1,0,0,0,0.000000," ","integrate(arcsinh(c*x)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(c x\right)}{e x + d}\,{d x}"," ",0,"integrate(arcsinh(c*x)/(e*x + d), x)","F",0
2,0,0,0,0.000000," ","integrate(arcsinh(c*x)^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(c x\right)^{2}}{e x + d}\,{d x}"," ",0,"integrate(arcsinh(c*x)^2/(e*x + d), x)","F",0
3,0,0,0,0.000000," ","integrate(arcsinh(c*x)^3/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(c x\right)^{3}}{e x + d}\,{d x}"," ",0,"integrate(arcsinh(c*x)^3/(e*x + d), x)","F",0
4,1,230,0,0.395844," ","integrate((e*x+d)^3*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + a d e^{2} x^{3} + \frac{3}{2} \, a d^{2} e x^{2} + \frac{3}{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} e + \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 e^{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 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,"1/4*a*e^3*x^4 + a*d*e^2*x^3 + 3/2*a*d^2*e*x^2 + 3/4*(2*x^2*arcsinh(c*x) - c*(sqrt(c^2*x^2 + 1)*x/c^2 - arcsinh(c*x)/c^3))*b*d^2*e + 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*e^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*e^3 + a*d^3*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^3/c","A",0
5,1,150,0,0.403690," ","integrate((e*x+d)^2*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e 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)} b d e + \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^{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,"1/3*a*e^2*x^3 + a*d*e*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))*b*d*e + 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^2 + a*d^2*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d^2/c","A",0
6,1,82,0,0.369712," ","integrate((e*x+d)*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e 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 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,"1/2*a*e*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*e + a*d*x + (c*x*arcsinh(c*x) - sqrt(c^2*x^2 + 1))*b*d/c","A",0
7,1,30,0,0.402199," ","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
8,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x+d),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"b*integrate(log(c*x + sqrt(c^2*x^2 + 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
9,1,94,0,0.457134," ","integrate((a+b*arcsinh(c*x))/(e*x+d)^2,x, algorithm=""maxima"")","-b {\left(\frac{\operatorname{arsinh}\left(c x\right)}{e^{2} x + d e} - \frac{c \operatorname{arsinh}\left(\frac{c d e x}{{\left| e^{2} x + d e \right|}} - \frac{e^{2}}{c {\left| e^{2} x + d e \right|}}\right)}{\sqrt{\frac{c^{2} d^{2}}{e^{2}} + 1} e^{2}}\right)} - \frac{a}{e^{2} x + d e}"," ",0,"-b*(arcsinh(c*x)/(e^2*x + d*e) - c*arcsinh(c*d*e*x/abs(e^2*x + d*e) - e^2/(c*abs(e^2*x + d*e)))/(sqrt(c^2*d^2/e^2 + 1)*e^2)) - a/(e^2*x + d*e)","A",0
