d^{\frac{3}{2}}}"," ",0,"b*x*arcsinh(c*x)/(sqrt(c^2*d*x^2 + d)*d) + a*x/(sqrt(c^2*d*x^2 + d)*d) - 1/2*b*log(x^2 + 1/c^2)/(c*d^(3/2))","A",0
161,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{c^{2} d x^{2} + d} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-a*(arcsinh(1/(c*abs(x)))/d^(3/2) - 1/(sqrt(c^2*d*x^2 + d)*d)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(3/2)*x), x)","F",0
162,1,119,0,0.413049," ","integrate((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, b c {\left(\frac{\log\left(c^{2} x^{2} + 1\right)}{d^{\frac{3}{2}}} + \frac{2 \, \log\left(x\right)}{d^{\frac{3}{2}}}\right)} - {\left(\frac{2 \, c^{2} x}{\sqrt{c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{c^{2} d x^{2} + d} d x}\right)} b \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, c^{2} x}{\sqrt{c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{c^{2} d x^{2} + d} d x}\right)} a"," ",0,"1/2*b*c*(log(c^2*x^2 + 1)/d^(3/2) + 2*log(x)/d^(3/2)) - (2*c^2*x/(sqrt(c^2*d*x^2 + d)*d) + 1/(sqrt(c^2*d*x^2 + d)*d*x))*b*arcsinh(c*x) - (2*c^2*x/(sqrt(c^2*d*x^2 + d)*d) + 1/(sqrt(c^2*d*x^2 + d)*d*x))*a","A",0
163,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\sqrt{c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{c^{2} d x^{2} + d} d x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"1/2*(3*c^2*arcsinh(1/(c*abs(x)))/d^(3/2) - 3*c^2/(sqrt(c^2*d*x^2 + d)*d) - 1/(sqrt(c^2*d*x^2 + d)*d*x^2))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(3/2)*x^3), x)","F",0
164,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\sqrt{c^{2} d x^{2} + d} d} + \frac{4 \, c^{2}}{\sqrt{c^{2} d x^{2} + d} d x} - \frac{1}{\sqrt{c^{2} d x^{2} + d} d x^{3}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"1/3*(8*c^4*x/(sqrt(c^2*d*x^2 + d)*d) + 4*c^2/(sqrt(c^2*d*x^2 + d)*d*x) - 1/(sqrt(c^2*d*x^2 + d)*d*x^3))*a + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(3/2)*x^4), x)","F",0
165,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{3 \, x^{5}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{5 \, x {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)}}{c^{2}} + \frac{5 \, x}{\sqrt{c^{2} d x^{2} + d} c^{6} d^{2}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7} d^{\frac{5}{2}}}\right)} + b \int \frac{x^{6} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/6*a*(3*x^5/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 5*x*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d))/c^2 + 5*x/(sqrt(c^2*d*x^2 + d)*c^6*d^2) - 15*arcsinh(c*x)/(c^7*d^(5/2))) + b*integrate(x^6*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, b {\left(\frac{{\left(3 \, c^{4} \sqrt{d} x^{4} + 12 \, c^{2} \sqrt{d} x^{2} + 8 \, \sqrt{d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{8} d^{3} x^{2} + c^{6} d^{3}\right)} \sqrt{c^{2} x^{2} + 1}} + 3 \, \int \frac{3 \, c^{4} \sqrt{d} x^{4} + 12 \, c^{2} \sqrt{d} x^{2} + 8 \, \sqrt{d}}{3 \, {\left(c^{11} d^{3} x^{6} + 2 \, c^{9} d^{3} x^{4} + c^{7} d^{3} x^{2} + {\left(c^{10} d^{3} x^{5} + 2 \, c^{8} d^{3} x^{3} + c^{6} d^{3} x\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x} - 3 \, \int \frac{3 \, c^{4} \sqrt{d} x^{4} + 12 \, c^{2} \sqrt{d} x^{2} + 8 \, \sqrt{d}}{3 \, {\left(c^{8} d^{3} x^{3} + c^{6} d^{3} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} + \frac{1}{3} \, a {\left(\frac{3 \, x^{4}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{12 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d} + \frac{8}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d}\right)}"," ",0,"1/3*b*((3*c^4*sqrt(d)*x^4 + 12*c^2*sqrt(d)*x^2 + 8*sqrt(d))*log(c*x + sqrt(c^2*x^2 + 1))/((c^8*d^3*x^2 + c^6*d^3)*sqrt(c^2*x^2 + 1)) + 3*integrate(1/3*(3*c^4*sqrt(d)*x^4 + 12*c^2*sqrt(d)*x^2 + 8*sqrt(d))/(c^11*d^3*x^6 + 2*c^9*d^3*x^4 + c^7*d^3*x^2 + (c^10*d^3*x^5 + 2*c^8*d^3*x^3 + c^6*d^3*x)*sqrt(c^2*x^2 + 1)), x) - 3*integrate(1/3*(3*c^4*sqrt(d)*x^4 + 12*c^2*sqrt(d)*x^2 + 8*sqrt(d))/((c^8*d^3*x^3 + c^6*d^3*x)*sqrt(c^2*x^2 + 1)), x)) + 1/3*a*(3*x^4/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 12*x^2/((c^2*d*x^2 + d)^(3/2)*c^4*d) + 8/((c^2*d*x^2 + d)^(3/2)*c^6*d))","F",0
167,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} + \frac{x}{\sqrt{c^{2} d x^{2} + d} c^{4} d^{2}} - \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} a + b \int \frac{x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*(x*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d)) + x/(sqrt(c^2*d*x^2 + d)*c^4*d^2) - 3*arcsinh(c*x)/(c^5*d^(5/2)))*a + b*integrate(x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(5/2), x)","F",0
168,1,138,0,0.588927," ","integrate(x^3*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, b c {\left(\frac{x}{c^{6} d^{\frac{5}{2}} x^{2} + c^{4} d^{\frac{5}{2}}} - \frac{5 \, \arctan\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)}"," ",0,"-1/6*b*c*(x/(c^6*d^(5/2)*x^2 + c^4*d^(5/2)) - 5*arctan(c*x)/(c^5*d^(5/2))) - 1/3*b*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d))*arcsinh(c*x) - 1/3*a*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d))","A",0
169,1,137,0,0.390374," ","integrate(x^2*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, b c {\left(\frac{1}{c^{6} d^{\frac{5}{2}} x^{2} + c^{4} d^{\frac{5}{2}}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{x}{\sqrt{c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{x}{\sqrt{c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)}"," ",0,"-1/6*b*c*(1/(c^6*d^(5/2)*x^2 + c^4*d^(5/2)) + log(c^2*x^2 + 1)/(c^4*d^(5/2))) + 1/3*b*(x/(sqrt(c^2*d*x^2 + d)*c^2*d^2) - x/((c^2*d*x^2 + d)^(3/2)*c^2*d))*arcsinh(c*x) + 1/3*a*(x/(sqrt(c^2*d*x^2 + d)*c^2*d^2) - x/((c^2*d*x^2 + d)^(3/2)*c^2*d))","A",0
170,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","b \int \frac{x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x} - \frac{a}{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"b*integrate(x*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(5/2), x) - 1/3*a/((c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
171,1,126,0,0.356928," ","integrate((a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} + c^{2} d^{\frac{5}{2}}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{2 \, x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)}"," ",0,"1/6*b*c*(1/(c^4*d^(5/2)*x^2 + c^2*d^(5/2)) - 2*log(c^2*x^2 + 1)/(c^2*d^(5/2))) + 1/3*b*(2*x/(sqrt(c^2*d*x^2 + d)*d^2) + x/((c^2*d*x^2 + d)^(3/2)*d))*arcsinh(c*x) + 1/3*a*(2*x/(sqrt(c^2*d*x^2 + d)*d^2) + x/((c^2*d*x^2 + d)^(3/2)*d))","A",0
172,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{c^{2} d x^{2} + d} d^{2}} - \frac{1}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"-1/3*a*(3*arcsinh(1/(c*abs(x)))/d^(5/2) - 3/(sqrt(c^2*d*x^2 + d)*d^2) - 1/((c^2*d*x^2 + d)^(3/2)*d)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(5/2)*x), x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{8 \, c^{2} x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{4 \, c^{2} x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{3}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"-1/3*a*(8*c^2*x/(sqrt(c^2*d*x^2 + d)*d^2) + 4*c^2*x/((c^2*d*x^2 + d)^(3/2)*d) + 3/((c^2*d*x^2 + d)^(3/2)*d*x)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(5/2)*x^2), x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/x^3/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{15 \, c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{15 \, c^{2}}{\sqrt{c^{2} d x^{2} + d} d^{2}} - \frac{5 \, c^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{3}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"1/6*a*(15*c^2*arcsinh(1/(c*abs(x)))/d^(5/2) - 15*c^2/(sqrt(c^2*d*x^2 + d)*d^2) - 5*c^2/((c^2*d*x^2 + d)^(3/2)*d) - 3/((c^2*d*x^2 + d)^(3/2)*d*x^2)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(5/2)*x^3), x)","F",0
175,1,236,0,0.439367," ","integrate((a+b*arcsinh(c*x))/x^4/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, b c {\left(\frac{8 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{d^{\frac{5}{2}}} + \frac{16 \, c^{2} \log\left(x\right)}{d^{\frac{5}{2}}} + \frac{1}{c^{2} d^{\frac{5}{2}} x^{4} + d^{\frac{5}{2}} x^{2}}\right)} + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{6 \, c^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} b \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{6 \, c^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a"," ",0,"-1/6*b*c*(8*c^2*log(c^2*x^2 + 1)/d^(5/2) + 16*c^2*log(x)/d^(5/2) + 1/(c^2*d^(5/2)*x^4 + d^(5/2)*x^2)) + 1/3*(16*c^4*x/(sqrt(c^2*d*x^2 + d)*d^2) + 8*c^4*x/((c^2*d*x^2 + d)^(3/2)*d) + 6*c^2/((c^2*d*x^2 + d)^(3/2)*d*x) - 1/((c^2*d*x^2 + d)^(3/2)*d*x^3))*b*arcsinh(c*x) + 1/3*(16*c^4*x/(sqrt(c^2*d*x^2 + d)*d^2) + 8*c^4*x/((c^2*d*x^2 + d)^(3/2)*d) + 6*c^2/((c^2*d*x^2 + d)^(3/2)*d*x) - 1/((c^2*d*x^2 + d)^(3/2)*d*x^3))*a","A",0
176,1,143,0,0.421517," ","integrate(arcsinh(a*x)/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{1}{60} \, a {\left(\frac{3}{{\left(a^{6} c^{\frac{5}{2}} x^{4} + 2 \, a^{4} c^{\frac{5}{2}} x^{2} + a^{2} c^{\frac{5}{2}}\right)} c} + \frac{8}{{\left(a^{4} c^{\frac{3}{2}} x^{2} + a^{2} c^{\frac{3}{2}}\right)} c^{2}} - \frac{16 \, \log\left(x^{2} + \frac{1}{a^{2}}\right)}{a^{2} c^{\frac{7}{2}}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{a^{2} c x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"1/60*a*(3/((a^6*c^(5/2)*x^4 + 2*a^4*c^(5/2)*x^2 + a^2*c^(5/2))*c) + 8/((a^4*c^(3/2)*x^2 + a^2*c^(3/2))*c^2) - 16*log(x^2 + 1/a^2)/(a^2*c^(7/2))) + 1/15*(8*x/(sqrt(a^2*c*x^2 + c)*c^3) + 4*x/((a^2*c*x^2 + c)^(3/2)*c^2) + 3*x/((a^2*c*x^2 + c)^(5/2)*c))*arcsinh(a*x)","A",0
177,1,83,0,0.415581," ","integrate(x^4*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{x^{4}}{a^{2}} - \frac{3 \, x^{2}}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)^{2}}{a^{6}}\right)} a + \frac{1}{8} \, {\left(\frac{2 \, \sqrt{a^{2} x^{2} + 1} x^{3}}{a^{2}} - \frac{3 \, \sqrt{a^{2} x^{2} + 1} x}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a^{5}}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"-1/16*(x^4/a^2 - 3*x^2/a^4 + 3*arcsinh(a*x)^2/a^6)*a + 1/8*(2*sqrt(a^2*x^2 + 1)*x^3/a^2 - 3*sqrt(a^2*x^2 + 1)*x/a^4 + 3*arcsinh(a*x)/a^5)*arcsinh(a*x)","A",0
178,1,59,0,0.401247," ","integrate(x^3*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{9} \, a {\left(\frac{x^{3}}{a^{2}} - \frac{6 \, x}{a^{4}}\right)} + \frac{1}{3} \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x^{2}}{a^{2}} - \frac{2 \, \sqrt{a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"-1/9*a*(x^3/a^2 - 6*x/a^4) + 1/3*(sqrt(a^2*x^2 + 1)*x^2/a^2 - 2*sqrt(a^2*x^2 + 1)/a^4)*arcsinh(a*x)","A",0
179,1,55,0,0.537594," ","integrate(x^2*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{x^{2}}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)^{2}}{a^{4}}\right)} + \frac{1}{2} \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)} \operatorname{arsinh}\left(a x\right)"," ",0,"-1/4*a*(x^2/a^2 - arcsinh(a*x)^2/a^4) + 1/2*(sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)*arcsinh(a*x)","A",0
180,1,26,0,0.412356," ","integrate(x*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}{a^{2}}"," ",0,"-x/a + sqrt(a^2*x^2 + 1)*arcsinh(a*x)/a^2","A",0
181,1,11,0,0.400915," ","integrate(arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)^{2}}{2 \, a}"," ",0,"1/2*arcsinh(a*x)^2/a","A",0
182,0,0,0,0.000000," ","integrate(arcsinh(a*x)/x/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsinh(a*x)/(sqrt(a^2*x^2 + 1)*x), x)","F",0
183,1,25,0,0.468778," ","integrate(arcsinh(a*x)/x^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","a \log\left(x\right) - \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}{x}"," ",0,"a*log(x) - sqrt(a^2*x^2 + 1)*arcsinh(a*x)/x","A",0
184,0,0,0,0.000000," ","integrate(arcsinh(a*x)/x^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsinh(a*x)/(sqrt(a^2*x^2 + 1)*x^3), x)","F",0
185,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{a c^{6} d^{3} x^{m + 7}}{m + 7} + \frac{3 \, a c^{4} d^{3} x^{m + 5}}{m + 5} + \frac{3 \, a c^{2} d^{3} x^{m + 3}}{m + 3} + \frac{a d^{3} x^{m + 1}}{m + 1} + \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{6} d^{3} x^{7} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{4} d^{3} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{2} d^{3} x^{3} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b d^{3} x\right)} x^{m} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105} - \int \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{7} d^{3} x^{7} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{5} d^{3} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{3} d^{3} x^{3} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c d^{3} x\right)} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{3} x^{3} + {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c x + {\left({\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} + m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x} - \int \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{8} d^{3} x^{8} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{6} d^{3} x^{6} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{4} d^{3} x^{4} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c^{2} d^{3} x^{2}\right)} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} + m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}\,{d x}"," ",0,"a*c^6*d^3*x^(m + 7)/(m + 7) + 3*a*c^4*d^3*x^(m + 5)/(m + 5) + 3*a*c^2*d^3*x^(m + 3)/(m + 3) + a*d^3*x^(m + 1)/(m + 1) + ((m^3 + 9*m^2 + 23*m + 15)*b*c^6*d^3*x^7 + 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^4*d^3*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^2*d^3*x^3 + (m^3 + 15*m^2 + 71*m + 105)*b*d^3*x)*x^m*log(c*x + sqrt(c^2*x^2 + 1))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105) - integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c^7*d^3*x^7 + 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^5*d^3*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^3*d^3*x^3 + (m^3 + 15*m^2 + 71*m + 105)*b*c*d^3*x)*x^m/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^3*x^3 + (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c*x + ((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 + m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*sqrt(c^2*x^2 + 1)), x) - integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c^8*d^3*x^8 + 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^6*d^3*x^6 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^4*d^3*x^4 + (m^3 + 15*m^2 + 71*m + 105)*b*c^2*d^3*x^2)*x^m/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 + m^4 + 16*m^3 + 86*m^2 + 176*m + 105), x)","F",0
186,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{a c^{4} d^{2} x^{m + 5}}{m + 5} + \frac{2 \, a c^{2} d^{2} x^{m + 3}}{m + 3} + \frac{a d^{2} x^{m + 1}}{m + 1} + \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{4} d^{2} x^{5} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{2} d^{2} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} b d^{2} x\right)} x^{m} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{m^{3} + 9 \, m^{2} + 23 \, m + 15} - \int \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{5} d^{2} x^{5} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{3} d^{2} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} b c d^{2} x\right)} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{3} x^{3} + {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c x + {\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} + m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x} - \int \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{6} d^{2} x^{6} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{4} d^{2} x^{4} + {\left(m^{2} + 8 \, m + 15\right)} b c^{2} d^{2} x^{2}\right)} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} + m^{3} + 9 \, m^{2} + 23 \, m + 15}\,{d x}"," ",0,"a*c^4*d^2*x^(m + 5)/(m + 5) + 2*a*c^2*d^2*x^(m + 3)/(m + 3) + a*d^2*x^(m + 1)/(m + 1) + ((m^2 + 4*m + 3)*b*c^4*d^2*x^5 + 2*(m^2 + 6*m + 5)*b*c^2*d^2*x^3 + (m^2 + 8*m + 15)*b*d^2*x)*x^m*log(c*x + sqrt(c^2*x^2 + 1))/(m^3 + 9*m^2 + 23*m + 15) - integrate(((m^2 + 4*m + 3)*b*c^5*d^2*x^5 + 2*(m^2 + 6*m + 5)*b*c^3*d^2*x^3 + (m^2 + 8*m + 15)*b*c*d^2*x)*x^m/((m^3 + 9*m^2 + 23*m + 15)*c^3*x^3 + (m^3 + 9*m^2 + 23*m + 15)*c*x + ((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 + m^3 + 9*m^2 + 23*m + 15)*sqrt(c^2*x^2 + 1)), x) - integrate(((m^2 + 4*m + 3)*b*c^6*d^2*x^6 + 2*(m^2 + 6*m + 5)*b*c^4*d^2*x^4 + (m^2 + 8*m + 15)*b*c^2*d^2*x^2)*x^m/((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 + m^3 + 9*m^2 + 23*m + 15), x)","F",0
187,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{a c^{2} d x^{m + 3}}{m + 3} + \frac{a d x^{m + 1}}{m + 1} + \frac{{\left(b c^{2} d {\left(m + 1\right)} x^{3} + b d {\left(m + 3\right)} x\right)} x^{m} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{m^{2} + 4 \, m + 3} - \int \frac{{\left(b c^{3} d {\left(m + 1\right)} x^{3} + b c d {\left(m + 3\right)} x\right)} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{3} x^{3} + {\left(m^{2} + 4 \, m + 3\right)} c x + {\left({\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} + m^{2} + 4 \, m + 3\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x} - \int \frac{{\left(b c^{4} d {\left(m + 1\right)} x^{4} + b c^{2} d {\left(m + 3\right)} x^{2}\right)} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} + m^{2} + 4 \, m + 3}\,{d x}"," ",0,"a*c^2*d*x^(m + 3)/(m + 3) + a*d*x^(m + 1)/(m + 1) + (b*c^2*d*(m + 1)*x^3 + b*d*(m + 3)*x)*x^m*log(c*x + sqrt(c^2*x^2 + 1))/(m^2 + 4*m + 3) - integrate((b*c^3*d*(m + 1)*x^3 + b*c*d*(m + 3)*x)*x^m/((m^2 + 4*m + 3)*c^3*x^3 + (m^2 + 4*m + 3)*c*x + ((m^2 + 4*m + 3)*c^2*x^2 + m^2 + 4*m + 3)*sqrt(c^2*x^2 + 1)), x) - integrate((b*c^4*d*(m + 1)*x^4 + b*c^2*d*(m + 3)*x^2)*x^m/((m^2 + 4*m + 3)*c^2*x^2 + m^2 + 4*m + 3), x)","F",0
188,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}}{c^{2} d x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*x^m/(c^2*d*x^2 + d), x)","F",0
189,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}}{{\left(c^{2} d x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*x^m/(c^2*d*x^2 + d)^2, x)","F",0
190,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}}{{\left(c^{2} d x^{2} + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*x^m/(c^2*d*x^2 + d)^3, x)","F",0
191,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)*x^m, x)","F",0
192,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)*x^m, x)","F",0
193,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^(1/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)*x^m, x)","F",0
194,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}}{\sqrt{c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*x^m/sqrt(c^2*d*x^2 + d), x)","F",0
195,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*x^m/(c^2*d*x^2 + d)^(3/2), x)","F",0
196,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{m}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*x^m/(c^2*d*x^2 + d)^(5/2), x)","F",0
197,0,0,0,0.000000," ","integrate(x^m*arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{arsinh}\left(a x\right)}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsinh(a*x)/sqrt(a^2*x^2 + 1), x)","F",0
198,1,441,0,0.540595," ","integrate(x^4*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} c^{2} d x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{7} \, a^{2} c^{2} d x^{7} + \frac{1}{5} \, b^{2} d x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{5} \, a^{2} d x^{5} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{2} d - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} c^{2} d + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d"," ",0,"1/7*b^2*c^2*d*x^7*arcsinh(c*x)^2 + 1/7*a^2*c^2*d*x^7 + 1/5*b^2*d*x^5*arcsinh(c*x)^2 + 1/5*a^2*d*x^5 + 2/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*c^2*d - 2/25725*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*c^2*d + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*d - 2/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*d","A",0
199,1,442,0,0.470039," ","integrate(x^3*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} c^{2} d x^{6} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{6} \, a^{2} c^{2} d x^{6} + \frac{1}{4} \, b^{2} d x^{4} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{144} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{2} d + \frac{1}{864} \, {\left({\left(\frac{8 \, x^{6}}{c^{2}} - \frac{15 \, x^{4}}{c^{4}} + \frac{45 \, x^{2}}{c^{6}} - \frac{45 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{8}}\right)} c^{2} - 6 \, {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{2} d + \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} a b d + \frac{1}{32} \, {\left({\left(\frac{x^{4}}{c^{2}} - \frac{3 \, x^{2}}{c^{4}} + \frac{3 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6}}\right)} c^{2} - 2 \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} d"," ",0,"1/6*b^2*c^2*d*x^6*arcsinh(c*x)^2 + 1/6*a^2*c^2*d*x^6 + 1/4*b^2*d*x^4*arcsinh(c*x)^2 + 1/4*a^2*d*x^4 + 1/144*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*a*b*c^2*d + 1/864*((8*x^6/c^2 - 15*x^4/c^4 + 45*x^2/c^6 - 45*log(c*x + sqrt(c^2*x^2 + 1))^2/c^8)*c^2 - 6*(8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c*arcsinh(c*x))*b^2*c^2*d + 1/16*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*a*b*d + 1/32*((x^4/c^2 - 3*x^2/c^4 + 3*log(c*x + sqrt(c^2*x^2 + 1))^2/c^6)*c^2 - 2*(2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c*arcsinh(c*x))*b^2*d","B",0
200,1,346,0,0.439497," ","integrate(x^2*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} c^{2} d x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{5} \, a^{2} c^{2} d x^{5} + \frac{1}{3} \, b^{2} d x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{2} d - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{2} d + \frac{1}{3} \, a^{2} d x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} d"," ",0,"1/5*b^2*c^2*d*x^5*arcsinh(c*x)^2 + 1/5*a^2*c^2*d*x^5 + 1/3*b^2*d*x^3*arcsinh(c*x)^2 + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*c^2*d - 2/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*c^2*d + 1/3*a^2*d*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*d - 2/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*d","A",0
201,1,347,0,0.365384," ","integrate(x*(c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} c^{2} d x^{4} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} c^{2} d x^{4} + \frac{1}{2} \, b^{2} d x^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} a b c^{2} d + \frac{1}{32} \, {\left({\left(\frac{x^{4}}{c^{2}} - \frac{3 \, x^{2}}{c^{4}} + \frac{3 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6}}\right)} c^{2} - 2 \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{2} d + \frac{1}{2} \, a^{2} d x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)}\right)} a b d + \frac{1}{4} \, {\left(c^{2} {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4}}\right)} - 2 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)} \operatorname{arsinh}\left(c x\right)\right)} b^{2} d"," ",0,"1/4*b^2*c^2*d*x^4*arcsinh(c*x)^2 + 1/4*a^2*c^2*d*x^4 + 1/2*b^2*d*x^2*arcsinh(c*x)^2 + 1/16*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*a*b*c^2*d + 1/32*((x^4/c^2 - 3*x^2/c^4 + 3*log(c*x + sqrt(c^2*x^2 + 1))^2/c^6)*c^2 - 2*(2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c*arcsinh(c*x))*b^2*c^2*d + 1/2*a^2*d*x^2 + 1/2*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*a*b*d + 1/4*(c^2*(x^2/c^2 - log(c*x + sqrt(c^2*x^2 + 1))^2/c^4) - 2*c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3)*arcsinh(c*x))*b^2*d","B",0
202,1,230,0,0.721591," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} c^{2} d x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{3} \, a^{2} c^{2} d x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{2} d - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} c^{2} d + b^{2} d x \operatorname{arsinh}\left(c x\right)^{2} + 2 \, b^{2} d {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b d}{c}"," ",0,"1/3*b^2*c^2*d*x^3*arcsinh(c*x)^2 + 1/3*a^2*c^2*d*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*c^2*d - 2/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*c^2*d + b^2*d*x*arcsinh(c*x)^2 + 2*b^2*d*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*d*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*d/c","B",0
203,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c^{2} d x^{2} + a^{2} d \log\left(x\right) + \int b^{2} c^{2} d x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 2 \, a b c^{2} d x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{b^{2} d \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, a b d \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/2*a^2*c^2*d*x^2 + a^2*d*log(x) + integrate(b^2*c^2*d*x*log(c*x + sqrt(c^2*x^2 + 1))^2 + 2*a*b*c^2*d*x*log(c*x + sqrt(c^2*x^2 + 1)) + b^2*d*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*a*b*d*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
204,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x^2,x, algorithm=""maxima"")","b^{2} c^{2} d x \operatorname{arsinh}\left(c x\right)^{2} + 2 \, b^{2} c^{2} d {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} c^{2} d x + 2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b c d - 2 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} a b d - b^{2} d {\left(\frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} - \int \frac{2 \, {\left(c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} c^{2} x + c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{3} x^{4} + c x^{2} + {\left(c^{2} x^{3} + x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} - \frac{a^{2} d}{x}"," ",0,"b^2*c^2*d*x*arcsinh(c*x)^2 + 2*b^2*c^2*d*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*c^2*d*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*c*d - 2*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*a*b*d - b^2*d*(log(c*x + sqrt(c^2*x^2 + 1))^2/x - integrate(2*(c^3*x^2 + sqrt(c^2*x^2 + 1)*c^2*x + c)*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*x^4 + c*x^2 + (c^2*x^3 + x)*sqrt(c^2*x^2 + 1)), x)) - a^2*d/x","F",0
205,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x^3,x, algorithm=""maxima"")","a^{2} c^{2} d \log\left(x\right) - a b d {\left(\frac{\sqrt{c^{2} x^{2} + 1} c}{x} + \frac{\operatorname{arsinh}\left(c x\right)}{x^{2}}\right)} - \frac{a^{2} d}{2 \, x^{2}} + \int \frac{b^{2} c^{2} d \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, a b c^{2} d \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x} + \frac{b^{2} d \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}}\,{d x}"," ",0,"a^2*c^2*d*log(x) - a*b*d*(sqrt(c^2*x^2 + 1)*c/x + arcsinh(c*x)/x^2) - 1/2*a^2*d/x^2 + integrate(b^2*c^2*d*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*a*b*c^2*d*log(c*x + sqrt(c^2*x^2 + 1))/x + b^2*d*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3, x)","F",0
206,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)*(a+b*arcsinh(c*x))^2/x^4,x, algorithm=""maxima"")","-2 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} a b c^{2} d + \frac{1}{3} \, {\left({\left(c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \operatorname{arsinh}\left(c x\right)}{x^{3}}\right)} a b d - \frac{a^{2} c^{2} d}{x} - \frac{a^{2} d}{3 \, x^{3}} - \frac{{\left(3 \, b^{2} c^{2} d x^{2} + b^{2} d\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{3 \, x^{3}} + \int \frac{2 \, {\left(3 \, b^{2} c^{5} d x^{4} + 4 \, b^{2} c^{3} d x^{2} + b^{2} c d + {\left(3 \, b^{2} c^{4} d x^{3} + b^{2} c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c^{3} x^{6} + c x^{4} + {\left(c^{2} x^{5} + x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"-2*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*a*b*c^2*d + 1/3*((c^2*arcsinh(1/(c*abs(x))) - sqrt(c^2*x^2 + 1)/x^2)*c - 2*arcsinh(c*x)/x^3)*a*b*d - a^2*c^2*d/x - 1/3*a^2*d/x^3 - 1/3*(3*b^2*c^2*d*x^2 + b^2*d)*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 + integrate(2/3*(3*b^2*c^5*d*x^4 + 4*b^2*c^3*d*x^2 + b^2*c*d + (3*b^2*c^4*d*x^3 + b^2*c^2*d*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*x^6 + c*x^4 + (c^2*x^5 + x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
207,1,760,0,0.453226," ","integrate(x^4*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} c^{4} d^{2} x^{9} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{9} \, a^{2} c^{4} d^{2} x^{9} + \frac{2}{7} \, b^{2} c^{2} d^{2} x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{7} \, a^{2} c^{2} d^{2} x^{7} + \frac{1}{5} \, b^{2} d^{2} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{2835} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} a b c^{4} d^{2} - \frac{2}{893025} \, {\left(315 \, {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{1225 \, c^{8} x^{9} - 1800 \, c^{6} x^{7} + 3024 \, c^{4} x^{5} - 6720 \, c^{2} x^{3} + 40320 \, x}{c^{8}}\right)} b^{2} c^{4} d^{2} + \frac{1}{5} \, a^{2} d^{2} x^{5} + \frac{4}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{2} d^{2} - \frac{4}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} c^{2} d^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d^{2} - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d^{2}"," ",0,"1/9*b^2*c^4*d^2*x^9*arcsinh(c*x)^2 + 1/9*a^2*c^4*d^2*x^9 + 2/7*b^2*c^2*d^2*x^7*arcsinh(c*x)^2 + 2/7*a^2*c^2*d^2*x^7 + 1/5*b^2*d^2*x^5*arcsinh(c*x)^2 + 2/2835*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*a*b*c^4*d^2 - 2/893025*(315*(35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c*arcsinh(c*x) - (1225*c^8*x^9 - 1800*c^6*x^7 + 3024*c^4*x^5 - 6720*c^2*x^3 + 40320*x)/c^8)*b^2*c^4*d^2 + 1/5*a^2*d^2*x^5 + 4/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*c^2*d^2 - 4/25725*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*c^2*d^2 + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*d^2 - 2/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*d^2","B",0
208,1,762,0,0.613454," ","integrate(x^3*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} c^{4} d^{2} x^{8} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{8} \, a^{2} c^{4} d^{2} x^{8} + \frac{1}{3} \, b^{2} c^{2} d^{2} x^{6} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{3} \, a^{2} c^{2} d^{2} x^{6} + \frac{1}{4} \, b^{2} d^{2} x^{4} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{1536} \, {\left(384 \, x^{8} \operatorname{arsinh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c\right)} a b c^{4} d^{2} + \frac{1}{9216} \, {\left({\left(\frac{36 \, x^{8}}{c^{2}} - \frac{56 \, x^{6}}{c^{4}} + \frac{105 \, x^{4}}{c^{6}} - \frac{315 \, x^{2}}{c^{8}} + \frac{315 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{10}}\right)} c^{2} - 6 \, {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{4} d^{2} + \frac{1}{4} \, a^{2} d^{2} x^{4} + \frac{1}{72} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{2} d^{2} + \frac{1}{432} \, {\left({\left(\frac{8 \, x^{6}}{c^{2}} - \frac{15 \, x^{4}}{c^{4}} + \frac{45 \, x^{2}}{c^{6}} - \frac{45 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{8}}\right)} c^{2} - 6 \, {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{2} d^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} a b d^{2} + \frac{1}{32} \, {\left({\left(\frac{x^{4}}{c^{2}} - \frac{3 \, x^{2}}{c^{4}} + \frac{3 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6}}\right)} c^{2} - 2 \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} d^{2}"," ",0,"1/8*b^2*c^4*d^2*x^8*arcsinh(c*x)^2 + 1/8*a^2*c^4*d^2*x^8 + 1/3*b^2*c^2*d^2*x^6*arcsinh(c*x)^2 + 1/3*a^2*c^2*d^2*x^6 + 1/4*b^2*d^2*x^4*arcsinh(c*x)^2 + 1/1536*(384*x^8*arcsinh(c*x) - (48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c)*a*b*c^4*d^2 + 1/9216*((36*x^8/c^2 - 56*x^6/c^4 + 105*x^4/c^6 - 315*x^2/c^8 + 315*log(c*x + sqrt(c^2*x^2 + 1))^2/c^10)*c^2 - 6*(48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c*arcsinh(c*x))*b^2*c^4*d^2 + 1/4*a^2*d^2*x^4 + 1/72*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*a*b*c^2*d^2 + 1/432*((8*x^6/c^2 - 15*x^4/c^4 + 45*x^2/c^6 - 45*log(c*x + sqrt(c^2*x^2 + 1))^2/c^8)*c^2 - 6*(8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c*arcsinh(c*x))*b^2*c^2*d^2 + 1/16*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*a*b*d^2 + 1/32*((x^4/c^2 - 3*x^2/c^4 + 3*log(c*x + sqrt(c^2*x^2 + 1))^2/c^6)*c^2 - 2*(2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c*arcsinh(c*x))*b^2*d^2","B",0
209,1,619,0,0.377336," ","integrate(x^2*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} c^{4} d^{2} x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{7} \, a^{2} c^{4} d^{2} x^{7} + \frac{2}{5} \, b^{2} c^{2} d^{2} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{5} \, a^{2} c^{2} d^{2} x^{5} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{4} d^{2} - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} c^{4} d^{2} + \frac{1}{3} \, b^{2} d^{2} x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{4}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{2} d^{2} - \frac{4}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{2} d^{2} + \frac{1}{3} \, a^{2} d^{2} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d^{2} - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} d^{2}"," ",0,"1/7*b^2*c^4*d^2*x^7*arcsinh(c*x)^2 + 1/7*a^2*c^4*d^2*x^7 + 2/5*b^2*c^2*d^2*x^5*arcsinh(c*x)^2 + 2/5*a^2*c^2*d^2*x^5 + 2/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*c^4*d^2 - 2/25725*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*c^4*d^2 + 1/3*b^2*d^2*x^3*arcsinh(c*x)^2 + 4/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*c^2*d^2 - 4/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*c^2*d^2 + 1/3*a^2*d^2*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*d^2 - 2/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*d^2","B",0
210,1,621,0,0.545008," ","integrate(x*(c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} c^{4} d^{2} x^{6} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{6} \, a^{2} c^{4} d^{2} x^{6} + \frac{1}{2} \, b^{2} c^{2} d^{2} x^{4} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} c^{2} d^{2} x^{4} + \frac{1}{144} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{4} d^{2} + \frac{1}{864} \, {\left({\left(\frac{8 \, x^{6}}{c^{2}} - \frac{15 \, x^{4}}{c^{4}} + \frac{45 \, x^{2}}{c^{6}} - \frac{45 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{8}}\right)} c^{2} - 6 \, {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{4} d^{2} + \frac{1}{2} \, b^{2} d^{2} x^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{8} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} a b c^{2} d^{2} + \frac{1}{16} \, {\left({\left(\frac{x^{4}}{c^{2}} - \frac{3 \, x^{2}}{c^{4}} + \frac{3 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6}}\right)} c^{2} - 2 \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{2} d^{2} + \frac{1}{2} \, a^{2} d^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)}\right)} a b d^{2} + \frac{1}{4} \, {\left(c^{2} {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4}}\right)} - 2 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)} \operatorname{arsinh}\left(c x\right)\right)} b^{2} d^{2}"," ",0,"1/6*b^2*c^4*d^2*x^6*arcsinh(c*x)^2 + 1/6*a^2*c^4*d^2*x^6 + 1/2*b^2*c^2*d^2*x^4*arcsinh(c*x)^2 + 1/2*a^2*c^2*d^2*x^4 + 1/144*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*a*b*c^4*d^2 + 1/864*((8*x^6/c^2 - 15*x^4/c^4 + 45*x^2/c^6 - 45*log(c*x + sqrt(c^2*x^2 + 1))^2/c^8)*c^2 - 6*(8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c*arcsinh(c*x))*b^2*c^4*d^2 + 1/2*b^2*d^2*x^2*arcsinh(c*x)^2 + 1/8*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*a*b*c^2*d^2 + 1/16*((x^4/c^2 - 3*x^2/c^4 + 3*log(c*x + sqrt(c^2*x^2 + 1))^2/c^6)*c^2 - 2*(2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c*arcsinh(c*x))*b^2*c^2*d^2 + 1/2*a^2*d^2*x^2 + 1/2*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*a*b*d^2 + 1/4*(c^2*(x^2/c^2 - log(c*x + sqrt(c^2*x^2 + 1))^2/c^4) - 2*c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3)*arcsinh(c*x))*b^2*d^2","B",0
211,1,457,0,0.541194," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} c^{4} d^{2} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{5} \, a^{2} c^{4} d^{2} x^{5} + \frac{2}{3} \, b^{2} c^{2} d^{2} x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{4} d^{2} - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{4} d^{2} + \frac{2}{3} \, a^{2} c^{2} d^{2} x^{3} + \frac{4}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{2} d^{2} - \frac{4}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} c^{2} d^{2} + b^{2} d^{2} x \operatorname{arsinh}\left(c x\right)^{2} + 2 \, b^{2} d^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b d^{2}}{c}"," ",0,"1/5*b^2*c^4*d^2*x^5*arcsinh(c*x)^2 + 1/5*a^2*c^4*d^2*x^5 + 2/3*b^2*c^2*d^2*x^3*arcsinh(c*x)^2 + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*c^4*d^2 - 2/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*c^4*d^2 + 2/3*a^2*c^2*d^2*x^3 + 4/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*c^2*d^2 - 4/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*c^2*d^2 + b^2*d^2*x*arcsinh(c*x)^2 + 2*b^2*d^2*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*d^2*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*d^2/c","B",0