10,1,158,0,0.389810," ","integrate((a+b*arcsinh(c*x))/(e*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\frac{\sqrt{c^{2} x^{2} + 1}}{c^{2} d^{2} e x + c^{2} d^{3} + e^{3} x + d e^{2}} - \frac{c^{2} d \operatorname{arsinh}\left(\frac{c d x}{e {\left| x + \frac{d}{e} \right|}} - \frac{1}{c {\left| x + \frac{d}{e} \right|}}\right)}{{\left(\frac{c^{2} d^{2}}{e^{2}} + 1\right)}^{\frac{3}{2}} e^{4}}\right)} + \frac{\operatorname{arsinh}\left(c x\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} b - \frac{a}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/2*(c*(sqrt(c^2*x^2 + 1)/(c^2*d^2*e*x + c^2*d^3 + e^3*x + d*e^2) - c^2*d*arcsinh(c*d*x/(e*abs(x + d/e)) - 1/(c*abs(x + d/e)))/((c^2*d^2/e^2 + 1)^(3/2)*e^4)) + arcsinh(c*x)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*b - 1/2*a/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
11,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(6 \, c \int \frac{1}{3 \, {\left(c^{3} e^{4} x^{6} + 3 \, c^{3} d e^{3} x^{5} + 3 \, c d^{2} e^{2} x^{2} + c d^{3} e x + {\left(3 \, c^{3} d^{2} e^{2} + c e^{4}\right)} x^{4} + {\left(c^{3} d^{3} e + 3 \, c d e^{3}\right)} x^{3} + {\left(c^{2} e^{4} x^{5} + 3 \, c^{2} d e^{3} x^{4} + 3 \, d^{2} e^{2} x + d^{3} e + {\left(3 \, c^{2} d^{2} e^{2} + e^{4}\right)} x^{3} + {\left(c^{2} d^{3} e + 3 \, d e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}\right)}}\,{d x} - \frac{2 \, {\left(c^{6} d^{3} - 3 \, c^{4} d e^{2}\right)} \log\left(e x + d\right)}{c^{6} d^{6} e + 3 \, c^{4} d^{4} e^{3} + 3 \, c^{2} d^{2} e^{5} + e^{7}} + \frac{3 \, c^{6} d^{6} + 2 \, c^{4} d^{4} e^{2} - c^{2} d^{2} e^{4} + 2 \, {\left(c^{6} d^{4} e^{2} - c^{2} e^{6}\right)} x^{2} + {\left(5 \, c^{6} d^{5} e + 2 \, c^{4} d^{3} e^{3} - 3 \, c^{2} d e^{5}\right)} x + {\left(c^{6} d^{6} - 3 \, c^{4} d^{4} e^{2} + {\left(c^{6} d^{3} e^{3} - 3 \, c^{4} d e^{5}\right)} x^{3} + 3 \, {\left(c^{6} d^{4} e^{2} - 3 \, c^{4} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(c^{6} d^{5} e - 3 \, c^{4} d^{3} e^{3}\right)} x\right)} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(c^{6} d^{6} + 3 \, c^{4} d^{4} e^{2} + 3 \, c^{2} d^{2} e^{4} + e^{6}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{6} d^{9} e + 3 \, c^{4} d^{7} e^{3} + 3 \, c^{2} d^{5} e^{5} + d^{3} e^{7} + {\left(c^{6} d^{6} e^{4} + 3 \, c^{4} d^{4} e^{6} + 3 \, c^{2} d^{2} e^{8} + e^{10}\right)} x^{3} + 3 \, {\left(c^{6} d^{7} e^{3} + 3 \, c^{4} d^{5} e^{5} + 3 \, c^{2} d^{3} e^{7} + d e^{9}\right)} x^{2} + 3 \, {\left(c^{6} d^{8} e^{2} + 3 \, c^{4} d^{6} e^{4} + 3 \, c^{2} d^{4} e^{6} + d^{2} e^{8}\right)} x} - \frac{i \, {\left(3 \, c^{6} d^{2} - c^{4} e^{2}\right)} {\left(\log\left(i \, c x + 1\right) - \log\left(-i \, c x + 1\right)\right)}}{{\left(c^{6} d^{6} + 3 \, c^{4} d^{4} e^{2} + 3 \, c^{2} d^{2} e^{4} + e^{6}\right)} c}\right)} b - \frac{a}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"1/6*(6*c*integrate(1/3/(c^3*e^4*x^6 + 3*c^3*d*e^3*x^5 + 3*c*d^2*e^2*x^2 + c*d^3*e*x + (3*c^3*d^2*e^2 + c*e^4)*x^4 + (c^3*d^3*e + 3*c*d*e^3)*x^3 + (c^2*e^4*x^5 + 3*c^2*d*e^3*x^4 + 3*d^2*e^2*x + d^3*e + (3*c^2*d^2*e^2 + e^4)*x^3 + (c^2*d^3*e + 3*d*e^3)*x^2)*sqrt(c^2*x^2 + 1)), x) - 2*(c^6*d^3 - 3*c^4*d*e^2)*log(e*x + d)/(c^6*d^6*e + 3*c^4*d^4*e^3 + 3*c^2*d^2*e^5 + e^7) + (3*c^6*d^6 + 2*c^4*d^4*e^2 - c^2*d^2*e^4 + 2*(c^6*d^4*e^2 - c^2*e^6)*x^2 + (5*c^6*d^5*e + 2*c^4*d^3*e^3 - 3*c^2*d*e^5)*x + (c^6*d^6 - 3*c^4*d^4*e^2 + (c^6*d^3*e^3 - 3*c^4*d*e^5)*x^3 + 3*(c^6*d^4*e^2 - 3*c^4*d^2*e^4)*x^2 + 3*(c^6*d^5*e - 3*c^4*d^3*e^3)*x)*log(c^2*x^2 + 1) - 2*(c^6*d^6 + 3*c^4*d^4*e^2 + 3*c^2*d^2*e^4 + e^6)*log(c*x + sqrt(c^2*x^2 + 1)))/(c^6*d^9*e + 3*c^4*d^7*e^3 + 3*c^2*d^5*e^5 + d^3*e^7 + (c^6*d^6*e^4 + 3*c^4*d^4*e^6 + 3*c^2*d^2*e^8 + e^10)*x^3 + 3*(c^6*d^7*e^3 + 3*c^4*d^5*e^5 + 3*c^2*d^3*e^7 + d*e^9)*x^2 + 3*(c^6*d^8*e^2 + 3*c^4*d^6*e^4 + 3*c^2*d^4*e^6 + d^2*e^8)*x) - I*(3*c^6*d^2 - c^4*e^2)*(log(I*c*x + 1) - log(-I*c*x + 1))/((c^6*d^6 + 3*c^4*d^4*e^2 + 3*c^2*d^2*e^4 + e^6)*c))*b - 1/3*a/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","F",0
12,1,590,0,0.503266," ","integrate((e*x+d)^3*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} e^{3} x^{4} \operatorname{arsinh}\left(c x\right)^{2} + b^{2} d e^{2} x^{3} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} e^{3} x^{4} + \frac{3}{2} \, b^{2} d^{2} e x^{2} \operatorname{arsinh}\left(c x\right)^{2} + a^{2} d e^{2} x^{3} + b^{2} d^{3} x \operatorname{arsinh}\left(c x\right)^{2} + \frac{3}{2} \, a^{2} d^{2} e x^{2} + \frac{3}{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} e + \frac{3}{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} e + \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 e^{2} - \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 e^{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 e^{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} 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,"1/4*b^2*e^3*x^4*arcsinh(c*x)^2 + b^2*d*e^2*x^3*arcsinh(c*x)^2 + 1/4*a^2*e^3*x^4 + 3/2*b^2*d^2*e*x^2*arcsinh(c*x)^2 + a^2*d*e^2*x^3 + b^2*d^3*x*arcsinh(c*x)^2 + 3/2*a^2*d^2*e*x^2 + 3/2*(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*e + 3/4*(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*e + 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*e^2 - 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*e^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*e^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*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
13,1,378,0,0.430387," ","integrate((e*x+d)^2*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} e^{2} x^{3} \operatorname{arsinh}\left(c x\right)^{2} + b^{2} d e x^{2} \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{3} \, a^{2} e^{2} x^{3} + b^{2} d^{2} x \operatorname{arsinh}\left(c x\right)^{2} + a^{2} d e x^{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 e + \frac{1}{2} \, {\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 e + \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^{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} 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,"1/3*b^2*e^2*x^3*arcsinh(c*x)^2 + b^2*d*e*x^2*arcsinh(c*x)^2 + 1/3*a^2*e^2*x^3 + b^2*d^2*x*arcsinh(c*x)^2 + a^2*d*e*x^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*e + 1/2*(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*e + 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 - 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 + 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
14,1,219,0,0.369016," ","integrate((e*x+d)*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} e x^{2} \operatorname{arsinh}\left(c x\right)^{2} + b^{2} d x \operatorname{arsinh}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} e 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 e + \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} 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,"1/2*b^2*e*x^2*arcsinh(c*x)^2 + b^2*d*x*arcsinh(c*x)^2 + 1/2*a^2*e*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*e + 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*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
15,1,72,0,0.333742," ","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
16,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{b^{2} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{e x + d} + \frac{2 \, a b \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{e x + d}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(b^2*log(c*x + sqrt(c^2*x^2 + 1))^2/(e*x + d) + 2*a*b*log(c*x + sqrt(c^2*x^2 + 1))/(e*x + d), x)","F",0
17,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x+d)^2,x, algorithm=""maxima"")","-b^{2} {\left(\frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{e^{2} x + d e} - \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} e^{2} x^{4} + c^{3} d e x^{3} + c e^{2} x^{2} + c d e x + {\left(c^{2} e^{2} x^{3} + c^{2} d e x^{2} + e^{2} x + d e\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} - 2 \, a b {\left(\frac{\operatorname{arsinh}\left(c x\right)}{e^{2} x + d e} - \frac{c \operatorname{arsinh}\left(\frac{c d e x}{{\left| e^{2} x + d e \right|}} - \frac{e^{2}}{c {\left| e^{2} x + d e \right|}}\right)}{\sqrt{\frac{c^{2} d^{2}}{e^{2}} + 1} e^{2}}\right)} - \frac{a^{2}}{e^{2} x + d e}"," ",0,"-b^2*(log(c*x + sqrt(c^2*x^2 + 1))^2/(e^2*x + d*e) - 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*e^2*x^4 + c^3*d*e*x^3 + c*e^2*x^2 + c*d*e*x + (c^2*e^2*x^3 + c^2*d*e*x^2 + e^2*x + d*e)*sqrt(c^2*x^2 + 1)), x)) - 2*a*b*(arcsinh(c*x)/(e^2*x + d*e) - c*arcsinh(c*d*e*x/abs(e^2*x + d*e) - e^2/(c*abs(e^2*x + d*e)))/(sqrt(c^2*d^2/e^2 + 1)*e^2)) - a^2/(e^2*x + d*e)","F",0