212,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c^{4} d^{2} x^{4} + a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} \log\left(x\right) + \int b^{2} c^{4} d^{2} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 2 \, a b c^{4} d^{2} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, b^{2} c^{2} d^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 4 \, a b c^{2} d^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{b^{2} d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, a b d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/4*a^2*c^4*d^2*x^4 + a^2*c^2*d^2*x^2 + a^2*d^2*log(x) + integrate(b^2*c^4*d^2*x^3*log(c*x + sqrt(c^2*x^2 + 1))^2 + 2*a*b*c^4*d^2*x^3*log(c*x + sqrt(c^2*x^2 + 1)) + 2*b^2*c^2*d^2*x*log(c*x + sqrt(c^2*x^2 + 1))^2 + 4*a*b*c^2*d^2*x*log(c*x + sqrt(c^2*x^2 + 1)) + b^2*d^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*a*b*d^2*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
213,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c^{4} d^{2} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{4} d^{2} + 2 \, b^{2} c^{2} d^{2} x \operatorname{arsinh}\left(c x\right)^{2} + 4 \, b^{2} c^{2} d^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + 2 \, a^{2} c^{2} d^{2} x + 4 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b c d^{2} - 2 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} a b d^{2} - \frac{a^{2} d^{2}}{x} + \frac{{\left(b^{2} c^{4} d^{2} x^{4} - 3 \, b^{2} d^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{3 \, x} - \int \frac{2 \, {\left(b^{2} c^{7} d^{2} x^{6} + b^{2} c^{5} d^{2} x^{4} - 3 \, b^{2} c^{3} d^{2} x^{2} - 3 \, b^{2} c d^{2} + {\left(b^{2} c^{6} d^{2} x^{5} - 3 \, b^{2} c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c^{3} x^{4} + c x^{2} + {\left(c^{2} x^{3} + x\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"1/3*a^2*c^4*d^2*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*c^4*d^2 + 2*b^2*c^2*d^2*x*arcsinh(c*x)^2 + 4*b^2*c^2*d^2*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + 2*a^2*c^2*d^2*x + 4*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*c*d^2 - 2*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*a*b*d^2 - a^2*d^2/x + 1/3*(b^2*c^4*d^2*x^4 - 3*b^2*d^2)*log(c*x + sqrt(c^2*x^2 + 1))^2/x - integrate(2/3*(b^2*c^7*d^2*x^6 + b^2*c^5*d^2*x^4 - 3*b^2*c^3*d^2*x^2 - 3*b^2*c*d^2 + (b^2*c^6*d^2*x^5 - 3*b^2*c^2*d^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*x^4 + c*x^2 + (c^2*x^3 + x)*sqrt(c^2*x^2 + 1)), x)","F",0
214,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c^{4} d^{2} x^{2} + 2 \, a^{2} c^{2} d^{2} \log\left(x\right) - a b d^{2} {\left(\frac{\sqrt{c^{2} x^{2} + 1} c}{x} + \frac{\operatorname{arsinh}\left(c x\right)}{x^{2}}\right)} - \frac{a^{2} d^{2}}{2 \, x^{2}} + \int b^{2} c^{4} d^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 2 \, a b c^{4} d^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{2 \, b^{2} c^{2} d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{4 \, a b c^{2} d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x} + \frac{b^{2} d^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}}\,{d x}"," ",0,"1/2*a^2*c^4*d^2*x^2 + 2*a^2*c^2*d^2*log(x) - a*b*d^2*(sqrt(c^2*x^2 + 1)*c/x + arcsinh(c*x)/x^2) - 1/2*a^2*d^2/x^2 + integrate(b^2*c^4*d^2*x*log(c*x + sqrt(c^2*x^2 + 1))^2 + 2*a*b*c^4*d^2*x*log(c*x + sqrt(c^2*x^2 + 1)) + 2*b^2*c^2*d^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 4*a*b*c^2*d^2*log(c*x + sqrt(c^2*x^2 + 1))/x + b^2*d^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3, x)","F",0
215,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2*(a+b*arcsinh(c*x))^2/x^4,x, algorithm=""maxima"")","b^{2} c^{4} d^{2} x \operatorname{arsinh}\left(c x\right)^{2} + 2 \, b^{2} c^{4} d^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} c^{4} d^{2} x + 2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b c^{3} d^{2} - 4 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} a b c^{2} d^{2} + \frac{1}{3} \, {\left({\left(c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \operatorname{arsinh}\left(c x\right)}{x^{3}}\right)} a b d^{2} - \frac{2 \, a^{2} c^{2} d^{2}}{x} - \frac{a^{2} d^{2}}{3 \, x^{3}} - \frac{{\left(6 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{3 \, x^{3}} + \int \frac{2 \, {\left(6 \, b^{2} c^{5} d^{2} x^{4} + 7 \, b^{2} c^{3} d^{2} x^{2} + b^{2} c d^{2} + {\left(6 \, b^{2} c^{4} d^{2} x^{3} + b^{2} c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c^{3} x^{6} + c x^{4} + {\left(c^{2} x^{5} + x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"b^2*c^4*d^2*x*arcsinh(c*x)^2 + 2*b^2*c^4*d^2*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*c^4*d^2*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*c^3*d^2 - 4*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*a*b*c^2*d^2 + 1/3*((c^2*arcsinh(1/(c*abs(x))) - sqrt(c^2*x^2 + 1)/x^2)*c - 2*arcsinh(c*x)/x^3)*a*b*d^2 - 2*a^2*c^2*d^2/x - 1/3*a^2*d^2/x^3 - 1/3*(6*b^2*c^2*d^2*x^2 + b^2*d^2)*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 + integrate(2/3*(6*b^2*c^5*d^2*x^4 + 7*b^2*c^3*d^2*x^2 + b^2*c*d^2 + (6*b^2*c^4*d^2*x^3 + b^2*c^2*d^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*x^6 + c*x^4 + (c^2*x^5 + x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
216,1,1109,0,0.465008," ","integrate(x^4*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{11} \, b^{2} c^{6} d^{3} x^{11} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{11} \, a^{2} c^{6} d^{3} x^{11} + \frac{1}{3} \, b^{2} c^{4} d^{3} x^{9} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{3} \, a^{2} c^{4} d^{3} x^{9} + \frac{3}{7} \, b^{2} c^{2} d^{3} x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{7} \, a^{2} c^{2} d^{3} x^{7} + \frac{2}{7623} \, {\left(693 \, x^{11} \operatorname{arsinh}\left(c x\right) - {\left(\frac{63 \, \sqrt{c^{2} x^{2} + 1} x^{10}}{c^{2}} - \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{6}} - \frac{96 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{10}} - \frac{256 \, \sqrt{c^{2} x^{2} + 1}}{c^{12}}\right)} c\right)} a b c^{6} d^{3} - \frac{2}{26413695} \, {\left(3465 \, {\left(\frac{63 \, \sqrt{c^{2} x^{2} + 1} x^{10}}{c^{2}} - \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{6}} - \frac{96 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{10}} - \frac{256 \, \sqrt{c^{2} x^{2} + 1}}{c^{12}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{19845 \, c^{10} x^{11} - 26950 \, c^{8} x^{9} + 39600 \, c^{6} x^{7} - 66528 \, c^{4} x^{5} + 147840 \, c^{2} x^{3} - 887040 \, x}{c^{10}}\right)} b^{2} c^{6} d^{3} + \frac{1}{5} \, b^{2} d^{3} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{945} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} a b c^{4} d^{3} - \frac{2}{297675} \, {\left(315 \, {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{1225 \, c^{8} x^{9} - 1800 \, c^{6} x^{7} + 3024 \, c^{4} x^{5} - 6720 \, c^{2} x^{3} + 40320 \, x}{c^{8}}\right)} b^{2} c^{4} d^{3} + \frac{1}{5} \, a^{2} d^{3} x^{5} + \frac{6}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{2} d^{3} - \frac{2}{8575} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} c^{2} d^{3} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d^{3} - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d^{3}"," ",0,"1/11*b^2*c^6*d^3*x^11*arcsinh(c*x)^2 + 1/11*a^2*c^6*d^3*x^11 + 1/3*b^2*c^4*d^3*x^9*arcsinh(c*x)^2 + 1/3*a^2*c^4*d^3*x^9 + 3/7*b^2*c^2*d^3*x^7*arcsinh(c*x)^2 + 3/7*a^2*c^2*d^3*x^7 + 2/7623*(693*x^11*arcsinh(c*x) - (63*sqrt(c^2*x^2 + 1)*x^10/c^2 - 70*sqrt(c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(c^2*x^2 + 1)*x^6/c^6 - 96*sqrt(c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(c^2*x^2 + 1)*x^2/c^10 - 256*sqrt(c^2*x^2 + 1)/c^12)*c)*a*b*c^6*d^3 - 2/26413695*(3465*(63*sqrt(c^2*x^2 + 1)*x^10/c^2 - 70*sqrt(c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(c^2*x^2 + 1)*x^6/c^6 - 96*sqrt(c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(c^2*x^2 + 1)*x^2/c^10 - 256*sqrt(c^2*x^2 + 1)/c^12)*c*arcsinh(c*x) - (19845*c^10*x^11 - 26950*c^8*x^9 + 39600*c^6*x^7 - 66528*c^4*x^5 + 147840*c^2*x^3 - 887040*x)/c^10)*b^2*c^6*d^3 + 1/5*b^2*d^3*x^5*arcsinh(c*x)^2 + 2/945*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*a*b*c^4*d^3 - 2/297675*(315*(35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c*arcsinh(c*x) - (1225*c^8*x^9 - 1800*c^6*x^7 + 3024*c^4*x^5 - 6720*c^2*x^3 + 40320*x)/c^8)*b^2*c^4*d^3 + 1/5*a^2*d^3*x^5 + 6/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*c^2*d^3 - 2/8575*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*c^2*d^3 + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*d^3 - 2/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*d^3","B",0
217,1,1112,0,0.602782," ","integrate(x^3*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{10} \, b^{2} c^{6} d^{3} x^{10} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{10} \, a^{2} c^{6} d^{3} x^{10} + \frac{3}{8} \, b^{2} c^{4} d^{3} x^{8} \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{8} \, a^{2} c^{4} d^{3} x^{8} + \frac{1}{2} \, b^{2} c^{2} d^{3} x^{6} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} c^{2} d^{3} x^{6} + \frac{1}{6400} \, {\left(1280 \, x^{10} \operatorname{arsinh}\left(c x\right) - {\left(\frac{128 \, \sqrt{c^{2} x^{2} + 1} x^{9}}{c^{2}} - \frac{144 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{6}} - \frac{210 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{c^{2} x^{2} + 1} x}{c^{10}} - \frac{315 \, \operatorname{arsinh}\left(c x\right)}{c^{11}}\right)} c\right)} a b c^{6} d^{3} + \frac{1}{64000} \, {\left({\left(\frac{128 \, x^{10}}{c^{2}} - \frac{180 \, x^{8}}{c^{4}} + \frac{280 \, x^{6}}{c^{6}} - \frac{525 \, x^{4}}{c^{8}} + \frac{1575 \, x^{2}}{c^{10}} - \frac{1575 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{12}}\right)} c^{2} - 10 \, {\left(\frac{128 \, \sqrt{c^{2} x^{2} + 1} x^{9}}{c^{2}} - \frac{144 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{6}} - \frac{210 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{c^{2} x^{2} + 1} x}{c^{10}} - \frac{315 \, \operatorname{arsinh}\left(c x\right)}{c^{11}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{6} d^{3} + \frac{1}{4} \, b^{2} d^{3} x^{4} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{512} \, {\left(384 \, x^{8} \operatorname{arsinh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c\right)} a b c^{4} d^{3} + \frac{1}{3072} \, {\left({\left(\frac{36 \, x^{8}}{c^{2}} - \frac{56 \, x^{6}}{c^{4}} + \frac{105 \, x^{4}}{c^{6}} - \frac{315 \, x^{2}}{c^{8}} + \frac{315 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{10}}\right)} c^{2} - 6 \, {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{4} d^{3} + \frac{1}{4} \, a^{2} d^{3} x^{4} + \frac{1}{48} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{2} d^{3} + \frac{1}{288} \, {\left({\left(\frac{8 \, x^{6}}{c^{2}} - \frac{15 \, x^{4}}{c^{4}} + \frac{45 \, x^{2}}{c^{6}} - \frac{45 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{8}}\right)} c^{2} - 6 \, {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{2} d^{3} + \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} a b d^{3} + \frac{1}{32} \, {\left({\left(\frac{x^{4}}{c^{2}} - \frac{3 \, x^{2}}{c^{4}} + \frac{3 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6}}\right)} c^{2} - 2 \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} d^{3}"," ",0,"1/10*b^2*c^6*d^3*x^10*arcsinh(c*x)^2 + 1/10*a^2*c^6*d^3*x^10 + 3/8*b^2*c^4*d^3*x^8*arcsinh(c*x)^2 + 3/8*a^2*c^4*d^3*x^8 + 1/2*b^2*c^2*d^3*x^6*arcsinh(c*x)^2 + 1/2*a^2*c^2*d^3*x^6 + 1/6400*(1280*x^10*arcsinh(c*x) - (128*sqrt(c^2*x^2 + 1)*x^9/c^2 - 144*sqrt(c^2*x^2 + 1)*x^7/c^4 + 168*sqrt(c^2*x^2 + 1)*x^5/c^6 - 210*sqrt(c^2*x^2 + 1)*x^3/c^8 + 315*sqrt(c^2*x^2 + 1)*x/c^10 - 315*arcsinh(c*x)/c^11)*c)*a*b*c^6*d^3 + 1/64000*((128*x^10/c^2 - 180*x^8/c^4 + 280*x^6/c^6 - 525*x^4/c^8 + 1575*x^2/c^10 - 1575*log(c*x + sqrt(c^2*x^2 + 1))^2/c^12)*c^2 - 10*(128*sqrt(c^2*x^2 + 1)*x^9/c^2 - 144*sqrt(c^2*x^2 + 1)*x^7/c^4 + 168*sqrt(c^2*x^2 + 1)*x^5/c^6 - 210*sqrt(c^2*x^2 + 1)*x^3/c^8 + 315*sqrt(c^2*x^2 + 1)*x/c^10 - 315*arcsinh(c*x)/c^11)*c*arcsinh(c*x))*b^2*c^6*d^3 + 1/4*b^2*d^3*x^4*arcsinh(c*x)^2 + 1/512*(384*x^8*arcsinh(c*x) - (48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c)*a*b*c^4*d^3 + 1/3072*((36*x^8/c^2 - 56*x^6/c^4 + 105*x^4/c^6 - 315*x^2/c^8 + 315*log(c*x + sqrt(c^2*x^2 + 1))^2/c^10)*c^2 - 6*(48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c*arcsinh(c*x))*b^2*c^4*d^3 + 1/4*a^2*d^3*x^4 + 1/48*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*a*b*c^2*d^3 + 1/288*((8*x^6/c^2 - 15*x^4/c^4 + 45*x^2/c^6 - 45*log(c*x + sqrt(c^2*x^2 + 1))^2/c^8)*c^2 - 6*(8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c*arcsinh(c*x))*b^2*c^2*d^3 + 1/16*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*a*b*d^3 + 1/32*((x^4/c^2 - 3*x^2/c^4 + 3*log(c*x + sqrt(c^2*x^2 + 1))^2/c^6)*c^2 - 2*(2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c*arcsinh(c*x))*b^2*d^3","B",0
218,1,922,0,0.449078," ","integrate(x^2*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} c^{6} d^{3} x^{9} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{9} \, a^{2} c^{6} d^{3} x^{9} + \frac{3}{7} \, b^{2} c^{4} d^{3} x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{7} \, a^{2} c^{4} d^{3} x^{7} + \frac{3}{5} \, b^{2} c^{2} d^{3} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{2835} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} a b c^{6} d^{3} - \frac{2}{893025} \, {\left(315 \, {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{1225 \, c^{8} x^{9} - 1800 \, c^{6} x^{7} + 3024 \, c^{4} x^{5} - 6720 \, c^{2} x^{3} + 40320 \, x}{c^{8}}\right)} b^{2} c^{6} d^{3} + \frac{3}{5} \, a^{2} c^{2} d^{3} x^{5} + \frac{6}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{4} d^{3} - \frac{2}{8575} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} c^{4} d^{3} + \frac{1}{3} \, b^{2} d^{3} x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{2} d^{3} - \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{2} d^{3} + \frac{1}{3} \, a^{2} d^{3} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d^{3} - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} d^{3}"," ",0,"1/9*b^2*c^6*d^3*x^9*arcsinh(c*x)^2 + 1/9*a^2*c^6*d^3*x^9 + 3/7*b^2*c^4*d^3*x^7*arcsinh(c*x)^2 + 3/7*a^2*c^4*d^3*x^7 + 3/5*b^2*c^2*d^3*x^5*arcsinh(c*x)^2 + 2/2835*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*a*b*c^6*d^3 - 2/893025*(315*(35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c*arcsinh(c*x) - (1225*c^8*x^9 - 1800*c^6*x^7 + 3024*c^4*x^5 - 6720*c^2*x^3 + 40320*x)/c^8)*b^2*c^6*d^3 + 3/5*a^2*c^2*d^3*x^5 + 6/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*c^4*d^3 - 2/8575*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*c^4*d^3 + 1/3*b^2*d^3*x^3*arcsinh(c*x)^2 + 2/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*c^2*d^3 - 2/375*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*c^2*d^3 + 1/3*a^2*d^3*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*d^3 - 2/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*d^3","B",0
219,1,925,0,0.453085," ","integrate(x*(c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} c^{6} d^{3} x^{8} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{8} \, a^{2} c^{6} d^{3} x^{8} + \frac{1}{2} \, b^{2} c^{4} d^{3} x^{6} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} c^{4} d^{3} x^{6} + \frac{3}{4} \, b^{2} c^{2} d^{3} x^{4} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{1536} \, {\left(384 \, x^{8} \operatorname{arsinh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c\right)} a b c^{6} d^{3} + \frac{1}{9216} \, {\left({\left(\frac{36 \, x^{8}}{c^{2}} - \frac{56 \, x^{6}}{c^{4}} + \frac{105 \, x^{4}}{c^{6}} - \frac{315 \, x^{2}}{c^{8}} + \frac{315 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{10}}\right)} c^{2} - 6 \, {\left(\frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{7}}{c^{2}} - \frac{56 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{6}} - \frac{105 \, \sqrt{c^{2} x^{2} + 1} x}{c^{8}} + \frac{105 \, \operatorname{arsinh}\left(c x\right)}{c^{9}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{6} d^{3} + \frac{3}{4} \, a^{2} c^{2} d^{3} x^{4} + \frac{1}{48} \, {\left(48 \, x^{6} \operatorname{arsinh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{4} d^{3} + \frac{1}{288} \, {\left({\left(\frac{8 \, x^{6}}{c^{2}} - \frac{15 \, x^{4}}{c^{4}} + \frac{45 \, x^{2}}{c^{6}} - \frac{45 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{8}}\right)} c^{2} - 6 \, {\left(\frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{5}}{c^{2}} - \frac{10 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \operatorname{arsinh}\left(c x\right)}{c^{7}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{4} d^{3} + \frac{1}{2} \, b^{2} d^{3} x^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{16} \, {\left(8 \, x^{4} \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c\right)} a b c^{2} d^{3} + \frac{3}{32} \, {\left({\left(\frac{x^{4}}{c^{2}} - \frac{3 \, x^{2}}{c^{4}} + \frac{3 \, \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6}}\right)} c^{2} - 2 \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} + 1} x^{3}}{c^{2}} - \frac{3 \, \sqrt{c^{2} x^{2} + 1} x}{c^{4}} + \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5}}\right)} c \operatorname{arsinh}\left(c x\right)\right)} b^{2} c^{2} d^{3} + \frac{1}{2} \, a^{2} d^{3} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)}\right)} a b d^{3} + \frac{1}{4} \, {\left(c^{2} {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4}}\right)} - 2 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x}{c^{2}} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3}}\right)} \operatorname{arsinh}\left(c x\right)\right)} b^{2} d^{3}"," ",0,"1/8*b^2*c^6*d^3*x^8*arcsinh(c*x)^2 + 1/8*a^2*c^6*d^3*x^8 + 1/2*b^2*c^4*d^3*x^6*arcsinh(c*x)^2 + 1/2*a^2*c^4*d^3*x^6 + 3/4*b^2*c^2*d^3*x^4*arcsinh(c*x)^2 + 1/1536*(384*x^8*arcsinh(c*x) - (48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c)*a*b*c^6*d^3 + 1/9216*((36*x^8/c^2 - 56*x^6/c^4 + 105*x^4/c^6 - 315*x^2/c^8 + 315*log(c*x + sqrt(c^2*x^2 + 1))^2/c^10)*c^2 - 6*(48*sqrt(c^2*x^2 + 1)*x^7/c^2 - 56*sqrt(c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(c^2*x^2 + 1)*x^3/c^6 - 105*sqrt(c^2*x^2 + 1)*x/c^8 + 105*arcsinh(c*x)/c^9)*c*arcsinh(c*x))*b^2*c^6*d^3 + 3/4*a^2*c^2*d^3*x^4 + 1/48*(48*x^6*arcsinh(c*x) - (8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c)*a*b*c^4*d^3 + 1/288*((8*x^6/c^2 - 15*x^4/c^4 + 45*x^2/c^6 - 45*log(c*x + sqrt(c^2*x^2 + 1))^2/c^8)*c^2 - 6*(8*sqrt(c^2*x^2 + 1)*x^5/c^2 - 10*sqrt(c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(c^2*x^2 + 1)*x/c^6 - 15*arcsinh(c*x)/c^7)*c*arcsinh(c*x))*b^2*c^4*d^3 + 1/2*b^2*d^3*x^2*arcsinh(c*x)^2 + 3/16*(8*x^4*arcsinh(c*x) - (2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c)*a*b*c^2*d^3 + 3/32*((x^4/c^2 - 3*x^2/c^4 + 3*log(c*x + sqrt(c^2*x^2 + 1))^2/c^6)*c^2 - 2*(2*sqrt(c^2*x^2 + 1)*x^3/c^2 - 3*sqrt(c^2*x^2 + 1)*x/c^4 + 3*arcsinh(c*x)/c^5)*c*arcsinh(c*x))*b^2*c^2*d^3 + 1/2*a^2*d^3*x^2 + 1/2*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*a*b*d^3 + 1/4*(c^2*(x^2/c^2 - log(c*x + sqrt(c^2*x^2 + 1))^2/c^4) - 2*c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3)*arcsinh(c*x))*b^2*d^3","B",0
220,1,712,0,0.468109," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} c^{6} d^{3} x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{7} \, a^{2} c^{6} d^{3} x^{7} + \frac{3}{5} \, b^{2} c^{4} d^{3} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{5} \, a^{2} c^{4} d^{3} x^{5} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{6} d^{3} - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} c^{6} d^{3} + b^{2} c^{2} d^{3} x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{4} d^{3} - \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{4} d^{3} + a^{2} c^{2} d^{3} x^{3} + \frac{2}{3} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{2} d^{3} - \frac{2}{9} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} c^{2} d^{3} + b^{2} d^{3} x \operatorname{arsinh}\left(c x\right)^{2} + 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b d^{3}}{c}"," ",0,"1/7*b^2*c^6*d^3*x^7*arcsinh(c*x)^2 + 1/7*a^2*c^6*d^3*x^7 + 3/5*b^2*c^4*d^3*x^5*arcsinh(c*x)^2 + 3/5*a^2*c^4*d^3*x^5 + 2/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*c^6*d^3 - 2/25725*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*c^6*d^3 + b^2*c^2*d^3*x^3*arcsinh(c*x)^2 + 2/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*c^4*d^3 - 2/375*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*c^4*d^3 + a^2*c^2*d^3*x^3 + 2/3*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*c^2*d^3 - 2/9*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*c^2*d^3 + b^2*d^3*x*arcsinh(c*x)^2 + 2*b^2*d^3*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*d^3*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*d^3/c","B",0
221,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} c^{6} d^{3} x^{6} + \frac{3}{4} \, a^{2} c^{4} d^{3} x^{4} + \frac{3}{2} \, a^{2} c^{2} d^{3} x^{2} + a^{2} d^{3} \log\left(x\right) + \int b^{2} c^{6} d^{3} x^{5} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 2 \, a b c^{6} d^{3} x^{5} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3 \, b^{2} c^{4} d^{3} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 6 \, a b c^{4} d^{3} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3 \, b^{2} c^{2} d^{3} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 6 \, a b c^{2} d^{3} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{b^{2} d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, a b d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"1/6*a^2*c^6*d^3*x^6 + 3/4*a^2*c^4*d^3*x^4 + 3/2*a^2*c^2*d^3*x^2 + a^2*d^3*log(x) + integrate(b^2*c^6*d^3*x^5*log(c*x + sqrt(c^2*x^2 + 1))^2 + 2*a*b*c^6*d^3*x^5*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b^2*c^4*d^3*x^3*log(c*x + sqrt(c^2*x^2 + 1))^2 + 6*a*b*c^4*d^3*x^3*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b^2*c^2*d^3*x*log(c*x + sqrt(c^2*x^2 + 1))^2 + 6*a*b*c^2*d^3*x*log(c*x + sqrt(c^2*x^2 + 1)) + b^2*d^3*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*a*b*d^3*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
222,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} c^{6} d^{3} x^{5} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{6} d^{3} + a^{2} c^{4} d^{3} x^{3} + \frac{2}{3} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{4} d^{3} + 3 \, b^{2} c^{2} d^{3} x \operatorname{arsinh}\left(c x\right)^{2} + 6 \, b^{2} c^{2} d^{3} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + 3 \, a^{2} c^{2} d^{3} x + 6 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b c d^{3} - 2 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} a b d^{3} - \frac{a^{2} d^{3}}{x} + \frac{{\left(b^{2} c^{6} d^{3} x^{6} + 5 \, b^{2} c^{4} d^{3} x^{4} - 5 \, b^{2} d^{3}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{5 \, x} - \int \frac{2 \, {\left(b^{2} c^{9} d^{3} x^{8} + 6 \, b^{2} c^{7} d^{3} x^{6} + 5 \, b^{2} c^{5} d^{3} x^{4} - 5 \, b^{2} c^{3} d^{3} x^{2} - 5 \, b^{2} c d^{3} + {\left(b^{2} c^{8} d^{3} x^{7} + 5 \, b^{2} c^{6} d^{3} x^{5} - 5 \, b^{2} c^{2} d^{3} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{5 \, {\left(c^{3} x^{4} + c x^{2} + {\left(c^{2} x^{3} + x\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"1/5*a^2*c^6*d^3*x^5 + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*c^6*d^3 + a^2*c^4*d^3*x^3 + 2/3*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*c^4*d^3 + 3*b^2*c^2*d^3*x*arcsinh(c*x)^2 + 6*b^2*c^2*d^3*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + 3*a^2*c^2*d^3*x + 6*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*c*d^3 - 2*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*a*b*d^3 - a^2*d^3/x + 1/5*(b^2*c^6*d^3*x^6 + 5*b^2*c^4*d^3*x^4 - 5*b^2*d^3)*log(c*x + sqrt(c^2*x^2 + 1))^2/x - integrate(2/5*(b^2*c^9*d^3*x^8 + 6*b^2*c^7*d^3*x^6 + 5*b^2*c^5*d^3*x^4 - 5*b^2*c^3*d^3*x^2 - 5*b^2*c*d^3 + (b^2*c^8*d^3*x^7 + 5*b^2*c^6*d^3*x^5 - 5*b^2*c^2*d^3*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*x^4 + c*x^2 + (c^2*x^3 + x)*sqrt(c^2*x^2 + 1)), x)","F",0
223,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c^{6} d^{3} x^{4} + \frac{3}{2} \, a^{2} c^{4} d^{3} x^{2} + 3 \, a^{2} c^{2} d^{3} \log\left(x\right) - a b d^{3} {\left(\frac{\sqrt{c^{2} x^{2} + 1} c}{x} + \frac{\operatorname{arsinh}\left(c x\right)}{x^{2}}\right)} - \frac{a^{2} d^{3}}{2 \, x^{2}} + \int b^{2} c^{6} d^{3} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 2 \, a b c^{6} d^{3} x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 3 \, b^{2} c^{4} d^{3} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2} + 6 \, a b c^{4} d^{3} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + \frac{3 \, b^{2} c^{2} d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{6 \, a b c^{2} d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x} + \frac{b^{2} d^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}}\,{d x}"," ",0,"1/4*a^2*c^6*d^3*x^4 + 3/2*a^2*c^4*d^3*x^2 + 3*a^2*c^2*d^3*log(x) - a*b*d^3*(sqrt(c^2*x^2 + 1)*c/x + arcsinh(c*x)/x^2) - 1/2*a^2*d^3/x^2 + integrate(b^2*c^6*d^3*x^3*log(c*x + sqrt(c^2*x^2 + 1))^2 + 2*a*b*c^6*d^3*x^3*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b^2*c^4*d^3*x*log(c*x + sqrt(c^2*x^2 + 1))^2 + 6*a*b*c^4*d^3*x*log(c*x + sqrt(c^2*x^2 + 1)) + 3*b^2*c^2*d^3*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 6*a*b*c^2*d^3*log(c*x + sqrt(c^2*x^2 + 1))/x + b^2*d^3*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3, x)","F",0
224,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^3*(a+b*arcsinh(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c^{6} d^{3} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{6} d^{3} + 3 \, b^{2} c^{4} d^{3} x \operatorname{arsinh}\left(c x\right)^{2} + 6 \, b^{2} c^{4} d^{3} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + 3 \, a^{2} c^{4} d^{3} x + 6 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b c^{3} d^{3} - 6 \, {\left(c \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arsinh}\left(c x\right)}{x}\right)} a b c^{2} d^{3} + \frac{1}{3} \, {\left({\left(c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \operatorname{arsinh}\left(c x\right)}{x^{3}}\right)} a b d^{3} - \frac{3 \, a^{2} c^{2} d^{3}}{x} - \frac{a^{2} d^{3}}{3 \, x^{3}} + \frac{{\left(b^{2} c^{6} d^{3} x^{6} - 9 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{3 \, x^{3}} - \int \frac{2 \, {\left(b^{2} c^{9} d^{3} x^{8} + b^{2} c^{7} d^{3} x^{6} - 9 \, b^{2} c^{5} d^{3} x^{4} - 10 \, b^{2} c^{3} d^{3} x^{2} - b^{2} c d^{3} + {\left(b^{2} c^{8} d^{3} x^{7} - 9 \, b^{2} c^{4} d^{3} x^{3} - b^{2} c^{2} d^{3} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c^{3} x^{6} + c x^{4} + {\left(c^{2} x^{5} + x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"1/3*a^2*c^6*d^3*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*c^6*d^3 + 3*b^2*c^4*d^3*x*arcsinh(c*x)^2 + 6*b^2*c^4*d^3*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + 3*a^2*c^4*d^3*x + 6*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*c^3*d^3 - 6*(c*arcsinh(1/(c*abs(x))) + arcsinh(c*x)/x)*a*b*c^2*d^3 + 1/3*((c^2*arcsinh(1/(c*abs(x))) - sqrt(c^2*x^2 + 1)/x^2)*c - 2*arcsinh(c*x)/x^3)*a*b*d^3 - 3*a^2*c^2*d^3/x - 1/3*a^2*d^3/x^3 + 1/3*(b^2*c^6*d^3*x^6 - 9*b^2*c^2*d^3*x^2 - b^2*d^3)*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 - integrate(2/3*(b^2*c^9*d^3*x^8 + b^2*c^7*d^3*x^6 - 9*b^2*c^5*d^3*x^4 - 10*b^2*c^3*d^3*x^2 - b^2*c*d^3 + (b^2*c^8*d^3*x^7 - 9*b^2*c^4*d^3*x^3 - b^2*c^2*d^3*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*x^6 + c*x^4 + (c^2*x^5 + x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
225,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4} d} + \frac{3 \, \arctan\left(c x\right)}{c^{5} d}\right)} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{2} + d} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{2} + d}\,{d x}"," ",0,"1/3*a^2*((c^2*x^3 - 3*x)/(c^4*d) + 3*arctan(c*x)/(c^5*d)) + integrate(b^2*x^4*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d) + 2*a*b*x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d), x)","F",0
226,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{x^{2}}{c^{2} d} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d}\right)} + \frac{{\left(b^{2} c^{2} x^{2} - b^{2} \log\left(c^{2} x^{2} + 1\right)\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{2 \, c^{4} d} + \int -\frac{{\left(b^{2} c^{2} x^{2} - {\left(2 \, a b c^{4} - b^{2} c^{4}\right)} x^{4} - {\left(b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c^{2} x^{2} + 1\right) - {\left(b^{2} c x \log\left(c^{2} x^{2} + 1\right) + {\left(2 \, a b c^{3} - b^{2} c^{3}\right)} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d x^{3} + c^{4} d x + {\left(c^{5} d x^{2} + c^{3} d\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"1/2*a^2*(x^2/(c^2*d) - log(c^2*x^2 + 1)/(c^4*d)) + 1/2*(b^2*c^2*x^2 - b^2*log(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d) + integrate(-(b^2*c^2*x^2 - (2*a*b*c^4 - b^2*c^4)*x^4 - (b^2*c^2*x^2 + b^2)*log(c^2*x^2 + 1) - (b^2*c*x*log(c^2*x^2 + 1) + (2*a*b*c^3 - b^2*c^3)*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d*x^3 + c^4*d*x + (c^5*d*x^2 + c^3*d)*sqrt(c^2*x^2 + 1)), x)","F",0
227,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","a^{2} {\left(\frac{x}{c^{2} d} - \frac{\arctan\left(c x\right)}{c^{3} d}\right)} + \int \frac{b^{2} x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{2} + d} + \frac{2 \, a b x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{2} + d}\,{d x}"," ",0,"a^2*(x/(c^2*d) - arctan(c*x)/(c^3*d)) + integrate(b^2*x^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d) + 2*a*b*x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d), x)","F",0
228,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{b^{2} \log\left(c^{2} x^{2} + 1\right) \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{2 \, c^{2} d} + \frac{a^{2} \log\left(c^{2} d x^{2} + d\right)}{2 \, c^{2} d} - \int -\frac{{\left(2 \, a b c^{2} x^{2} - {\left(b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c^{2} x^{2} + 1\right) - {\left(b^{2} c x \log\left(c^{2} x^{2} + 1\right) - 2 \, a b c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d x^{3} + c^{2} d x + {\left(c^{3} d x^{2} + c d\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"1/2*b^2*log(c^2*x^2 + 1)*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d) + 1/2*a^2*log(c^2*d*x^2 + d)/(c^2*d) - integrate(-(2*a*b*c^2*x^2 - (b^2*c^2*x^2 + b^2)*log(c^2*x^2 + 1) - (b^2*c*x*log(c^2*x^2 + 1) - 2*a*b*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d*x^3 + c^2*d*x + (c^3*d*x^2 + c*d)*sqrt(c^2*x^2 + 1)), x)","F",0
229,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(c x\right)}{c d} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{2} + d} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{2} + d}\,{d x}"," ",0,"a^2*arctan(c*x)/(c*d) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d), x)","F",0
230,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c^{2} x^{2} + 1\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{3} + d x} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{3} + d x}\,{d x}"," ",0,"-1/2*a^2*(log(c^2*x^2 + 1)/d - 2*log(x)/d) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^3 + d*x) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^3 + d*x), x)","F",0
231,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d),x, algorithm=""maxima"")","-a^{2} {\left(\frac{c \arctan\left(c x\right)}{d} + \frac{1}{d x}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{4} + d x^{2}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{4} + d x^{2}}\,{d x}"," ",0,"-a^2*(c*arctan(c*x)/d + 1/(d*x)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^4 + d*x^2) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^4 + d*x^2), x)","F",0
232,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} \log\left(c^{2} x^{2} + 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} - \frac{1}{d x^{2}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{5} + d x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{5} + d x^{3}}\,{d x}"," ",0,"1/2*(c^2*log(c^2*x^2 + 1)/d - 2*c^2*log(x)/d - 1/(d*x^2))*a^2 + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^5 + d*x^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^5 + d*x^3), x)","F",0
233,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, c^{3} \arctan\left(c x\right)}{d} + \frac{3 \, c^{2} x^{2} - 1}{d x^{3}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{2} d x^{6} + d x^{4}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{2} d x^{6} + d x^{4}}\,{d x}"," ",0,"1/3*(3*c^3*arctan(c*x)/d + (3*c^2*x^2 - 1)/(d*x^3))*a^2 + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^6 + d*x^4) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^6 + d*x^4), x)","F",0
234,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{x}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + \frac{2 \, x}{c^{4} d^{2}} - \frac{3 \, \arctan\left(c x\right)}{c^{5} d^{2}}\right)} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a^2*(x/(c^6*d^2*x^2 + c^4*d^2) + 2*x/(c^4*d^2) - 3*arctan(c*x)/(c^5*d^2)) + integrate(b^2*x^4*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2) + 2*a*b*x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x)","F",0
235,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{1}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d^{2}}\right)} + \frac{{\left(b^{2} + {\left(b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c^{2} x^{2} + 1\right)\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{2 \, {\left(c^{6} d^{2} x^{2} + c^{4} d^{2}\right)}} - \int -\frac{{\left(2 \, a b c^{4} x^{4} - b^{2} c^{2} x^{2} - b^{2} - {\left(b^{2} c^{4} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c^{2} x^{2} + 1\right) + {\left(2 \, a b c^{3} x^{3} - b^{2} c x - {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \log\left(c^{2} x^{2} + 1\right)\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{8} d^{2} x^{5} + 2 \, c^{6} d^{2} x^{3} + c^{4} d^{2} x + {\left(c^{7} d^{2} x^{4} + 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"1/2*a^2*(1/(c^6*d^2*x^2 + c^4*d^2) + log(c^2*x^2 + 1)/(c^4*d^2)) + 1/2*(b^2 + (b^2*c^2*x^2 + b^2)*log(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^2*x^2 + c^4*d^2) - integrate(-(2*a*b*c^4*x^4 - b^2*c^2*x^2 - b^2 - (b^2*c^4*x^4 + 2*b^2*c^2*x^2 + b^2)*log(c^2*x^2 + 1) + (2*a*b*c^3*x^3 - b^2*c*x - (b^2*c^3*x^3 + b^2*c*x)*log(c^2*x^2 + 1))*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^8*d^2*x^5 + 2*c^6*d^2*x^3 + c^4*d^2*x + (c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2)*sqrt(c^2*x^2 + 1)), x)","F",0
236,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{x}{c^{4} d^{2} x^{2} + c^{2} d^{2}} - \frac{\arctan\left(c x\right)}{c^{3} d^{2}}\right)} + \int \frac{b^{2} x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}} + \frac{2 \, a b x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a^2*(x/(c^4*d^2*x^2 + c^2*d^2) - arctan(c*x)/(c^3*d^2)) + integrate(b^2*x^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2) + 2*a*b*x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x)","F",0
237,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{2 \, {\left(c^{4} d^{2} x^{2} + c^{2} d^{2}\right)}} - \frac{a^{2}}{2 \, {\left(c^{4} d^{2} x^{2} + c^{2} d^{2}\right)}} + \int \frac{{\left({\left(2 \, a b c^{2} + b^{2} c^{2}\right)} x^{2} + \sqrt{c^{2} x^{2} + 1} {\left(2 \, a b c + b^{2} c\right)} x + b^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{2} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{2} d^{2} x + {\left(c^{5} d^{2} x^{4} + 2 \, c^{3} d^{2} x^{2} + c d^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-1/2*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^2 + c^2*d^2) - 1/2*a^2/(c^4*d^2*x^2 + c^2*d^2) + integrate(((2*a*b*c^2 + b^2*c^2)*x^2 + sqrt(c^2*x^2 + 1)*(2*a*b*c + b^2*c)*x + b^2)*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^2*x^5 + 2*c^4*d^2*x^3 + c^2*d^2*x + (c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2)*sqrt(c^2*x^2 + 1)), x)","F",0
238,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{x}{c^{2} d^{2} x^{2} + d^{2}} + \frac{\arctan\left(c x\right)}{c d^{2}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a^2*(x/(c^2*d^2*x^2 + d^2) + arctan(c*x)/(c*d^2)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x)","F",0
239,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{1}{c^{2} d^{2} x^{2} + d^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{5} + 2 \, c^{2} d^{2} x^{3} + d^{2} x} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{5} + 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"1/2*a^2*(1/(c^2*d^2*x^2 + d^2) - log(c^2*x^2 + 1)/d^2 + 2*log(x)/d^2) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^5 + 2*c^2*d^2*x^3 + d^2*x) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^5 + 2*c^2*d^2*x^3 + d^2*x), x)","F",0
240,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{3 \, c^{2} x^{2} + 2}{c^{2} d^{2} x^{3} + d^{2} x} + \frac{3 \, c \arctan\left(c x\right)}{d^{2}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{6} + 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{6} + 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}\,{d x}"," ",0,"-1/2*a^2*((3*c^2*x^2 + 2)/(c^2*d^2*x^3 + d^2*x) + 3*c*arctan(c*x)/d^2) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^6 + 2*c^2*d^2*x^4 + d^2*x^2) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^6 + 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
241,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{2 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{d^{2}} - \frac{4 \, c^{2} \log\left(x\right)}{d^{2}} - \frac{2 \, c^{2} x^{2} + 1}{c^{2} d^{2} x^{4} + d^{2} x^{2}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{7} + 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{7} + 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"1/2*a^2*(2*c^2*log(c^2*x^2 + 1)/d^2 - 4*c^2*log(x)/d^2 - (2*c^2*x^2 + 1)/(c^2*d^2*x^4 + d^2*x^2)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^7 + 2*c^2*d^2*x^5 + d^2*x^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^7 + 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
242,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{15 \, c^{3} \arctan\left(c x\right)}{d^{2}} + \frac{15 \, c^{4} x^{4} + 10 \, c^{2} x^{2} - 2}{c^{2} d^{2} x^{5} + d^{2} x^{3}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{4} d^{2} x^{8} + 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{4} d^{2} x^{8} + 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}\,{d x}"," ",0,"1/6*(15*c^3*arctan(c*x)/d^2 + (15*c^4*x^4 + 10*c^2*x^2 - 2)/(c^2*d^2*x^5 + d^2*x^3))*a^2 + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^4*d^2*x^8 + 2*c^2*d^2*x^6 + d^2*x^4) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^4*d^2*x^8 + 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
243,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} {\left(\frac{5 \, c^{2} x^{3} + 3 \, x}{c^{8} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} - \frac{3 \, \arctan\left(c x\right)}{c^{5} d^{3}}\right)} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}}\,{d x}"," ",0,"-1/8*a^2*((5*c^2*x^3 + 3*x)/(c^8*d^3*x^4 + 2*c^6*d^3*x^2 + c^4*d^3) - 3*arctan(c*x)/(c^5*d^3)) + integrate(b^2*x^4*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3) + 2*a*b*x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3), x)","F",0
244,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, c^{2} x^{2} + 1\right)} a^{2}}{4 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}} - \frac{{\left(2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{4 \, {\left(c^{8} d^{3} x^{4} + 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}} + \int \frac{{\left(3 \, b^{2} c^{2} x^{2} + 2 \, {\left(2 \, a b c^{4} + b^{2} c^{4}\right)} x^{4} + b^{2} + {\left(b^{2} c x + 2 \, {\left(2 \, a b c^{3} + b^{2} c^{3}\right)} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{2 \, {\left(c^{10} d^{3} x^{7} + 3 \, c^{8} d^{3} x^{5} + 3 \, c^{6} d^{3} x^{3} + c^{4} d^{3} x + {\left(c^{9} d^{3} x^{6} + 3 \, c^{7} d^{3} x^{4} + 3 \, c^{5} d^{3} x^{2} + c^{3} d^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"-1/4*(2*c^2*x^2 + 1)*a^2/(c^8*d^3*x^4 + 2*c^6*d^3*x^2 + c^4*d^3) - 1/4*(2*b^2*c^2*x^2 + b^2)*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^8*d^3*x^4 + 2*c^6*d^3*x^2 + c^4*d^3) + integrate(1/2*(3*b^2*c^2*x^2 + 2*(2*a*b*c^4 + b^2*c^4)*x^4 + b^2 + (b^2*c*x + 2*(2*a*b*c^3 + b^2*c^3)*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^10*d^3*x^7 + 3*c^8*d^3*x^5 + 3*c^6*d^3*x^3 + c^4*d^3*x + (c^9*d^3*x^6 + 3*c^7*d^3*x^4 + 3*c^5*d^3*x^2 + c^3*d^3)*sqrt(c^2*x^2 + 1)), x)","F",0
245,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} {\left(\frac{c^{2} x^{3} - x}{c^{6} d^{3} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} + \frac{\arctan\left(c x\right)}{c^{3} d^{3}}\right)} + \int \frac{b^{2} x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{2 \, a b x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a^2*((c^2*x^3 - x)/(c^6*d^3*x^4 + 2*c^4*d^3*x^2 + c^2*d^3) + arctan(c*x)/(c^3*d^3)) + integrate(b^2*x^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3) + 2*a*b*x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3), x)","F",0
246,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{4 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}} - \frac{a^{2}}{4 \, {\left(c^{6} d^{3} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}} + \int \frac{{\left({\left(4 \, a b c^{2} + b^{2} c^{2}\right)} x^{2} + \sqrt{c^{2} x^{2} + 1} {\left(4 \, a b c + b^{2} c\right)} x + b^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{2 \, {\left(c^{8} d^{3} x^{7} + 3 \, c^{6} d^{3} x^{5} + 3 \, c^{4} d^{3} x^{3} + c^{2} d^{3} x + {\left(c^{7} d^{3} x^{6} + 3 \, c^{5} d^{3} x^{4} + 3 \, c^{3} d^{3} x^{2} + c d^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"-1/4*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^4 + 2*c^4*d^3*x^2 + c^2*d^3) - 1/4*a^2/(c^6*d^3*x^4 + 2*c^4*d^3*x^2 + c^2*d^3) + integrate(1/2*((4*a*b*c^2 + b^2*c^2)*x^2 + sqrt(c^2*x^2 + 1)*(4*a*b*c + b^2*c)*x + b^2)*log(c*x + sqrt(c^2*x^2 + 1))/(c^8*d^3*x^7 + 3*c^6*d^3*x^5 + 3*c^4*d^3*x^3 + c^2*d^3*x + (c^7*d^3*x^6 + 3*c^5*d^3*x^4 + 3*c^3*d^3*x^2 + c*d^3)*sqrt(c^2*x^2 + 1)), x)","F",0
247,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} {\left(\frac{3 \, c^{2} x^{3} + 5 \, x}{c^{4} d^{3} x^{4} + 2 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{3 \, \arctan\left(c x\right)}{c d^{3}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{6} + 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a^2*((3*c^2*x^3 + 5*x)/(c^4*d^3*x^4 + 2*c^2*d^3*x^2 + d^3) + 3*arctan(c*x)/(c*d^3)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^6 + 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 + d^3), x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} {\left(\frac{2 \, c^{2} x^{2} + 3}{c^{4} d^{3} x^{4} + 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{7} + 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} + d^{3} x} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{7} + 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} + d^{3} x}\,{d x}"," ",0,"1/4*a^2*((2*c^2*x^2 + 3)/(c^4*d^3*x^4 + 2*c^2*d^3*x^2 + d^3) - 2*log(c^2*x^2 + 1)/d^3 + 4*log(x)/d^3) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^7 + 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 + d^3*x) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^7 + 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 + d^3*x), x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} {\left(\frac{15 \, c^{4} x^{4} + 25 \, c^{2} x^{2} + 8}{c^{4} d^{3} x^{5} + 2 \, c^{2} d^{3} x^{3} + d^{3} x} + \frac{15 \, c \arctan\left(c x\right)}{d^{3}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{8} + 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{8} + 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} + d^{3} x^{2}}\,{d x}"," ",0,"-1/8*a^2*((15*c^4*x^4 + 25*c^2*x^2 + 8)/(c^4*d^3*x^5 + 2*c^2*d^3*x^3 + d^3*x) + 15*c*arctan(c*x)/d^3) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^8 + 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 + d^3*x^2) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^8 + 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 + d^3*x^2), x)","F",0
250,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{6 \, c^{4} x^{4} + 9 \, c^{2} x^{2} + 2}{c^{4} d^{3} x^{6} + 2 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} - \frac{6 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{d^{3}} + \frac{12 \, c^{2} \log\left(x\right)}{d^{3}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{9} + 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} + d^{3} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{9} + 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\,{d x}"," ",0,"-1/4*a^2*((6*c^4*x^4 + 9*c^2*x^2 + 2)/(c^4*d^3*x^6 + 2*c^2*d^3*x^4 + d^3*x^2) - 6*c^2*log(c^2*x^2 + 1)/d^3 + 12*c^2*log(x)/d^3) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^9 + 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 + d^3*x^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^9 + 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 + d^3*x^3), x)","F",0
251,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{24} \, a^{2} {\left(\frac{105 \, c^{3} \arctan\left(c x\right)}{d^{3}} + \frac{105 \, c^{6} x^{6} + 175 \, c^{4} x^{4} + 56 \, c^{2} x^{2} - 8}{c^{4} d^{3} x^{7} + 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{c^{6} d^{3} x^{10} + 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} + d^{3} x^{4}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{3} x^{10} + 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} + d^{3} x^{4}}\,{d x}"," ",0,"1/24*a^2*(105*c^3*arctan(c*x)/d^3 + (105*c^6*x^6 + 175*c^4*x^4 + 56*c^2*x^2 - 8)/(c^4*d^3*x^7 + 2*c^2*d^3*x^5 + d^3*x^3)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^6*d^3*x^10 + 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 + d^3*x^4) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(c^6*d^3*x^10 + 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 + d^3*x^4), x)","F",0
252,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
253,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
254,-2,0,0,0.000000," ","integrate((pi*c^2*x^2+pi)^(1/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
255,1,47,0,0.355633," ","integrate((a+b*arcsinh(c*x))^2/(pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \operatorname{arsinh}\left(c x\right)^{3}}{3 \, \sqrt{\pi} c} + \frac{a b \operatorname{arsinh}\left(c x\right)^{2}}{\sqrt{\pi} c} + \frac{a^{2} \operatorname{arsinh}\left(c x\right)}{\sqrt{\pi} c}"," ",0,"1/3*b^2*arcsinh(c*x)^3/(sqrt(pi)*c) + a*b*arcsinh(c*x)^2/(sqrt(pi)*c) + a^2*arcsinh(c*x)/(sqrt(pi)*c)","B",0
256,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(pi*c^2*x^2+pi)^(3/2),x, algorithm=""maxima"")","b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}}\,{d x} + \frac{2 \, a b x \operatorname{arsinh}\left(c x\right)}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} + \frac{a^{2} x}{\pi \sqrt{\pi + \pi c^{2} x^{2}}} - \frac{a b \log\left(x^{2} + \frac{1}{c^{2}}\right)}{\pi^{\frac{3}{2}} c}"," ",0,"b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(pi + pi*c^2*x^2)^(3/2), x) + 2*a*b*x*arcsinh(c*x)/(pi*sqrt(pi + pi*c^2*x^2)) + a^2*x/(pi*sqrt(pi + pi*c^2*x^2)) - a*b*log(x^2 + 1/c^2)/(pi^(3/2)*c)","F",0
257,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(pi*c^2*x^2+pi)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{1}{\pi^{\frac{5}{2}} c^{4} x^{2} + \pi^{\frac{5}{2}} c^{2}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{\pi^{\frac{5}{2}} c^{2}}\right)} + \frac{2}{3} \, a b {\left(\frac{x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{x}{\pi {\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, x}{\pi^{2} \sqrt{\pi + \pi c^{2} x^{2}}}\right)} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(\pi + \pi c^{2} x^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*b*c*(1/(pi^(5/2)*c^4*x^2 + pi^(5/2)*c^2) - 2*log(c^2*x^2 + 1)/(pi^(5/2)*c^2)) + 2/3*a*b*(x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 2*x/(pi^2*sqrt(pi + pi*c^2*x^2)))*arcsinh(c*x) + 1/3*a^2*(x/(pi*(pi + pi*c^2*x^2)^(3/2)) + 2*x/(pi^2*sqrt(pi + pi*c^2*x^2))) + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(pi + pi*c^2*x^2)^(5/2), x)","F",0
258,1,302,0,0.457289," ","integrate(x^3*(a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, b^{2} {\left(\frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{15} \, a b {\left(\frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{15} \, a^{2} {\left(\frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} + \frac{2}{3375} \, b^{2} {\left(\frac{27 \, \sqrt{c^{2} x^{2} + 1} c^{2} \sqrt{d} x^{4} - 11 \, \sqrt{c^{2} x^{2} + 1} \sqrt{d} x^{2} - \frac{428 \, \sqrt{c^{2} x^{2} + 1} \sqrt{d}}{c^{2}}}{c^{2}} - \frac{15 \, {\left(9 \, c^{4} \sqrt{d} x^{5} + 5 \, c^{2} \sqrt{d} x^{3} - 30 \, \sqrt{d} x\right)} \operatorname{arsinh}\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(9 \, c^{4} \sqrt{d} x^{5} + 5 \, c^{2} \sqrt{d} x^{3} - 30 \, \sqrt{d} x\right)} a b}{225 \, c^{3}}"," ",0,"1/15*b^2*(3*(c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(3/2)/(c^4*d))*arcsinh(c*x)^2 + 2/15*a*b*(3*(c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(3/2)/(c^4*d))*arcsinh(c*x) + 1/15*a^2*(3*(c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(3/2)/(c^4*d)) + 2/3375*b^2*((27*sqrt(c^2*x^2 + 1)*c^2*sqrt(d)*x^4 - 11*sqrt(c^2*x^2 + 1)*sqrt(d)*x^2 - 428*sqrt(c^2*x^2 + 1)*sqrt(d)/c^2)/c^2 - 15*(9*c^4*sqrt(d)*x^5 + 5*c^2*sqrt(d)*x^3 - 30*sqrt(d)*x)*arcsinh(c*x)/c^3) - 2/225*(9*c^4*sqrt(d)*x^5 + 5*c^2*sqrt(d)*x^3 - 30*sqrt(d)*x)*a*b/c^3","A",0
259,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
260,1,183,0,0.425571," ","integrate(x*(a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{2}{27} \, b^{2} {\left(\frac{\sqrt{c^{2} x^{2} + 1} d^{\frac{3}{2}} x^{2} + \frac{7 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{3}{2}}}{c^{2}}}{d} - \frac{3 \, {\left(c^{2} d^{\frac{3}{2}} x^{3} + 3 \, d^{\frac{3}{2}} x\right)} \operatorname{arsinh}\left(c x\right)}{c d}\right)} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \operatorname{arsinh}\left(c x\right)^{2}}{3 \, c^{2} d} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \operatorname{arsinh}\left(c x\right)}{3 \, c^{2} d} - \frac{2 \, {\left(c^{2} d^{\frac{3}{2}} x^{3} + 3 \, d^{\frac{3}{2}} x\right)} a b}{9 \, c d} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2}}{3 \, c^{2} d}"," ",0,"2/27*b^2*((sqrt(c^2*x^2 + 1)*d^(3/2)*x^2 + 7*sqrt(c^2*x^2 + 1)*d^(3/2)/c^2)/d - 3*(c^2*d^(3/2)*x^3 + 3*d^(3/2)*x)*arcsinh(c*x)/(c*d)) + 1/3*(c^2*d*x^2 + d)^(3/2)*b^2*arcsinh(c*x)^2/(c^2*d) + 2/3*(c^2*d*x^2 + d)^(3/2)*a*b*arcsinh(c*x)/(c^2*d) - 2/9*(c^2*d^(3/2)*x^3 + 3*d^(3/2)*x)*a*b/(c*d) + 1/3*(c^2*d*x^2 + d)^(3/2)*a^2/(c^2*d)","A",0
261,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
262,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \sqrt{c^{2} d x^{2} + d}\right)} a^{2} + \int \frac{\sqrt{c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, \sqrt{c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*arcsinh(1/(c*abs(x))) - sqrt(c^2*d*x^2 + d))*a^2 + integrate(sqrt(c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*sqrt(c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
263,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","{\left(c \sqrt{d} \operatorname{arsinh}\left(c x\right) - \frac{\sqrt{c^{2} d x^{2} + d}}{x}\right)} a^{2} + \int \frac{\sqrt{c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{2}} + \frac{2 \, \sqrt{c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{2}}\,{d x}"," ",0,"(c*sqrt(d)*arcsinh(c*x) - sqrt(c^2*d*x^2 + d)/x)*a^2 + integrate(sqrt(c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x^2 + 2*sqrt(c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x^2, x)","F",0
264,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - \sqrt{c^{2} d x^{2} + d} c^{2} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a^{2} + \int \frac{\sqrt{c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}} + \frac{2 \, \sqrt{c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(c^2*sqrt(d)*arcsinh(1/(c*abs(x))) - sqrt(c^2*d*x^2 + d)*c^2 + (c^2*d*x^2 + d)^(3/2)/(d*x^2))*a^2 + integrate(sqrt(c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 + 2*sqrt(c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
265,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(c^2*d*x^2+d)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{{\left(\left(-1\right)^{2 \, c^{2} d x^{2} + 2 \, d} c^{2} d^{\frac{3}{2}} \log\left(2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) - c^{2} d^{\frac{3}{2}} \log\left(x^{2} + \frac{1}{c^{2}}\right) + \frac{\sqrt{c^{4} d x^{4} + 2 \, c^{2} d x^{2} + d} d}{x^{2}}\right)} a b c}{3 \, d} - \frac{1}{3} \, b^{2} {\left(\frac{{\left(c^{2} \sqrt{d} x^{2} + \sqrt{d}\right)} \sqrt{c^{2} x^{2} + 1} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}} - 3 \, \int \frac{2 \, {\left({\left(c^{2} x^{2} + 1\right)} c^{2} \sqrt{d} x + {\left(c^{3} \sqrt{d} x^{2} + c \sqrt{d}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c x^{4} + \sqrt{c^{2} x^{2} + 1} x^{3}\right)}}\,{d x}\right)} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \operatorname{arsinh}\left(c x\right)}{3 \, d x^{3}} - \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2}}{3 \, d x^{3}}"," ",0,"-1/3*((-1)^(2*c^2*d*x^2 + 2*d)*c^2*d^(3/2)*log(2*c^2*d + 2*d/x^2) - c^2*d^(3/2)*log(x^2 + 1/c^2) + sqrt(c^4*d*x^4 + 2*c^2*d*x^2 + d)*d/x^2)*a*b*c/d - 1/3*b^2*((c^2*sqrt(d)*x^2 + sqrt(d))*sqrt(c^2*x^2 + 1)*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 - 3*integrate(2/3*((c^2*x^2 + 1)*c^2*sqrt(d)*x + (c^3*sqrt(d)*x^2 + c*sqrt(d))*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c*x^4 + sqrt(c^2*x^2 + 1)*x^3), x)) - 2/3*(c^2*d*x^2 + d)^(3/2)*a*b*arcsinh(c*x)/(d*x^3) - 1/3*(c^2*d*x^2 + d)^(3/2)*a^2/(d*x^3)","F",0
266,1,346,0,0.438486," ","integrate(x^3*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} b^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{35} \, {\left(\frac{5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a b \operatorname{arsinh}\left(c x\right) + \frac{1}{35} \, {\left(\frac{5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a^{2} + \frac{2}{385875} \, b^{2} {\left(\frac{1125 \, \sqrt{c^{2} x^{2} + 1} c^{4} d^{\frac{3}{2}} x^{6} + 2178 \, \sqrt{c^{2} x^{2} + 1} c^{2} d^{\frac{3}{2}} x^{4} - 1679 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{3}{2}} x^{2} - \frac{18692 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{3}{2}}}{c^{2}}}{c^{2}} - \frac{105 \, {\left(75 \, c^{6} d^{\frac{3}{2}} x^{7} + 168 \, c^{4} d^{\frac{3}{2}} x^{5} + 35 \, c^{2} d^{\frac{3}{2}} x^{3} - 210 \, d^{\frac{3}{2}} x\right)} \operatorname{arsinh}\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(75 \, c^{6} d^{\frac{3}{2}} x^{7} + 168 \, c^{4} d^{\frac{3}{2}} x^{5} + 35 \, c^{2} d^{\frac{3}{2}} x^{3} - 210 \, d^{\frac{3}{2}} x\right)} a b}{3675 \, c^{3}}"," ",0,"1/35*(5*(c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(5/2)/(c^4*d))*b^2*arcsinh(c*x)^2 + 2/35*(5*(c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(5/2)/(c^4*d))*a*b*arcsinh(c*x) + 1/35*(5*(c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(5/2)/(c^4*d))*a^2 + 2/385875*b^2*((1125*sqrt(c^2*x^2 + 1)*c^4*d^(3/2)*x^6 + 2178*sqrt(c^2*x^2 + 1)*c^2*d^(3/2)*x^4 - 1679*sqrt(c^2*x^2 + 1)*d^(3/2)*x^2 - 18692*sqrt(c^2*x^2 + 1)*d^(3/2)/c^2)/c^2 - 105*(75*c^6*d^(3/2)*x^7 + 168*c^4*d^(3/2)*x^5 + 35*c^2*d^(3/2)*x^3 - 210*d^(3/2)*x)*arcsinh(c*x)/c^3) - 2/3675*(75*c^6*d^(3/2)*x^7 + 168*c^4*d^(3/2)*x^5 + 35*c^2*d^(3/2)*x^3 - 210*d^(3/2)*x)*a*b/c^3","A",0
267,-2,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
268,1,230,0,0.387947," ","integrate(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \operatorname{arsinh}\left(c x\right)^{2}}{5 \, c^{2} d} + \frac{2}{1125} \, b^{2} {\left(\frac{9 \, \sqrt{c^{2} x^{2} + 1} c^{2} d^{\frac{5}{2}} x^{4} + 38 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{5}{2}} x^{2} + \frac{149 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{5}{2}}}{c^{2}}}{d} - \frac{15 \, {\left(3 \, c^{4} d^{\frac{5}{2}} x^{5} + 10 \, c^{2} d^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} x\right)} \operatorname{arsinh}\left(c x\right)}{c d}\right)} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \operatorname{arsinh}\left(c x\right)}{5 \, c^{2} d} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a^{2}}{5 \, c^{2} d} - \frac{2 \, {\left(3 \, c^{4} d^{\frac{5}{2}} x^{5} + 10 \, c^{2} d^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} x\right)} a b}{75 \, c d}"," ",0,"1/5*(c^2*d*x^2 + d)^(5/2)*b^2*arcsinh(c*x)^2/(c^2*d) + 2/1125*b^2*((9*sqrt(c^2*x^2 + 1)*c^2*d^(5/2)*x^4 + 38*sqrt(c^2*x^2 + 1)*d^(5/2)*x^2 + 149*sqrt(c^2*x^2 + 1)*d^(5/2)/c^2)/d - 15*(3*c^4*d^(5/2)*x^5 + 10*c^2*d^(5/2)*x^3 + 15*d^(5/2)*x)*arcsinh(c*x)/(c*d)) + 2/5*(c^2*d*x^2 + d)^(5/2)*a*b*arcsinh(c*x)/(c^2*d) + 1/5*(c^2*d*x^2 + d)^(5/2)*a^2/(c^2*d) - 2/75*(3*c^4*d^(5/2)*x^5 + 10*c^2*d^(5/2)*x^3 + 15*d^(5/2)*x)*a*b/(c*d)","A",0
269,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
270,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{c^{2} d x^{2} + d} d\right)} a^{2} + \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-1/3*(3*d^(3/2)*arcsinh(1/(c*abs(x))) - (c^2*d*x^2 + d)^(3/2) - 3*sqrt(c^2*d*x^2 + d)*d)*a^2 + integrate((c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*(c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
271,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
272,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, c^{2} d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, \sqrt{c^{2} d x^{2} + d} c^{2} d + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a^{2} + \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(3*c^2*d^(3/2)*arcsinh(1/(c*abs(x))) - (c^2*d*x^2 + d)^(3/2)*c^2 - 3*sqrt(c^2*d*x^2 + d)*c^2*d + (c^2*d*x^2 + d)^(5/2)/(d*x^2))*a^2 + integrate((c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 + 2*(c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
273,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
274,1,390,0,0.417043," ","integrate(x^3*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{63} \, {\left(\frac{7 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} b^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{63} \, {\left(\frac{7 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a b \operatorname{arsinh}\left(c x\right) + \frac{1}{63} \, {\left(\frac{7 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} - \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a^{2} + \frac{2}{250047} \, b^{2} {\left(\frac{343 \, \sqrt{c^{2} x^{2} + 1} c^{6} d^{\frac{5}{2}} x^{8} + 1147 \, \sqrt{c^{2} x^{2} + 1} c^{4} d^{\frac{5}{2}} x^{6} + 1005 \, \sqrt{c^{2} x^{2} + 1} c^{2} d^{\frac{5}{2}} x^{4} - 899 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{5}{2}} x^{2} - \frac{6140 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{5}{2}}}{c^{2}}}{c^{2}} - \frac{63 \, {\left(49 \, c^{8} d^{\frac{5}{2}} x^{9} + 171 \, c^{6} d^{\frac{5}{2}} x^{7} + 189 \, c^{4} d^{\frac{5}{2}} x^{5} + 21 \, c^{2} d^{\frac{5}{2}} x^{3} - 126 \, d^{\frac{5}{2}} x\right)} \operatorname{arsinh}\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(49 \, c^{8} d^{\frac{5}{2}} x^{9} + 171 \, c^{6} d^{\frac{5}{2}} x^{7} + 189 \, c^{4} d^{\frac{5}{2}} x^{5} + 21 \, c^{2} d^{\frac{5}{2}} x^{3} - 126 \, d^{\frac{5}{2}} x\right)} a b}{3969 \, c^{3}}"," ",0,"1/63*(7*(c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(7/2)/(c^4*d))*b^2*arcsinh(c*x)^2 + 2/63*(7*(c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(7/2)/(c^4*d))*a*b*arcsinh(c*x) + 1/63*(7*(c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) - 2*(c^2*d*x^2 + d)^(7/2)/(c^4*d))*a^2 + 2/250047*b^2*((343*sqrt(c^2*x^2 + 1)*c^6*d^(5/2)*x^8 + 1147*sqrt(c^2*x^2 + 1)*c^4*d^(5/2)*x^6 + 1005*sqrt(c^2*x^2 + 1)*c^2*d^(5/2)*x^4 - 899*sqrt(c^2*x^2 + 1)*d^(5/2)*x^2 - 6140*sqrt(c^2*x^2 + 1)*d^(5/2)/c^2)/c^2 - 63*(49*c^8*d^(5/2)*x^9 + 171*c^6*d^(5/2)*x^7 + 189*c^4*d^(5/2)*x^5 + 21*c^2*d^(5/2)*x^3 - 126*d^(5/2)*x)*arcsinh(c*x)/c^3) - 2/3969*(49*c^8*d^(5/2)*x^9 + 171*c^6*d^(5/2)*x^7 + 189*c^4*d^(5/2)*x^5 + 21*c^2*d^(5/2)*x^3 - 126*d^(5/2)*x)*a*b/c^3","A",0
275,-2,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
276,1,274,0,0.490044," ","integrate(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b^{2} \operatorname{arsinh}\left(c x\right)^{2}}{7 \, c^{2} d} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a b \operatorname{arsinh}\left(c x\right)}{7 \, c^{2} d} + \frac{2}{25725} \, b^{2} {\left(\frac{75 \, \sqrt{c^{2} x^{2} + 1} c^{4} d^{\frac{7}{2}} x^{6} + 351 \, \sqrt{c^{2} x^{2} + 1} c^{2} d^{\frac{7}{2}} x^{4} + 757 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{7}{2}} x^{2} + \frac{2161 \, \sqrt{c^{2} x^{2} + 1} d^{\frac{7}{2}}}{c^{2}}}{d} - \frac{105 \, {\left(5 \, c^{6} d^{\frac{7}{2}} x^{7} + 21 \, c^{4} d^{\frac{7}{2}} x^{5} + 35 \, c^{2} d^{\frac{7}{2}} x^{3} + 35 \, d^{\frac{7}{2}} x\right)} \operatorname{arsinh}\left(c x\right)}{c d}\right)} + \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a^{2}}{7 \, c^{2} d} - \frac{2 \, {\left(5 \, c^{6} d^{\frac{7}{2}} x^{7} + 21 \, c^{4} d^{\frac{7}{2}} x^{5} + 35 \, c^{2} d^{\frac{7}{2}} x^{3} + 35 \, d^{\frac{7}{2}} x\right)} a b}{245 \, c d}"," ",0,"1/7*(c^2*d*x^2 + d)^(7/2)*b^2*arcsinh(c*x)^2/(c^2*d) + 2/7*(c^2*d*x^2 + d)^(7/2)*a*b*arcsinh(c*x)/(c^2*d) + 2/25725*b^2*((75*sqrt(c^2*x^2 + 1)*c^4*d^(7/2)*x^6 + 351*sqrt(c^2*x^2 + 1)*c^2*d^(7/2)*x^4 + 757*sqrt(c^2*x^2 + 1)*d^(7/2)*x^2 + 2161*sqrt(c^2*x^2 + 1)*d^(7/2)/c^2)/d - 105*(5*c^6*d^(7/2)*x^7 + 21*c^4*d^(7/2)*x^5 + 35*c^2*d^(7/2)*x^3 + 35*d^(7/2)*x)*arcsinh(c*x)/(c*d)) + 1/7*(c^2*d*x^2 + d)^(7/2)*a^2/(c^2*d) - 2/245*(5*c^6*d^(7/2)*x^7 + 21*c^4*d^(7/2)*x^5 + 35*c^2*d^(7/2)*x^3 + 35*d^(7/2)*x)*a*b/(c*d)","A",0
277,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
278,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(15 \, d^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d - 15 \, \sqrt{c^{2} d x^{2} + d} d^{2}\right)} a^{2} + \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x}\,{d x}"," ",0,"-1/15*(15*d^(5/2)*arcsinh(1/(c*abs(x))) - 3*(c^2*d*x^2 + d)^(5/2) - 5*(c^2*d*x^2 + d)^(3/2)*d - 15*sqrt(c^2*d*x^2 + d)*d^2)*a^2 + integrate((c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x + 2*(c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x, x)","F",0
279,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
280,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(15 \, c^{2} d^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right) - 3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2} - 5 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d - 15 \, \sqrt{c^{2} d x^{2} + d} c^{2} d^{2} + \frac{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{2}}\right)} a^{2} + \int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{x^{3}} + \frac{2 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/6*(15*c^2*d^(5/2)*arcsinh(1/(c*abs(x))) - 3*(c^2*d*x^2 + d)^(5/2)*c^2 - 5*(c^2*d*x^2 + d)^(3/2)*c^2*d - 15*sqrt(c^2*d*x^2 + d)*c^2*d^2 + 3*(c^2*d*x^2 + d)^(7/2)/(d*x^2))*a^2 + integrate((c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/x^3 + 2*(c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/x^3, x)","F",0
281,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
282,0,0,0,0.000000," ","integrate(x^4*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4} \operatorname{arsinh}\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^4*arcsinh(a*x)^2/sqrt(a^2*x^2 + 1), x)","F",0
283,1,101,0,0.464303," ","integrate(x^3*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x^{2}}{a^{2}} - \frac{2 \, \sqrt{a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arsinh}\left(a x\right)^{2} + \frac{2 \, {\left(\sqrt{a^{2} x^{2} + 1} x^{2} - \frac{20 \, \sqrt{a^{2} x^{2} + 1}}{a^{2}}\right)}}{27 \, a^{2}} - \frac{2 \, {\left(a^{2} x^{3} - 6 \, x\right)} \operatorname{arsinh}\left(a x\right)}{9 \, a^{3}}"," ",0,"1/3*(sqrt(a^2*x^2 + 1)*x^2/a^2 - 2*sqrt(a^2*x^2 + 1)/a^4)*arcsinh(a*x)^2 + 2/27*(sqrt(a^2*x^2 + 1)*x^2 - 20*sqrt(a^2*x^2 + 1)/a^2)/a^2 - 2/9*(a^2*x^3 - 6*x)*arcsinh(a*x)/a^3","A",0
284,0,0,0,0.000000," ","integrate(x^2*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{arsinh}\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arcsinh(a*x)^2/sqrt(a^2*x^2 + 1), x)","F",0
285,1,48,0,0.518545," ","integrate(x*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)^{2}}{a^{2}} - \frac{2 \, {\left(a x \operatorname{arsinh}\left(a x\right) - \sqrt{a^{2} x^{2} + 1}\right)}}{a^{2}}"," ",0,"sqrt(a^2*x^2 + 1)*arcsinh(a*x)^2/a^2 - 2*(a*x*arcsinh(a*x) - sqrt(a^2*x^2 + 1))/a^2","A",0
286,1,11,0,0.460783," ","integrate(arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)^{3}}{3 \, a}"," ",0,"1/3*arcsinh(a*x)^3/a","A",0
287,0,0,0,0.000000," ","integrate(arcsinh(a*x)^2/x/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsinh(a*x)^2/(sqrt(a^2*x^2 + 1)*x), x)","F",0
288,0,0,0,0.000000," ","integrate(arcsinh(a*x)^2/x^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a^{2} x^{2} + 1} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)^{2}}{x} + \int \frac{2 \, {\left(a^{3} x^{2} + \sqrt{a^{2} x^{2} + 1} a^{2} x + a\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)}{\sqrt{a^{2} x^{2} + 1} a x^{2} + {\left(a^{2} x^{2} + 1\right)} x}\,{d x}"," ",0,"-sqrt(a^2*x^2 + 1)*log(a*x + sqrt(a^2*x^2 + 1))^2/x + integrate(2*(a^3*x^2 + sqrt(a^2*x^2 + 1)*a^2*x + a)*log(a*x + sqrt(a^2*x^2 + 1))/(sqrt(a^2*x^2 + 1)*a*x^2 + (a^2*x^2 + 1)*x), x)","F",0
289,0,0,0,0.000000," ","integrate(arcsinh(a*x)^2/x^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^2/(sqrt(a^2*x^2 + 1)*x^3), x)","F",0
290,1,353,0,0.517649," ","integrate(x^5*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, \sqrt{c^{2} d x^{2} + d} x^{4}}{c^{2} d} - \frac{4 \, \sqrt{c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{c^{2} d x^{2} + d}}{c^{6} d}\right)} b^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{15} \, {\left(\frac{3 \, \sqrt{c^{2} d x^{2} + d} x^{4}}{c^{2} d} - \frac{4 \, \sqrt{c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{c^{2} d x^{2} + d}}{c^{6} d}\right)} a b \operatorname{arsinh}\left(c x\right) + \frac{1}{15} \, {\left(\frac{3 \, \sqrt{c^{2} d x^{2} + d} x^{4}}{c^{2} d} - \frac{4 \, \sqrt{c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{c^{2} d x^{2} + d}}{c^{6} d}\right)} a^{2} + \frac{2}{3375} \, b^{2} {\left(\frac{27 \, \sqrt{c^{2} x^{2} + 1} c^{2} x^{4} - 136 \, \sqrt{c^{2} x^{2} + 1} x^{2} + \frac{2072 \, \sqrt{c^{2} x^{2} + 1}}{c^{2}}}{c^{4} \sqrt{d}} - \frac{15 \, {\left(9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x\right)} \operatorname{arsinh}\left(c x\right)}{c^{5} \sqrt{d}}\right)} - \frac{2 \, {\left(9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x\right)} a b}{225 \, c^{5} \sqrt{d}}"," ",0,"1/15*(3*sqrt(c^2*d*x^2 + d)*x^4/(c^2*d) - 4*sqrt(c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(c^2*d*x^2 + d)/(c^6*d))*b^2*arcsinh(c*x)^2 + 2/15*(3*sqrt(c^2*d*x^2 + d)*x^4/(c^2*d) - 4*sqrt(c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(c^2*d*x^2 + d)/(c^6*d))*a*b*arcsinh(c*x) + 1/15*(3*sqrt(c^2*d*x^2 + d)*x^4/(c^2*d) - 4*sqrt(c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(c^2*d*x^2 + d)/(c^6*d))*a^2 + 2/3375*b^2*((27*sqrt(c^2*x^2 + 1)*c^2*x^4 - 136*sqrt(c^2*x^2 + 1)*x^2 + 2072*sqrt(c^2*x^2 + 1)/c^2)/(c^4*sqrt(d)) - 15*(9*c^4*x^5 - 20*c^2*x^3 + 120*x)*arcsinh(c*x)/(c^5*sqrt(d))) - 2/225*(9*c^4*x^5 - 20*c^2*x^3 + 120*x)*a*b/(c^5*sqrt(d))","A",0
291,-2,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
292,1,243,0,0.521518," ","integrate(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} {\left(\frac{\sqrt{c^{2} d x^{2} + d} x^{2}}{c^{2} d} - \frac{2 \, \sqrt{c^{2} d x^{2} + d}}{c^{4} d}\right)} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{3} \, a b {\left(\frac{\sqrt{c^{2} d x^{2} + d} x^{2}}{c^{2} d} - \frac{2 \, \sqrt{c^{2} d x^{2} + d}}{c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{\sqrt{c^{2} d x^{2} + d} x^{2}}{c^{2} d} - \frac{2 \, \sqrt{c^{2} d x^{2} + d}}{c^{4} d}\right)} + \frac{2}{27} \, b^{2} {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2} - \frac{20 \, \sqrt{c^{2} x^{2} + 1}}{c^{2}}}{c^{2} \sqrt{d}} - \frac{3 \, {\left(c^{2} x^{3} - 6 \, x\right)} \operatorname{arsinh}\left(c x\right)}{c^{3} \sqrt{d}}\right)} - \frac{2 \, {\left(c^{2} x^{3} - 6 \, x\right)} a b}{9 \, c^{3} \sqrt{d}}"," ",0,"1/3*b^2*(sqrt(c^2*d*x^2 + d)*x^2/(c^2*d) - 2*sqrt(c^2*d*x^2 + d)/(c^4*d))*arcsinh(c*x)^2 + 2/3*a*b*(sqrt(c^2*d*x^2 + d)*x^2/(c^2*d) - 2*sqrt(c^2*d*x^2 + d)/(c^4*d))*arcsinh(c*x) + 1/3*a^2*(sqrt(c^2*d*x^2 + d)*x^2/(c^2*d) - 2*sqrt(c^2*d*x^2 + d)/(c^4*d)) + 2/27*b^2*((sqrt(c^2*x^2 + 1)*x^2 - 20*sqrt(c^2*x^2 + 1)/c^2)/(c^2*sqrt(d)) - 3*(c^2*x^3 - 6*x)*arcsinh(c*x)/(c^3*sqrt(d))) - 2/9*(c^2*x^3 - 6*x)*a*b/(c^3*sqrt(d))","A",0
293,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
294,1,125,0,0.512842," ","integrate(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-2 \, b^{2} {\left(\frac{x \operatorname{arsinh}\left(c x\right)}{c \sqrt{d}} - \frac{\sqrt{c^{2} x^{2} + 1}}{c^{2} \sqrt{d}}\right)} - \frac{2 \, a b x}{c \sqrt{d}} + \frac{\sqrt{c^{2} d x^{2} + d} b^{2} \operatorname{arsinh}\left(c x\right)^{2}}{c^{2} d} + \frac{2 \, \sqrt{c^{2} d x^{2} + d} a b \operatorname{arsinh}\left(c x\right)}{c^{2} d} + \frac{\sqrt{c^{2} d x^{2} + d} a^{2}}{c^{2} d}"," ",0,"-2*b^2*(x*arcsinh(c*x)/(c*sqrt(d)) - sqrt(c^2*x^2 + 1)/(c^2*sqrt(d))) - 2*a*b*x/(c*sqrt(d)) + sqrt(c^2*d*x^2 + d)*b^2*arcsinh(c*x)^2/(c^2*d) + 2*sqrt(c^2*d*x^2 + d)*a*b*arcsinh(c*x)/(c^2*d) + sqrt(c^2*d*x^2 + d)*a^2/(c^2*d)","A",0
295,1,47,0,0.407418," ","integrate((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \operatorname{arsinh}\left(c x\right)^{3}}{3 \, c \sqrt{d}} + \frac{a b \operatorname{arsinh}\left(c x\right)^{2}}{c \sqrt{d}} + \frac{a^{2} \operatorname{arsinh}\left(c x\right)}{c \sqrt{d}}"," ",0,"1/3*b^2*arcsinh(c*x)^3/(c*sqrt(d)) + a*b*arcsinh(c*x)^2/(c*sqrt(d)) + a^2*arcsinh(c*x)/(c*sqrt(d))","A",0
296,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\sqrt{d}} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{c^{2} d x^{2} + d} x} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{c^{2} d x^{2} + d} x}\,{d x}"," ",0,"-a^2*arcsinh(1/(c*abs(x)))/sqrt(d) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(sqrt(c^2*d*x^2 + d)*x) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(c^2*d*x^2 + d)*x), x)","F",0
297,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\left(-1\right)^{2 \, c^{2} d x^{2} + 2 \, d} \sqrt{d} \log\left(2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) - \sqrt{d} \log\left(x^{2} + \frac{1}{c^{2}}\right)\right)} a b c}{d} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{c^{2} d x^{2} + d} x^{2}}\,{d x} - \frac{2 \, \sqrt{c^{2} d x^{2} + d} a b \operatorname{arsinh}\left(c x\right)}{d x} - \frac{\sqrt{c^{2} d x^{2} + d} a^{2}}{d x}"," ",0,"-((-1)^(2*c^2*d*x^2 + 2*d)*sqrt(d)*log(2*c^2*d + 2*d/x^2) - sqrt(d)*log(x^2 + 1/c^2))*a*b*c/d + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(sqrt(c^2*d*x^2 + d)*x^2), x) - 2*sqrt(c^2*d*x^2 + d)*a*b*arcsinh(c*x)/(d*x) - sqrt(c^2*d*x^2 + d)*a^2/(d*x)","F",0
298,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{\sqrt{d}} - \frac{\sqrt{c^{2} d x^{2} + d}}{d x^{2}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{c^{2} d x^{2} + d} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{c^{2} d x^{2} + d} x^{3}}\,{d x}"," ",0,"1/2*(c^2*arcsinh(1/(c*abs(x)))/sqrt(d) - sqrt(c^2*d*x^2 + d)/(d*x^2))*a^2 + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(sqrt(c^2*d*x^2 + d)*x^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(sqrt(c^2*d*x^2 + d)*x^3), x)","F",0
299,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{4 \, c^{2} \log\left(x\right)}{\sqrt{d}} + \frac{1}{\sqrt{d} x^{2}}\right)} a b c + \frac{2}{3} \, a b {\left(\frac{2 \, \sqrt{c^{2} d x^{2} + d} c^{2}}{d x} - \frac{\sqrt{c^{2} d x^{2} + d}}{d x^{3}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{2 \, \sqrt{c^{2} d x^{2} + d} c^{2}}{d x} - \frac{\sqrt{c^{2} d x^{2} + d}}{d x^{3}}\right)} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{c^{2} d x^{2} + d} x^{4}}\,{d x}"," ",0,"-1/3*(4*c^2*log(x)/sqrt(d) + 1/(sqrt(d)*x^2))*a*b*c + 2/3*a*b*(2*sqrt(c^2*d*x^2 + d)*c^2/(d*x) - sqrt(c^2*d*x^2 + d)/(d*x^3))*arcsinh(c*x) + 1/3*a^2*(2*sqrt(c^2*d*x^2 + d)*c^2/(d*x) - sqrt(c^2*d*x^2 + d)/(d*x^3)) + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(sqrt(c^2*d*x^2 + d)*x^4), x)","F",0
300,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{x^{4}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} - \frac{4 \, x^{2}}{\sqrt{c^{2} d x^{2} + d} c^{4} d} - \frac{8}{\sqrt{c^{2} d x^{2} + d} c^{6} d}\right)} + \frac{{\left(b^{2} c^{4} \sqrt{d} x^{4} - 4 \, b^{2} c^{2} \sqrt{d} x^{2} - 8 \, b^{2} \sqrt{d}\right)} \sqrt{c^{2} x^{2} + 1} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{3 \, {\left(c^{8} d^{2} x^{2} + c^{6} d^{2}\right)}} + \int \frac{2 \, {\left({\left(4 \, b^{2} c^{3} x^{3} + {\left(3 \, a b c^{5} - b^{2} c^{5}\right)} x^{5} + 8 \, b^{2} c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(3 \, b^{2} c^{4} x^{4} + {\left(3 \, a b c^{6} - b^{2} c^{6}\right)} x^{6} + 12 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c^{10} d^{\frac{3}{2}} x^{5} + 2 \, c^{8} d^{\frac{3}{2}} x^{3} + c^{6} d^{\frac{3}{2}} x + {\left(c^{9} d^{\frac{3}{2}} x^{4} + 2 \, c^{7} d^{\frac{3}{2}} x^{2} + c^{5} d^{\frac{3}{2}}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"1/3*a^2*(x^4/(sqrt(c^2*d*x^2 + d)*c^2*d) - 4*x^2/(sqrt(c^2*d*x^2 + d)*c^4*d) - 8/(sqrt(c^2*d*x^2 + d)*c^6*d)) + 1/3*(b^2*c^4*sqrt(d)*x^4 - 4*b^2*c^2*sqrt(d)*x^2 - 8*b^2*sqrt(d))*sqrt(c^2*x^2 + 1)*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^8*d^2*x^2 + c^6*d^2) + integrate(2/3*((4*b^2*c^3*x^3 + (3*a*b*c^5 - b^2*c^5)*x^5 + 8*b^2*c*x)*(c^2*x^2 + 1) + (3*b^2*c^4*x^4 + (3*a*b*c^6 - b^2*c^6)*x^6 + 12*b^2*c^2*x^2 + 8*b^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^10*d^(3/2)*x^5 + 2*c^8*d^(3/2)*x^3 + c^6*d^(3/2)*x + (c^9*d^(3/2)*x^4 + 2*c^7*d^(3/2)*x^2 + c^5*d^(3/2))*sqrt(c^2*x^2 + 1)), x)","F",0
301,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{x^{3}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \frac{3 \, x}{\sqrt{c^{2} d x^{2} + d} c^{4} d} - \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*a^2*(x^3/(sqrt(c^2*d*x^2 + d)*c^2*d) + 3*x/(sqrt(c^2*d*x^2 + d)*c^4*d) - 3*arcsinh(c*x)/(c^5*d^(3/2))) + integrate(b^2*x^4*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(3/2) + 2*a*b*x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(3/2), x)","F",0