18,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2/(e*x+d)^3,x, algorithm=""maxima"")","-{\left(c {\left(\frac{\sqrt{c^{2} x^{2} + 1}}{c^{2} d^{2} e x + c^{2} d^{3} + e^{3} x + d e^{2}} - \frac{c^{2} d \operatorname{arsinh}\left(\frac{c d x}{e {\left| x + \frac{d}{e} \right|}} - \frac{1}{c {\left| x + \frac{d}{e} \right|}}\right)}{{\left(\frac{c^{2} d^{2}}{e^{2}} + 1\right)}^{\frac{3}{2}} e^{4}}\right)} + \frac{\operatorname{arsinh}\left(c x\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} a b - \frac{1}{2} \, b^{2} {\left(\frac{\log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e} - 2 \, \int \frac{{\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} e^{3} x^{5} + 2 \, c^{3} d e^{2} x^{4} + 2 \, c d e^{2} x^{2} + c d^{2} e x + {\left(c^{3} d^{2} e + c e^{3}\right)} x^{3} + {\left(c^{2} e^{3} x^{4} + 2 \, c^{2} d e^{2} x^{3} + 2 \, d e^{2} x + d^{2} e + {\left(c^{2} d^{2} e + e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} - \frac{a^{2}}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-(c*(sqrt(c^2*x^2 + 1)/(c^2*d^2*e*x + c^2*d^3 + e^3*x + d*e^2) - c^2*d*arcsinh(c*d*x/(e*abs(x + d/e)) - 1/(c*abs(x + d/e)))/((c^2*d^2/e^2 + 1)^(3/2)*e^4)) + arcsinh(c*x)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*a*b - 1/2*b^2*(log(c*x + sqrt(c^2*x^2 + 1))^2/(e^3*x^2 + 2*d*e^2*x + d^2*e) - 2*integrate((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*e^3*x^5 + 2*c^3*d*e^2*x^4 + 2*c*d*e^2*x^2 + c*d^2*e*x + (c^3*d^2*e + c*e^3)*x^3 + (c^2*e^3*x^4 + 2*c^2*d*e^2*x^3 + 2*d*e^2*x + d^2*e + (c^2*d^2*e + e^3)*x^2)*sqrt(c^2*x^2 + 1)), x)) - 1/2*a^2/(e^3*x^2 + 2*d*e^2*x + d^2*e)","F",0
19,0,0,0,0.000000," ","integrate((e*x+d)^3/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{3}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^3/(b*arcsinh(c*x) + a), x)","F",0
20,0,0,0,0.000000," ","integrate((e*x+d)^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{2}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^2/(b*arcsinh(c*x) + a), x)","F",0
21,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{e x + d}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)/(b*arcsinh(c*x) + a), x)","F",0
22,0,0,0,0.000000," ","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
23,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)*(b*arcsinh(c*x) + a)), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)}^{2} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)^2*(b*arcsinh(c*x) + a)), x)","F",0
25,0,0,0,0.000000," ","integrate((e*x+d)^2/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} e^{2} x^{5} + 2 \, c^{3} d e x^{4} + 2 \, c d e x^{2} + c d^{2} x + {\left(c^{3} d^{2} + c e^{2}\right)} x^{3} + {\left(c^{2} e^{2} x^{4} + 2 \, c^{2} d e x^{3} + 2 \, d e x + {\left(c^{2} d^{2} + e^{2}\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{3 \, c^{5} e^{2} x^{6} + 4 \, c^{5} d e x^{5} + 8 \, c^{3} d e x^{3} + {\left(c^{5} d^{2} + 6 \, c^{3} e^{2}\right)} x^{4} + 4 \, c d e x + c d^{2} + {\left(2 \, c^{3} d^{2} + 3 \, c e^{2}\right)} x^{2} + {\left(3 \, c^{3} e^{2} x^{4} + 4 \, c^{3} d e x^{3} - c d^{2} + {\left(c^{3} d^{2} + c e^{2}\right)} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(6 \, c^{4} e^{2} x^{5} + 8 \, c^{4} d e x^{4} + 8 \, c^{2} d e x^{2} + {\left(2 \, c^{4} d^{2} + 7 \, c^{2} e^{2}\right)} x^{3} + 2 \, d e + {\left(c^{2} d^{2} + 2 \, e^{2}\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^5 + 2*c^3*d*e*x^4 + 2*c*d*e*x^2 + c*d^2*x + (c^3*d^2 + c*e^2)*x^3 + (c^2*e^2*x^4 + 2*c^2*d*e*x^3 + 2*d*e*x + (c^2*d^2 + e^2)*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((3*c^5*e^2*x^6 + 4*c^5*d*e*x^5 + 8*c^3*d*e*x^3 + (c^5*d^2 + 6*c^3*e^2)*x^4 + 4*c*d*e*x + c*d^2 + (2*c^3*d^2 + 3*c*e^2)*x^2 + (3*c^3*e^2*x^4 + 4*c^3*d*e*x^3 - c*d^2 + (c^3*d^2 + c*e^2)*x^2)*(c^2*x^2 + 1) + (6*c^4*e^2*x^5 + 8*c^4*d*e*x^4 + 8*c^2*d*e*x^2 + (2*c^4*d^2 + 7*c^2*e^2)*x^3 + 2*d*e + (c^2*d^2 + 2*e^2)*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
26,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} e x^{4} + c^{3} d x^{3} + c e x^{2} + c d x + {\left(c^{2} e x^{3} + c^{2} d x^{2} + e x + 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{2 \, c^{5} e x^{5} + c^{5} d x^{4} + 4 \, c^{3} e x^{3} + 2 \, c^{3} d x^{2} + 2 \, c e x + {\left(2 \, c^{3} e x^{3} + c^{3} d x^{2} - c d\right)} {\left(c^{2} x^{2} + 1\right)} + c d + {\left(4 \, c^{4} e x^{4} + 2 \, c^{4} d x^{3} + 4 \, c^{2} e x^{2} + c^{2} d x + e\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^4 + c^3*d*x^3 + c*e*x^2 + c*d*x + (c^2*e*x^3 + c^2*d*x^2 + e*x + 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((2*c^5*e*x^5 + c^5*d*x^4 + 4*c^3*e*x^3 + 2*c^3*d*x^2 + 2*c*e*x + (2*c^3*e*x^3 + c^3*d*x^2 - c*d)*(c^2*x^2 + 1) + c*d + (4*c^4*e*x^4 + 2*c^4*d*x^3 + 4*c^2*e*x^2 + c^2*d*x + e)*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
27,0,0,0,0.000000," ","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
28,0,0,0,0.000000," ","integrate(1/(e*x+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^{3} + a b c^{3} d x^{2} + a b c e x + a b c d + {\left(b^{2} c^{3} e x^{3} + b^{2} c^{3} d x^{2} + b^{2} c e x + b^{2} c d + {\left(b^{2} c^{2} e x^{2} + 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^{2} + a b c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1}} + \int \frac{c^{5} d x^{4} + 2 \, c^{3} d x^{2} + {\left(c^{3} d x^{2} - 2 \, c e x - c d\right)} {\left(c^{2} x^{2} + 1\right)} + c d + {\left(2 \, c^{4} d x^{3} - 2 \, c^{2} e x^{2} + c^{2} d x - e\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} e^{2} x^{6} + 2 \, a b c^{5} d e x^{5} + 4 \, a b c^{3} d e x^{3} + {\left(c^{5} d^{2} + 2 \, c^{3} e^{2}\right)} a b x^{4} + 2 \, a b c d e x + a b c d^{2} + {\left(2 \, c^{3} d^{2} + c e^{2}\right)} a b x^{2} + {\left(a b c^{3} e^{2} x^{4} + 2 \, a b c^{3} d e x^{3} + a b c^{3} d^{2} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} e^{2} x^{6} + 2 \, b^{2} c^{5} d e x^{5} + 4 \, b^{2} c^{3} d e x^{3} + {\left(c^{5} d^{2} + 2 \, c^{3} e^{2}\right)} b^{2} x^{4} + 2 \, b^{2} c d e x + b^{2} c d^{2} + {\left(2 \, c^{3} d^{2} + c e^{2}\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{2} x^{4} + 2 \, b^{2} c^{3} d e x^{3} + 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^{5} + 2 \, b^{2} c^{4} d e x^{4} + 2 \, b^{2} c^{2} d e x^{2} + b^{2} c^{2} d^{2} x + {\left(c^{4} d^{2} + c^{2} e^{2}\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^{5} + 