302,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-2 \, a b c {\left(\frac{x}{c^{4} d^{\frac{3}{2}}} + \frac{\arctan\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + 2 \, a b {\left(\frac{x^{2}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \frac{2}{\sqrt{c^{2} d x^{2} + d} c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) + a^{2} {\left(\frac{x^{2}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \frac{2}{\sqrt{c^{2} d x^{2} + d} c^{4} d}\right)} + b^{2} {\left(\frac{{\left(c^{2} x^{2} + 2\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{c^{2} x^{2} + 1} c^{4} d^{\frac{3}{2}}} - \int \frac{2 \, {\left(c^{4} x^{4} + 3 \, c^{2} x^{2} + {\left(c^{3} x^{3} + 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1} + 2\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{5} d^{\frac{3}{2}} x^{2} + c^{3} d^{\frac{3}{2}}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{6} d^{\frac{3}{2}} x^{3} + c^{4} d^{\frac{3}{2}} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)}"," ",0,"-2*a*b*c*(x/(c^4*d^(3/2)) + arctan(c*x)/(c^5*d^(3/2))) + 2*a*b*(x^2/(sqrt(c^2*d*x^2 + d)*c^2*d) + 2/(sqrt(c^2*d*x^2 + d)*c^4*d))*arcsinh(c*x) + a^2*(x^2/(sqrt(c^2*d*x^2 + d)*c^2*d) + 2/(sqrt(c^2*d*x^2 + d)*c^4*d)) + b^2*((c^2*x^2 + 2)*log(c*x + sqrt(c^2*x^2 + 1))^2/(sqrt(c^2*x^2 + 1)*c^4*d^(3/2)) - integrate(2*(c^4*x^4 + 3*c^2*x^2 + (c^3*x^3 + 2*c*x)*sqrt(c^2*x^2 + 1) + 2)*log(c*x + sqrt(c^2*x^2 + 1))/((c^5*d^(3/2)*x^2 + c^3*d^(3/2))*(c^2*x^2 + 1) + (c^6*d^(3/2)*x^3 + c^4*d^(3/2)*x)*sqrt(c^2*x^2 + 1)), x))","F",0
303,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{x}{\sqrt{c^{2} d x^{2} + d} c^{2} d} - \frac{\operatorname{arsinh}\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + \int \frac{b^{2} x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, a b x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-a^2*(x/(sqrt(c^2*d*x^2 + d)*c^2*d) - arcsinh(c*x)/(c^3*d^(3/2))) + integrate(b^2*x^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(3/2) + 2*a*b*x^2*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(3/2), x)","F",0
304,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{a^{2}}{\sqrt{c^{2} d x^{2} + d} c^{2} d} + \int \frac{b^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, a b x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-a^2/(sqrt(c^2*d*x^2 + d)*c^2*d) + integrate(b^2*x*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(3/2) + 2*a*b*x*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(3/2), x)","F",0
305,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x} + \frac{2 \, a b x \operatorname{arsinh}\left(c x\right)}{\sqrt{c^{2} d x^{2} + d} d} + \frac{a^{2} x}{\sqrt{c^{2} d x^{2} + d} d} - \frac{a b \log\left(x^{2} + \frac{1}{c^{2}}\right)}{c d^{\frac{3}{2}}}"," ",0,"b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(3/2), x) + 2*a*b*x*arcsinh(c*x)/(sqrt(c^2*d*x^2 + d)*d) + a^2*x/(sqrt(c^2*d*x^2 + d)*d) - a*b*log(x^2 + 1/c^2)/(c*d^(3/2))","F",0
306,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{c^{2} d x^{2} + d} d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-a^2*(arcsinh(1/(c*abs(x)))/d^(3/2) - 1/(sqrt(c^2*d*x^2 + d)*d)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(3/2)*x) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(3/2)*x), x)","F",0
307,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a b c {\left(\frac{\log\left(c^{2} x^{2} + 1\right)}{d^{\frac{3}{2}}} + \frac{2 \, \log\left(x\right)}{d^{\frac{3}{2}}}\right)} - 2 \, {\left(\frac{2 \, c^{2} x}{\sqrt{c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{c^{2} d x^{2} + d} d x}\right)} a b \operatorname{arsinh}\left(c x\right) - {\left(\frac{2 \, c^{2} x}{\sqrt{c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{c^{2} d x^{2} + d} d x}\right)} a^{2} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"a*b*c*(log(c^2*x^2 + 1)/d^(3/2) + 2*log(x)/d^(3/2)) - 2*(2*c^2*x/(sqrt(c^2*d*x^2 + d)*d) + 1/(sqrt(c^2*d*x^2 + d)*d*x))*a*b*arcsinh(c*x) - (2*c^2*x/(sqrt(c^2*d*x^2 + d)*d) + 1/(sqrt(c^2*d*x^2 + d)*d*x))*a^2 + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(3/2)*x^2), x)","F",0
308,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\sqrt{c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{c^{2} d x^{2} + d} d x^{2}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"1/2*(3*c^2*arcsinh(1/(c*abs(x)))/d^(3/2) - 3*c^2/(sqrt(c^2*d*x^2 + d)*d) - 1/(sqrt(c^2*d*x^2 + d)*d*x^2))*a^2 + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(3/2)*x^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(3/2)*x^3), x)","F",0
309,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\sqrt{c^{2} d x^{2} + d} d} + \frac{4 \, c^{2}}{\sqrt{c^{2} d x^{2} + d} d x} - \frac{1}{\sqrt{c^{2} d x^{2} + d} d x^{3}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"1/3*(8*c^4*x/(sqrt(c^2*d*x^2 + d)*d) + 4*c^2/(sqrt(c^2*d*x^2 + d)*d*x) - 1/(sqrt(c^2*d*x^2 + d)*d*x^3))*a^2 + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(3/2)*x^4) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(3/2)*x^4), x)","F",0
310,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{3 \, x^{4}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{12 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d} + \frac{8}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d}\right)} + \frac{{\left(3 \, b^{2} c^{4} \sqrt{d} x^{4} + 12 \, b^{2} c^{2} \sqrt{d} x^{2} + 8 \, b^{2} \sqrt{d}\right)} \sqrt{c^{2} x^{2} + 1} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{3 \, {\left(c^{10} d^{3} x^{4} + 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}\right)}} + \int -\frac{2 \, {\left({\left(12 \, b^{2} c^{3} x^{3} - 3 \, {\left(a b c^{5} - b^{2} c^{5}\right)} x^{5} + 8 \, b^{2} c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(15 \, b^{2} c^{4} x^{4} - 3 \, {\left(a b c^{6} - b^{2} c^{6}\right)} x^{6} + 20 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{3 \, {\left(c^{12} d^{\frac{5}{2}} x^{7} + 3 \, c^{10} d^{\frac{5}{2}} x^{5} + 3 \, c^{8} d^{\frac{5}{2}} x^{3} + c^{6} d^{\frac{5}{2}} x + {\left(c^{11} d^{\frac{5}{2}} x^{6} + 3 \, c^{9} d^{\frac{5}{2}} x^{4} + 3 \, c^{7} d^{\frac{5}{2}} x^{2} + c^{5} d^{\frac{5}{2}}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x}"," ",0,"1/3*a^2*(3*x^4/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 12*x^2/((c^2*d*x^2 + d)^(3/2)*c^4*d) + 8/((c^2*d*x^2 + d)^(3/2)*c^6*d)) + 1/3*(3*b^2*c^4*sqrt(d)*x^4 + 12*b^2*c^2*sqrt(d)*x^2 + 8*b^2*sqrt(d))*sqrt(c^2*x^2 + 1)*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^10*d^3*x^4 + 2*c^8*d^3*x^2 + c^6*d^3) + integrate(-2/3*((12*b^2*c^3*x^3 - 3*(a*b*c^5 - b^2*c^5)*x^5 + 8*b^2*c*x)*(c^2*x^2 + 1) + (15*b^2*c^4*x^4 - 3*(a*b*c^6 - b^2*c^6)*x^6 + 20*b^2*c^2*x^2 + 8*b^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1))/(c^12*d^(5/2)*x^7 + 3*c^10*d^(5/2)*x^5 + 3*c^8*d^(5/2)*x^3 + c^6*d^(5/2)*x + (c^11*d^(5/2)*x^6 + 3*c^9*d^(5/2)*x^4 + 3*c^7*d^(5/2)*x^2 + c^5*d^(5/2))*sqrt(c^2*x^2 + 1)), x)","F",0
311,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} + \frac{x}{\sqrt{c^{2} d x^{2} + d} c^{4} d^{2}} - \frac{3 \, \operatorname{arsinh}\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} a^{2} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*(x*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d)) + x/(sqrt(c^2*d*x^2 + d)*c^4*d^2) - 3*arcsinh(c*x)/(c^5*d^(5/2)))*a^2 + integrate(b^2*x^4*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(5/2) + 2*a*b*x^4*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(5/2), x)","F",0
312,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a b c {\left(\frac{x}{c^{6} d^{\frac{5}{2}} x^{2} + c^{4} d^{\frac{5}{2}}} - \frac{5 \, \arctan\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} - \frac{2}{3} \, a b {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{3 \, x^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \frac{2}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} + b^{2} \int \frac{x^{3} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*a*b*c*(x/(c^6*d^(5/2)*x^2 + c^4*d^(5/2)) - 5*arctan(c*x)/(c^5*d^(5/2))) - 2/3*a*b*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d))*arcsinh(c*x) - 1/3*a^2*(3*x^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + 2/((c^2*d*x^2 + d)^(3/2)*c^4*d)) + b^2*integrate(x^3*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(5/2), x)","F",0
313,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a b c {\left(\frac{1}{c^{6} d^{\frac{5}{2}} x^{2} + c^{4} d^{\frac{5}{2}}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b {\left(\frac{x}{\sqrt{c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{x}{\sqrt{c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} + b^{2} \int \frac{x^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*a*b*c*(1/(c^6*d^(5/2)*x^2 + c^4*d^(5/2)) + log(c^2*x^2 + 1)/(c^4*d^(5/2))) + 2/3*a*b*(x/(sqrt(c^2*d*x^2 + d)*c^2*d^2) - x/((c^2*d*x^2 + d)^(3/2)*c^2*d))*arcsinh(c*x) + 1/3*a^2*(x/(sqrt(c^2*d*x^2 + d)*c^2*d^2) - x/((c^2*d*x^2 + d)^(3/2)*c^2*d)) + b^2*integrate(x^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(5/2), x)","F",0
314,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{a^{2}}{3 \, {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \int \frac{b^{2} x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}} + \frac{2 \, a b x \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*a^2/((c^2*d*x^2 + d)^(3/2)*c^2*d) + integrate(b^2*x*log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(5/2) + 2*a*b*x*log(c*x + sqrt(c^2*x^2 + 1))/(c^2*d*x^2 + d)^(5/2), x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} + c^{2} d^{\frac{5}{2}}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b {\left(\frac{2 \, x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{2 \, x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*b*c*(1/(c^4*d^(5/2)*x^2 + c^2*d^(5/2)) - 2*log(c^2*x^2 + 1)/(c^2*d^(5/2))) + 2/3*a*b*(2*x/(sqrt(c^2*d*x^2 + d)*d^2) + x/((c^2*d*x^2 + d)^(3/2)*d))*arcsinh(c*x) + 1/3*a^2*(2*x/(sqrt(c^2*d*x^2 + d)*d^2) + x/((c^2*d*x^2 + d)^(3/2)*d)) + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(c^2*d*x^2 + d)^(5/2), x)","F",0
316,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{3 \, \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{c^{2} d x^{2} + d} d^{2}} - \frac{1}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"-1/3*a^2*(3*arcsinh(1/(c*abs(x)))/d^(5/2) - 3/(sqrt(c^2*d*x^2 + d)*d^2) - 1/((c^2*d*x^2 + d)^(3/2)*d)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(5/2)*x) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(5/2)*x), x)","F",0
317,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{8 \, c^{2} x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{4 \, c^{2} x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{3}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"-1/3*a^2*(8*c^2*x/(sqrt(c^2*d*x^2 + d)*d^2) + 4*c^2*x/((c^2*d*x^2 + d)^(3/2)*d) + 3/((c^2*d*x^2 + d)^(3/2)*d*x)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(5/2)*x^2) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(5/2)*x^2), x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^3/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} {\left(\frac{15 \, c^{2} \operatorname{arsinh}\left(\frac{1}{c {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{15 \, c^{2}}{\sqrt{c^{2} d x^{2} + d} d^{2}} - \frac{5 \, c^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{3}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"1/6*a^2*(15*c^2*arcsinh(1/(c*abs(x)))/d^(5/2) - 15*c^2/(sqrt(c^2*d*x^2 + d)*d^2) - 5*c^2/((c^2*d*x^2 + d)^(3/2)*d) - 3/((c^2*d*x^2 + d)^(3/2)*d*x^2)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(5/2)*x^3) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/((c^2*d*x^2 + d)^(5/2)*x^3), x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/x^4/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a b c {\left(\frac{8 \, c^{2} \log\left(c^{2} x^{2} + 1\right)}{d^{\frac{5}{2}}} + \frac{16 \, c^{2} \log\left(x\right)}{d^{\frac{5}{2}}} + \frac{1}{c^{2} d^{\frac{5}{2}} x^{4} + d^{\frac{5}{2}} x^{2}}\right)} + \frac{2}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{6 \, c^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a b \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{6 \, c^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a^{2} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}\,{d x}"," ",0,"-1/3*a*b*c*(8*c^2*log(c^2*x^2 + 1)/d^(5/2) + 16*c^2*log(x)/d^(5/2) + 1/(c^2*d^(5/2)*x^4 + d^(5/2)*x^2)) + 2/3*(16*c^4*x/(sqrt(c^2*d*x^2 + d)*d^2) + 8*c^4*x/((c^2*d*x^2 + d)^(3/2)*d) + 6*c^2/((c^2*d*x^2 + d)^(3/2)*d*x) - 1/((c^2*d*x^2 + d)^(3/2)*d*x^3))*a*b*arcsinh(c*x) + 1/3*(16*c^4*x/(sqrt(c^2*d*x^2 + d)*d^2) + 8*c^4*x/((c^2*d*x^2 + d)^(3/2)*d) + 6*c^2/((c^2*d*x^2 + d)^(3/2)*d*x) - 1/((c^2*d*x^2 + d)^(3/2)*d*x^3))*a^2 + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/((c^2*d*x^2 + d)^(5/2)*x^4), x)","F",0
320,0,0,0,0.000000," ","integrate(arcsinh(a*x)^2/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^2/(a^2*c*x^2 + c)^(7/2), x)","F",0
321,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} x^{m}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)^2*x^m, x)","F",0
322,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} x^{m}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)^2*x^m, x)","F",0
323,0,0,0,0.000000," ","integrate(x^m*(c^2*d*x^2+d)^(1/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\int \sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} x^{m}\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)^2*x^m, x)","F",0
324,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} x^{m}}{\sqrt{c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^2*x^m/sqrt(c^2*d*x^2 + d), x)","F",0
325,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} x^{m}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^2*x^m/(c^2*d*x^2 + d)^(3/2), x)","F",0
326,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(c*x))^2/(c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} x^{m}}{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^2*x^m/(c^2*d*x^2 + d)^(5/2), x)","F",0
327,0,0,0,0.000000," ","integrate(x^m*arcsinh(a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{arsinh}\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsinh(a*x)^2/sqrt(a^2*x^2 + 1), x)","F",0
328,1,276,0,0.323062," ","integrate((a^2*c*x^2+c)^3*arcsinh(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{1225} \, {\left(75 \, \sqrt{a^{2} x^{2} + 1} a^{4} c^{3} x^{6} + 351 \, \sqrt{a^{2} x^{2} + 1} a^{2} c^{3} x^{4} + 757 \, \sqrt{a^{2} x^{2} + 1} c^{3} x^{2} + \frac{2161 \, \sqrt{a^{2} x^{2} + 1} c^{3}}{a^{2}}\right)} a \operatorname{arsinh}\left(a x\right)^{2} + \frac{1}{35} \, {\left(5 \, a^{6} c^{3} x^{7} + 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} + 35 \, c^{3} x\right)} \operatorname{arsinh}\left(a x\right)^{3} - \frac{2}{13505625} \, {\left(16875 \, \sqrt{a^{2} x^{2} + 1} a^{4} c^{3} x^{6} + 134541 \, \sqrt{a^{2} x^{2} + 1} a^{2} c^{3} x^{4} + 747937 \, \sqrt{a^{2} x^{2} + 1} c^{3} x^{2} + \frac{22329151 \, \sqrt{a^{2} x^{2} + 1} c^{3}}{a^{2}} - \frac{105 \, {\left(1125 \, a^{6} c^{3} x^{7} + 7371 \, a^{4} c^{3} x^{5} + 26495 \, a^{2} c^{3} x^{3} + 226905 \, c^{3} x\right)} \operatorname{arsinh}\left(a x\right)}{a}\right)} a"," ",0,"-1/1225*(75*sqrt(a^2*x^2 + 1)*a^4*c^3*x^6 + 351*sqrt(a^2*x^2 + 1)*a^2*c^3*x^4 + 757*sqrt(a^2*x^2 + 1)*c^3*x^2 + 2161*sqrt(a^2*x^2 + 1)*c^3/a^2)*a*arcsinh(a*x)^2 + 1/35*(5*a^6*c^3*x^7 + 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 + 35*c^3*x)*arcsinh(a*x)^3 - 2/13505625*(16875*sqrt(a^2*x^2 + 1)*a^4*c^3*x^6 + 134541*sqrt(a^2*x^2 + 1)*a^2*c^3*x^4 + 747937*sqrt(a^2*x^2 + 1)*c^3*x^2 + 22329151*sqrt(a^2*x^2 + 1)*c^3/a^2 - 105*(1125*a^6*c^3*x^7 + 7371*a^4*c^3*x^5 + 26495*a^2*c^3*x^3 + 226905*c^3*x)*arcsinh(a*x)/a)*a","A",0
329,1,210,0,0.318934," ","integrate((a^2*c*x^2+c)^2*arcsinh(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{75} \, {\left(9 \, \sqrt{a^{2} x^{2} + 1} a^{2} c^{2} x^{4} + 38 \, \sqrt{a^{2} x^{2} + 1} c^{2} x^{2} + \frac{149 \, \sqrt{a^{2} x^{2} + 1} c^{2}}{a^{2}}\right)} a \operatorname{arsinh}\left(a x\right)^{2} + \frac{1}{15} \, {\left(3 \, a^{4} c^{2} x^{5} + 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \operatorname{arsinh}\left(a x\right)^{3} - \frac{2}{16875} \, {\left(81 \, \sqrt{a^{2} x^{2} + 1} a^{2} c^{2} x^{4} + 842 \, \sqrt{a^{2} x^{2} + 1} c^{2} x^{2} - \frac{15 \, {\left(27 \, a^{4} c^{2} x^{5} + 190 \, a^{2} c^{2} x^{3} + 2235 \, c^{2} x\right)} \operatorname{arsinh}\left(a x\right)}{a} + \frac{31841 \, \sqrt{a^{2} x^{2} + 1} c^{2}}{a^{2}}\right)} a"," ",0,"-1/75*(9*sqrt(a^2*x^2 + 1)*a^2*c^2*x^4 + 38*sqrt(a^2*x^2 + 1)*c^2*x^2 + 149*sqrt(a^2*x^2 + 1)*c^2/a^2)*a*arcsinh(a*x)^2 + 1/15*(3*a^4*c^2*x^5 + 10*a^2*c^2*x^3 + 15*c^2*x)*arcsinh(a*x)^3 - 2/16875*(81*sqrt(a^2*x^2 + 1)*a^2*c^2*x^4 + 842*sqrt(a^2*x^2 + 1)*c^2*x^2 - 15*(27*a^4*c^2*x^5 + 190*a^2*c^2*x^3 + 2235*c^2*x)*arcsinh(a*x)/a + 31841*sqrt(a^2*x^2 + 1)*c^2/a^2)*a","A",0
330,1,124,0,0.561654," ","integrate((a^2*c*x^2+c)*arcsinh(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\sqrt{a^{2} x^{2} + 1} c x^{2} + \frac{7 \, \sqrt{a^{2} x^{2} + 1} c}{a^{2}}\right)} a \operatorname{arsinh}\left(a x\right)^{2} + \frac{1}{3} \, {\left(a^{2} c x^{3} + 3 \, c x\right)} \operatorname{arsinh}\left(a x\right)^{3} - \frac{2}{27} \, {\left(\sqrt{a^{2} x^{2} + 1} c x^{2} - \frac{3 \, {\left(a^{2} c x^{3} + 21 \, c x\right)} \operatorname{arsinh}\left(a x\right)}{a} + \frac{61 \, \sqrt{a^{2} x^{2} + 1} c}{a^{2}}\right)} a"," ",0,"-1/3*(sqrt(a^2*x^2 + 1)*c*x^2 + 7*sqrt(a^2*x^2 + 1)*c/a^2)*a*arcsinh(a*x)^2 + 1/3*(a^2*c*x^3 + 3*c*x)*arcsinh(a*x)^3 - 2/27*(sqrt(a^2*x^2 + 1)*c*x^2 - 3*(a^2*c*x^3 + 21*c*x)*arcsinh(a*x)/a + 61*sqrt(a^2*x^2 + 1)*c/a^2)*a","A",0
331,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(a^2*c*x^2 + c), x)","F",0
332,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(a^2*c*x^2 + c)^2, x)","F",0
333,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(a^2*c*x^2 + c)^3, x)","F",0
334,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arcsinh(a*x)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
335,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
336,-2,0,0,0.000000," ","integrate(arcsinh(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
337,1,14,0,0.367298," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)^{4}}{4 \, a \sqrt{c}}"," ",0,"1/4*arcsinh(a*x)^4/(a*sqrt(c))","A",0
338,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(a^2*c*x^2 + c)^(3/2), x)","F",0
339,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
340,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(a^2*c*x^2 + c)^(7/2), x)","F",0
341,0,0,0,0.000000," ","integrate(x^m*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{arsinh}\left(a x\right)^{3}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsinh(a*x)^3/sqrt(a^2*x^2 + 1), x)","F",0
342,0,0,0,0.000000," ","integrate(x^4*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4} \operatorname{arsinh}\left(a x\right)^{3}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^4*arcsinh(a*x)^3/sqrt(a^2*x^2 + 1), x)","F",0
343,1,127,0,0.406189," ","integrate(x^3*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x^{2}}{a^{2}} - \frac{2 \, \sqrt{a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arsinh}\left(a x\right)^{3} + \frac{2}{27} \, a {\left(\frac{3 \, {\left(\sqrt{a^{2} x^{2} + 1} x^{2} - \frac{20 \, \sqrt{a^{2} x^{2} + 1}}{a^{2}}\right)} \operatorname{arsinh}\left(a x\right)}{a^{3}} - \frac{a^{2} x^{3} - 60 \, x}{a^{4}}\right)} - \frac{{\left(a^{2} x^{3} - 6 \, x\right)} \operatorname{arsinh}\left(a x\right)^{2}}{3 \, a^{3}}"," ",0,"1/3*(sqrt(a^2*x^2 + 1)*x^2/a^2 - 2*sqrt(a^2*x^2 + 1)/a^4)*arcsinh(a*x)^3 + 2/27*a*(3*(sqrt(a^2*x^2 + 1)*x^2 - 20*sqrt(a^2*x^2 + 1)/a^2)*arcsinh(a*x)/a^3 - (a^2*x^3 - 60*x)/a^4) - 1/3*(a^2*x^3 - 6*x)*arcsinh(a*x)^2/a^3","A",0
344,0,0,0,0.000000," ","integrate(x^2*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{arsinh}\left(a x\right)^{3}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arcsinh(a*x)^3/sqrt(a^2*x^2 + 1), x)","F",0
345,1,61,0,0.321114," ","integrate(x*arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{3 \, x \operatorname{arsinh}\left(a x\right)^{2}}{a} + \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)^{3}}{a^{2}} - \frac{6 \, {\left(x - \frac{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}{a}\right)}}{a}"," ",0,"-3*x*arcsinh(a*x)^2/a + sqrt(a^2*x^2 + 1)*arcsinh(a*x)^3/a^2 - 6*(x - sqrt(a^2*x^2 + 1)*arcsinh(a*x)/a)/a","A",0
346,1,11,0,0.350240," ","integrate(arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)^{4}}{4 \, a}"," ",0,"1/4*arcsinh(a*x)^4/a","A",0
347,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/x/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{\sqrt{a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(sqrt(a^2*x^2 + 1)*x), x)","F",0
348,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/x^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a^{2} x^{2} + 1} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)^{3}}{x} + \int \frac{3 \, {\left(a^{3} x^{2} + \sqrt{a^{2} x^{2} + 1} a^{2} x + a\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)^{2}}{\sqrt{a^{2} x^{2} + 1} a x^{2} + {\left(a^{2} x^{2} + 1\right)} x}\,{d x}"," ",0,"-sqrt(a^2*x^2 + 1)*log(a*x + sqrt(a^2*x^2 + 1))^3/x + integrate(3*(a^3*x^2 + sqrt(a^2*x^2 + 1)*a^2*x + a)*log(a*x + sqrt(a^2*x^2 + 1))^2/(sqrt(a^2*x^2 + 1)*a*x^2 + (a^2*x^2 + 1)*x), x)","F",0
349,0,0,0,0.000000," ","integrate(arcsinh(a*x)^3/x^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{3}}{\sqrt{a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^3/(sqrt(a^2*x^2 + 1)*x^3), x)","F",0
350,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arcsinh(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{3}}{\operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^3/arcsinh(a*x), x)","F",0
351,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arcsinh(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{2}}{\operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2/arcsinh(a*x), x)","F",0
352,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arcsinh(a*x),x, algorithm=""maxima"")","\int \frac{a^{2} c x^{2} + c}{\operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)/arcsinh(a*x), x)","F",0
353,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)/arcsinh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)*arcsinh(a*x)), x)","F",0
354,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arcsinh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{2} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^2*arcsinh(a*x)), x)","F",0
355,0,0,0,0.000000," ","integrate(x^4*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1} x^{4}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)*x^4/(b*arcsinh(c*x) + a), x)","F",0
356,0,0,0,0.000000," ","integrate(x^3*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1} x^{3}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)*x^3/(b*arcsinh(c*x) + a), x)","F",0
357,0,0,0,0.000000," ","integrate(x^2*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)*x^2/(b*arcsinh(c*x) + a), x)","F",0
358,0,0,0,0.000000," ","integrate(x*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1} x}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)*x/(b*arcsinh(c*x) + a), x)","F",0
359,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)/(b*arcsinh(c*x) + a), x)","F",0
360,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)/((b*arcsinh(c*x) + a)*x), x)","F",0
361,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)/((b*arcsinh(c*x) + a)*x^2), x)","F",0
362,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x^3/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)/((b*arcsinh(c*x) + a)*x^3), x)","F",0
363,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x^4/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)/((b*arcsinh(c*x) + a)*x^4), x)","F",0
364,0,0,0,0.000000," ","integrate(x^3*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)*x^3/(b*arcsinh(c*x) + a), x)","F",0
365,0,0,0,0.000000," ","integrate(x^2*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)*x^2/(b*arcsinh(c*x) + a), x)","F",0
366,0,0,0,0.000000," ","integrate(x*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)*x/(b*arcsinh(c*x) + a), x)","F",0
367,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)/(b*arcsinh(c*x) + a), x)","F",0
368,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)/((b*arcsinh(c*x) + a)*x), x)","F",0
369,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)/((b*arcsinh(c*x) + a)*x^2), x)","F",0
370,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x^3/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)/((b*arcsinh(c*x) + a)*x^3), x)","F",0
371,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x^4/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)/((b*arcsinh(c*x) + a)*x^4), x)","F",0
372,0,0,0,0.000000," ","integrate(x^3*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{3}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)*x^3/(b*arcsinh(c*x) + a), x)","F",0
373,0,0,0,0.000000," ","integrate(x^2*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{2}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)*x^2/(b*arcsinh(c*x) + a), x)","F",0
374,0,0,0,0.000000," ","integrate(x*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)*x/(b*arcsinh(c*x) + a), x)","F",0
375,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)/(b*arcsinh(c*x) + a), x)","F",0
376,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)/((b*arcsinh(c*x) + a)*x), x)","F",0
377,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)/((b*arcsinh(c*x) + a)*x^2), x)","F",0
378,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x^3/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)/((b*arcsinh(c*x) + a)*x^3), x)","F",0
379,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x^4/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)/((b*arcsinh(c*x) + a)*x^4), x)","F",0
380,0,0,0,0.000000," ","integrate(x^4/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/(sqrt(a^2*x^2 + 1)*arcsinh(a*x)), x)","F",0
381,0,0,0,0.000000," ","integrate(x^3/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/(sqrt(a^2*x^2 + 1)*arcsinh(a*x)), x)","F",0
382,0,0,0,0.000000," ","integrate(x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/(sqrt(a^2*x^2 + 1)*arcsinh(a*x)), x)","F",0
383,0,0,0,0.000000," ","integrate(x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/(sqrt(a^2*x^2 + 1)*arcsinh(a*x)), x)","F",0
384,0,0,0,0.000000," ","integrate(x/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{a^{2} x^{2} + 1} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/(sqrt(a^2*x^2 + 1)*arcsinh(a*x)), x)","F",0
385,1,9,0,0.419219," ","integrate(1/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\operatorname{arsinh}\left(a x\right)\right)}{a}"," ",0,"log(arcsinh(a*x))/a","A",0
386,0,0,0,0.000000," ","integrate(1/x/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} x^{2} + 1} x \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 + 1)*x*arcsinh(a*x)), x)","F",0
387,0,0,0,0.000000," ","integrate(1/x^2/arcsinh(a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} x^{2} + 1} x^{2} \operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 + 1)*x^2*arcsinh(a*x)), x)","F",0
388,0,0,0,0.000000," ","integrate(x^5/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{5}}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^5/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
389,0,0,0,0.000000," ","integrate(x^4/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^4/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
390,0,0,0,0.000000," ","integrate(x^3/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^3/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
391,0,0,0,0.000000," ","integrate(x^2/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
392,0,0,0,0.000000," ","integrate(x/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
393,1,16,0,0.413466," ","integrate(1/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(b \operatorname{arsinh}\left(c x\right) + a\right)}{b c}"," ",0,"log(b*arcsinh(c*x) + a)/(b*c)","A",0
394,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)*x), x)","F",0
395,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)*x^2), x)","F",0
396,0,0,0,0.000000," ","integrate(x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/((c^2*x^2 + 1)^(3/2)*(b*arcsinh(c*x) + a)), x)","F",0
397,0,0,0,0.000000," ","integrate(x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{x}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/((c^2*x^2 + 1)^(3/2)*(b*arcsinh(c*x) + a)), x)","F",0
398,0,0,0,0.000000," ","integrate(1/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((c^2*x^2 + 1)^(3/2)*(b*arcsinh(c*x) + a)), x)","F",0
399,0,0,0,0.000000," ","integrate(1/x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((c^2*x^2 + 1)^(3/2)*(b*arcsinh(c*x) + a)*x), x)","F",0
400,0,0,0,0.000000," ","integrate(1/x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((c^2*x^2 + 1)^(3/2)*(b*arcsinh(c*x) + a)*x^2), x)","F",0
401,0,0,0,0.000000," ","integrate(x^m*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{m}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(5/2)*x^m/(b*arcsinh(c*x) + a), x)","F",0
402,0,0,0,0.000000," ","integrate(x^m*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)^(3/2)*x^m/(b*arcsinh(c*x) + a), x)","F",0
403,0,0,0,0.000000," ","integrate(x^m*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} x^{2} + 1} x^{m}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)*x^m/(b*arcsinh(c*x) + a), x)","F",0
404,0,0,0,0.000000," ","integrate(x^m/(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
405,0,0,0,0.000000," ","integrate(x^m/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/((c^2*x^2 + 1)^(3/2)*(b*arcsinh(c*x) + a)), x)","F",0
406,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arcsinh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{9} c^{3} x^{9} + 4 \, a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} + 4 \, a^{3} c^{3} x^{3} + a c^{3} x + {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \sqrt{a^{2} x^{2} + 1}}{{\left(a^{3} x^{2} + \sqrt{a^{2} x^{2} + 1} a^{2} x + a\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)} + \int \frac{7 \, a^{10} c^{3} x^{10} + 29 \, a^{8} c^{3} x^{8} + 46 \, a^{6} c^{3} x^{6} + 34 \, a^{4} c^{3} x^{4} + 11 \, a^{2} c^{3} x^{2} + c^{3} + {\left(7 \, a^{8} c^{3} x^{8} + 20 \, a^{6} c^{3} x^{6} + 18 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} - c^{3}\right)} {\left(a^{2} x^{2} + 1\right)} + 7 \, {\left(2 \, a^{9} c^{3} x^{9} + 7 \, a^{7} c^{3} x^{7} + 9 \, a^{5} c^{3} x^{5} + 5 \, a^{3} c^{3} x^{3} + a c^{3} x\right)} \sqrt{a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} + {\left(a^{2} x^{2} + 1\right)} a^{2} x^{2} + 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} + a x\right)} \sqrt{a^{2} x^{2} + 1} + 1\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)}\,{d x}"," ",0,"-(a^9*c^3*x^9 + 4*a^7*c^3*x^7 + 6*a^5*c^3*x^5 + 4*a^3*c^3*x^3 + a*c^3*x + (a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*sqrt(a^2*x^2 + 1))/((a^3*x^2 + sqrt(a^2*x^2 + 1)*a^2*x + a)*log(a*x + sqrt(a^2*x^2 + 1))) + integrate((7*a^10*c^3*x^10 + 29*a^8*c^3*x^8 + 46*a^6*c^3*x^6 + 34*a^4*c^3*x^4 + 11*a^2*c^3*x^2 + c^3 + (7*a^8*c^3*x^8 + 20*a^6*c^3*x^6 + 18*a^4*c^3*x^4 + 4*a^2*c^3*x^2 - c^3)*(a^2*x^2 + 1) + 7*(2*a^9*c^3*x^9 + 7*a^7*c^3*x^7 + 9*a^5*c^3*x^5 + 5*a^3*c^3*x^3 + a*c^3*x)*sqrt(a^2*x^2 + 1))/((a^4*x^4 + (a^2*x^2 + 1)*a^2*x^2 + 2*a^2*x^2 + 2*(a^3*x^3 + a*x)*sqrt(a^2*x^2 + 1) + 1)*log(a*x + sqrt(a^2*x^2 + 1))), x)","F",0
407,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arcsinh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{7} c^{2} x^{7} + 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} + a c^{2} x + {\left(a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} x^{2} + 1}}{{\left(a^{3} x^{2} + \sqrt{a^{2} x^{2} + 1} a^{2} x + a\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)} + \int \frac{5 \, a^{8} c^{2} x^{8} + 16 \, a^{6} c^{2} x^{6} + 18 \, a^{4} c^{2} x^{4} + 8 \, a^{2} c^{2} x^{2} + {\left(5 \, a^{6} c^{2} x^{6} + 9 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} - c^{2}\right)} {\left(a^{2} x^{2} + 1\right)} + c^{2} + 5 \, {\left(2 \, a^{7} c^{2} x^{7} + 5 \, a^{5} c^{2} x^{5} + 4 \, a^{3} c^{2} x^{3} + a c^{2} x\right)} \sqrt{a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} + {\left(a^{2} x^{2} + 1\right)} a^{2} x^{2} + 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} + a x\right)} \sqrt{a^{2} x^{2} + 1} + 1\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)}\,{d x}"," ",0,"-(a^7*c^2*x^7 + 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 + a*c^2*x + (a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*sqrt(a^2*x^2 + 1))/((a^3*x^2 + sqrt(a^2*x^2 + 1)*a^2*x + a)*log(a*x + sqrt(a^2*x^2 + 1))) + integrate((5*a^8*c^2*x^8 + 16*a^6*c^2*x^6 + 18*a^4*c^2*x^4 + 8*a^2*c^2*x^2 + (5*a^6*c^2*x^6 + 9*a^4*c^2*x^4 + 3*a^2*c^2*x^2 - c^2)*(a^2*x^2 + 1) + c^2 + 5*(2*a^7*c^2*x^7 + 5*a^5*c^2*x^5 + 4*a^3*c^2*x^3 + a*c^2*x)*sqrt(a^2*x^2 + 1))/((a^4*x^4 + (a^2*x^2 + 1)*a^2*x^2 + 2*a^2*x^2 + 2*(a^3*x^3 + a*x)*sqrt(a^2*x^2 + 1) + 1)*log(a*x + sqrt(a^2*x^2 + 1))), x)","F",0
408,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arcsinh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{5} c x^{5} + 2 \, a^{3} c x^{3} + a c x + {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \sqrt{a^{2} x^{2} + 1}}{{\left(a^{3} x^{2} + \sqrt{a^{2} x^{2} + 1} a^{2} x + a\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)} + \int \frac{3 \, a^{6} c x^{6} + 7 \, a^{4} c x^{4} + 5 \, a^{2} c x^{2} + {\left(3 \, a^{4} c x^{4} + 2 \, a^{2} c x^{2} - c\right)} {\left(a^{2} x^{2} + 1\right)} + 3 \, {\left(2 \, a^{5} c x^{5} + 3 \, a^{3} c x^{3} + a c x\right)} \sqrt{a^{2} x^{2} + 1} + c}{{\left(a^{4} x^{4} + {\left(a^{2} x^{2} + 1\right)} a^{2} x^{2} + 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} + a x\right)} \sqrt{a^{2} x^{2} + 1} + 1\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)}\,{d x}"," ",0,"-(a^5*c*x^5 + 2*a^3*c*x^3 + a*c*x + (a^4*c*x^4 + 2*a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1))/((a^3*x^2 + sqrt(a^2*x^2 + 1)*a^2*x + a)*log(a*x + sqrt(a^2*x^2 + 1))) + integrate((3*a^6*c*x^6 + 7*a^4*c*x^4 + 5*a^2*c*x^2 + (3*a^4*c*x^4 + 2*a^2*c*x^2 - c)*(a^2*x^2 + 1) + 3*(2*a^5*c*x^5 + 3*a^3*c*x^3 + a*c*x)*sqrt(a^2*x^2 + 1) + c)/((a^4*x^4 + (a^2*x^2 + 1)*a^2*x^2 + 2*a^2*x^2 + 2*(a^3*x^3 + a*x)*sqrt(a^2*x^2 + 1) + 1)*log(a*x + sqrt(a^2*x^2 + 1))), x)","F",0
409,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)/arcsinh(a*x)^2,x, algorithm=""maxima"")","-\frac{a x + \sqrt{a^{2} x^{2} + 1}}{{\left(a^{3} c x^{2} + \sqrt{a^{2} x^{2} + 1} a^{2} c x + a c\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)} - \int \frac{a^{4} x^{4} + {\left(a^{2} x^{2} + 1\right)}^{2} + {\left(2 \, a^{3} x^{3} + a x\right)} \sqrt{a^{2} x^{2} + 1} - 1}{{\left(a^{6} c x^{6} + 3 \, a^{4} c x^{4} + 3 \, a^{2} c x^{2} + {\left(a^{4} c x^{4} + a^{2} c x^{2}\right)} {\left(a^{2} x^{2} + 1\right)} + 2 \, {\left(a^{5} c x^{5} + 2 \, a^{3} c x^{3} + a c x\right)} \sqrt{a^{2} x^{2} + 1} + c\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)}\,{d x}"," ",0,"-(a*x + sqrt(a^2*x^2 + 1))/((a^3*c*x^2 + sqrt(a^2*x^2 + 1)*a^2*c*x + a*c)*log(a*x + sqrt(a^2*x^2 + 1))) - integrate((a^4*x^4 + (a^2*x^2 + 1)^2 + (2*a^3*x^3 + a*x)*sqrt(a^2*x^2 + 1) - 1)/((a^6*c*x^6 + 3*a^4*c*x^4 + 3*a^2*c*x^2 + (a^4*c*x^4 + a^2*c*x^2)*(a^2*x^2 + 1) + 2*(a^5*c*x^5 + 2*a^3*c*x^3 + a*c*x)*sqrt(a^2*x^2 + 1) + c)*log(a*x + sqrt(a^2*x^2 + 1))), x)","F",0
410,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arcsinh(a*x)^2,x, algorithm=""maxima"")","-\frac{a x + \sqrt{a^{2} x^{2} + 1}}{{\left(a^{5} c^{2} x^{4} + 2 \, a^{3} c^{2} x^{2} + a c^{2} + {\left(a^{4} c^{2} x^{3} + a^{2} c^{2} x\right)} \sqrt{a^{2} x^{2} + 1}\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)} - \int \frac{3 \, a^{4} x^{4} + 2 \, a^{2} x^{2} + {\left(3 \, a^{2} x^{2} + 1\right)} {\left(a^{2} x^{2} + 1\right)} + 3 \, {\left(2 \, a^{3} x^{3} + a x\right)} \sqrt{a^{2} x^{2} + 1} - 1}{{\left(a^{8} c^{2} x^{8} + 4 \, a^{6} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{4} + 4 \, a^{2} c^{2} x^{2} + {\left(a^{6} c^{2} x^{6} + 2 \, a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2}\right)} {\left(a^{2} x^{2} + 1\right)} + c^{2} + 2 \, {\left(a^{7} c^{2} x^{7} + 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} + a c^{2} x\right)} \sqrt{a^{2} x^{2} + 1}\right)} \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right)}\,{d x}"," ",0,"-(a*x + sqrt(a^2*x^2 + 1))/((a^5*c^2*x^4 + 2*a^3*c^2*x^2 + a*c^2 + (a^4*c^2*x^3 + a^2*c^2*x)*sqrt(a^2*x^2 + 1))*log(a*x + sqrt(a^2*x^2 + 1))) - integrate((3*a^4*x^4 + 2*a^2*x^2 + (3*a^2*x^2 + 1)*(a^2*x^2 + 1) + 3*(2*a^3*x^3 + a*x)*sqrt(a^2*x^2 + 1) - 1)/((a^8*c^2*x^8 + 4*a^6*c^2*x^6 + 6*a^4*c^2*x^4 + 4*a^2*c^2*x^2 + (a^6*c^2*x^6 + 2*a^4*c^2*x^4 + a^2*c^2*x^2)*(a^2*x^2 + 1) + c^2 + 2*(a^7*c^2*x^7 + 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 + a*c^2*x)*sqrt(a^2*x^2 + 1))*log(a*x + sqrt(a^2*x^2 + 1))), x)","F",0
411,0,0,0,0.000000," ","integrate(x^3*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{5} + x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{3} x^{6} + c x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(5 \, c^{3} x^{5} + 2 \, c x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(10 \, c^{4} x^{6} + 11 \, c^{2} x^{4} + 3 \, x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(5 \, c^{5} x^{7} + 9 \, c^{3} x^{5} + 4 \, c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^5 + x^3)*(c^2*x^2 + 1) + (c^3*x^6 + c*x^4)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((5*c^3*x^5 + 2*c*x^3)*(c^2*x^2 + 1)^(3/2) + (10*c^4*x^6 + 11*c^2*x^4 + 3*x^2)*(c^2*x^2 + 1) + (5*c^5*x^7 + 9*c^3*x^5 + 4*c*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
412,0,0,0,0.000000," ","integrate(x^2*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{4} + x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{3} x^{5} + c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(4 \, c^{3} x^{4} + c x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(4 \, c^{4} x^{5} + 4 \, c^{2} x^{3} + x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(4 \, c^{5} x^{6} + 7 \, c^{3} x^{4} + 3 \, c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^4 + x^2)*(c^2*x^2 + 1) + (c^3*x^5 + c*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((4*c^3*x^4 + c*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(4*c^4*x^5 + 4*c^2*x^3 + x)*(c^2*x^2 + 1) + (4*c^5*x^6 + 7*c^3*x^4 + 3*c*x^2)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
413,0,0,0,0.000000," ","integrate(x*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{3} + x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{3} x^{4} + c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{3 \, {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3} x^{3} + {\left(6 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(3 \, c^{5} x^{5} + 5 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^3 + x)*(c^2*x^2 + 1) + (c^3*x^4 + c*x^2)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate((3*(c^2*x^2 + 1)^(3/2)*c^3*x^3 + (6*c^4*x^4 + 5*c^2*x^2 + 1)*(c^2*x^2 + 1) + (3*c^5*x^5 + 5*c^3*x^3 + 2*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
414,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{2} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(2 \, c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(2 \, c^{3} x^{3} + c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{2} + 2 \, a b c^{2} x^{2} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{2} + 2 \, b^{2} c^{2} x^{2} + b^{2} + 2 \, {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^2 + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((2*c^2*x^2 - 1)*(c^2*x^2 + 1)^(3/2) + 2*(2*c^3*x^3 + c*x)*(c^2*x^2 + 1) + (2*c^4*x^4 + 3*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/(a*b*c^4*x^4 + (c^2*x^2 + 1)*a*b*c^2*x^2 + 2*a*b*c^2*x^2 + a*b + (b^2*c^4*x^4 + (c^2*x^2 + 1)*b^2*c^2*x^2 + 2*b^2*c^2*x^2 + b^2 + 2*(b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
415,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{2} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{3} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{2} + a b c x + {\left(b^{2} c^{3} x^{3} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{2} + b^{2} c x\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(c^{3} x^{3} - 2 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(2 \, c^{4} x^{4} - c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + c^{3} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{6} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{4} + 2 \, a b c^{3} x^{4} + a b c x^{2} + {\left(b^{2} c^{5} x^{6} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{4} + 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2} + 2 \, {\left(b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{5} + a b c^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^2 + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^3 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^2 + a*b*c*x + (b^2*c^3*x^3 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^2 + b^2*c*x)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((c^3*x^3 - 2*c*x)*(c^2*x^2 + 1)^(3/2) + (2*c^4*x^4 - c^2*x^2 - 1)*(c^2*x^2 + 1) + (c^5*x^5 + c^3*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^6 + (c^2*x^2 + 1)*a*b*c^3*x^4 + 2*a*b*c^3*x^4 + a*b*c*x^2 + (b^2*c^5*x^6 + (c^2*x^2 + 1)*b^2*c^3*x^4 + 2*b^2*c^3*x^4 + b^2*c*x^2 + 2*(b^2*c^4*x^5 + b^2*c^2*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^5 + a*b*c^2*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
416,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x^2/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{2} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{4} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{3} + a b c x^{2} + {\left(b^{2} c^{3} x^{4} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{3} + b^{2} c x^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} - \int \frac{3 \, {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} c x + 2 \, {\left(2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{7} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{5} + 2 \, a b c^{3} x^{5} + a b c x^{3} + {\left(b^{2} c^{5} x^{7} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{5} + 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3} + 2 \, {\left(b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{6} + a b c^{2} x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^2 + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^4 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^3 + a*b*c*x^2 + (b^2*c^3*x^4 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^3 + b^2*c*x^2)*log(c*x + sqrt(c^2*x^2 + 1))) - integrate((3*(c^2*x^2 + 1)^(3/2)*c*x + 2*(2*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^7 + (c^2*x^2 + 1)*a*b*c^3*x^5 + 2*a*b*c^3*x^5 + a*b*c*x^3 + (b^2*c^5*x^7 + (c^2*x^2 + 1)*b^2*c^3*x^5 + 2*b^2*c^3*x^5 + b^2*c*x^3 + 2*(b^2*c^4*x^6 + b^2*c^2*x^4)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^6 + a*b*c^2*x^4)*sqrt(c^2*x^2 + 1)), x)","F",0
417,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x^3/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{2} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{5} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{4} + a b c x^{3} + {\left(b^{2} c^{3} x^{5} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{4} + b^{2} c x^{3}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} - \int \frac{{\left(c^{3} x^{3} + 4 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(2 \, c^{4} x^{4} + 7 \, c^{2} x^{2} + 3\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + 3 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{8} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{6} + 2 \, a b c^{3} x^{6} + a b c x^{4} + {\left(b^{2} c^{5} x^{8} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{6} + 2 \, b^{2} c^{3} x^{6} + b^{2} c x^{4} + 2 \, {\left(b^{2} c^{4} x^{7} + b^{2} c^{2} x^{5}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{7} + a b c^{2} x^{5}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^2 + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^5 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^4 + a*b*c*x^3 + (b^2*c^3*x^5 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^4 + b^2*c*x^3)*log(c*x + sqrt(c^2*x^2 + 1))) - integrate(((c^3*x^3 + 4*c*x)*(c^2*x^2 + 1)^(3/2) + (2*c^4*x^4 + 7*c^2*x^2 + 3)*(c^2*x^2 + 1) + (c^5*x^5 + 3*c^3*x^3 + 2*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^8 + (c^2*x^2 + 1)*a*b*c^3*x^6 + 2*a*b*c^3*x^6 + a*b*c*x^4 + (b^2*c^5*x^8 + (c^2*x^2 + 1)*b^2*c^3*x^6 + 2*b^2*c^3*x^6 + b^2*c*x^4 + 2*(b^2*c^4*x^7 + b^2*c^2*x^5)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^7 + a*b*c^2*x^5)*sqrt(c^2*x^2 + 1)), x)","F",0
418,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/x^4/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{2} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{6} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{5} + a b c x^{4} + {\left(b^{2} c^{3} x^{6} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{5} + b^{2} c x^{4}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} - \int \frac{{\left(2 \, c^{3} x^{3} + 5 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(2 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 2\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{5} x^{5} + 5 \, c^{3} x^{3} + 3 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{9} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{7} + 2 \, a b c^{3} x^{7} + a b c x^{5} + {\left(b^{2} c^{5} x^{9} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{7} + 2 \, b^{2} c^{3} x^{7} + b^{2} c x^{5} + 2 \, {\left(b^{2} c^{4} x^{8} + b^{2} c^{2} x^{6}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{8} + a b c^{2} x^{6}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^2 + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^6 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^5 + a*b*c*x^4 + (b^2*c^3*x^6 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^5 + b^2*c*x^4)*log(c*x + sqrt(c^2*x^2 + 1))) - integrate(((2*c^3*x^3 + 5*c*x)*(c^2*x^2 + 1)^(3/2) + 2*(2*c^4*x^4 + 5*c^2*x^2 + 2)*(c^2*x^2 + 1) + (2*c^5*x^5 + 5*c^3*x^3 + 3*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^9 + (c^2*x^2 + 1)*a*b*c^3*x^7 + 2*a*b*c^3*x^7 + a*b*c*x^5 + (b^2*c^5*x^9 + (c^2*x^2 + 1)*b^2*c^3*x^7 + 2*b^2*c^3*x^7 + b^2*c*x^5 + 2*(b^2*c^4*x^8 + b^2*c^2*x^6)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^8 + a*b*c^2*x^6)*sqrt(c^2*x^2 + 1)), x)","F",0
419,0,0,0,0.000000," ","integrate(x^3*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{7} + 2 \, c^{2} x^{5} + x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{8} + 2 \, c^{3} x^{6} + c x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(7 \, c^{5} x^{7} + 9 \, c^{3} x^{5} + 2 \, c x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(14 \, c^{6} x^{8} + 27 \, c^{4} x^{6} + 16 \, c^{2} x^{4} + 3 \, x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(7 \, c^{7} x^{9} + 18 \, c^{5} x^{7} + 15 \, c^{3} x^{5} + 4 \, c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^7 + 2*c^2*x^5 + x^3)*(c^2*x^2 + 1) + (c^5*x^8 + 2*c^3*x^6 + c*x^4)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((7*c^5*x^7 + 9*c^3*x^5 + 2*c*x^3)*(c^2*x^2 + 1)^(3/2) + (14*c^6*x^8 + 27*c^4*x^6 + 16*c^2*x^4 + 3*x^2)*(c^2*x^2 + 1) + (7*c^7*x^9 + 18*c^5*x^7 + 15*c^3*x^5 + 4*c*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
420,0,0,0,0.000000," ","integrate(x^2*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{6} + 2 \, c^{2} x^{4} + x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{7} + 2 \, c^{3} x^{5} + c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(6 \, c^{5} x^{6} + 7 \, c^{3} x^{4} + c x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(6 \, c^{6} x^{7} + 11 \, c^{4} x^{5} + 6 \, c^{2} x^{3} + x\right)} {\left(c^{2} x^{2} + 1\right)} + 3 \, {\left(2 \, c^{7} x^{8} + 5 \, c^{5} x^{6} + 4 \, c^{3} x^{4} + c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^6 + 2*c^2*x^4 + x^2)*(c^2*x^2 + 1) + (c^5*x^7 + 2*c^3*x^5 + c*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((6*c^5*x^6 + 7*c^3*x^4 + c*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(6*c^6*x^7 + 11*c^4*x^5 + 6*c^2*x^3 + x)*(c^2*x^2 + 1) + 3*(2*c^7*x^8 + 5*c^5*x^6 + 4*c^3*x^4 + c*x^2)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
421,0,0,0,0.000000," ","integrate(x*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{5} + 2 \, c^{2} x^{3} + x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{6} + 2 \, c^{3} x^{4} + c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{5 \, {\left(c^{5} x^{5} + c^{3} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(10 \, c^{6} x^{6} + 17 \, c^{4} x^{4} + 8 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(5 \, c^{7} x^{7} + 12 \, c^{5} x^{5} + 9 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^5 + 2*c^2*x^3 + x)*(c^2*x^2 + 1) + (c^5*x^6 + 2*c^3*x^4 + c*x^2)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate((5*(c^5*x^5 + c^3*x^3)*(c^2*x^2 + 1)^(3/2) + (10*c^6*x^6 + 17*c^4*x^4 + 8*c^2*x^2 + 1)*(c^2*x^2 + 1) + (5*c^7*x^7 + 12*c^5*x^5 + 9*c^3*x^3 + 2*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
422,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(4 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 4 \, {\left(2 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(4 \, c^{6} x^{6} + 9 \, c^{4} x^{4} + 6 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{2} + 2 \, a b c^{2} x^{2} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{2} + 2 \, b^{2} c^{2} x^{2} + b^{2} + 2 \, {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^4 + 2*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((4*c^4*x^4 + 3*c^2*x^2 - 1)*(c^2*x^2 + 1)^(3/2) + 4*(2*c^5*x^5 + 3*c^3*x^3 + c*x)*(c^2*x^2 + 1) + (4*c^6*x^6 + 9*c^4*x^4 + 6*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/(a*b*c^4*x^4 + (c^2*x^2 + 1)*a*b*c^2*x^2 + 2*a*b*c^2*x^2 + a*b + (b^2*c^4*x^4 + (c^2*x^2 + 1)*b^2*c^2*x^2 + 2*b^2*c^2*x^2 + b^2 + 2*(b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
423,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{3} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{2} + a b c x + {\left(b^{2} c^{3} x^{3} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{2} + b^{2} c x\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(3 \, c^{5} x^{5} + c^{3} x^{3} - 2 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(6 \, c^{6} x^{6} + 7 \, c^{4} x^{4} - 1\right)} {\left(c^{2} x^{2} + 1\right)} + 3 \, {\left(c^{7} x^{7} + 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{6} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{4} + 2 \, a b c^{3} x^{4} + a b c x^{2} + {\left(b^{2} c^{5} x^{6} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{4} + 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2} + 2 \, {\left(b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{5} + a b c^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^4 + 2*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^3 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^2 + a*b*c*x + (b^2*c^3*x^3 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^2 + b^2*c*x)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((3*c^5*x^5 + c^3*x^3 - 2*c*x)*(c^2*x^2 + 1)^(3/2) + (6*c^6*x^6 + 7*c^4*x^4 - 1)*(c^2*x^2 + 1) + 3*(c^7*x^7 + 2*c^5*x^5 + c^3*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^6 + (c^2*x^2 + 1)*a*b*c^3*x^4 + 2*a*b*c^3*x^4 + a*b*c*x^2 + (b^2*c^5*x^6 + (c^2*x^2 + 1)*b^2*c^3*x^4 + 2*b^2*c^3*x^4 + b^2*c*x^2 + 2*(b^2*c^4*x^5 + b^2*c^2*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^5 + a*b*c^2*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
424,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x^2/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{4} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{3} + a b c x^{2} + {\left(b^{2} c^{3} x^{4} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{3} + b^{2} c x^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(2 \, c^{5} x^{5} - c^{3} x^{3} - 3 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(2 \, c^{6} x^{6} + c^{4} x^{4} - 2 \, c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{7} x^{7} + 3 \, c^{5} x^{5} - c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{7} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{5} + 2 \, a b c^{3} x^{5} + a b c x^{3} + {\left(b^{2} c^{5} x^{7} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{5} + 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3} + 2 \, {\left(b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{6} + a b c^{2} x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^4 + 2*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^4 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^3 + a*b*c*x^2 + (b^2*c^3*x^4 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^3 + b^2*c*x^2)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((2*c^5*x^5 - c^3*x^3 - 3*c*x)*(c^2*x^2 + 1)^(3/2) + 2*(2*c^6*x^6 + c^4*x^4 - 2*c^2*x^2 - 1)*(c^2*x^2 + 1) + (2*c^7*x^7 + 3*c^5*x^5 - c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^7 + (c^2*x^2 + 1)*a*b*c^3*x^5 + 2*a*b*c^3*x^5 + a*b*c*x^3 + (b^2*c^5*x^7 + (c^2*x^2 + 1)*b^2*c^3*x^5 + 2*b^2*c^3*x^5 + b^2*c*x^3 + 2*(b^2*c^4*x^6 + b^2*c^2*x^4)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^6 + a*b*c^2*x^4)*sqrt(c^2*x^2 + 1)), x)","F",0
425,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x^3/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{5} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{4} + a b c x^{3} + {\left(b^{2} c^{3} x^{5} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{4} + b^{2} c x^{3}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(c^{5} x^{5} - 3 \, c^{3} x^{3} - 4 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(2 \, c^{6} x^{6} - 3 \, c^{4} x^{4} - 8 \, c^{2} x^{2} - 3\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{7} - 3 \, c^{3} x^{3} - 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{8} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{6} + 2 \, a b c^{3} x^{6} + a b c x^{4} + {\left(b^{2} c^{5} x^{8} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{6} + 2 \, b^{2} c^{3} x^{6} + b^{2} c x^{4} + 2 \, {\left(b^{2} c^{4} x^{7} + b^{2} c^{2} x^{5}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{7} + a b c^{2} x^{5}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^4 + 2*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^5 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^4 + a*b*c*x^3 + (b^2*c^3*x^5 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^4 + b^2*c*x^3)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((c^5*x^5 - 3*c^3*x^3 - 4*c*x)*(c^2*x^2 + 1)^(3/2) + (2*c^6*x^6 - 3*c^4*x^4 - 8*c^2*x^2 - 3)*(c^2*x^2 + 1) + (c^7*x^7 - 3*c^3*x^3 - 2*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^8 + (c^2*x^2 + 1)*a*b*c^3*x^6 + 2*a*b*c^3*x^6 + a*b*c*x^4 + (b^2*c^5*x^8 + (c^2*x^2 + 1)*b^2*c^3*x^6 + 2*b^2*c^3*x^6 + b^2*c*x^4 + 2*(b^2*c^4*x^7 + b^2*c^2*x^5)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^7 + a*b*c^2*x^5)*sqrt(c^2*x^2 + 1)), x)","F",0
426,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(3/2)/x^4/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{6} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{5} + a b c x^{4} + {\left(b^{2} c^{3} x^{6} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{5} + b^{2} c x^{4}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} - \int \frac{5 \, {\left(c^{3} x^{3} + c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 4 \, {\left(2 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + 3 \, {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{9} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{7} + 2 \, a b c^{3} x^{7} + a b c x^{5} + {\left(b^{2} c^{5} x^{9} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{7} + 2 \, b^{2} c^{3} x^{7} + b^{2} c x^{5} + 2 \, {\left(b^{2} c^{4} x^{8} + b^{2} c^{2} x^{6}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{8} + a b c^{2} x^{6}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^4 + 2*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^6 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^5 + a*b*c*x^4 + (b^2*c^3*x^6 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^5 + b^2*c*x^4)*log(c*x + sqrt(c^2*x^2 + 1))) - integrate((5*(c^3*x^3 + c*x)*(c^2*x^2 + 1)^(3/2) + 4*(2*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1) + 3*(c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^9 + (c^2*x^2 + 1)*a*b*c^3*x^7 + 2*a*b*c^3*x^7 + a*b*c*x^5 + (b^2*c^5*x^9 + (c^2*x^2 + 1)*b^2*c^3*x^7 + 2*b^2*c^3*x^7 + b^2*c*x^5 + 2*(b^2*c^4*x^8 + b^2*c^2*x^6)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^8 + a*b*c^2*x^6)*sqrt(c^2*x^2 + 1)), x)","F",0
427,0,0,0,0.000000," ","integrate(x^3*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{9} + 3 \, c^{4} x^{7} + 3 \, c^{2} x^{5} + x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{10} + 3 \, c^{5} x^{8} + 3 \, c^{3} x^{6} + c x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(9 \, c^{7} x^{9} + 20 \, c^{5} x^{7} + 13 \, c^{3} x^{5} + 2 \, c x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(6 \, c^{8} x^{10} + 17 \, c^{6} x^{8} + 17 \, c^{4} x^{6} + 7 \, c^{2} x^{4} + x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(9 \, c^{9} x^{11} + 31 \, c^{7} x^{9} + 39 \, c^{5} x^{7} + 21 \, c^{3} x^{5} + 4 \, c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^9 + 3*c^4*x^7 + 3*c^2*x^5 + x^3)*(c^2*x^2 + 1) + (c^7*x^10 + 3*c^5*x^8 + 3*c^3*x^6 + c*x^4)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((9*c^7*x^9 + 20*c^5*x^7 + 13*c^3*x^5 + 2*c*x^3)*(c^2*x^2 + 1)^(3/2) + 3*(6*c^8*x^10 + 17*c^6*x^8 + 17*c^4*x^6 + 7*c^2*x^4 + x^2)*(c^2*x^2 + 1) + (9*c^9*x^11 + 31*c^7*x^9 + 39*c^5*x^7 + 21*c^3*x^5 + 4*c*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
428,0,0,0,0.000000," ","integrate(x^2*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{8} + 3 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{9} + 3 \, c^{5} x^{7} + 3 \, c^{3} x^{5} + c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(8 \, c^{7} x^{8} + 17 \, c^{5} x^{6} + 10 \, c^{3} x^{4} + c x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(8 \, c^{8} x^{9} + 22 \, c^{6} x^{7} + 21 \, c^{4} x^{5} + 8 \, c^{2} x^{3} + x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(8 \, c^{9} x^{10} + 27 \, c^{7} x^{8} + 33 \, c^{5} x^{6} + 17 \, c^{3} x^{4} + 3 \, c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^8 + 3*c^4*x^6 + 3*c^2*x^4 + x^2)*(c^2*x^2 + 1) + (c^7*x^9 + 3*c^5*x^7 + 3*c^3*x^5 + c*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((8*c^7*x^8 + 17*c^5*x^6 + 10*c^3*x^4 + c*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(8*c^8*x^9 + 22*c^6*x^7 + 21*c^4*x^5 + 8*c^2*x^3 + x)*(c^2*x^2 + 1) + (8*c^9*x^10 + 27*c^7*x^8 + 33*c^5*x^6 + 17*c^3*x^4 + 3*c*x^2)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
429,0,0,0,0.000000," ","integrate(x*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{7} + 3 \, c^{4} x^{5} + 3 \, c^{2} x^{3} + x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{8} + 3 \, c^{5} x^{6} + 3 \, c^{3} x^{4} + c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{7 \, {\left(c^{7} x^{7} + 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(14 \, c^{8} x^{8} + 37 \, c^{6} x^{6} + 33 \, c^{4} x^{4} + 11 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(7 \, c^{9} x^{9} + 23 \, c^{7} x^{7} + 27 \, c^{5} x^{5} + 13 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^7 + 3*c^4*x^5 + 3*c^2*x^3 + x)*(c^2*x^2 + 1) + (c^7*x^8 + 3*c^5*x^6 + 3*c^3*x^4 + c*x^2)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate((7*(c^7*x^7 + 2*c^5*x^5 + c^3*x^3)*(c^2*x^2 + 1)^(3/2) + (14*c^8*x^8 + 37*c^6*x^6 + 33*c^4*x^4 + 11*c^2*x^2 + 1)*(c^2*x^2 + 1) + (7*c^9*x^9 + 23*c^7*x^7 + 27*c^5*x^5 + 13*c^3*x^3 + 2*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
430,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{6} + 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(6 \, c^{6} x^{6} + 11 \, c^{4} x^{4} + 4 \, c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(2 \, c^{7} x^{7} + 5 \, c^{5} x^{5} + 4 \, c^{3} x^{3} + c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(6 \, c^{8} x^{8} + 19 \, c^{6} x^{6} + 21 \, c^{4} x^{4} + 9 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{2} + 2 \, a b c^{2} x^{2} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{2} + 2 \, b^{2} c^{2} x^{2} + b^{2} + 2 \, {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^6 + 3*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((6*c^6*x^6 + 11*c^4*x^4 + 4*c^2*x^2 - 1)*(c^2*x^2 + 1)^(3/2) + 6*(2*c^7*x^7 + 5*c^5*x^5 + 4*c^3*x^3 + c*x)*(c^2*x^2 + 1) + (6*c^8*x^8 + 19*c^6*x^6 + 21*c^4*x^4 + 9*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/(a*b*c^4*x^4 + (c^2*x^2 + 1)*a*b*c^2*x^2 + 2*a*b*c^2*x^2 + a*b + (b^2*c^4*x^4 + (c^2*x^2 + 1)*b^2*c^2*x^2 + 2*b^2*c^2*x^2 + b^2 + 2*(b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
431,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{6} + 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{3} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{2} + a b c x + {\left(b^{2} c^{3} x^{3} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{2} + b^{2} c x\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(5 \, c^{7} x^{7} + 8 \, c^{5} x^{5} + c^{3} x^{3} - 2 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + {\left(10 \, c^{8} x^{8} + 23 \, c^{6} x^{6} + 15 \, c^{4} x^{4} + c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)} + 5 \, {\left(c^{9} x^{9} + 3 \, c^{7} x^{7} + 3 \, c^{5} x^{5} + c^{3} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{6} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{4} + 2 \, a b c^{3} x^{4} + a b c x^{2} + {\left(b^{2} c^{5} x^{6} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{4} + 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2} + 2 \, {\left(b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{5} + a b c^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^6 + 3*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^3 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^2 + a*b*c*x + (b^2*c^3*x^3 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^2 + b^2*c*x)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((5*c^7*x^7 + 8*c^5*x^5 + c^3*x^3 - 2*c*x)*(c^2*x^2 + 1)^(3/2) + (10*c^8*x^8 + 23*c^6*x^6 + 15*c^4*x^4 + c^2*x^2 - 1)*(c^2*x^2 + 1) + 5*(c^9*x^9 + 3*c^7*x^7 + 3*c^5*x^5 + c^3*x^3)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^6 + (c^2*x^2 + 1)*a*b*c^3*x^4 + 2*a*b*c^3*x^4 + a*b*c*x^2 + (b^2*c^5*x^6 + (c^2*x^2 + 1)*b^2*c^3*x^4 + 2*b^2*c^3*x^4 + b^2*c*x^2 + 2*(b^2*c^4*x^5 + b^2*c^2*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^5 + a*b*c^2*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
432,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x^2/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{6} + 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{4} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{3} + a b c x^{2} + {\left(b^{2} c^{3} x^{4} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{3} + b^{2} c x^{2}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(4 \, c^{7} x^{7} + 5 \, c^{5} x^{5} - 2 \, c^{3} x^{3} - 3 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(4 \, c^{8} x^{8} + 8 \, c^{6} x^{6} + 3 \, c^{4} x^{4} - 2 \, c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(4 \, c^{9} x^{9} + 11 \, c^{7} x^{7} + 9 \, c^{5} x^{5} + c^{3} x^{3} - c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{7} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{5} + 2 \, a b c^{3} x^{5} + a b c x^{3} + {\left(b^{2} c^{5} x^{7} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{5} + 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3} + 2 \, {\left(b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{6} + a b c^{2} x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^6 + 3*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^4 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^3 + a*b*c*x^2 + (b^2*c^3*x^4 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^3 + b^2*c*x^2)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((4*c^7*x^7 + 5*c^5*x^5 - 2*c^3*x^3 - 3*c*x)*(c^2*x^2 + 1)^(3/2) + 2*(4*c^8*x^8 + 8*c^6*x^6 + 3*c^4*x^4 - 2*c^2*x^2 - 1)*(c^2*x^2 + 1) + (4*c^9*x^9 + 11*c^7*x^7 + 9*c^5*x^5 + c^3*x^3 - c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^7 + (c^2*x^2 + 1)*a*b*c^3*x^5 + 2*a*b*c^3*x^5 + a*b*c*x^3 + (b^2*c^5*x^7 + (c^2*x^2 + 1)*b^2*c^3*x^5 + 2*b^2*c^3*x^5 + b^2*c*x^3 + 2*(b^2*c^4*x^6 + b^2*c^2*x^4)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^6 + a*b*c^2*x^4)*sqrt(c^2*x^2 + 1)), x)","F",0
433,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x^3/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{6} + 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{5} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{4} + a b c x^{3} + {\left(b^{2} c^{3} x^{5} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{4} + b^{2} c x^{3}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(3 \, c^{7} x^{7} + 2 \, c^{5} x^{5} - 5 \, c^{3} x^{3} - 4 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(2 \, c^{8} x^{8} + 3 \, c^{6} x^{6} - c^{4} x^{4} - 3 \, c^{2} x^{2} - 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(3 \, c^{9} x^{9} + 7 \, c^{7} x^{7} + 3 \, c^{5} x^{5} - 3 \, c^{3} x^{3} - 2 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{8} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{6} + 2 \, a b c^{3} x^{6} + a b c x^{4} + {\left(b^{2} c^{5} x^{8} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{6} + 2 \, b^{2} c^{3} x^{6} + b^{2} c x^{4} + 2 \, {\left(b^{2} c^{4} x^{7} + b^{2} c^{2} x^{5}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{7} + a b c^{2} x^{5}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^6 + 3*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^5 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^4 + a*b*c*x^3 + (b^2*c^3*x^5 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^4 + b^2*c*x^3)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((3*c^7*x^7 + 2*c^5*x^5 - 5*c^3*x^3 - 4*c*x)*(c^2*x^2 + 1)^(3/2) + 3*(2*c^8*x^8 + 3*c^6*x^6 - c^4*x^4 - 3*c^2*x^2 - 1)*(c^2*x^2 + 1) + (3*c^9*x^9 + 7*c^7*x^7 + 3*c^5*x^5 - 3*c^3*x^3 - 2*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^8 + (c^2*x^2 + 1)*a*b*c^3*x^6 + 2*a*b*c^3*x^6 + a*b*c*x^4 + (b^2*c^5*x^8 + (c^2*x^2 + 1)*b^2*c^3*x^6 + 2*b^2*c^3*x^6 + b^2*c*x^4 + 2*(b^2*c^4*x^7 + b^2*c^2*x^5)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^7 + a*b*c^2*x^5)*sqrt(c^2*x^2 + 1)), x)","F",0
434,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(5/2)/x^4/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{6} + 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{6} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x^{5} + a b c x^{4} + {\left(b^{2} c^{3} x^{6} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x^{5} + b^{2} c x^{4}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(2 \, c^{7} x^{7} - c^{5} x^{5} - 8 \, c^{3} x^{3} - 5 \, c x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(2 \, c^{8} x^{8} + c^{6} x^{6} - 6 \, c^{4} x^{4} - 7 \, c^{2} x^{2} - 2\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{9} x^{9} + 3 \, c^{7} x^{7} - 3 \, c^{5} x^{5} - 7 \, c^{3} x^{3} - 3 \, c x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{9} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{7} + 2 \, a b c^{3} x^{7} + a b c x^{5} + {\left(b^{2} c^{5} x^{9} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{7} + 2 \, b^{2} c^{3} x^{7} + b^{2} c x^{5} + 2 \, {\left(b^{2} c^{4} x^{8} + b^{2} c^{2} x^{6}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{8} + a b c^{2} x^{6}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^6 + 3*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1) + (c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^6 + sqrt(c^2*x^2 + 1)*a*b*c^2*x^5 + a*b*c*x^4 + (b^2*c^3*x^6 + sqrt(c^2*x^2 + 1)*b^2*c^2*x^5 + b^2*c*x^4)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((2*c^7*x^7 - c^5*x^5 - 8*c^3*x^3 - 5*c*x)*(c^2*x^2 + 1)^(3/2) + 2*(2*c^8*x^8 + c^6*x^6 - 6*c^4*x^4 - 7*c^2*x^2 - 2)*(c^2*x^2 + 1) + (2*c^9*x^9 + 3*c^7*x^7 - 3*c^5*x^5 - 7*c^3*x^3 - 3*c*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^9 + (c^2*x^2 + 1)*a*b*c^3*x^7 + 2*a*b*c^3*x^7 + a*b*c*x^5 + (b^2*c^5*x^9 + (c^2*x^2 + 1)*b^2*c^3*x^7 + 2*b^2*c^3*x^7 + b^2*c*x^5 + 2*(b^2*c^4*x^8 + b^2*c^2*x^6)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^8 + a*b*c^2*x^6)*sqrt(c^2*x^2 + 1)), x)","F",0
435,0,0,0,0.000000," ","integrate(x^5/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{8} + c x^{6} + {\left(c^{2} x^{7} + x^{5}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{5 \, c^{5} x^{9} + 11 \, c^{3} x^{7} + 6 \, c x^{5} + {\left(5 \, c^{3} x^{7} + 4 \, c x^{5}\right)} {\left(c^{2} x^{2} + 1\right)} + 5 \, {\left(2 \, c^{4} x^{8} + 3 \, c^{2} x^{6} + x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^8 + c*x^6 + (c^2*x^7 + x^5)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((5*c^5*x^9 + 11*c^3*x^7 + 6*c*x^5 + (5*c^3*x^7 + 4*c*x^5)*(c^2*x^2 + 1) + 5*(2*c^4*x^8 + 3*c^2*x^6 + x^4)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
436,0,0,0,0.000000," ","integrate(x^4/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{7} + c x^{5} + {\left(c^{2} x^{6} + x^{4}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{4 \, c^{5} x^{8} + 9 \, c^{3} x^{6} + 5 \, c x^{4} + {\left(4 \, c^{3} x^{6} + 3 \, c x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + 4 \, {\left(2 \, c^{4} x^{7} + 3 \, c^{2} x^{5} + x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^7 + c*x^5 + (c^2*x^6 + x^4)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((4*c^5*x^8 + 9*c^3*x^6 + 5*c*x^4 + (4*c^3*x^6 + 3*c*x^4)*(c^2*x^2 + 1) + 4*(2*c^4*x^7 + 3*c^2*x^5 + x^3)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
437,0,0,0,0.000000," ","integrate(x^3/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{6} + c x^{4} + {\left(c^{2} x^{5} + x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{3 \, c^{5} x^{7} + 7 \, c^{3} x^{5} + 4 \, c x^{3} + {\left(3 \, c^{3} x^{5} + 2 \, c x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + 3 \, {\left(2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^6 + c*x^4 + (c^2*x^5 + x^3)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((3*c^5*x^7 + 7*c^3*x^5 + 4*c*x^3 + (3*c^3*x^5 + 2*c*x^3)*(c^2*x^2 + 1) + 3*(2*c^4*x^6 + 3*c^2*x^4 + x^2)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
438,0,0,0,0.000000," ","integrate(x^2/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{5} + c x^{3} + {\left(c^{2} x^{4} + x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{2 \, c^{5} x^{6} + 5 \, c^{3} x^{4} + 3 \, c x^{2} + {\left(2 \, c^{3} x^{4} + c x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(2 \, c^{4} x^{5} + 3 \, c^{2} x^{3} + x\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^5 + c*x^3 + (c^2*x^4 + x^2)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((2*c^5*x^6 + 5*c^3*x^4 + 3*c*x^2 + (2*c^3*x^4 + c*x^2)*(c^2*x^2 + 1) + 2*(2*c^4*x^5 + 3*c^2*x^3 + x)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
439,0,0,0,0.000000," ","integrate(x/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{4} + c x^{2} + {\left(c^{2} x^{3} + x\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} c^{3} x^{3} + 3 \, c^{3} x^{3} + 2 \, c x + {\left(2 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^4 + c*x^2 + (c^2*x^3 + x)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((c^5*x^5 + (c^2*x^2 + 1)*c^3*x^3 + 3*c^3*x^3 + 2*c*x + (2*c^4*x^4 + 3*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
440,1,18,0,0.359345," ","integrate(1/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} b c}"," ",0,"-1/((b*arcsinh(c*x) + a)*b*c)","A",0
441,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{2} + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{2} + {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{c^{5} x^{5} + c^{3} x^{3} + {\left(c^{3} x^{3} + 2 \, c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{4} + 2 \, {\left(a b c^{4} x^{5} + a b c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{4} + 2 \, {\left(b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{6} + 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{6} + 2 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/((c^2*x^2 + 1)*a*b*c^2*x^2 + ((c^2*x^2 + 1)*b^2*c^2*x^2 + (b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)) - integrate((c^5*x^5 + c^3*x^3 + (c^3*x^3 + 2*c*x)*(c^2*x^2 + 1) + (2*c^4*x^4 + 3*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^4 + 2*(a*b*c^4*x^5 + a*b*c^2*x^3)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^4 + 2*(b^2*c^4*x^5 + b^2*c^2*x^3)*(c^2*x^2 + 1) + (b^2*c^5*x^6 + 2*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^6 + 2*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c^2*x^2 + 1)), x)","F",0
442,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsinh(c*x))^2/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{3} + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{3} + {\left(b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{2 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + {\left(2 \, c^{3} x^{3} + 3 \, c x\right)} {\left(c^{2} x^{2} + 1\right)} + c x + 2 \, {\left(2 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{5} + 2 \, {\left(a b c^{4} x^{6} + a b c^{2} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{5} + 2 \, {\left(b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{7} + 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{7} + 2 \, a b c^{3} x^{5} + a b c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/((c^2*x^2 + 1)*a*b*c^2*x^3 + ((c^2*x^2 + 1)*b^2*c^2*x^3 + (b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c^2*x^2 + 1)) - integrate((2*c^5*x^5 + 3*c^3*x^3 + (2*c^3*x^3 + 3*c*x)*(c^2*x^2 + 1) + c*x + 2*(2*c^4*x^4 + 3*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^5 + 2*(a*b*c^4*x^6 + a*b*c^2*x^4)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^5 + 2*(b^2*c^4*x^6 + b^2*c^2*x^4)*(c^2*x^2 + 1) + (b^2*c^5*x^7 + 2*b^2*c^3*x^5 + b^2*c*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^7 + 2*a*b*c^3*x^5 + a*b*c*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