2 \, a b c^{4} d e x^{4} + 2 \, a b c^{2} d e x^{2} + a b c^{2} d^{2} x + {\left(c^{4} d^{2} + c^{2} e^{2}\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^3 + a*b*c^3*d*x^2 + a*b*c*e*x + a*b*c*d + (b^2*c^3*e*x^3 + b^2*c^3*d*x^2 + b^2*c*e*x + b^2*c*d + (b^2*c^2*e*x^2 + 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^2 + a*b*c^2*d*x)*sqrt(c^2*x^2 + 1)) + integrate((c^5*d*x^4 + 2*c^3*d*x^2 + (c^3*d*x^2 - 2*c*e*x - c*d)*(c^2*x^2 + 1) + c*d + (2*c^4*d*x^3 - 2*c^2*e*x^2 + c^2*d*x - e)*sqrt(c^2*x^2 + 1))/(a*b*c^5*e^2*x^6 + 2*a*b*c^5*d*e*x^5 + 4*a*b*c^3*d*e*x^3 + (c^5*d^2 + 2*c^3*e^2)*a*b*x^4 + 2*a*b*c*d*e*x + a*b*c*d^2 + (2*c^3*d^2 + c*e^2)*a*b*x^2 + (a*b*c^3*e^2*x^4 + 2*a*b*c^3*d*e*x^3 + a*b*c^3*d^2*x^2)*(c^2*x^2 + 1) + (b^2*c^5*e^2*x^6 + 2*b^2*c^5*d*e*x^5 + 4*b^2*c^3*d*e*x^3 + (c^5*d^2 + 2*c^3*e^2)*b^2*x^4 + 2*b^2*c*d*e*x + b^2*c*d^2 + (2*c^3*d^2 + c*e^2)*b^2*x^2 + (b^2*c^3*e^2*x^4 + 2*b^2*c^3*d*e*x^3 + b^2*c^3*d^2*x^2)*(c^2*x^2 + 1) + 2*(b^2*c^4*e^2*x^5 + 2*b^2*c^4*d*e*x^4 + 2*b^2*c^2*d*e*x^2 + b^2*c^2*d^2*x + (c^4*d^2 + c^2*e^2)*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^5 + 2*a*b*c^4*d*e*x^4 + 2*a*b*c^2*d*e*x^2 + a*b*c^2*d^2*x + (c^4*d^2 + c^2*e^2)*a*b*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
29,0,0,0,0.000000," ","integrate(1/(e*x+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^{4} + 2 \, a b c^{3} d e x^{3} + 2 \, a b c d e x + a b c d^{2} + {\left(c^{3} d^{2} + c e^{2}\right)} a b x^{2} + {\left(b^{2} c^{3} e^{2} x^{4} + 2 \, b^{2} c^{3} d e x^{3} + 2 \, b^{2} c d e x + b^{2} c d^{2} + {\left(c^{3} d^{2} + c e^{2}\right)} b^{2} x^{2} + {\left(b^{2} c^{2} e^{2} x^{3} + 2 \, b^{2} c^{2} d e x^{2} + 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^{3} + 2 \, a b c^{2} d e x^{2} + a b c^{2} d^{2} x\right)} \sqrt{c^{2} x^{2} + 1}} - \int \frac{c^{5} e x^{5} - c^{5} d x^{4} + 2 \, c^{3} e x^{3} - 2 \, c^{3} d x^{2} + c e x + {\left(c^{3} e x^{3} - c^{3} d x^{2} + 3 \, c e x + c d\right)} {\left(c^{2} x^{2} + 1\right)} - c d + {\left(2 \, c^{4} e x^{4} - 2 \, c^{4} d x^{3} + 5 \, c^{2} e x^{2} - c^{2} d x + 2 \, e\right)} \sqrt{c^{2} x^{2} + 1}}{a b c^{5} e^{3} x^{7} + 3 \, a b c^{5} d e^{2} x^{6} + {\left(3 \, c^{5} d^{2} e + 2 \, c^{3} e^{3}\right)} a b x^{5} + 3 \, a b c d^{2} e x + {\left(c^{5} d^{3} + 6 \, c^{3} d e^{2}\right)} a b x^{4} + a b c d^{3} + {\left(6 \, c^{3} d^{2} e + c e^{3}\right)} a b x^{3} + {\left(2 \, c^{3} d^{3} + 3 \, c d e^{2}\right)} a b x^{2} + {\left(a b c^{3} e^{3} x^{5} + 3 \, a b c^{3} d e^{2} x^{4} + 3 \, a b c^{3} d^{2} e x^{3} + a b c^{3} d^{3} x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} e^{3} x^{7} + 3 \, b^{2} c^{5} d e^{2} x^{6} + {\left(3 \, c^{5} d^{2} e + 2 \, c^{3} e^{3}\right)} b^{2} x^{5} + 3 \, b^{2} c d^{2} e x + {\left(c^{5} d^{3} + 6 \, c^{3} d e^{2}\right)} b^{2} x^{4} + b^{2} c d^{3} + {\left(6 \, c^{3} d^{2} e + c e^{3}\right)} b^{2} x^{3} + {\left(2 \, c^{3} d^{3} + 3 \, c d e^{2}\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{3} x^{5} + 