443,0,0,0,0.000000," ","integrate(x^3/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{4} + \sqrt{c^{2} x^{2} + 1} x^{3}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{c^{5} x^{7} + 5 \, c^{3} x^{5} + 4 \, c x^{3} + {\left(c^{3} x^{5} + 2 \, c x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{4} x^{6} + 7 \, c^{2} x^{4} + 3 \, x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{6} x^{5} + 2 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{6} x^{5} + 2 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{7} x^{6} + 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{7} x^{6} + 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x^4 + sqrt(c^2*x^2 + 1)*x^3)/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((c^5*x^7 + 5*c^3*x^5 + 4*c*x^3 + (c^3*x^5 + 2*c*x^3)*(c^2*x^2 + 1) + (2*c^4*x^6 + 7*c^2*x^4 + 3*x^2)*sqrt(c^2*x^2 + 1))/((a*b*c^5*x^4 + a*b*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^6*x^5 + 2*a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^5*x^4 + b^2*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^6*x^5 + 2*b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^7*x^6 + 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^7*x^6 + 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
444,0,0,0,0.000000," ","integrate(x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{3} + \sqrt{c^{2} x^{2} + 1} x^{2}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{3 \, c^{3} x^{4} + {\left(c^{2} x^{2} + 1\right)} c x^{2} + 3 \, c x^{2} + 2 \, {\left(2 \, c^{2} x^{3} + x\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{6} x^{5} + 2 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{6} x^{5} + 2 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{7} x^{6} + 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{7} x^{6} + 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x^3 + sqrt(c^2*x^2 + 1)*x^2)/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate((3*c^3*x^4 + (c^2*x^2 + 1)*c*x^2 + 3*c*x^2 + 2*(2*c^2*x^3 + x)*sqrt(c^2*x^2 + 1))/((a*b*c^5*x^4 + a*b*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^6*x^5 + 2*a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^5*x^4 + b^2*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^6*x^5 + 2*b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^7*x^6 + 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^7*x^6 + 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
445,0,0,0,0.000000," ","integrate(x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{2} + \sqrt{c^{2} x^{2} + 1} x}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} c^{3} x^{3} - c^{3} x^{3} - 2 \, c x + {\left(2 \, c^{4} x^{4} - c^{2} x^{2} - 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{6} x^{5} + 2 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{6} x^{5} + 2 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{7} x^{6} + 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{7} x^{6} + 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x^2 + sqrt(c^2*x^2 + 1)*x)/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) - integrate((c^5*x^5 + (c^2*x^2 + 1)*c^3*x^3 - c^3*x^3 - 2*c*x + (2*c^4*x^4 - c^2*x^2 - 1)*sqrt(c^2*x^2 + 1))/((a*b*c^5*x^4 + a*b*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^6*x^5 + 2*a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^5*x^4 + b^2*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^6*x^5 + 2*b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^7*x^6 + 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^7*x^6 + 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
446,0,0,0,0.000000," ","integrate(1/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{2 \, c^{4} x^{4} + c^{2} x^{2} + {\left(2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1} - 1}{{\left(a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{5} x^{5} + 2 \, a b c^{3} x^{3} + a b c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{5} x^{5} + 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{6} x^{6} + 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} + b^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{6} x^{6} + 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} + a b\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) - integrate((2*c^4*x^4 + c^2*x^2 + (2*c^2*x^2 + 1)*(c^2*x^2 + 1) + 2*(2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1) - 1)/((a*b*c^4*x^4 + a*b*c^2*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^5*x^5 + 2*a*b*c^3*x^3 + a*b*c*x)*(c^2*x^2 + 1) + ((b^2*c^4*x^4 + b^2*c^2*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^5*x^5 + 2*b^2*c^3*x^3 + b^2*c*x)*(c^2*x^2 + 1) + (b^2*c^6*x^6 + 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 + b^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^6*x^6 + 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 + a*b)*sqrt(c^2*x^2 + 1)), x)","F",0
447,0,0,0,0.000000," ","integrate(1/x/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{2} + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{2} + {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + {\left(3 \, c^{3} x^{3} + 2 \, c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(6 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{5} x^{6} + a b c^{3} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{6} x^{7} + 2 \, a b c^{4} x^{5} + a b c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{5} x^{6} + b^{2} c^{3} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{6} x^{7} + 2 \, b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{7} x^{8} + 3 \, b^{2} c^{5} x^{6} + 3 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{7} x^{8} + 3 \, a b c^{5} x^{6} + 3 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x^2 + ((c^2*x^2 + 1)*b^2*c^2*x^2 + (b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)) - integrate((3*c^5*x^5 + 3*c^3*x^3 + (3*c^3*x^3 + 2*c*x)*(c^2*x^2 + 1) + (6*c^4*x^4 + 5*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((a*b*c^5*x^6 + a*b*c^3*x^4)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^6*x^7 + 2*a*b*c^4*x^5 + a*b*c^2*x^3)*(c^2*x^2 + 1) + ((b^2*c^5*x^6 + b^2*c^3*x^4)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^6*x^7 + 2*b^2*c^4*x^5 + b^2*c^2*x^3)*(c^2*x^2 + 1) + (b^2*c^7*x^8 + 3*b^2*c^5*x^6 + 3*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^7*x^8 + 3*a*b*c^5*x^6 + 3*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c^2*x^2 + 1)), x)","F",0
448,0,0,0,0.000000," ","integrate(1/x^2/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c^{2} x^{2} + 1}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{3} + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{3} + {\left(b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{4 \, c^{5} x^{5} + 5 \, c^{3} x^{3} + {\left(4 \, c^{3} x^{3} + 3 \, c x\right)} {\left(c^{2} x^{2} + 1\right)} + c x + 2 \, {\left(4 \, c^{4} x^{4} + 4 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{5} x^{7} + a b c^{3} x^{5}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{6} x^{8} + 2 \, a b c^{4} x^{6} + a b c^{2} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{5} x^{7} + b^{2} c^{3} x^{5}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{6} x^{8} + 2 \, b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{7} x^{9} + 3 \, b^{2} c^{5} x^{7} + 3 \, b^{2} c^{3} x^{5} + b^{2} c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{7} x^{9} + 3 \, a b c^{5} x^{7} + 3 \, a b c^{3} x^{5} + a b c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c^2*x^2 + 1))/((c^2*x^2 + 1)*a*b*c^2*x^3 + ((c^2*x^2 + 1)*b^2*c^2*x^3 + (b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c^2*x^2 + 1)) - integrate((4*c^5*x^5 + 5*c^3*x^3 + (4*c^3*x^3 + 3*c*x)*(c^2*x^2 + 1) + c*x + 2*(4*c^4*x^4 + 4*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((a*b*c^5*x^7 + a*b*c^3*x^5)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^6*x^8 + 2*a*b*c^4*x^6 + a*b*c^2*x^4)*(c^2*x^2 + 1) + ((b^2*c^5*x^7 + b^2*c^3*x^5)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^6*x^8 + 2*b^2*c^4*x^6 + b^2*c^2*x^4)*(c^2*x^2 + 1) + (b^2*c^7*x^9 + 3*b^2*c^5*x^7 + 3*b^2*c^3*x^5 + b^2*c*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^7*x^9 + 3*a*b*c^5*x^7 + 3*a*b*c^3*x^5 + a*b*c*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
449,0,0,0,0.000000," ","integrate(x^3/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{4} + \sqrt{c^{2} x^{2} + 1} x^{3}}{{\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{c^{5} x^{7} - 3 \, c^{3} x^{5} - 4 \, c x^{3} + {\left(c^{3} x^{5} - 2 \, c x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(2 \, c^{4} x^{6} - 5 \, c^{2} x^{4} - 3 \, x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{7} x^{6} + 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{8} x^{7} + 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{7} x^{6} + 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{8} x^{7} + 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{9} x^{8} + 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} + 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{9} x^{8} + 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} + 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x^4 + sqrt(c^2*x^2 + 1)*x^3)/((a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) - integrate((c^5*x^7 - 3*c^3*x^5 - 4*c*x^3 + (c^3*x^5 - 2*c*x^3)*(c^2*x^2 + 1) + (2*c^4*x^6 - 5*c^2*x^4 - 3*x^2)*sqrt(c^2*x^2 + 1))/((a*b*c^7*x^6 + 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^8*x^7 + 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^7*x^6 + 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^8*x^7 + 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^9*x^8 + 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 + 4*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^9*x^8 + 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 + 4*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
450,0,0,0,0.000000," ","integrate(x^2/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{3} + \sqrt{c^{2} x^{2} + 1} x^{2}}{{\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{2 \, c^{5} x^{6} - c^{3} x^{4} - 3 \, c x^{2} + {\left(2 \, c^{3} x^{4} - c x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(2 \, c^{4} x^{5} - c^{2} x^{3} - x\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{7} x^{6} + 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{8} x^{7} + 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{7} x^{6} + 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{8} x^{7} + 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{9} x^{8} + 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} + 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{9} x^{8} + 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} + 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x^3 + sqrt(c^2*x^2 + 1)*x^2)/((a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) - integrate((2*c^5*x^6 - c^3*x^4 - 3*c*x^2 + (2*c^3*x^4 - c*x^2)*(c^2*x^2 + 1) + 2*(2*c^4*x^5 - c^2*x^3 - x)*sqrt(c^2*x^2 + 1))/((a*b*c^7*x^6 + 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^8*x^7 + 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^7*x^6 + 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^8*x^7 + 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^9*x^8 + 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 + 4*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^9*x^8 + 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 + 4*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
451,0,0,0,0.000000," ","integrate(x/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{2} + \sqrt{c^{2} x^{2} + 1} x}{{\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{3 \, c^{5} x^{5} + 3 \, {\left(c^{2} x^{2} + 1\right)} c^{3} x^{3} + c^{3} x^{3} - 2 \, c x + {\left(6 \, c^{4} x^{4} + c^{2} x^{2} - 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{7} x^{6} + 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{8} x^{7} + 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{7} x^{6} + 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{8} x^{7} + 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{9} x^{8} + 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} + 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{9} x^{8} + 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} + 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x^2 + sqrt(c^2*x^2 + 1)*x)/((a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) - integrate((3*c^5*x^5 + 3*(c^2*x^2 + 1)*c^3*x^3 + c^3*x^3 - 2*c*x + (6*c^4*x^4 + c^2*x^2 - 1)*sqrt(c^2*x^2 + 1))/((a*b*c^7*x^6 + 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^8*x^7 + 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^7*x^6 + 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^8*x^7 + 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^9*x^8 + 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 + 4*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^9*x^8 + 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 + 4*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)), x)","F",0
452,0,0,0,0.000000," ","integrate(1/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{4 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + {\left(4 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} + 4 \, {\left(2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1} - 1}{{\left(a b c^{6} x^{6} + 2 \, a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{7} x^{7} + 3 \, a b c^{5} x^{5} + 3 \, a b c^{3} x^{3} + a b c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{6} x^{6} + 2 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{7} x^{7} + 3 \, b^{2} c^{5} x^{5} + 3 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{8} x^{8} + 4 \, b^{2} c^{6} x^{6} + 6 \, b^{2} c^{4} x^{4} + 4 \, b^{2} c^{2} x^{2} + b^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{8} x^{8} + 4 \, a b c^{6} x^{6} + 6 \, a b c^{4} x^{4} + 4 \, a b c^{2} x^{2} + a b\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c^2*x^2 + 1))/((a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) - integrate((4*c^4*x^4 + 3*c^2*x^2 + (4*c^2*x^2 + 1)*(c^2*x^2 + 1) + 4*(2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1) - 1)/((a*b*c^6*x^6 + 2*a*b*c^4*x^4 + a*b*c^2*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^7*x^7 + 3*a*b*c^5*x^5 + 3*a*b*c^3*x^3 + a*b*c*x)*(c^2*x^2 + 1) + ((b^2*c^6*x^6 + 2*b^2*c^4*x^4 + b^2*c^2*x^2)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^7*x^7 + 3*b^2*c^5*x^5 + 3*b^2*c^3*x^3 + b^2*c*x)*(c^2*x^2 + 1) + (b^2*c^8*x^8 + 4*b^2*c^6*x^6 + 6*b^2*c^4*x^4 + 4*b^2*c^2*x^2 + b^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^8*x^8 + 4*a*b*c^6*x^6 + 6*a*b*c^4*x^4 + 4*a*b*c^2*x^2 + a*b)*sqrt(c^2*x^2 + 1)), x)","F",0
453,0,0,0,0.000000," ","integrate(1/x/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{5} + 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{5} + 2 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{5 \, c^{5} x^{5} + 5 \, c^{3} x^{3} + {\left(5 \, c^{3} x^{3} + 2 \, c x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(10 \, c^{4} x^{4} + 7 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{7} x^{8} + 2 \, a b c^{5} x^{6} + a b c^{3} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{8} x^{9} + 3 \, a b c^{6} x^{7} + 3 \, a b c^{4} x^{5} + a b c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{7} x^{8} + 2 \, b^{2} c^{5} x^{6} + b^{2} c^{3} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{8} x^{9} + 3 \, b^{2} c^{6} x^{7} + 3 \, b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{9} x^{10} + 4 \, b^{2} c^{7} x^{8} + 6 \, b^{2} c^{5} x^{6} + 4 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{9} x^{10} + 4 \, a b c^{7} x^{8} + 6 \, a b c^{5} x^{6} + 4 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c^2*x^2 + 1))/((a*b*c^4*x^4 + a*b*c^2*x^2)*(c^2*x^2 + 1) + ((b^2*c^4*x^4 + b^2*c^2*x^2)*(c^2*x^2 + 1) + (b^2*c^5*x^5 + 2*b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^5 + 2*a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)) - integrate((5*c^5*x^5 + 5*c^3*x^3 + (5*c^3*x^3 + 2*c*x)*(c^2*x^2 + 1) + (10*c^4*x^4 + 7*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((a*b*c^7*x^8 + 2*a*b*c^5*x^6 + a*b*c^3*x^4)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^8*x^9 + 3*a*b*c^6*x^7 + 3*a*b*c^4*x^5 + a*b*c^2*x^3)*(c^2*x^2 + 1) + ((b^2*c^7*x^8 + 2*b^2*c^5*x^6 + b^2*c^3*x^4)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^8*x^9 + 3*b^2*c^6*x^7 + 3*b^2*c^4*x^5 + b^2*c^2*x^3)*(c^2*x^2 + 1) + (b^2*c^9*x^10 + 4*b^2*c^7*x^8 + 6*b^2*c^5*x^6 + 4*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^9*x^10 + 4*a*b*c^7*x^8 + 6*a*b*c^5*x^6 + 4*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c^2*x^2 + 1)), x)","F",0
454,0,0,0,0.000000," ","integrate(1/x^2/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{4} x^{5} + a b c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{6} + 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{6} + 2 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{6 \, c^{5} x^{5} + 7 \, c^{3} x^{3} + 3 \, {\left(2 \, c^{3} x^{3} + c x\right)} {\left(c^{2} x^{2} + 1\right)} + c x + 2 \, {\left(6 \, c^{4} x^{4} + 5 \, c^{2} x^{2} + 1\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{7} x^{9} + 2 \, a b c^{5} x^{7} + a b c^{3} x^{5}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{8} x^{10} + 3 \, a b c^{6} x^{8} + 3 \, a b c^{4} x^{6} + a b c^{2} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{7} x^{9} + 2 \, b^{2} c^{5} x^{7} + b^{2} c^{3} x^{5}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{8} x^{10} + 3 \, b^{2} c^{6} x^{8} + 3 \, b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{9} x^{11} + 4 \, b^{2} c^{7} x^{9} + 6 \, b^{2} c^{5} x^{7} + 4 \, b^{2} c^{3} x^{5} + b^{2} c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{9} x^{11} + 4 \, a b c^{7} x^{9} + 6 \, a b c^{5} x^{7} + 4 \, a b c^{3} x^{5} + a b c x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c^2*x^2 + 1))/((a*b*c^4*x^5 + a*b*c^2*x^3)*(c^2*x^2 + 1) + ((b^2*c^4*x^5 + b^2*c^2*x^3)*(c^2*x^2 + 1) + (b^2*c^5*x^6 + 2*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^6 + 2*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c^2*x^2 + 1)) - integrate((6*c^5*x^5 + 7*c^3*x^3 + 3*(2*c^3*x^3 + c*x)*(c^2*x^2 + 1) + c*x + 2*(6*c^4*x^4 + 5*c^2*x^2 + 1)*sqrt(c^2*x^2 + 1))/((a*b*c^7*x^9 + 2*a*b*c^5*x^7 + a*b*c^3*x^5)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^8*x^10 + 3*a*b*c^6*x^8 + 3*a*b*c^4*x^6 + a*b*c^2*x^4)*(c^2*x^2 + 1) + ((b^2*c^7*x^9 + 2*b^2*c^5*x^7 + b^2*c^3*x^5)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^8*x^10 + 3*b^2*c^6*x^8 + 3*b^2*c^4*x^6 + b^2*c^2*x^4)*(c^2*x^2 + 1) + (b^2*c^9*x^11 + 4*b^2*c^7*x^9 + 6*b^2*c^5*x^7 + 4*b^2*c^3*x^5 + b^2*c*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^9*x^11 + 4*a*b*c^7*x^9 + 6*a*b*c^5*x^7 + 4*a*b*c^3*x^5 + a*b*c*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
455,0,0,0,0.000000," ","integrate(x^m*(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{6} x^{6} + 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1} x^{m}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(c^{7} {\left(m + 6\right)} x^{7} + c^{5} {\left(3 \, m + 11\right)} x^{5} + c^{3} {\left(3 \, m + 4\right)} x^{3} + c {\left(m - 1\right)} x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m} + {\left(2 \, c^{8} {\left(m + 6\right)} x^{8} + c^{6} {\left(7 \, m + 30\right)} x^{6} + 3 \, c^{4} {\left(3 \, m + 8\right)} x^{4} + c^{2} {\left(5 \, m + 6\right)} x^{2} + m\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(c^{9} {\left(m + 6\right)} x^{9} + c^{7} {\left(4 \, m + 19\right)} x^{7} + 3 \, c^{5} {\left(2 \, m + 7\right)} x^{5} + c^{3} {\left(4 \, m + 9\right)} x^{3} + c {\left(m + 1\right)} x\right)} \sqrt{c^{2} x^{2} + 1} x^{m}}{a b c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{3} + 2 \, a b c^{3} x^{3} + a b c x + {\left(b^{2} c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{3} + 2 \, b^{2} c^{3} x^{3} + b^{2} c x + 2 \, {\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{4} + a b c^{2} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^6*x^6 + 3*c^4*x^4 + 3*c^2*x^2 + 1)*(c^2*x^2 + 1)*x^m + (c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1)*x^m)/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((c^7*(m + 6)*x^7 + c^5*(3*m + 11)*x^5 + c^3*(3*m + 4)*x^3 + c*(m - 1)*x)*(c^2*x^2 + 1)^(3/2)*x^m + (2*c^8*(m + 6)*x^8 + c^6*(7*m + 30)*x^6 + 3*c^4*(3*m + 8)*x^4 + c^2*(5*m + 6)*x^2 + m)*(c^2*x^2 + 1)*x^m + (c^9*(m + 6)*x^9 + c^7*(4*m + 19)*x^7 + 3*c^5*(2*m + 7)*x^5 + c^3*(4*m + 9)*x^3 + c*(m + 1)*x)*sqrt(c^2*x^2 + 1)*x^m)/(a*b*c^5*x^5 + (c^2*x^2 + 1)*a*b*c^3*x^3 + 2*a*b*c^3*x^3 + a*b*c*x + (b^2*c^5*x^5 + (c^2*x^2 + 1)*b^2*c^3*x^3 + 2*b^2*c^3*x^3 + b^2*c*x + 2*(b^2*c^4*x^4 + b^2*c^2*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^4 + a*b*c^2*x^2)*sqrt(c^2*x^2 + 1)), x)","F",0
456,0,0,0,0.000000," ","integrate(x^m*(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(c^{5} x^{5} + 2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1} x^{m}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(c^{5} {\left(m + 4\right)} x^{5} + c^{3} {\left(2 \, m + 3\right)} x^{3} + c {\left(m - 1\right)} x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m} + {\left(2 \, c^{6} {\left(m + 4\right)} x^{6} + c^{4} {\left(5 \, m + 12\right)} x^{4} + 4 \, c^{2} {\left(m + 1\right)} x^{2} + m\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(c^{7} {\left(m + 4\right)} x^{7} + 3 \, c^{5} {\left(m + 3\right)} x^{5} + 3 \, c^{3} {\left(m + 2\right)} x^{3} + c {\left(m + 1\right)} x\right)} \sqrt{c^{2} x^{2} + 1} x^{m}}{a b c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{3} + 2 \, a b c^{3} x^{3} + a b c x + {\left(b^{2} c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{3} + 2 \, b^{2} c^{3} x^{3} + b^{2} c x + 2 \, {\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{4} + a b c^{2} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^4*x^4 + 2*c^2*x^2 + 1)*(c^2*x^2 + 1)*x^m + (c^5*x^5 + 2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1)*x^m)/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((c^5*(m + 4)*x^5 + c^3*(2*m + 3)*x^3 + c*(m - 1)*x)*(c^2*x^2 + 1)^(3/2)*x^m + (2*c^6*(m + 4)*x^6 + c^4*(5*m + 12)*x^4 + 4*c^2*(m + 1)*x^2 + m)*(c^2*x^2 + 1)*x^m + (c^7*(m + 4)*x^7 + 3*c^5*(m + 3)*x^5 + 3*c^3*(m + 2)*x^3 + c*(m + 1)*x)*sqrt(c^2*x^2 + 1)*x^m)/(a*b*c^5*x^5 + (c^2*x^2 + 1)*a*b*c^3*x^3 + 2*a*b*c^3*x^3 + a*b*c*x + (b^2*c^5*x^5 + (c^2*x^2 + 1)*b^2*c^3*x^3 + 2*b^2*c^3*x^3 + b^2*c*x + 2*(b^2*c^4*x^4 + b^2*c^2*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^4 + a*b*c^2*x^2)*sqrt(c^2*x^2 + 1)), x)","F",0
457,0,0,0,0.000000," ","integrate(x^m*(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{2} x^{m} + {\left(c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1} x^{m}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(c^{3} {\left(m + 2\right)} x^{3} + c {\left(m - 1\right)} x\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m} + {\left(2 \, c^{4} {\left(m + 2\right)} x^{4} + c^{2} {\left(3 \, m + 2\right)} x^{2} + m\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(c^{5} {\left(m + 2\right)} x^{5} + c^{3} {\left(2 \, m + 3\right)} x^{3} + c {\left(m + 1\right)} x\right)} \sqrt{c^{2} x^{2} + 1} x^{m}}{a b c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{3} + 2 \, a b c^{3} x^{3} + a b c x + {\left(b^{2} c^{5} x^{5} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{3} + 2 \, b^{2} c^{3} x^{3} + b^{2} c x + 2 \, {\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{4} + a b c^{2} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^2*x^m + (c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1)*x^m)/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((c^3*(m + 2)*x^3 + c*(m - 1)*x)*(c^2*x^2 + 1)^(3/2)*x^m + (2*c^4*(m + 2)*x^4 + c^2*(3*m + 2)*x^2 + m)*(c^2*x^2 + 1)*x^m + (c^5*(m + 2)*x^5 + c^3*(2*m + 3)*x^3 + c*(m + 1)*x)*sqrt(c^2*x^2 + 1)*x^m)/(a*b*c^5*x^5 + (c^2*x^2 + 1)*a*b*c^3*x^3 + 2*a*b*c^3*x^3 + a*b*c*x + (b^2*c^5*x^5 + (c^2*x^2 + 1)*b^2*c^3*x^3 + 2*b^2*c^3*x^3 + b^2*c*x + 2*(b^2*c^4*x^4 + b^2*c^2*x^2)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^4 + a*b*c^2*x^2)*sqrt(c^2*x^2 + 1)), x)","F",0
458,0,0,0,0.000000," ","integrate(x^m/(c^2*x^2+1)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m} + {\left(c^{3} x^{3} + c x\right)} x^{m}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{{\left(c^{3} m x^{3} + c {\left(m - 1\right)} x\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(2 \, c^{4} m x^{4} + 3 \, c^{2} m x^{2} + m\right)} \sqrt{c^{2} x^{2} + 1} x^{m} + {\left(c^{5} m x^{5} + c^{3} {\left(2 \, m + 1\right)} x^{3} + c {\left(m + 1\right)} x\right)} x^{m}}{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b c^{3} x^{3} + 2 \, {\left(a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} c^{3} x^{3} + 2 \, {\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{5} + 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{5} + 2 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^(3/2)*x^m + (c^3*x^3 + c*x)*x^m)/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate(((c^3*m*x^3 + c*(m - 1)*x)*(c^2*x^2 + 1)*x^m + (2*c^4*m*x^4 + 3*c^2*m*x^2 + m)*sqrt(c^2*x^2 + 1)*x^m + (c^5*m*x^5 + c^3*(2*m + 1)*x^3 + c*(m + 1)*x)*x^m)/((c^2*x^2 + 1)^(3/2)*a*b*c^3*x^3 + 2*(a*b*c^4*x^4 + a*b*c^2*x^2)*(c^2*x^2 + 1) + ((c^2*x^2 + 1)^(3/2)*b^2*c^3*x^3 + 2*(b^2*c^4*x^4 + b^2*c^2*x^2)*(c^2*x^2 + 1) + (b^2*c^5*x^5 + 2*b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^5 + 2*a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
459,0,0,0,0.000000," ","integrate(x^m/(c^2*x^2+1)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x x^{m} + \sqrt{c^{2} x^{2} + 1} x^{m}}{{\left(c^{2} x^{2} + 1\right)} a b c^{2} x + {\left({\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{{\left(c^{3} {\left(m - 2\right)} x^{3} + c {\left(m - 1\right)} x\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(2 \, c^{4} {\left(m - 2\right)} x^{4} + c^{2} {\left(3 \, m - 2\right)} x^{2} + m\right)} \sqrt{c^{2} x^{2} + 1} x^{m} + {\left(c^{5} {\left(m - 2\right)} x^{5} + c^{3} {\left(2 \, m - 1\right)} x^{3} + c {\left(m + 1\right)} x\right)} x^{m}}{{\left(a b c^{5} x^{5} + a b c^{3} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{6} x^{6} + 2 \, a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{5} x^{5} + b^{2} c^{3} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{6} x^{6} + 2 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{7} x^{7} + 3 \, b^{2} c^{5} x^{5} + 3 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{7} x^{7} + 3 \, a b c^{5} x^{5} + 3 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x*x^m + sqrt(c^2*x^2 + 1)*x^m)/((c^2*x^2 + 1)*a*b*c^2*x + ((c^2*x^2 + 1)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate(((c^3*(m - 2)*x^3 + c*(m - 1)*x)*(c^2*x^2 + 1)*x^m + (2*c^4*(m - 2)*x^4 + c^2*(3*m - 2)*x^2 + m)*sqrt(c^2*x^2 + 1)*x^m + (c^5*(m - 2)*x^5 + c^3*(2*m - 1)*x^3 + c*(m + 1)*x)*x^m)/((a*b*c^5*x^5 + a*b*c^3*x^3)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^6*x^6 + 2*a*b*c^4*x^4 + a*b*c^2*x^2)*(c^2*x^2 + 1) + ((b^2*c^5*x^5 + b^2*c^3*x^3)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^6*x^6 + 2*b^2*c^4*x^4 + b^2*c^2*x^2)*(c^2*x^2 + 1) + (b^2*c^7*x^7 + 3*b^2*c^5*x^5 + 3*b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^7*x^7 + 3*a*b*c^5*x^5 + 3*a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
460,0,0,0,0.000000," ","integrate(x^m/(c^2*x^2+1)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x x^{m} + \sqrt{c^{2} x^{2} + 1} x^{m}}{{\left(a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} x^{4} + 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} x^{4} + 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{{\left(c^{3} {\left(m - 4\right)} x^{3} + c {\left(m - 1\right)} x\right)} {\left(c^{2} x^{2} + 1\right)} x^{m} + {\left(2 \, c^{4} {\left(m - 4\right)} x^{4} + c^{2} {\left(3 \, m - 4\right)} x^{2} + m\right)} \sqrt{c^{2} x^{2} + 1} x^{m} + {\left(c^{5} {\left(m - 4\right)} x^{5} + c^{3} {\left(2 \, m - 3\right)} x^{3} + c {\left(m + 1\right)} x\right)} x^{m}}{{\left(a b c^{7} x^{7} + 2 \, a b c^{5} x^{5} + a b c^{3} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{8} x^{8} + 3 \, a b c^{6} x^{6} + 3 \, a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left({\left(b^{2} c^{7} x^{7} + 2 \, b^{2} c^{5} x^{5} + b^{2} c^{3} x^{3}\right)} {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{2} c^{8} x^{8} + 3 \, b^{2} c^{6} x^{6} + 3 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{9} x^{9} + 4 \, b^{2} c^{7} x^{7} + 6 \, b^{2} c^{5} x^{5} + 4 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{9} x^{9} + 4 \, a b c^{7} x^{7} + 6 \, a b c^{5} x^{5} + 4 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c*x*x^m + sqrt(c^2*x^2 + 1)*x^m)/((a*b*c^4*x^3 + a*b*c^2*x)*(c^2*x^2 + 1) + ((b^2*c^4*x^3 + b^2*c^2*x)*(c^2*x^2 + 1) + (b^2*c^5*x^4 + 2*b^2*c^3*x^2 + b^2*c)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*x^4 + 2*a*b*c^3*x^2 + a*b*c)*sqrt(c^2*x^2 + 1)) + integrate(((c^3*(m - 4)*x^3 + c*(m - 1)*x)*(c^2*x^2 + 1)*x^m + (2*c^4*(m - 4)*x^4 + c^2*(3*m - 4)*x^2 + m)*sqrt(c^2*x^2 + 1)*x^m + (c^5*(m - 4)*x^5 + c^3*(2*m - 3)*x^3 + c*(m + 1)*x)*x^m)/((a*b*c^7*x^7 + 2*a*b*c^5*x^5 + a*b*c^3*x^3)*(c^2*x^2 + 1)^(3/2) + 2*(a*b*c^8*x^8 + 3*a*b*c^6*x^6 + 3*a*b*c^4*x^4 + a*b*c^2*x^2)*(c^2*x^2 + 1) + ((b^2*c^7*x^7 + 2*b^2*c^5*x^5 + b^2*c^3*x^3)*(c^2*x^2 + 1)^(3/2) + 2*(b^2*c^8*x^8 + 3*b^2*c^6*x^6 + 3*b^2*c^4*x^4 + b^2*c^2*x^2)*(c^2*x^2 + 1) + (b^2*c^9*x^9 + 4*b^2*c^7*x^7 + 6*b^2*c^5*x^5 + 4*b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^9*x^9 + 4*a*b*c^7*x^7 + 6*a*b*c^5*x^5 + 4*a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
461,1,11,0,0.641672," ","integrate(1/arcsinh(a*x)^3/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2 \, a \operatorname{arsinh}\left(a x\right)^{2}}"," ",0,"-1/2/(a*arcsinh(a*x)^2)","A",0
462,0,0,0,0.000000," ","integrate(x^3*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)} x^{3}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)*x^3/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)} x^{2}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)*x^2/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
464,0,0,0,0.000000," ","integrate(x*(c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)} x}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)*x/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
465,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{c^{2} d x^{2} + d}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
466,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)/x/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{c^{2} d x^{2} + d}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)/((b*arcsinh(c*x) + a)^(3/2)*x), x)","F",0
467,0,0,0,0.000000," ","integrate(x^3*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{2} x^{3}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^2*x^3/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{2} x^{2}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^2*x^2/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
469,0,0,0,0.000000," ","integrate(x*(c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{2} x}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^2*x/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
470,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{2}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^2/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
471,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^2/x/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{2}}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^2/((b*arcsinh(c*x) + a)^(3/2)*x), x)","F",0
472,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*sqrt(arcsinh(a*x)), x)","F",0
473,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)*arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} \sqrt{\operatorname{arsinh}\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*sqrt(arcsinh(a*x)), x)","F",0
474,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arsinh}\left(a x\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(arcsinh(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
475,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arsinh}\left(a x\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(arcsinh(a*x))/(a^2*c*x^2 + c)^(3/2), x)","F",0
476,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arsinh}\left(a x\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(arcsinh(a*x))/(a^2*c*x^2 + c)^(5/2), x)","F",0
477,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arcsinh(a*x)^(3/2), x)","F",0
478,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} \operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arcsinh(a*x)^(3/2), x)","F",0
479,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^(3/2)/sqrt(a^2*c*x^2 + c), x)","F",0
480,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^(3/2)/(a^2*c*x^2 + c)^(3/2), x)","F",0
481,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arcsinh(a*x)^(5/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arcsinh(a*x)^(5/2), x)","F",0
482,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} \operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arcsinh(a*x)^(5/2), x)","F",0
483,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^(5/2)/sqrt(a^2*c*x^2 + c), x)","F",0
484,0,0,0,0.000000," ","integrate(arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^(5/2)/(a^2*c*x^2 + c)^(3/2), x)","F",0
485,0,0,0,0.000000," ","integrate((a^2+x^2)^(3/2)*arcsinh(x/a)^(1/2),x, algorithm=""maxima"")","\int {\left(a^{2} + x^{2}\right)}^{\frac{3}{2}} \sqrt{\operatorname{arsinh}\left(\frac{x}{a}\right)}\,{d x}"," ",0,"integrate((a^2 + x^2)^(3/2)*sqrt(arcsinh(x/a)), x)","F",0
486,0,0,0,0.000000," ","integrate((a^2+x^2)^(1/2)*arcsinh(x/a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} + x^{2}} \sqrt{\operatorname{arsinh}\left(\frac{x}{a}\right)}\,{d x}"," ",0,"integrate(sqrt(a^2 + x^2)*sqrt(arcsinh(x/a)), x)","F",0
487,0,0,0,0.000000," ","integrate(arcsinh(x/a)^(1/2)/(a^2+x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arsinh}\left(\frac{x}{a}\right)}}{\sqrt{a^{2} + x^{2}}}\,{d x}"," ",0,"integrate(sqrt(arcsinh(x/a))/sqrt(a^2 + x^2), x)","F",0
488,0,0,0,0.000000," ","integrate(arcsinh(x/a)^(1/2)/(a^2+x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arsinh}\left(\frac{x}{a}\right)}}{{\left(a^{2} + x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(arcsinh(x/a))/(a^2 + x^2)^(3/2), x)","F",0
489,0,0,0,0.000000," ","integrate(arcsinh(x/a)^(1/2)/(a^2+x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arsinh}\left(\frac{x}{a}\right)}}{{\left(a^{2} + x^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(arcsinh(x/a))/(a^2 + x^2)^(5/2), x)","F",0
490,0,0,0,0.000000," ","integrate((a^2+x^2)^(3/2)*arcsinh(x/a)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} + x^{2}\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{x}{a}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a^2 + x^2)^(3/2)*arcsinh(x/a)^(3/2), x)","F",0
491,0,0,0,0.000000," ","integrate(arcsinh(x/a)^(3/2)*(a^2+x^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} + x^{2}} \operatorname{arsinh}\left(\frac{x}{a}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a^2 + x^2)*arcsinh(x/a)^(3/2), x)","F",0
492,0,0,0,0.000000," ","integrate(arcsinh(x/a)^(3/2)/(a^2+x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(\frac{x}{a}\right)^{\frac{3}{2}}}{\sqrt{a^{2} + x^{2}}}\,{d x}"," ",0,"integrate(arcsinh(x/a)^(3/2)/sqrt(a^2 + x^2), x)","F",0
493,0,0,0,0.000000," ","integrate(arcsinh(x/a)^(3/2)/(a^2+x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(\frac{x}{a}\right)^{\frac{3}{2}}}{{\left(a^{2} + x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsinh(x/a)^(3/2)/(a^2 + x^2)^(3/2), x)","F",0
494,0,0,0,0.000000," ","integrate(x/(x^2+1)^(1/2)/arcsinh(x)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{x^{2} + 1} \sqrt{\operatorname{arsinh}\left(x\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^2 + 1)*sqrt(arcsinh(x))), x)","F",0
495,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\sqrt{\operatorname{arsinh}\left(a x\right)}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/sqrt(arcsinh(a*x)), x)","F",0
496,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{\operatorname{arsinh}\left(a x\right)}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/sqrt(arcsinh(a*x)), x)","F",0
497,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{\sqrt{\operatorname{arsinh}\left(a x\right)}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/sqrt(arcsinh(a*x)), x)","F",0
498,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} \sqrt{\operatorname{arsinh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*sqrt(arcsinh(a*x))), x)","F",0
499,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\operatorname{arsinh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*sqrt(arcsinh(a*x))), x)","F",0
500,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\operatorname{arsinh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*sqrt(arcsinh(a*x))), x)","F",0
501,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/arcsinh(a*x)^(3/2), x)","F",0
502,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/arcsinh(a*x)^(3/2), x)","F",0
503,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{\operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/arcsinh(a*x)^(3/2), x)","F",0
504,0,0,0,0.000000," ","integrate(1/arcsinh(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} \operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*arcsinh(a*x)^(3/2)), x)","F",0
505,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*arcsinh(a*x)^(3/2)), x)","F",0
506,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \operatorname{arsinh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*arcsinh(a*x)^(3/2)), x)","F",0
507,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/arcsinh(a*x)^(5/2), x)","F",0
508,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arcsinh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{\operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/arcsinh(a*x)^(5/2), x)","F",0
509,0,0,0,0.000000," ","integrate(1/arcsinh(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} \operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*arcsinh(a*x)^(5/2)), x)","F",0
510,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arcsinh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*arcsinh(a*x)^(5/2)), x)","F",0
511,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arcsinh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \operatorname{arsinh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*arcsinh(a*x)^(5/2)), x)","F",0
512,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)^n*x^2, x)","F",0
513,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)^n*x, x)","F",0
514,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)^n, x)","F",0
515,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)^n/x, x)","F",0
516,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^n*(c^2*d*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c^{2} d x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c^2*d*x^2 + d)*(b*arcsinh(c*x) + a)^n/x^2, x)","F",0
517,0,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)^n*x^2, x)","F",0
518,0,0,0,0.000000," ","integrate(x*(c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)^n*x, x)","F",0
519,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)^n, x)","F",0
520,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)^n/x, x)","F",0
521,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)^n/x^2, x)","F",0
522,0,0,0,0.000000," ","integrate(x^2*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)^n*x^2, x)","F",0
523,0,0,0,0.000000," ","integrate(x*(c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)^n*x, x)","F",0
524,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)^n, x)","F",0
525,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)^n/x, x)","F",0
526,0,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)^n/x^2, x)","F",0
527,0,0,0,0.000000," ","integrate(x^m*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \operatorname{arsinh}\left(a x\right)^{n}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsinh(a*x)^n/sqrt(a^2*x^2 + 1), x)","F",0
528,0,0,0,0.000000," ","integrate(x^3*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{arsinh}\left(a x\right)^{n}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^3*arcsinh(a*x)^n/sqrt(a^2*x^2 + 1), x)","F",0
529,0,0,0,0.000000," ","integrate(x^2*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \operatorname{arsinh}\left(a x\right)^{n}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arcsinh(a*x)^n/sqrt(a^2*x^2 + 1), x)","F",0
530,0,0,0,0.000000," ","integrate(x*arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x \operatorname{arsinh}\left(a x\right)^{n}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x*arcsinh(a*x)^n/sqrt(a^2*x^2 + 1), x)","F",0
531,1,17,0,0.386974," ","integrate(arcsinh(a*x)^n/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)^{n + 1}}{a {\left(n + 1\right)}}"," ",0,"arcsinh(a*x)^(n + 1)/(a*(n + 1))","A",0
532,0,0,0,0.000000," ","integrate(arcsinh(a*x)^n/x/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{n}}{\sqrt{a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsinh(a*x)^n/(sqrt(a^2*x^2 + 1)*x), x)","F",0
533,0,0,0,0.000000," ","integrate(arcsinh(a*x)^n/x^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x\right)^{n}}{\sqrt{a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(arcsinh(a*x)^n/(sqrt(a^2*x^2 + 1)*x^2), x)","F",0
534,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
535,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
536,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)*(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
537,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","a {\left(\frac{f \operatorname{arsinh}\left(c x\right)}{c d \sqrt{\frac{f}{d}}} - \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{c d}\right)} + b \int \frac{\sqrt{-i \, c f x + f} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{i \, c d x + d}}\,{d x}"," ",0,"a*(f*arcsinh(c*x)/(c*d*sqrt(f/d)) - I*sqrt(c^2*d*f*x^2 + d*f)/(c*d)) + b*integrate(sqrt(-I*c*f*x + f)*log(c*x + sqrt(c^2*x^2 + 1))/sqrt(I*c*d*x + d), x)","F",0
538,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{i \, c^{2} d^{2} x + c d^{2}} - \frac{f \operatorname{arsinh}\left(c x\right)}{c d^{2} \sqrt{\frac{f}{d}}}\right)} + b \int \frac{\sqrt{-i \, c f x + f} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(2*I*sqrt(c^2*d*f*x^2 + d*f)/(I*c^2*d^2*x + c*d^2) - f*arcsinh(c*x)/(c*d^2*sqrt(f/d))) + b*integrate(sqrt(-I*c*f*x + f)*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(3/2), x)","F",0
539,1,219,0,0.598584," ","integrate((a+b*arcsinh(c*x))*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, b c {\left(\frac{6 \, \sqrt{f}}{3 i \, c^{3} d^{\frac{5}{2}} x + 3 \, c^{2} d^{\frac{5}{2}}} + \frac{\sqrt{f} \log\left(c x - i\right)}{c^{2} d^{\frac{5}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}} + \frac{3 i \, \sqrt{c^{2} d f x^{2} + d f}}{3 i \, c^{2} d^{3} x + 3 \, c d^{3}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}} + \frac{3 i \, \sqrt{c^{2} d f x^{2} + d f}}{3 i \, c^{2} d^{3} x + 3 \, c d^{3}}\right)}"," ",0,"1/3*b*c*(6*sqrt(f)/(3*I*c^3*d^(5/2)*x + 3*c^2*d^(5/2)) + sqrt(f)*log(c*x - I)/(c^2*d^(5/2))) - 1/3*b*(2*I*sqrt(c^2*d*f*x^2 + d*f)/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3) + 3*I*sqrt(c^2*d*f*x^2 + d*f)/(3*I*c^2*d^3*x + 3*c*d^3))*arcsinh(c*x) - 1/3*a*(2*I*sqrt(c^2*d*f*x^2 + d*f)/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3) + 3*I*sqrt(c^2*d*f*x^2 + d*f)/(3*I*c^2*d^3*x + 3*c*d^3))","A",0
540,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
541,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
542,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
543,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
544,0,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}} + \frac{6 i \, \sqrt{c^{2} d f x^{2} + d f} f}{i \, c^{2} d^{2} x + c d^{2}} - \frac{3 \, f^{2} \operatorname{arsinh}\left(c x\right)}{c d^{2} \sqrt{\frac{f}{d}}}\right)} + b \int \frac{{\left(-i \, c f x + f\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(I*(c^2*d*f*x^2 + d*f)^(3/2)/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3) + 6*I*sqrt(c^2*d*f*x^2 + d*f)*f/(I*c^2*d^2*x + c*d^2) - 3*f^2*arcsinh(c*x)/(c*d^2*sqrt(f/d))) + b*integrate((-I*c*f*x + f)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(3/2), x)","F",0
545,0,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(-\frac{3 i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{-3 i \, c^{4} d^{4} x^{3} - 9 \, c^{3} d^{4} x^{2} + 9 i \, c^{2} d^{4} x + 3 \, c d^{4}} + \frac{2 i \, \sqrt{c^{2} d f x^{2} + d f} f}{c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}} + \frac{21 i \, \sqrt{c^{2} d f x^{2} + d f} f}{3 i \, c^{2} d^{3} x + 3 \, c d^{3}} - \frac{3 \, f^{2} \operatorname{arsinh}\left(c x\right)}{c d^{3} \sqrt{\frac{f}{d}}}\right)} + b \int \frac{{\left(-i \, c f x + f\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*a*(-3*I*(c^2*d*f*x^2 + d*f)^(3/2)/(-3*I*c^4*d^4*x^3 - 9*c^3*d^4*x^2 + 9*I*c^2*d^4*x + 3*c*d^4) + 2*I*sqrt(c^2*d*f*x^2 + d*f)*f/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3) + 21*I*sqrt(c^2*d*f*x^2 + d*f)*f/(3*I*c^2*d^3*x + 3*c*d^3) - 3*f^2*arcsinh(c*x)/(c*d^3*sqrt(f/d))) + b*integrate((-I*c*f*x + f)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(5/2), x)","F",0
546,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
547,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
548,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
549,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
550,0,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} f^{3} x^{3}}{\sqrt{c^{2} d f x^{2} + d f} d} + \frac{8 i \, c f^{3} x^{2}}{\sqrt{c^{2} d f x^{2} + d f} d} + \frac{17 \, f^{3} x}{\sqrt{c^{2} d f x^{2} + d f} d} - \frac{15 \, f^{3} \operatorname{arsinh}\left(c x\right)}{\sqrt{d f} c d} + \frac{24 i \, f^{3}}{\sqrt{c^{2} d f x^{2} + d f} c d}\right)} a + b \int \frac{{\left(-i \, c f x + f\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*(c^2*f^3*x^3/(sqrt(c^2*d*f*x^2 + d*f)*d) + 8*I*c*f^3*x^2/(sqrt(c^2*d*f*x^2 + d*f)*d) + 17*f^3*x/(sqrt(c^2*d*f*x^2 + d*f)*d) - 15*f^3*arcsinh(c*x)/(sqrt(d*f)*c*d) + 24*I*f^3/(sqrt(c^2*d*f*x^2 + d*f)*c*d))*a + b*integrate((-I*c*f*x + f)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(3/2), x)","F",0
551,0,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{3 i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{5}{2}}}{c^{5} d^{5} x^{4} - 4 i \, c^{4} d^{5} x^{3} - 6 \, c^{3} d^{5} x^{2} + 4 i \, c^{2} d^{5} x + c d^{5}} - \frac{15 i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} f}{-3 i \, c^{4} d^{4} x^{3} - 9 \, c^{3} d^{4} x^{2} + 9 i \, c^{2} d^{4} x + 3 \, c d^{4}} + \frac{10 i \, \sqrt{c^{2} d f x^{2} + d f} f^{2}}{c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}} + \frac{105 i \, \sqrt{c^{2} d f x^{2} + d f} f^{2}}{3 i \, c^{2} d^{3} x + 3 \, c d^{3}} - \frac{15 \, f^{3} \operatorname{arsinh}\left(c x\right)}{c d^{3} \sqrt{\frac{f}{d}}}\right)} a + b \int \frac{{\left(-i \, c f x + f\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-1/3*(3*I*(c^2*d*f*x^2 + d*f)^(5/2)/(c^5*d^5*x^4 - 4*I*c^4*d^5*x^3 - 6*c^3*d^5*x^2 + 4*I*c^2*d^5*x + c*d^5) - 15*I*(c^2*d*f*x^2 + d*f)^(3/2)*f/(-3*I*c^4*d^4*x^3 - 9*c^3*d^4*x^2 + 9*I*c^2*d^4*x + 3*c*d^4) + 10*I*sqrt(c^2*d*f*x^2 + d*f)*f^2/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3) + 105*I*sqrt(c^2*d*f*x^2 + d*f)*f^2/(3*I*c^2*d^3*x + 3*c*d^3) - 15*f^3*arcsinh(c*x)/(c*d^3*sqrt(f/d)))*a + b*integrate((-I*c*f*x + f)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(5/2), x)","F",0
552,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
553,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
554,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","a {\left(\frac{d \operatorname{arsinh}\left(c x\right)}{c f \sqrt{\frac{d}{f}}} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{c f}\right)} + b \int \frac{\sqrt{i \, c d x + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{-i \, c f x + f}}\,{d x}"," ",0,"a*(d*arcsinh(c*x)/(c*f*sqrt(d/f)) + I*sqrt(c^2*d*f*x^2 + d*f)/(c*f)) + b*integrate(sqrt(I*c*d*x + d)*log(c*x + sqrt(c^2*x^2 + 1))/sqrt(-I*c*f*x + f), x)","F",0
555,1,32,0,0.508433," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\frac{b \operatorname{arsinh}\left(c x\right)^{2}}{2 \, \sqrt{d f} c} + \frac{a \operatorname{arsinh}\left(c x\right)}{\sqrt{d f} c}"," ",0,"1/2*b*arcsinh(c*x)^2/(sqrt(d*f)*c) + a*arcsinh(c*x)/(sqrt(d*f)*c)","A",0
556,1,98,0,0.743903," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\frac{i \, \sqrt{c^{2} d f x^{2} + d f} b \operatorname{arsinh}\left(c x\right)}{i \, c^{2} d^{2} f x + c d^{2} f} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f} a}{i \, c^{2} d^{2} f x + c d^{2} f} - \frac{b \log\left(i \, c x + 1\right)}{c d^{\frac{3}{2}} \sqrt{f}}"," ",0,"I*sqrt(c^2*d*f*x^2 + d*f)*b*arcsinh(c*x)/(I*c^2*d^2*f*x + c*d^2*f) + I*sqrt(c^2*d*f*x^2 + d*f)*a/(I*c^2*d^2*f*x + c*d^2*f) - b*log(I*c*x + 1)/(c*d^(3/2)*sqrt(f))","A",0
557,1,233,0,0.710987," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, b c {\left(\frac{3}{3 i \, c^{3} d^{\frac{5}{2}} \sqrt{f} x + 3 \, c^{2} d^{\frac{5}{2}} \sqrt{f}} - \frac{\log\left(c x - i\right)}{c^{2} d^{\frac{5}{2}} \sqrt{f}}\right)} + b {\left(-\frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{3 \, c^{3} d^{3} f x^{2} - 6 i \, c^{2} d^{3} f x - 3 \, c d^{3} f} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{3 i \, c^{2} d^{3} f x + 3 \, c d^{3} f}\right)} \operatorname{arsinh}\left(c x\right) + a {\left(-\frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{3 \, c^{3} d^{3} f x^{2} - 6 i \, c^{2} d^{3} f x - 3 \, c d^{3} f} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{3 i \, c^{2} d^{3} f x + 3 \, c d^{3} f}\right)}"," ",0,"1/3*b*c*(3/(3*I*c^3*d^(5/2)*sqrt(f)*x + 3*c^2*d^(5/2)*sqrt(f)) - log(c*x - I)/(c^2*d^(5/2)*sqrt(f))) + b*(-I*sqrt(c^2*d*f*x^2 + d*f)/(3*c^3*d^3*f*x^2 - 6*I*c^2*d^3*f*x - 3*c*d^3*f) + I*sqrt(c^2*d*f*x^2 + d*f)/(3*I*c^2*d^3*f*x + 3*c*d^3*f))*arcsinh(c*x) + a*(-I*sqrt(c^2*d*f*x^2 + d*f)/(3*c^3*d^3*f*x^2 - 6*I*c^2*d^3*f*x - 3*c*d^3*f) + I*sqrt(c^2*d*f*x^2 + d*f)/(3*I*c^2*d^3*f*x + 3*c*d^3*f))","A",0
558,0,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} d^{3} x^{3}}{\sqrt{c^{2} d f x^{2} + d f} f} - \frac{8 i \, c d^{3} x^{2}}{\sqrt{c^{2} d f x^{2} + d f} f} + \frac{17 \, d^{3} x}{\sqrt{c^{2} d f x^{2} + d f} f} - \frac{15 \, d^{3} \operatorname{arsinh}\left(c x\right)}{\sqrt{d f} c f} - \frac{24 i \, d^{3}}{\sqrt{c^{2} d f x^{2} + d f} c f}\right)} a + b \int \frac{{\left(i \, c d x + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*(c^2*d^3*x^3/(sqrt(c^2*d*f*x^2 + d*f)*f) - 8*I*c*d^3*x^2/(sqrt(c^2*d*f*x^2 + d*f)*f) + 17*d^3*x/(sqrt(c^2*d*f*x^2 + d*f)*f) - 15*d^3*arcsinh(c*x)/(sqrt(d*f)*c*f) - 24*I*d^3/(sqrt(c^2*d*f*x^2 + d*f)*c*f))*a + b*integrate((I*c*d*x + d)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(3/2), x)","F",0
559,0,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","a {\left(-\frac{i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{3} f^{3} x^{2} + 2 i \, c^{2} f^{3} x - c f^{3}} - \frac{6 i \, \sqrt{c^{2} d f x^{2} + d f} d}{-i \, c^{2} f^{2} x + c f^{2}} - \frac{3 \, d^{2} \operatorname{arsinh}\left(c x\right)}{c f^{2} \sqrt{\frac{d}{f}}}\right)} + b \int \frac{{\left(i \, c d x + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(-I*(c^2*d*f*x^2 + d*f)^(3/2)/(c^3*f^3*x^2 + 2*I*c^2*f^3*x - c*f^3) - 6*I*sqrt(c^2*d*f*x^2 + d*f)*d/(-I*c^2*f^2*x + c*f^2) - 3*d^2*arcsinh(c*x)/(c*f^2*sqrt(d/f))) + b*integrate((I*c*d*x + d)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(3/2), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","a {\left(-\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{-i \, c^{2} f^{2} x + c f^{2}} - \frac{d \operatorname{arsinh}\left(c x\right)}{c f^{2} \sqrt{\frac{d}{f}}}\right)} + b \int \frac{\sqrt{i \, c d x + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(-2*I*sqrt(c^2*d*f*x^2 + d*f)/(-I*c^2*f^2*x + c*f^2) - d*arcsinh(c*x)/(c*f^2*sqrt(d/f))) + b*integrate(sqrt(I*c*d*x + d)*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(3/2), x)","F",0
561,1,98,0,0.651910," ","integrate((a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2)/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","-\frac{i \, \sqrt{c^{2} d f x^{2} + d f} b \operatorname{arsinh}\left(c x\right)}{-i \, c^{2} d f^{2} x + c d f^{2}} - \frac{i \, \sqrt{c^{2} d f x^{2} + d f} a}{-i \, c^{2} d f^{2} x + c d f^{2}} - \frac{b \log\left(i \, c x - 1\right)}{c \sqrt{d} f^{\frac{3}{2}}}"," ",0,"-I*sqrt(c^2*d*f*x^2 + d*f)*b*arcsinh(c*x)/(-I*c^2*d*f^2*x + c*d*f^2) - I*sqrt(c^2*d*f*x^2 + d*f)*a/(-I*c^2*d*f^2*x + c*d*f^2) - b*log(I*c*x - 1)/(c*sqrt(d)*f^(3/2))","A",0
562,1,82,0,0.584183," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","\frac{b x \operatorname{arsinh}\left(c x\right)}{\sqrt{c^{2} d f x^{2} + d f} d f} + \frac{a x}{\sqrt{c^{2} d f x^{2} + d f} d f} - \frac{b \sqrt{\frac{1}{d f}} \log\left(x^{2} + \frac{1}{c^{2}}\right)}{2 \, c d f}"," ",0,"b*x*arcsinh(c*x)/(sqrt(c^2*d*f*x^2 + d*f)*d*f) + a*x/(sqrt(c^2*d*f*x^2 + d*f)*d*f) - 1/2*b*sqrt(1/(d*f))*log(x^2 + 1/c^2)/(c*d*f)","A",0
563,1,237,0,0.516173," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","\frac{1}{12} \, b c {\left(-\frac{2 i \, \sqrt{d} \sqrt{f}}{c^{3} d^{3} f^{2} x - i \, c^{2} d^{3} f^{2}} - \frac{3 \, \log\left(c x + i\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{3}{2}}} - \frac{5 \, \log\left(c x - i\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{3}{2}}}\right)} - \frac{1}{3} \, b {\left(-\frac{3 i}{3 i \, \sqrt{c^{2} d f x^{2} + d f} c^{2} d^{2} f x + 3 \, \sqrt{c^{2} d f x^{2} + d f} c d^{2} f} - \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d^{2} f}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a {\left(-\frac{3 i}{3 i \, \sqrt{c^{2} d f x^{2} + d f} c^{2} d^{2} f x + 3 \, \sqrt{c^{2} d f x^{2} + d f} c d^{2} f} - \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d^{2} f}\right)}"," ",0,"1/12*b*c*(-2*I*sqrt(d)*sqrt(f)/(c^3*d^3*f^2*x - I*c^2*d^3*f^2) - 3*log(c*x + I)/(c^2*d^(5/2)*f^(3/2)) - 5*log(c*x - I)/(c^2*d^(5/2)*f^(3/2))) - 1/3*b*(-3*I/(3*I*sqrt(c^2*d*f*x^2 + d*f)*c^2*d^2*f*x + 3*sqrt(c^2*d*f*x^2 + d*f)*c*d^2*f) - 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d^2*f))*arcsinh(c*x) - 1/3*a*(-3*I/(3*I*sqrt(c^2*d*f*x^2 + d*f)*c^2*d^2*f*x + 3*sqrt(c^2*d*f*x^2 + d*f)*c*d^2*f) - 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d^2*f))","A",0
564,0,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","{\left(\frac{i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{5}{2}}}{c^{5} f^{5} x^{4} + 4 i \, c^{4} f^{5} x^{3} - 6 \, c^{3} f^{5} x^{2} - 4 i \, c^{2} f^{5} x + c f^{5}} - \frac{5 i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d}{3 i \, c^{4} f^{4} x^{3} - 9 \, c^{3} f^{4} x^{2} - 9 i \, c^{2} f^{4} x + 3 \, c f^{4}} + \frac{10 i \, \sqrt{c^{2} d f x^{2} + d f} d^{2}}{3 \, c^{3} f^{3} x^{2} + 6 i \, c^{2} f^{3} x - 3 \, c f^{3}} + \frac{35 i \, \sqrt{c^{2} d f x^{2} + d f} d^{2}}{-3 i \, c^{2} f^{3} x + 3 \, c f^{3}} + \frac{5 \, d^{3} \operatorname{arsinh}\left(c x\right)}{c f^{3} \sqrt{\frac{d}{f}}}\right)} a + b \int \frac{{\left(i \, c d x + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"(I*(c^2*d*f*x^2 + d*f)^(5/2)/(c^5*f^5*x^4 + 4*I*c^4*f^5*x^3 - 6*c^3*f^5*x^2 - 4*I*c^2*f^5*x + c*f^5) - 5*I*(c^2*d*f*x^2 + d*f)^(3/2)*d/(3*I*c^4*f^4*x^3 - 9*c^3*f^4*x^2 - 9*I*c^2*f^4*x + 3*c*f^4) + 10*I*sqrt(c^2*d*f*x^2 + d*f)*d^2/(3*c^3*f^3*x^2 + 6*I*c^2*f^3*x - 3*c*f^3) + 35*I*sqrt(c^2*d*f*x^2 + d*f)*d^2/(-3*I*c^2*f^3*x + 3*c*f^3) + 5*d^3*arcsinh(c*x)/(c*f^3*sqrt(d/f)))*a + b*integrate((I*c*d*x + d)^(5/2)*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(5/2), x)","F",0
565,0,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","a {\left(-\frac{i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{3 i \, c^{4} f^{4} x^{3} - 9 \, c^{3} f^{4} x^{2} - 9 i \, c^{2} f^{4} x + 3 \, c f^{4}} + \frac{2 i \, \sqrt{c^{2} d f x^{2} + d f} d}{3 \, c^{3} f^{3} x^{2} + 6 i \, c^{2} f^{3} x - 3 \, c f^{3}} + \frac{7 i \, \sqrt{c^{2} d f x^{2} + d f} d}{-3 i \, c^{2} f^{3} x + 3 \, c f^{3}} + \frac{d^{2} \operatorname{arsinh}\left(c x\right)}{c f^{3} \sqrt{\frac{d}{f}}}\right)} + b \int \frac{{\left(i \, c d x + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"a*(-I*(c^2*d*f*x^2 + d*f)^(3/2)/(3*I*c^4*f^4*x^3 - 9*c^3*f^4*x^2 - 9*I*c^2*f^4*x + 3*c*f^4) + 2*I*sqrt(c^2*d*f*x^2 + d*f)*d/(3*c^3*f^3*x^2 + 6*I*c^2*f^3*x - 3*c*f^3) + 7*I*sqrt(c^2*d*f*x^2 + d*f)*d/(-3*I*c^2*f^3*x + 3*c*f^3) + d^2*arcsinh(c*x)/(c*f^3*sqrt(d/f))) + b*integrate((I*c*d*x + d)^(3/2)*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(5/2), x)","F",0
566,1,220,0,0.625556," ","integrate((a+b*arcsinh(c*x))*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b c {\left(\frac{6 \, \sqrt{d}}{3 i \, c^{3} f^{\frac{5}{2}} x - 3 \, c^{2} f^{\frac{5}{2}}} - \frac{\sqrt{d} \log\left(c x + i\right)}{c^{2} f^{\frac{5}{2}}}\right)} + b {\left(\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{3 \, c^{3} f^{3} x^{2} + 6 i \, c^{2} f^{3} x - 3 \, c f^{3}} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{-3 i \, c^{2} f^{3} x + 3 \, c f^{3}}\right)} \operatorname{arsinh}\left(c x\right) + a {\left(\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{3 \, c^{3} f^{3} x^{2} + 6 i \, c^{2} f^{3} x - 3 \, c f^{3}} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{-3 i \, c^{2} f^{3} x + 3 \, c f^{3}}\right)}"," ",0,"-1/3*b*c*(6*sqrt(d)/(3*I*c^3*f^(5/2)*x - 3*c^2*f^(5/2)) - sqrt(d)*log(c*x + I)/(c^2*f^(5/2))) + b*(2*I*sqrt(c^2*d*f*x^2 + d*f)/(3*c^3*f^3*x^2 + 6*I*c^2*f^3*x - 3*c*f^3) + I*sqrt(c^2*d*f*x^2 + d*f)/(-3*I*c^2*f^3*x + 3*c*f^3))*arcsinh(c*x) + a*(2*I*sqrt(c^2*d*f*x^2 + d*f)/(3*c^3*f^3*x^2 + 6*I*c^2*f^3*x - 3*c*f^3) + I*sqrt(c^2*d*f*x^2 + d*f)/(-3*I*c^2*f^3*x + 3*c*f^3))","A",0
567,1,232,0,0.638759," ","integrate((a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2)/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b c {\left(\frac{3}{3 i \, c^{3} \sqrt{d} f^{\frac{5}{2}} x - 3 \, c^{2} \sqrt{d} f^{\frac{5}{2}}} + \frac{\log\left(c x + i\right)}{c^{2} \sqrt{d} f^{\frac{5}{2}}}\right)} + b {\left(\frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{3 \, c^{3} d f^{3} x^{2} + 6 i \, c^{2} d f^{3} x - 3 \, c d f^{3}} - \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{-3 i \, c^{2} d f^{3} x + 3 \, c d f^{3}}\right)} \operatorname{arsinh}\left(c x\right) + a {\left(\frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{3 \, c^{3} d f^{3} x^{2} + 6 i \, c^{2} d f^{3} x - 3 \, c d f^{3}} - \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{-3 i \, c^{2} d f^{3} x + 3 \, c d f^{3}}\right)}"," ",0,"-1/3*b*c*(3/(3*I*c^3*sqrt(d)*f^(5/2)*x - 3*c^2*sqrt(d)*f^(5/2)) + log(c*x + I)/(c^2*sqrt(d)*f^(5/2))) + b*(I*sqrt(c^2*d*f*x^2 + d*f)/(3*c^3*d*f^3*x^2 + 6*I*c^2*d*f^3*x - 3*c*d*f^3) - I*sqrt(c^2*d*f*x^2 + d*f)/(-3*I*c^2*d*f^3*x + 3*c*d*f^3))*arcsinh(c*x) + a*(I*sqrt(c^2*d*f*x^2 + d*f)/(3*c^3*d*f^3*x^2 + 6*I*c^2*d*f^3*x - 3*c*d*f^3) - I*sqrt(c^2*d*f*x^2 + d*f)/(-3*I*c^2*d*f^3*x + 3*c*d*f^3))","A",0
568,1,237,0,0.619688," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\frac{1}{12} \, b c {\left(\frac{2 i \, \sqrt{d} \sqrt{f}}{c^{3} d^{2} f^{3} x + i \, c^{2} d^{2} f^{3}} - \frac{5 \, \log\left(c x + i\right)}{c^{2} d^{\frac{3}{2}} f^{\frac{5}{2}}} - \frac{3 \, \log\left(c x - i\right)}{c^{2} d^{\frac{3}{2}} f^{\frac{5}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{3 i}{-3 i \, \sqrt{c^{2} d f x^{2} + d f} c^{2} d f^{2} x + 3 \, \sqrt{c^{2} d f x^{2} + d f} c d f^{2}} - \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d f^{2}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{3 i}{-3 i \, \sqrt{c^{2} d f x^{2} + d f} c^{2} d f^{2} x + 3 \, \sqrt{c^{2} d f x^{2} + d f} c d f^{2}} - \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d f^{2}}\right)}"," ",0,"1/12*b*c*(2*I*sqrt(d)*sqrt(f)/(c^3*d^2*f^3*x + I*c^2*d^2*f^3) - 5*log(c*x + I)/(c^2*d^(3/2)*f^(5/2)) - 3*log(c*x - I)/(c^2*d^(3/2)*f^(5/2))) - 1/3*b*(3*I/(-3*I*sqrt(c^2*d*f*x^2 + d*f)*c^2*d*f^2*x + 3*sqrt(c^2*d*f*x^2 + d*f)*c*d*f^2) - 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d*f^2))*arcsinh(c*x) - 1/3*a*(3*I/(-3*I*sqrt(c^2*d*f*x^2 + d*f)*c^2*d*f^2*x + 3*sqrt(c^2*d*f*x^2 + d*f)*c*d*f^2) - 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d*f^2))","A",0
569,1,159,0,0.529830," ","integrate((a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} f^{\frac{5}{2}} x^{2} + c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{x}{{\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f} + \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d^{2} f^{2}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{x}{{\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f} + \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d^{2} f^{2}}\right)}"," ",0,"1/6*b*c*(1/(c^4*d^(5/2)*f^(5/2)*x^2 + c^2*d^(5/2)*f^(5/2)) - 2*log(c^2*x^2 + 1)/(c^2*d^(5/2)*f^(5/2))) + 1/3*b*(x/((c^2*d*f*x^2 + d*f)^(3/2)*d*f) + 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d^2*f^2))*arcsinh(c*x) + 1/3*a*(x/((c^2*d*f*x^2 + d*f)^(3/2)*d*f) + 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d^2*f^2))","A",0
570,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
571,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
572,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)*(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
573,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{f \operatorname{arsinh}\left(c x\right)}{c d \sqrt{\frac{f}{d}}} - \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{c d}\right)} + \int \frac{\sqrt{-i \, c f x + f} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{i \, c d x + d}} + \frac{2 \, \sqrt{-i \, c f x + f} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{i \, c d x + d}}\,{d x}"," ",0,"a^2*(f*arcsinh(c*x)/(c*d*sqrt(f/d)) - I*sqrt(c^2*d*f*x^2 + d*f)/(c*d)) + integrate(sqrt(-I*c*f*x + f)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/sqrt(I*c*d*x + d) + 2*sqrt(-I*c*f*x + f)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/sqrt(I*c*d*x + d), x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{i \, c^{2} d^{2} x + c d^{2}} - \frac{f \operatorname{arsinh}\left(c x\right)}{c d^{2} \sqrt{\frac{f}{d}}}\right)} + \int \frac{\sqrt{-i \, c f x + f} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}} + \frac{2 \, \sqrt{-i \, c f x + f} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a^2*(2*I*sqrt(c^2*d*f*x^2 + d*f)/(I*c^2*d^2*x + c*d^2) - f*arcsinh(c*x)/(c*d^2*sqrt(f/d))) + integrate(sqrt(-I*c*f*x + f)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(I*c*d*x + d)^(3/2) + 2*sqrt(-I*c*f*x + f)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(3/2), x)","F",0
575,-1,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(f-I*c*f*x)^(1/2)/(d+I*c*d*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
577,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
578,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
579,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
580,0,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}} + \frac{6 i \, \sqrt{c^{2} d f x^{2} + d f} f}{i \, c^{2} d^{2} x + c d^{2}} - \frac{3 \, f^{2} \operatorname{arsinh}\left(c x\right)}{c d^{2} \sqrt{\frac{f}{d}}}\right)} + \int \frac{{\left(-i \, c f x + f\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(-i \, c f x + f\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a^2*(I*(c^2*d*f*x^2 + d*f)^(3/2)/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3) + 6*I*sqrt(c^2*d*f*x^2 + d*f)*f/(I*c^2*d^2*x + c*d^2) - 3*f^2*arcsinh(c*x)/(c*d^2*sqrt(f/d))) + integrate((-I*c*f*x + f)^(3/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(I*c*d*x + d)^(3/2) + 2*(-I*c*f*x + f)^(3/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(3/2), x)","F",0
581,-1,0,0,0.000000," ","integrate((f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
583,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
584,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
585,-2,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
586,0,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} f^{3} x^{3}}{\sqrt{c^{2} d f x^{2} + d f} d} + \frac{8 i \, c f^{3} x^{2}}{\sqrt{c^{2} d f x^{2} + d f} d} + \frac{17 \, f^{3} x}{\sqrt{c^{2} d f x^{2} + d f} d} - \frac{15 \, f^{3} \operatorname{arsinh}\left(c x\right)}{\sqrt{d f} c d} + \frac{24 i \, f^{3}}{\sqrt{c^{2} d f x^{2} + d f} c d}\right)} a^{2} + \int \frac{{\left(-i \, c f x + f\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(-i \, c f x + f\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(i \, c d x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*(c^2*f^3*x^3/(sqrt(c^2*d*f*x^2 + d*f)*d) + 8*I*c*f^3*x^2/(sqrt(c^2*d*f*x^2 + d*f)*d) + 17*f^3*x/(sqrt(c^2*d*f*x^2 + d*f)*d) - 15*f^3*arcsinh(c*x)/(sqrt(d*f)*c*d) + 24*I*f^3/(sqrt(c^2*d*f*x^2 + d*f)*c*d))*a^2 + integrate((-I*c*f*x + f)^(5/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(I*c*d*x + d)^(3/2) + 2*(-I*c*f*x + f)^(5/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(I*c*d*x + d)^(3/2), x)","F",0
587,-1,0,0,0.000000," ","integrate((f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
589,-2,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
590,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{d \operatorname{arsinh}\left(c x\right)}{c f \sqrt{\frac{d}{f}}} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f}}{c f}\right)} + \int \frac{\sqrt{i \, c d x + d} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{-i \, c f x + f}} + \frac{2 \, \sqrt{i \, c d x + d} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{-i \, c f x + f}}\,{d x}"," ",0,"a^2*(d*arcsinh(c*x)/(c*f*sqrt(d/f)) + I*sqrt(c^2*d*f*x^2 + d*f)/(c*f)) + integrate(sqrt(I*c*d*x + d)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/sqrt(-I*c*f*x + f) + 2*sqrt(I*c*d*x + d)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/sqrt(-I*c*f*x + f), x)","F",0
591,1,53,0,0.587979," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \operatorname{arsinh}\left(c x\right)^{3}}{3 \, \sqrt{d f} c} + \frac{a b \operatorname{arsinh}\left(c x\right)^{2}}{\sqrt{d f} c} + \frac{a^{2} \operatorname{arsinh}\left(c x\right)}{\sqrt{d f} c}"," ",0,"1/3*b^2*arcsinh(c*x)^3/(sqrt(d*f)*c) + a*b*arcsinh(c*x)^2/(sqrt(d*f)*c) + a^2*arcsinh(c*x)/(sqrt(d*f)*c)","A",0
592,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(i \, c d x + d\right)}^{\frac{3}{2}} \sqrt{-i \, c f x + f}}\,{d x} + \frac{2 i \, \sqrt{c^{2} d f x^{2} + d f} a b \operatorname{arsinh}\left(c x\right)}{i \, c^{2} d^{2} f x + c d^{2} f} + \frac{i \, \sqrt{c^{2} d f x^{2} + d f} a^{2}}{i \, c^{2} d^{2} f x + c d^{2} f} - \frac{2 \, a b \log\left(i \, c x + 1\right)}{c d^{\frac{3}{2}} \sqrt{f}}"," ",0,"b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/((I*c*d*x + d)^(3/2)*sqrt(-I*c*f*x + f)), x) + 2*I*sqrt(c^2*d*f*x^2 + d*f)*a*b*arcsinh(c*x)/(I*c^2*d^2*f*x + c*d^2*f) + I*sqrt(c^2*d*f*x^2 + d*f)*a^2/(I*c^2*d^2*f*x + c*d^2*f) - 2*a*b*log(I*c*x + 1)/(c*d^(3/2)*sqrt(f))","F",0
593,-1,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{c^{2} d^{3} x^{3}}{\sqrt{c^{2} d f x^{2} + d f} f} - \frac{8 i \, c d^{3} x^{2}}{\sqrt{c^{2} d f x^{2} + d f} f} + \frac{17 \, d^{3} x}{\sqrt{c^{2} d f x^{2} + d f} f} - \frac{15 \, d^{3} \operatorname{arsinh}\left(c x\right)}{\sqrt{d f} c f} - \frac{24 i \, d^{3}}{\sqrt{c^{2} d f x^{2} + d f} c f}\right)} a^{2} + \int \frac{{\left(i \, c d x + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(i \, c d x + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*(c^2*d^3*x^3/(sqrt(c^2*d*f*x^2 + d*f)*f) - 8*I*c*d^3*x^2/(sqrt(c^2*d*f*x^2 + d*f)*f) + 17*d^3*x/(sqrt(c^2*d*f*x^2 + d*f)*f) - 15*d^3*arcsinh(c*x)/(sqrt(d*f)*c*f) - 24*I*d^3/(sqrt(c^2*d*f*x^2 + d*f)*c*f))*a^2 + integrate((I*c*d*x + d)^(5/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(-I*c*f*x + f)^(3/2) + 2*(I*c*d*x + d)^(5/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(3/2), x)","F",0
595,0,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(-\frac{i \, {\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{3} f^{3} x^{2} + 2 i \, c^{2} f^{3} x - c f^{3}} - \frac{6 i \, \sqrt{c^{2} d f x^{2} + d f} d}{-i \, c^{2} f^{2} x + c f^{2}} - \frac{3 \, d^{2} \operatorname{arsinh}\left(c x\right)}{c f^{2} \sqrt{\frac{d}{f}}}\right)} + \int \frac{{\left(i \, c d x + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(i \, c d x + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a^2*(-I*(c^2*d*f*x^2 + d*f)^(3/2)/(c^3*f^3*x^2 + 2*I*c^2*f^3*x - c*f^3) - 6*I*sqrt(c^2*d*f*x^2 + d*f)*d/(-I*c^2*f^2*x + c*f^2) - 3*d^2*arcsinh(c*x)/(c*f^2*sqrt(d/f))) + integrate((I*c*d*x + d)^(3/2)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(-I*c*f*x + f)^(3/2) + 2*(I*c*d*x + d)^(3/2)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(3/2), x)","F",0
596,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(-\frac{2 i \, \sqrt{c^{2} d f x^{2} + d f}}{-i \, c^{2} f^{2} x + c f^{2}} - \frac{d \operatorname{arsinh}\left(c x\right)}{c f^{2} \sqrt{\frac{d}{f}}}\right)} + \int \frac{\sqrt{i \, c d x + d} b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}} + \frac{2 \, \sqrt{i \, c d x + d} a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a^2*(-2*I*sqrt(c^2*d*f*x^2 + d*f)/(-I*c^2*f^2*x + c*f^2) - d*arcsinh(c*x)/(c*f^2*sqrt(d/f))) + integrate(sqrt(I*c*d*x + d)*b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(-I*c*f*x + f)^(3/2) + 2*sqrt(I*c*d*x + d)*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(-I*c*f*x + f)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2)/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{i \, c d x + d} {\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x} - \frac{2 i \, \sqrt{c^{2} d f x^{2} + d f} a b \operatorname{arsinh}\left(c x\right)}{-i \, c^{2} d f^{2} x + c d f^{2}} - \frac{i \, \sqrt{c^{2} d f x^{2} + d f} a^{2}}{-i \, c^{2} d f^{2} x + c d f^{2}} - \frac{2 \, a b \log\left(i \, c x - 1\right)}{c \sqrt{d} f^{\frac{3}{2}}}"," ",0,"b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/(sqrt(I*c*d*x + d)*(-I*c*f*x + f)^(3/2)), x) - 2*I*sqrt(c^2*d*f*x^2 + d*f)*a*b*arcsinh(c*x)/(-I*c^2*d*f^2*x + c*d*f^2) - I*sqrt(c^2*d*f*x^2 + d*f)*a^2/(-I*c^2*d*f^2*x + c*d*f^2) - 2*a*b*log(I*c*x - 1)/(c*sqrt(d)*f^(3/2))","F",0
598,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(i \, c d x + d\right)}^{\frac{3}{2}} {\left(-i \, c f x + f\right)}^{\frac{3}{2}}}\,{d x} + \frac{2 \, a b x \operatorname{arsinh}\left(c x\right)}{\sqrt{c^{2} d f x^{2} + d f} d f} + \frac{a^{2} x}{\sqrt{c^{2} d f x^{2} + d f} d f} - \frac{a b \sqrt{\frac{1}{d f}} \log\left(x^{2} + \frac{1}{c^{2}}\right)}{c d f}"," ",0,"b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/((I*c*d*x + d)^(3/2)*(-I*c*f*x + f)^(3/2)), x) + 2*a*b*x*arcsinh(c*x)/(sqrt(c^2*d*f*x^2 + d*f)*d*f) + a^2*x/(sqrt(c^2*d*f*x^2 + d*f)*d*f) - a*b*sqrt(1/(d*f))*log(x^2 + 1/c^2)/(c*d*f)","F",0
599,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
600,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(d+I*c*d*x)^(1/2)/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2)/(d+I*c*d*x)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2)/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
605,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2)/(f-I*c*f*x)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} f^{\frac{5}{2}} x^{2} + c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}} - \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b {\left(\frac{x}{{\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f} + \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d^{2} f^{2}}\right)} \operatorname{arsinh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{x}{{\left(c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f} + \frac{2 \, x}{\sqrt{c^{2} d f x^{2} + d f} d^{2} f^{2}}\right)} + b^{2} \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(i \, c d x + d\right)}^{\frac{5}{2}} {\left(-i \, c f x + f\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*b*c*(1/(c^4*d^(5/2)*f^(5/2)*x^2 + c^2*d^(5/2)*f^(5/2)) - 2*log(c^2*x^2 + 1)/(c^2*d^(5/2)*f^(5/2))) + 2/3*a*b*(x/((c^2*d*f*x^2 + d*f)^(3/2)*d*f) + 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d^2*f^2))*arcsinh(c*x) + 1/3*a^2*(x/((c^2*d*f*x^2 + d*f)^(3/2)*d*f) + 2*x/(sqrt(c^2*d*f*x^2 + d*f)*d^2*f^2)) + b^2*integrate(log(c*x + sqrt(c^2*x^2 + 1))^2/((I*c*d*x + d)^(5/2)*(-I*c*f*x + f)^(5/2)), x)","F",0
606,1,415,0,0.412278," ","integrate((e*x^2+d)^4*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{4} x^{9} + \frac{4}{7} \, a d e^{3} x^{7} + \frac{6}{5} \, a d^{2} e^{2} x^{5} + \frac{4}{3} \, a d^{3} e x^{3} + \frac{4}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3} e + \frac{2}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2} e^{2} + \frac{4}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b d e^{3} + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arsinh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} + 1} x^{8}}{c^{2}} - \frac{40 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{6}} - \frac{64 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b e^{4} + a d^{4} x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d^{4}}{c}"," ",0,"1/9*a*e^4*x^9 + 4/7*a*d*e^3*x^7 + 6/5*a*d^2*e^2*x^5 + 4/3*a*d^3*e*x^3 + 4/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*d^3*e + 2/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*d^2*e^2 + 4/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*d*e^3 + 1/2835*(315*x^9*arcsinh(c*x) - (35*sqrt(c^2*x^2 + 1)*x^8/c^2 - 40*sqrt(c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(c^2*x^2 + 1)*x^4/c^6 - 64*sqrt(c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(c^2*x^2 + 1)/c^10)*c)*b*e^4 + a*d^4*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^4/c","A",0
607,1,287,0,0.355606," ","integrate((e*x^2+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{3} x^{7} + \frac{3}{5} \, a d e^{2} x^{5} + a d^{2} e x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} e + \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d e^{2} + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b e^{3} + a d^{3} x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d^{3}}{c}"," ",0,"1/7*a*e^3*x^7 + 3/5*a*d*e^2*x^5 + a*d^2*e*x^3 + 1/3*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*d^2*e + 1/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*d*e^2 + 1/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*b*e^3 + a*d^3*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^3/c","A",0
608,1,180,0,0.445963," ","integrate((e*x^2+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} x^{5} + \frac{2}{3} \, a d e x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d e + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{2} + a d^{2} x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d^{2}}{c}"," ",0,"1/5*a*e^2*x^5 + 2/3*a*d*e*x^3 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*d*e + 1/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*b*e^2 + a*d^2*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^2/c","A",0
609,1,91,0,0.331398," ","integrate((e*x^2+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b e + a d x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b d}{c}"," ",0,"1/3*a*e*x^3 + 1/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*b*e + a*d*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d/c","A",0
610,1,30,0,0.318872," ","integrate(a+b*arcsinh(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} b}{c}"," ",0,"a*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b/c","A",0
611,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(e*x^2 + d), x) + a*arctan(e*x/sqrt(d*e))/sqrt(d*e)","F",0
612,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
613,1,684,0,0.527278," ","integrate((e*x^2+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} e^{3} x^{7} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{7} \, a^{2} e^{3} x^{7} + \frac{3}{5} \, b^{2} d e^{2} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{5} \, a^{2} d e^{2} x^{5} + b^{2} d^{2} e x^{3} \operatorname{arsinh}\left(c x\right)^{2} + a^{2} d^{2} e x^{3} + b^{2} d^{3} x \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{3} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d^{2} e - \frac{2}{9} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} d^{2} e + \frac{2}{25} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d e^{2} - \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d e^{2} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arsinh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b e^{3} - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} + 1} x^{6}}{c^{2}} - \frac{6 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{6}} - \frac{16 \, \sqrt{c^{2} x^{2} + 1}}{c^{8}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{75 \, c^{6} x^{7} - 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} - 1680 \, x}{c^{6}}\right)} b^{2} e^{3} + 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b d^{3}}{c}"," ",0,"1/7*b^2*e^3*x^7*arcsinh(c*x)^2 + 1/7*a^2*e^3*x^7 + 3/5*b^2*d*e^2*x^5*arcsinh(c*x)^2 + 3/5*a^2*d*e^2*x^5 + b^2*d^2*e*x^3*arcsinh(c*x)^2 + a^2*d^2*e*x^3 + b^2*d^3*x*arcsinh(c*x)^2 + 2/3*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*d^2*e - 2/9*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*d^2*e + 2/25*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*d*e^2 - 2/375*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*d*e^2 + 2/245*(35*x^7*arcsinh(c*x) - (5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c)*a*b*e^3 - 2/25725*(105*(5*sqrt(c^2*x^2 + 1)*x^6/c^2 - 6*sqrt(c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(c^2*x^2 + 1)*x^2/c^6 - 16*sqrt(c^2*x^2 + 1)/c^8)*c*arcsinh(c*x) - (75*c^6*x^7 - 126*c^4*x^5 + 280*c^2*x^3 - 1680*x)/c^6)*b^2*e^3 + 2*b^2*d^3*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*d^3*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*d^3/c","A",0
614,1,429,0,0.503851," ","integrate((e*x^2+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} e^{2} x^{5} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{5} \, a^{2} e^{2} x^{5} + \frac{2}{3} \, b^{2} d e x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{3} \, a^{2} d e x^{3} + b^{2} d^{2} x \operatorname{arsinh}\left(c x\right)^{2} + \frac{4}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d e - \frac{4}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} d e + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arsinh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b e^{2} - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} + 1} x^{4}}{c^{2}} - \frac{4 \, \sqrt{c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} + 1}}{c^{6}}\right)} c \operatorname{arsinh}\left(c x\right) - \frac{9 \, c^{4} x^{5} - 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} e^{2} + 2 \, b^{2} d^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b d^{2}}{c}"," ",0,"1/5*b^2*e^2*x^5*arcsinh(c*x)^2 + 1/5*a^2*e^2*x^5 + 2/3*b^2*d*e*x^3*arcsinh(c*x)^2 + 2/3*a^2*d*e*x^3 + b^2*d^2*x*arcsinh(c*x)^2 + 4/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*d*e - 4/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*d*e + 2/75*(15*x^5*arcsinh(c*x) - (3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c)*a*b*e^2 - 2/1125*(15*(3*sqrt(c^2*x^2 + 1)*x^4/c^2 - 4*sqrt(c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(c^2*x^2 + 1)/c^6)*c*arcsinh(c*x) - (9*c^4*x^5 - 20*c^2*x^3 + 120*x)/c^4)*b^2*e^2 + 2*b^2*d^2*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*d^2*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*d^2/c","A",0
615,1,218,0,0.436077," ","integrate((e*x^2+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} e x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{3} \, a^{2} e x^{3} + b^{2} d x \operatorname{arsinh}\left(c x\right)^{2} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arsinh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b e - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} + 1} x^{2}}{c^{2}} - \frac{2 \, \sqrt{c^{2} x^{2} + 1}}{c^{4}}\right)} \operatorname{arsinh}\left(c x\right) - \frac{c^{2} x^{3} - 6 \, x}{c^{2}}\right)} b^{2} e + 2 \, b^{2} d {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b d}{c}"," ",0,"1/3*b^2*e*x^3*arcsinh(c*x)^2 + 1/3*a^2*e*x^3 + b^2*d*x*arcsinh(c*x)^2 + 2/9*(3*x^3*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4))*a*b*e - 2/27*(3*c*(sqrt(c^2*x^2 + 1)*x^2/c^2 - 2*sqrt(c^2*x^2 + 1)/c^4)*arcsinh(c*x) - (c^2*x^3 - 6*x)/c^2)*b^2*e + 2*b^2*d*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*d*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b*d/c","A",0
616,1,72,0,0.605458," ","integrate((a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","b^{2} x \operatorname{arsinh}\left(c x\right)^{2} + 2 \, b^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} + 1} \operatorname{arsinh}\left(c x\right)}{c}\right)} + a^{2} x + \frac{2 \, {\left(c x \operatorname{arsinh}\left(c x\right) - \sqrt{c^{2} x^{2} + 1}\right)} a b}{c}"," ",0,"b^2*x*arcsinh(c*x)^2 + 2*b^2*(x - sqrt(c^2*x^2 + 1)*arcsinh(c*x)/c) + a^2*x + 2*(c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*a*b/c","A",0
617,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{e x^{2} + d} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"a^2*arctan(e*x/sqrt(d*e))/sqrt(d*e) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(e*x^2 + d) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(e*x^2 + d), x)","F",0
618,0,0,0,0.000000," ","integrate((e*x^2+d)^3/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{3}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^3/(b*arcsinh(c*x) + a), x)","F",0
619,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/(b*arcsinh(c*x) + a), x)","F",0
620,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)/(b*arcsinh(c*x) + a), x)","F",0
621,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsinh(c*x) + a), x)","F",0
622,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*(b*arcsinh(c*x) + a)), x)","F",0
623,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*(b*arcsinh(c*x) + a)), x)","F",0
624,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} e^{2} x^{7} + {\left(2 \, c^{3} d e + c e^{2}\right)} x^{5} + c d^{2} x + {\left(c^{3} d^{2} + 2 \, c d e\right)} x^{3} + {\left(c^{2} e^{2} x^{6} + {\left(2 \, c^{2} d e + e^{2}\right)} x^{4} + {\left(c^{2} d^{2} + 2 \, d e\right)} x^{2} + d^{2}\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{5 \, c^{5} e^{2} x^{8} + 2 \, {\left(3 \, c^{5} d e + 5 \, c^{3} e^{2}\right)} x^{6} + {\left(c^{5} d^{2} + 12 \, c^{3} d e + 5 \, c e^{2}\right)} x^{4} + c d^{2} + 2 \, {\left(c^{3} d^{2} + 3 \, c d e\right)} x^{2} + {\left(5 \, c^{3} e^{2} x^{6} + 3 \, {\left(2 \, c^{3} d e + c e^{2}\right)} x^{4} - c d^{2} + {\left(c^{3} d^{2} + 2 \, c d e\right)} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(10 \, c^{4} e^{2} x^{7} + {\left(12 \, c^{4} d e + 13 \, c^{2} e^{2}\right)} x^{5} + 2 \, {\left(c^{4} d^{2} + 7 \, c^{2} d e + 2 \, e^{2}\right)} x^{3} + {\left(c^{2} d^{2} + 4 \, d e\right)} x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*e^2*x^7 + (2*c^3*d*e + c*e^2)*x^5 + c*d^2*x + (c^3*d^2 + 2*c*d*e)*x^3 + (c^2*e^2*x^6 + (2*c^2*d*e + e^2)*x^4 + (c^2*d^2 + 2*d*e)*x^2 + d^2)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate((5*c^5*e^2*x^8 + 2*(3*c^5*d*e + 5*c^3*e^2)*x^6 + (c^5*d^2 + 12*c^3*d*e + 5*c*e^2)*x^4 + c*d^2 + 2*(c^3*d^2 + 3*c*d*e)*x^2 + (5*c^3*e^2*x^6 + 3*(2*c^3*d*e + c*e^2)*x^4 - c*d^2 + (c^3*d^2 + 2*c*d*e)*x^2)*(c^2*x^2 + 1) + (10*c^4*e^2*x^7 + (12*c^4*d*e + 13*c^2*e^2)*x^5 + 2*(c^4*d^2 + 7*c^2*d*e + 2*e^2)*x^3 + (c^2*d^2 + 4*d*e)*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
625,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} e x^{5} + {\left(c^{3} d + c e\right)} x^{3} + c d x + {\left(c^{2} e x^{4} + {\left(c^{2} d + e\right)} x^{2} + d\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{3 \, c^{5} e x^{6} + {\left(c^{5} d + 6 \, c^{3} e\right)} x^{4} + {\left(2 \, c^{3} d + 3 \, c e\right)} x^{2} + {\left(3 \, c^{3} e x^{4} + {\left(c^{3} d + c e\right)} x^{2} - c d\right)} {\left(c^{2} x^{2} + 1\right)} + c d + {\left(6 \, c^{4} e x^{5} + {\left(2 \, c^{4} d + 7 \, c^{2} e\right)} x^{3} + {\left(c^{2} d + 2 \, e\right)} x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{3} x^{2} + 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{3} x^{2} + 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} x^{3} + a b c^{2} x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*e*x^5 + (c^3*d + c*e)*x^3 + c*d*x + (c^2*e*x^4 + (c^2*d + e)*x^2 + d)*sqrt(c^2*x^2 + 1))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate((3*c^5*e*x^6 + (c^5*d + 6*c^3*e)*x^4 + (2*c^3*d + 3*c*e)*x^2 + (3*c^3*e*x^4 + (c^3*d + c*e)*x^2 - c*d)*(c^2*x^2 + 1) + c*d + (6*c^4*e*x^5 + (2*c^4*d + 7*c^2*e)*x^3 + (c^2*d + 2*e)*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*x^4 + (c^2*x^2 + 1)*a*b*c^3*x^2 + 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 + (c^2*x^2 + 1)*b^2*c^3*x^2 + 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 + b^2*c^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*x^3 + a*b*c^2*x)*sqrt(c^2*x^2 + 1)), x)","F",0
626,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{c^{4} x^{4} + 2 \, c^{2} x^{2} + {\left(c^{2} x^{2} + 1\right)} {\left(c^{2} x^{2} - 1\right)} + {\left(2 \, c^{3} x^{3} + c x\right)} \sqrt{c^{2} x^{2} + 1} + 1}{a b c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} a b c^{2} x^{2} + 2 \, a b c^{2} x^{2} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c^{2} x^{2} + 1\right)} b^{2} c^{2} x^{2} + 2 \, b^{2} c^{2} x^{2} + b^{2} + 2 \, {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{3} x^{3} + a b c x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate((c^4*x^4 + 2*c^2*x^2 + (c^2*x^2 + 1)*(c^2*x^2 - 1) + (2*c^3*x^3 + c*x)*sqrt(c^2*x^2 + 1) + 1)/(a*b*c^4*x^4 + (c^2*x^2 + 1)*a*b*c^2*x^2 + 2*a*b*c^2*x^2 + a*b + (b^2*c^4*x^4 + (c^2*x^2 + 1)*b^2*c^2*x^2 + 2*b^2*c^2*x^2 + b^2 + 2*(b^2*c^3*x^3 + b^2*c*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^3*x^3 + a*b*c*x)*sqrt(c^2*x^2 + 1)), x)","F",0
627,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a b c^{3} e x^{4} + {\left(c^{3} d + c e\right)} a b x^{2} + a b c d + {\left(b^{2} c^{3} e x^{4} + {\left(c^{3} d + c e\right)} b^{2} x^{2} + b^{2} c d + {\left(b^{2} c^{2} e x^{3} + b^{2} c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{2} e x^{3} + a b c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{c^{5} e x^{6} - {\left(c^{5} d - 2 \, c^{3} e\right)} x^{4} - {\left(2 \, c^{3} d - c e\right)} x^{2} + {\left(c^{3} e x^{4} - {\left(c^{3} d - 3 \, c e\right)} x^{2} + c d\right)} {\left(c^{2} x^{2} + 1\right)} - c d + {\left(2 \, c^{4} e x^{5} - {\left(2 \, c^{4} d - 5 \, c^{2} e\right)} x^{3} - {\left(c^{2} d - 2 \, e\right)} x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e + c^{3} e^{2}\right)} a b x^{6} + {\left(c^{5} d^{2} + 4 \, c^{3} d e + c e^{2}\right)} a b x^{4} + a b c d^{2} + 2 \, {\left(c^{3} d^{2} + c d e\right)} a b x^{2} + {\left(a b c^{3} e^{2} x^{6} + 2 \, a b c^{3} d e x^{4} + a b c^{3} d^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e + c^{3} e^{2}\right)} b^{2} x^{6} + {\left(c^{5} d^{2} + 4 \, c^{3} d e + c e^{2}\right)} b^{2} x^{4} + b^{2} c d^{2} + 2 \, {\left(c^{3} d^{2} + c d e\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{2} x^{6} + 2 \, b^{2} c^{3} d e x^{4} + b^{2} c^{3} d^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(b^{2} c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e + c^{2} e^{2}\right)} b^{2} x^{5} + b^{2} c^{2} d^{2} x + {\left(c^{4} d^{2} + 2 \, c^{2} d e\right)} b^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e + c^{2} e^{2}\right)} a b x^{5} + a b c^{2} d^{2} x + {\left(c^{4} d^{2} + 2 \, c^{2} d e\right)} a b x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/(a*b*c^3*e*x^4 + (c^3*d + c*e)*a*b*x^2 + a*b*c*d + (b^2*c^3*e*x^4 + (c^3*d + c*e)*b^2*x^2 + b^2*c*d + (b^2*c^2*e*x^3 + b^2*c^2*d*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^2*e*x^3 + a*b*c^2*d*x)*sqrt(c^2*x^2 + 1)) - integrate((c^5*e*x^6 - (c^5*d - 2*c^3*e)*x^4 - (2*c^3*d - c*e)*x^2 + (c^3*e*x^4 - (c^3*d - 3*c*e)*x^2 + c*d)*(c^2*x^2 + 1) - c*d + (2*c^4*e*x^5 - (2*c^4*d - 5*c^2*e)*x^3 - (c^2*d - 2*e)*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*e^2*x^8 + 2*(c^5*d*e + c^3*e^2)*a*b*x^6 + (c^5*d^2 + 4*c^3*d*e + c*e^2)*a*b*x^4 + a*b*c*d^2 + 2*(c^3*d^2 + c*d*e)*a*b*x^2 + (a*b*c^3*e^2*x^6 + 2*a*b*c^3*d*e*x^4 + a*b*c^3*d^2*x^2)*(c^2*x^2 + 1) + (b^2*c^5*e^2*x^8 + 2*(c^5*d*e + c^3*e^2)*b^2*x^6 + (c^5*d^2 + 4*c^3*d*e + c*e^2)*b^2*x^4 + b^2*c*d^2 + 2*(c^3*d^2 + c*d*e)*b^2*x^2 + (b^2*c^3*e^2*x^6 + 2*b^2*c^3*d*e*x^4 + b^2*c^3*d^2*x^2)*(c^2*x^2 + 1) + 2*(b^2*c^4*e^2*x^7 + (2*c^4*d*e + c^2*e^2)*b^2*x^5 + b^2*c^2*d^2*x + (c^4*d^2 + 2*c^2*d*e)*b^2*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*e^2*x^7 + (2*c^4*d*e + c^2*e^2)*a*b*x^5 + a*b*c^2*d^2*x + (c^4*d^2 + 2*c^2*d*e)*a*b*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
628,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a b c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e + c e^{2}\right)} a b x^{4} + a b c d^{2} + {\left(c^{3} d^{2} + 2 \, c d e\right)} a b x^{2} + {\left(b^{2} c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e + c e^{2}\right)} b^{2} x^{4} + b^{2} c d^{2} + {\left(c^{3} d^{2} + 2 \, c d e\right)} b^{2} x^{2} + {\left(b^{2} c^{2} e^{2} x^{5} + 2 \, b^{2} c^{2} d e x^{3} + b^{2} c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{2} e^{2} x^{5} + 2 \, a b c^{2} d e x^{3} + a b c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{3 \, c^{5} e x^{6} - {\left(c^{5} d - 6 \, c^{3} e\right)} x^{4} - {\left(2 \, c^{3} d - 3 \, c e\right)} x^{2} + {\left(3 \, c^{3} e x^{4} - {\left(c^{3} d - 5 \, c e\right)} x^{2} + c d\right)} {\left(c^{2} x^{2} + 1\right)} - c d + {\left(6 \, c^{4} e x^{5} - {\left(2 \, c^{4} d - 11 \, c^{2} e\right)} x^{3} - {\left(c^{2} d - 4 \, e\right)} x\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} + 2 \, c^{3} e^{3}\right)} a b x^{8} + {\left(3 \, c^{5} d^{2} e + 6 \, c^{3} d e^{2} + c e^{3}\right)} a b x^{6} + {\left(c^{5} d^{3} + 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} a b x^{4} + a b c d^{3} + {\left(2 \, c^{3} d^{3} + 3 \, c d^{2} e\right)} a b x^{2} + {\left(a b c^{3} e^{3} x^{8} + 3 \, a b c^{3} d e^{2} x^{6} + 3 \, a b c^{3} d^{2} e x^{4} + a b c^{3} d^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} + 2 \, c^{3} e^{3}\right)} b^{2} x^{8} + {\left(3 \, c^{5} d^{2} e + 6 \, c^{3} d e^{2} + c e^{3}\right)} b^{2} x^{6} + {\left(c^{5} d^{3} + 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} b^{2} x^{4} + b^{2} c d^{3} + {\left(2 \, c^{3} d^{3} + 3 \, c d^{2} e\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{3} x^{8} + 3 \, b^{2} c^{3} d e^{2} x^{6} + 3 \, b^{2} c^{3} d^{2} e x^{4} + b^{2} c^{3} d^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(b^{2} c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} + c^{2} e^{3}\right)} b^{2} x^{7} + b^{2} c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e + c^{2} d e^{2}\right)} b^{2} x^{5} + {\left(c^{4} d^{3} + 3 \, c^{2} d^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} + c^{2} e^{3}\right)} a b x^{7} + a b c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e + c^{2} d e^{2}\right)} a b x^{5} + {\left(c^{4} d^{3} + 3 \, c^{2} d^{2} e\right)} a b x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/(a*b*c^3*e^2*x^6 + (2*c^3*d*e + c*e^2)*a*b*x^4 + a*b*c*d^2 + (c^3*d^2 + 2*c*d*e)*a*b*x^2 + (b^2*c^3*e^2*x^6 + (2*c^3*d*e + c*e^2)*b^2*x^4 + b^2*c*d^2 + (c^3*d^2 + 2*c*d*e)*b^2*x^2 + (b^2*c^2*e^2*x^5 + 2*b^2*c^2*d*e*x^3 + b^2*c^2*d^2*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^2*e^2*x^5 + 2*a*b*c^2*d*e*x^3 + a*b*c^2*d^2*x)*sqrt(c^2*x^2 + 1)) - integrate((3*c^5*e*x^6 - (c^5*d - 6*c^3*e)*x^4 - (2*c^3*d - 3*c*e)*x^2 + (3*c^3*e*x^4 - (c^3*d - 5*c*e)*x^2 + c*d)*(c^2*x^2 + 1) - c*d + (6*c^4*e*x^5 - (2*c^4*d - 11*c^2*e)*x^3 - (c^2*d - 4*e)*x)*sqrt(c^2*x^2 + 1))/(a*b*c^5*e^3*x^10 + (3*c^5*d*e^2 + 2*c^3*e^3)*a*b*x^8 + (3*c^5*d^2*e + 6*c^3*d*e^2 + c*e^3)*a*b*x^6 + (c^5*d^3 + 6*c^3*d^2*e + 3*c*d*e^2)*a*b*x^4 + a*b*c*d^3 + (2*c^3*d^3 + 3*c*d^2*e)*a*b*x^2 + (a*b*c^3*e^3*x^8 + 3*a*b*c^3*d*e^2*x^6 + 3*a*b*c^3*d^2*e*x^4 + a*b*c^3*d^3*x^2)*(c^2*x^2 + 1) + (b^2*c^5*e^3*x^10 + (3*c^5*d*e^2 + 2*c^3*e^3)*b^2*x^8 + (3*c^5*d^2*e + 6*c^3*d*e^2 + c*e^3)*b^2*x^6 + (c^5*d^3 + 6*c^3*d^2*e + 3*c*d*e^2)*b^2*x^4 + b^2*c*d^3 + (2*c^3*d^3 + 3*c*d^2*e)*b^2*x^2 + (b^2*c^3*e^3*x^8 + 3*b^2*c^3*d*e^2*x^6 + 3*b^2*c^3*d^2*e*x^4 + b^2*c^3*d^3*x^2)*(c^2*x^2 + 1) + 2*(b^2*c^4*e^3*x^9 + (3*c^4*d*e^2 + c^2*e^3)*b^2*x^7 + b^2*c^2*d^3*x + 3*(c^4*d^2*e + c^2*d*e^2)*b^2*x^5 + (c^4*d^3 + 3*c^2*d^2*e)*b^2*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*e^3*x^9 + (3*c^4*d*e^2 + c^2*e^3)*a*b*x^7 + a*b*c^2*d^3*x + 3*(c^4*d^2*e + c^2*d*e^2)*a*b*x^5 + (c^4*d^3 + 3*c^2*d^2*e)*a*b*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
629,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{2} \sqrt{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*sqrt(b*arcsinh(c*x) + a), x)","F",0
630,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)} \sqrt{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)*sqrt(b*arcsinh(c*x) + a), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(c*x) + a), x)","F",0
632,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^(1/2)/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{\sqrt{b \operatorname{arsinh}\left(c x\right) + a}}{e x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(c*x) + a)/(e*x^2 + d), x)","F",0
633,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^(1/2)/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{b \operatorname{arsinh}\left(c x\right) + a}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(c*x) + a)/(e*x^2 + d)^2, x)","F",0
634,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arcsinh(c*x) + a)^(3/2), x)","F",0
635,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^(3/2), x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^(3/2)/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^(3/2)/(e*x^2 + d), x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^(3/2)/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^(3/2)/(e*x^2 + d)^2, x)","F",0
638,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{b \operatorname{arsinh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(b*arcsinh(c*x) + a), x)","F",0
639,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{\sqrt{b \operatorname{arsinh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(b*arcsinh(c*x) + a), x)","F",0
640,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arsinh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsinh(c*x) + a), x)","F",0
641,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} \sqrt{b \operatorname{arsinh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*sqrt(b*arcsinh(c*x) + a)), x)","F",0
642,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} \sqrt{b \operatorname{arsinh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*sqrt(b*arcsinh(c*x) + a)), x)","F",0
643,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)/(b*arcsinh(c*x) + a)^(3/2), x)","F",0
644,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^(-3/2), x)","F",0
645,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*(b*arcsinh(c*x) + a)^(3/2)), x)","F",0
646,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsinh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*(b*arcsinh(c*x) + a)^(3/2)), x)","F",0
647,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
648,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{e x^{2} + d}}\,{d x} + \frac{a \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}"," ",0,"b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/sqrt(e*x^2 + d), x) + a*arcsinh(e*x/sqrt(d*e))/sqrt(e)","F",0
649,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
650,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(e*x^2 + d)^(5/2), x)","F",0
651,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x^2+d)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{8 \, x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} + \frac{3 \, x}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"1/15*a*(8*x/(sqrt(e*x^2 + d)*d^3) + 4*x/((e*x^2 + d)^(3/2)*d^2) + 3*x/((e*x^2 + d)^(5/2)*d)) + b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(e*x^2 + d)^(7/2), x)","F",0
652,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
653,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{a^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{\sqrt{e x^{2} + d}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"a^2*arcsinh(e*x/sqrt(d*e))/sqrt(e) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/sqrt(e*x^2 + d) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/sqrt(e*x^2 + d), x)","F",0
654,-2,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
655,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a^2*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(e*x^2 + d)^(5/2) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(e*x^2 + d)^(5/2), x)","F",0
656,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{e x^{2} + d}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)/(b*arcsinh(c*x) + a), x)","F",0
657,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e x^{2} + d} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*x^2 + d)*(b*arcsinh(c*x) + a)), x)","F",0
658,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^(3/2)*(b*arcsinh(c*x) + a)), x)","F",0
659,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^(5/2)*(b*arcsinh(c*x) + a)), x)","F",0
660,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{e x^{2} + d} + {\left(c^{3} x^{3} + c x\right)} \sqrt{e x^{2} + d}}{a b c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} a b c^{2} x + a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c^{2} x^{2} + 1} b^{2} c^{2} x + b^{2} c\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)} + \int \frac{{\left(2 \, c^{3} e x^{4} + c^{3} d x^{2} - c d\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + {\left(4 \, c^{4} e x^{5} + 2 \, {\left(c^{4} d + 2 \, c^{2} e\right)} x^{3} + {\left(c^{2} d + e\right)} x\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left(2 \, c^{5} e x^{6} + {\left(c^{5} d + 4 \, c^{3} e\right)} x^{4} + 2 \, {\left(c^{3} d + c e\right)} x^{2} + c d\right)} \sqrt{e x^{2} + d}}{a b c^{5} e x^{6} + {\left(c^{5} d + 2 \, c^{3} e\right)} a b x^{4} + {\left(2 \, c^{3} d + c e\right)} a b x^{2} + a b c d + {\left(a b c^{3} e x^{4} + a b c^{3} d x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} e x^{6} + {\left(c^{5} d + 2 \, c^{3} e\right)} b^{2} x^{4} + {\left(2 \, c^{3} d + c e\right)} b^{2} x^{2} + b^{2} c d + {\left(b^{2} c^{3} e x^{4} + b^{2} c^{3} d x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(b^{2} c^{4} e x^{5} + b^{2} c^{2} d x + {\left(c^{4} d + c^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + 2 \, {\left(a b c^{4} e x^{5} + a b c^{2} d x + {\left(c^{4} d + c^{2} e\right)} a b x^{3}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^(3/2)*sqrt(e*x^2 + d) + (c^3*x^3 + c*x)*sqrt(e*x^2 + d))/(a*b*c^3*x^2 + sqrt(c^2*x^2 + 1)*a*b*c^2*x + a*b*c + (b^2*c^3*x^2 + sqrt(c^2*x^2 + 1)*b^2*c^2*x + b^2*c)*log(c*x + sqrt(c^2*x^2 + 1))) + integrate(((2*c^3*e*x^4 + c^3*d*x^2 - c*d)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (4*c^4*e*x^5 + 2*(c^4*d + 2*c^2*e)*x^3 + (c^2*d + e)*x)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (2*c^5*e*x^6 + (c^5*d + 4*c^3*e)*x^4 + 2*(c^3*d + c*e)*x^2 + c*d)*sqrt(e*x^2 + d))/(a*b*c^5*e*x^6 + (c^5*d + 2*c^3*e)*a*b*x^4 + (2*c^3*d + c*e)*a*b*x^2 + a*b*c*d + (a*b*c^3*e*x^4 + a*b*c^3*d*x^2)*(c^2*x^2 + 1) + (b^2*c^5*e*x^6 + (c^5*d + 2*c^3*e)*b^2*x^4 + (2*c^3*d + c*e)*b^2*x^2 + b^2*c*d + (b^2*c^3*e*x^4 + b^2*c^3*d*x^2)*(c^2*x^2 + 1) + 2*(b^2*c^4*e*x^5 + b^2*c^2*d*x + (c^4*d + c^2*e)*b^2*x^3)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*e*x^5 + a*b*c^2*d*x + (c^4*d + c^2*e)*a*b*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
661,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(c*x))^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{\sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} a b c^{2} x + {\left(\sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{e x^{2} + d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} x^{2} + a b c\right)} \sqrt{e x^{2} + d}} + \int \frac{c^{5} d x^{4} + 2 \, c^{3} d x^{2} + {\left(c^{2} x^{2} + 1\right)} {\left({\left(c^{3} d - 2 \, c e\right)} x^{2} - c d\right)} + c d + \sqrt{c^{2} x^{2} + 1} {\left(2 \, {\left(c^{4} d - c^{2} e\right)} x^{3} + {\left(c^{2} d - e\right)} x\right)}}{{\left(a b c^{3} e x^{4} + a b c^{3} d x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + 2 \, {\left(a b c^{4} e x^{5} + a b c^{2} d x + {\left(c^{4} d + c^{2} e\right)} a b x^{3}\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left({\left(b^{2} c^{3} e x^{4} + b^{2} c^{3} d x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + 2 \, {\left(b^{2} c^{4} e x^{5} + b^{2} c^{2} d x + {\left(c^{4} d + c^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left(b^{2} c^{5} e x^{6} + {\left(c^{5} d + 2 \, c^{3} e\right)} b^{2} x^{4} + {\left(2 \, c^{3} d + c e\right)} b^{2} x^{2} + b^{2} c d\right)} \sqrt{e x^{2} + d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} e x^{6} + {\left(c^{5} d + 2 \, c^{3} e\right)} a b x^{4} + {\left(2 \, c^{3} d + c e\right)} a b x^{2} + a b c d\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/(sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d)*a*b*c^2*x + (sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d)*b^2*c^2*x + (b^2*c^3*x^2 + b^2*c)*sqrt(e*x^2 + d))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*x^2 + a*b*c)*sqrt(e*x^2 + d)) + integrate((c^5*d*x^4 + 2*c^3*d*x^2 + (c^2*x^2 + 1)*((c^3*d - 2*c*e)*x^2 - c*d) + c*d + sqrt(c^2*x^2 + 1)*(2*(c^4*d - c^2*e)*x^3 + (c^2*d - e)*x))/((a*b*c^3*e*x^4 + a*b*c^3*d*x^2)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + 2*(a*b*c^4*e*x^5 + a*b*c^2*d*x + (c^4*d + c^2*e)*a*b*x^3)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + ((b^2*c^3*e*x^4 + b^2*c^3*d*x^2)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + 2*(b^2*c^4*e*x^5 + b^2*c^2*d*x + (c^4*d + c^2*e)*b^2*x^3)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (b^2*c^5*e*x^6 + (c^5*d + 2*c^3*e)*b^2*x^4 + (2*c^3*d + c*e)*b^2*x^2 + b^2*c*d)*sqrt(e*x^2 + d))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*e*x^6 + (c^5*d + 2*c^3*e)*a*b*x^4 + (2*c^3*d + c*e)*a*b*x^2 + a*b*c*d)*sqrt(e*x^2 + d)), x)","F",0
662,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a b c^{2} e x^{3} + a b c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left({\left(b^{2} c^{2} e x^{3} + b^{2} c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left(b^{2} c^{3} e x^{4} + {\left(c^{3} d + c e\right)} b^{2} x^{2} + b^{2} c d\right)} \sqrt{e x^{2} + d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} e x^{4} + {\left(c^{3} d + c e\right)} a b x^{2} + a b c d\right)} \sqrt{e x^{2} + d}} - \int \frac{2 \, c^{5} e x^{6} - {\left(c^{5} d - 4 \, c^{3} e\right)} x^{4} - 2 \, {\left(c^{3} d - c e\right)} x^{2} + {\left(2 \, c^{3} e x^{4} - {\left(c^{3} d - 4 \, c e\right)} x^{2} + c d\right)} {\left(c^{2} x^{2} + 1\right)} - c d + {\left(4 \, c^{4} e x^{5} - 2 \, {\left(c^{4} d - 4 \, c^{2} e\right)} x^{3} - {\left(c^{2} d - 3 \, e\right)} x\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{3} e^{2} x^{6} + 2 \, a b c^{3} d e x^{4} + a b c^{3} d^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + 2 \, {\left(a b c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e + c^{2} e^{2}\right)} a b x^{5} + a b c^{2} d^{2} x + {\left(c^{4} d^{2} + 2 \, c^{2} d e\right)} a b x^{3}\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left({\left(b^{2} c^{3} e^{2} x^{6} + 2 \, b^{2} c^{3} d e x^{4} + b^{2} c^{3} d^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + 2 \, {\left(b^{2} c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e + c^{2} e^{2}\right)} b^{2} x^{5} + b^{2} c^{2} d^{2} x + {\left(c^{4} d^{2} + 2 \, c^{2} d e\right)} b^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left(b^{2} c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e + c^{3} e^{2}\right)} b^{2} x^{6} + {\left(c^{5} d^{2} + 4 \, c^{3} d e + c e^{2}\right)} b^{2} x^{4} + b^{2} c d^{2} + 2 \, {\left(c^{3} d^{2} + c d e\right)} b^{2} x^{2}\right)} \sqrt{e x^{2} + d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e + c^{3} e^{2}\right)} a b x^{6} + {\left(c^{5} d^{2} + 4 \, c^{3} d e + c e^{2}\right)} a b x^{4} + a b c d^{2} + 2 \, {\left(c^{3} d^{2} + c d e\right)} a b x^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/((a*b*c^2*e*x^3 + a*b*c^2*d*x)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + ((b^2*c^2*e*x^3 + b^2*c^2*d*x)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (b^2*c^3*e*x^4 + (c^3*d + c*e)*b^2*x^2 + b^2*c*d)*sqrt(e*x^2 + d))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*e*x^4 + (c^3*d + c*e)*a*b*x^2 + a*b*c*d)*sqrt(e*x^2 + d)) - integrate((2*c^5*e*x^6 - (c^5*d - 4*c^3*e)*x^4 - 2*(c^3*d - c*e)*x^2 + (2*c^3*e*x^4 - (c^3*d - 4*c*e)*x^2 + c*d)*(c^2*x^2 + 1) - c*d + (4*c^4*e*x^5 - 2*(c^4*d - 4*c^2*e)*x^3 - (c^2*d - 3*e)*x)*sqrt(c^2*x^2 + 1))/((a*b*c^3*e^2*x^6 + 2*a*b*c^3*d*e*x^4 + a*b*c^3*d^2*x^2)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + 2*(a*b*c^4*e^2*x^7 + (2*c^4*d*e + c^2*e^2)*a*b*x^5 + a*b*c^2*d^2*x + (c^4*d^2 + 2*c^2*d*e)*a*b*x^3)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + ((b^2*c^3*e^2*x^6 + 2*b^2*c^3*d*e*x^4 + b^2*c^3*d^2*x^2)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + 2*(b^2*c^4*e^2*x^7 + (2*c^4*d*e + c^2*e^2)*b^2*x^5 + b^2*c^2*d^2*x + (c^4*d^2 + 2*c^2*d*e)*b^2*x^3)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (b^2*c^5*e^2*x^8 + 2*(c^5*d*e + c^3*e^2)*b^2*x^6 + (c^5*d^2 + 4*c^3*d*e + c*e^2)*b^2*x^4 + b^2*c*d^2 + 2*(c^3*d^2 + c*d*e)*b^2*x^2)*sqrt(e*x^2 + d))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*e^2*x^8 + 2*(c^5*d*e + c^3*e^2)*a*b*x^6 + (c^5*d^2 + 4*c^3*d*e + c*e^2)*a*b*x^4 + a*b*c*d^2 + 2*(c^3*d^2 + c*d*e)*a*b*x^2)*sqrt(e*x^2 + d)), x)","F",0
663,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + c x + {\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a b c^{2} e^{2} x^{5} + 2 \, a b c^{2} d e x^{3} + a b c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left({\left(b^{2} c^{2} e^{2} x^{5} + 2 \, b^{2} c^{2} d e x^{3} + b^{2} c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left(b^{2} c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e + c e^{2}\right)} b^{2} x^{4} + b^{2} c d^{2} + {\left(c^{3} d^{2} + 2 \, c d e\right)} b^{2} x^{2}\right)} \sqrt{e x^{2} + d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e + c e^{2}\right)} a b x^{4} + a b c d^{2} + {\left(c^{3} d^{2} + 2 \, c d e\right)} a b x^{2}\right)} \sqrt{e x^{2} + d}} - \int \frac{4 \, c^{5} e x^{6} - {\left(c^{5} d - 8 \, c^{3} e\right)} x^{4} - 2 \, {\left(c^{3} d - 2 \, c e\right)} x^{2} + {\left(4 \, c^{3} e x^{4} - {\left(c^{3} d - 6 \, c e\right)} x^{2} + c d\right)} {\left(c^{2} x^{2} + 1\right)} - c d + {\left(8 \, c^{4} e x^{5} - 2 \, {\left(c^{4} d - 7 \, c^{2} e\right)} x^{3} - {\left(c^{2} d - 5 \, e\right)} x\right)} \sqrt{c^{2} x^{2} + 1}}{{\left(a b c^{3} e^{3} x^{8} + 3 \, a b c^{3} d e^{2} x^{6} + 3 \, a b c^{3} d^{2} e x^{4} + a b c^{3} d^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + 2 \, {\left(a b c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} + c^{2} e^{3}\right)} a b x^{7} + a b c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e + c^{2} d e^{2}\right)} a b x^{5} + {\left(c^{4} d^{3} + 3 \, c^{2} d^{2} e\right)} a b x^{3}\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left({\left(b^{2} c^{3} e^{3} x^{8} + 3 \, b^{2} c^{3} d e^{2} x^{6} + 3 \, b^{2} c^{3} d^{2} e x^{4} + b^{2} c^{3} d^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} \sqrt{e x^{2} + d} + 2 \, {\left(b^{2} c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} + c^{2} e^{3}\right)} b^{2} x^{7} + b^{2} c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e + c^{2} d e^{2}\right)} b^{2} x^{5} + {\left(c^{4} d^{3} + 3 \, c^{2} d^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c^{2} x^{2} + 1} \sqrt{e x^{2} + d} + {\left(b^{2} c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} + 2 \, c^{3} e^{3}\right)} b^{2} x^{8} + {\left(3 \, c^{5} d^{2} e + 6 \, c^{3} d e^{2} + c e^{3}\right)} b^{2} x^{6} + {\left(c^{5} d^{3} + 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} b^{2} x^{4} + b^{2} c d^{3} + {\left(2 \, c^{3} d^{3} + 3 \, c d^{2} e\right)} b^{2} x^{2}\right)} \sqrt{e x^{2} + d}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right) + {\left(a b c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} + 2 \, c^{3} e^{3}\right)} a b x^{8} + {\left(3 \, c^{5} d^{2} e + 6 \, c^{3} d e^{2} + c e^{3}\right)} a b x^{6} + {\left(c^{5} d^{3} + 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} a b x^{4} + a b c d^{3} + {\left(2 \, c^{3} d^{3} + 3 \, c d^{2} e\right)} a b x^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-(c^3*x^3 + c*x + (c^2*x^2 + 1)^(3/2))/((a*b*c^2*e^2*x^5 + 2*a*b*c^2*d*e*x^3 + a*b*c^2*d^2*x)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + ((b^2*c^2*e^2*x^5 + 2*b^2*c^2*d*e*x^3 + b^2*c^2*d^2*x)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (b^2*c^3*e^2*x^6 + (2*c^3*d*e + c*e^2)*b^2*x^4 + b^2*c*d^2 + (c^3*d^2 + 2*c*d*e)*b^2*x^2)*sqrt(e*x^2 + d))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^3*e^2*x^6 + (2*c^3*d*e + c*e^2)*a*b*x^4 + a*b*c*d^2 + (c^3*d^2 + 2*c*d*e)*a*b*x^2)*sqrt(e*x^2 + d)) - integrate((4*c^5*e*x^6 - (c^5*d - 8*c^3*e)*x^4 - 2*(c^3*d - 2*c*e)*x^2 + (4*c^3*e*x^4 - (c^3*d - 6*c*e)*x^2 + c*d)*(c^2*x^2 + 1) - c*d + (8*c^4*e*x^5 - 2*(c^4*d - 7*c^2*e)*x^3 - (c^2*d - 5*e)*x)*sqrt(c^2*x^2 + 1))/((a*b*c^3*e^3*x^8 + 3*a*b*c^3*d*e^2*x^6 + 3*a*b*c^3*d^2*e*x^4 + a*b*c^3*d^3*x^2)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + 2*(a*b*c^4*e^3*x^9 + (3*c^4*d*e^2 + c^2*e^3)*a*b*x^7 + a*b*c^2*d^3*x + 3*(c^4*d^2*e + c^2*d*e^2)*a*b*x^5 + (c^4*d^3 + 3*c^2*d^2*e)*a*b*x^3)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + ((b^2*c^3*e^3*x^8 + 3*b^2*c^3*d*e^2*x^6 + 3*b^2*c^3*d^2*e*x^4 + b^2*c^3*d^3*x^2)*(c^2*x^2 + 1)*sqrt(e*x^2 + d) + 2*(b^2*c^4*e^3*x^9 + (3*c^4*d*e^2 + c^2*e^3)*b^2*x^7 + b^2*c^2*d^3*x + 3*(c^4*d^2*e + c^2*d*e^2)*b^2*x^5 + (c^4*d^3 + 3*c^2*d^2*e)*b^2*x^3)*sqrt(c^2*x^2 + 1)*sqrt(e*x^2 + d) + (b^2*c^5*e^3*x^10 + (3*c^5*d*e^2 + 2*c^3*e^3)*b^2*x^8 + (3*c^5*d^2*e + 6*c^3*d*e^2 + c*e^3)*b^2*x^6 + (c^5*d^3 + 6*c^3*d^2*e + 3*c*d*e^2)*b^2*x^4 + b^2*c*d^3 + (2*c^3*d^3 + 3*c*d^2*e)*b^2*x^2)*sqrt(e*x^2 + d))*log(c*x + sqrt(c^2*x^2 + 1)) + (a*b*c^5*e^3*x^10 + (3*c^5*d*e^2 + 2*c^3*e^3)*a*b*x^8 + (3*c^5*d^2*e + 6*c^3*d*e^2 + c*e^3)*a*b*x^6 + (c^5*d^3 + 6*c^3*d^2*e + 3*c*d*e^2)*a*b*x^4 + a*b*c*d^3 + (2*c^3*d^3 + 3*c*d^2*e)*a*b*x^2)*sqrt(e*x^2 + d)), x)","F",0