3 \, b^{2} c^{3} d e^{2} x^{4} + 3 \, b^{2} c^{3} d^{2} e x^{3} + 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^{6} + 3 \, b^{2} c^{4} d e^{2} x^{5} + 3 \, b^{2} c^{2} d^{2} e x^{2} + b^{2} c^{2} d^{3} x + {\left(3 \, c^{4} d^{2} e + c^{2} e^{3}\right)} b^{2} x^{4} + {\left(c^{4} d^{3} + 3 \, c^{2} d e^{2}\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^{6} + 3 \, a b c^{4} d e^{2} x^{5} + 3 \, a b c^{2} d^{2} e x^{2} + a b c^{2} d^{3} x + {\left(3 \, c^{4} d^{2} e + c^{2} e^{3}\right)} a b x^{4} + {\left(c^{4} d^{3} + 3 \, c^{2} d e^{2}\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^4 + 2*a*b*c^3*d*e*x^3 + 2*a*b*c*d*e*x + a*b*c*d^2 + (c^3*d^2 + c*e^2)*a*b*x^2 + (b^2*c^3*e^2*x^4 + 2*b^2*c^3*d*e*x^3 + 2*b^2*c*d*e*x + b^2*c*d^2 + (c^3*d^2 + c*e^2)*b^2*x^2 + (b^2*c^2*e^2*x^3 + 2*b^2*c^2*d*e*x^2 + 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^3 + 2*a*b*c^2*d*e*x^2 + a*b*c^2*d^2*x)*sqrt(c^2*x^2 + 1)) - integrate((c^5*e*x^5 - c^5*d*x^4 + 2*c^3*e*x^3 - 2*c^3*d*x^2 + c*e*x + (c^3*e*x^3 - c^3*d*x^2 + 3*c*e*x + c*d)*(c^2*x^2 + 1) - c*d + (2*c^4*e*x^4 - 2*c^4*d*x^3 + 5*c^2*e*x^2 - c^2*d*x + 2*e)*sqrt(c^2*x^2 + 1))/(a*b*c^5*e^3*x^7 + 3*a*b*c^5*d*e^2*x^6 + (3*c^5*d^2*e + 2*c^3*e^3)*a*b*x^5 + 3*a*b*c*d^2*e*x + (c^5*d^3 + 6*c^3*d*e^2)*a*b*x^4 + a*b*c*d^3 + (6*c^3*d^2*e + c*e^3)*a*b*x^3 + (2*c^3*d^3 + 3*c*d*e^2)*a*b*x^2 + (a*b*c^3*e^3*x^5 + 3*a*b*c^3*d*e^2*x^4 + 3*a*b*c^3*d^2*e*x^3 + a*b*c^3*d^3*x^2)*(c^2*x^2 + 1) + (b^2*c^5*e^3*x^7 + 3*b^2*c^5*d*e^2*x^6 + (3*c^5*d^2*e + 2*c^3*e^3)*b^2*x^5 + 3*b^2*c*d^2*e*x + (c^5*d^3 + 6*c^3*d*e^2)*b^2*x^4 + b^2*c*d^3 + (6*c^3*d^2*e + c*e^3)*b^2*x^3 + (2*c^3*d^3 + 3*c*d*e^2)*b^2*x^2 + (b^2*c^3*e^3*x^5 + 3*b^2*c^3*d*e^2*x^4 + 3*b^2*c^3*d^2*e*x^3 + b^2*c^3*d^3*x^2)*(c^2*x^2 + 1) + 2*(b^2*c^4*e^3*x^6 + 3*b^2*c^4*d*e^2*x^5 + 3*b^2*c^2*d^2*e*x^2 + b^2*c^2*d^3*x + (3*c^4*d^2*e + c^2*e^3)*b^2*x^4 + (c^4*d^3 + 3*c^2*d*e^2)*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^6 + 3*a*b*c^4*d*e^2*x^5 + 3*a*b*c^2*d^2*e*x^2 + a*b*c^2*d^3*x + (3*c^4*d^2*e + c^2*e^3)*a*b*x^4 + (c^4*d^3 + 3*c^2*d*e^2)*a*b*x^3)*sqrt(c^2*x^2 + 1)), x)","F",0
30,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} e x + b^{2} d\right)} {\left(e x + d\right)}^{m} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)^{2}}{e {\left(m + 1\right)}} + \frac{{\left(e x + d\right)}^{m + 1} a^{2}}{e {\left(m + 1\right)}} + \int -\frac{2 \, {\left({\left(b^{2} c^{2} d x - a b e {\left(m + 1\right)} - {\left(a b c^{2} e {\left(m + 1\right)} - b^{2} c^{2} e\right)} x^{2}\right)} \sqrt{c^{2} x^{2} + 1} {\left(e x + d\right)}^{m} + {\left(b^{2} c^{3} d x^{2} + b^{2} c d - {\left(a b c^{3} e {\left(m + 1\right)} - b^{2} c^{3} e\right)} x^{3} - {\left(a b c e {\left(m + 1\right)} - b^{2} c e\right)} x\right)} {\left(e x + d\right)}^{m}\right)} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{c^{3} e {\left(m + 1\right)} x^{3} + c e {\left(m + 1\right)} x + {\left(c^{2} e {\left(m + 1\right)} x^{2} + e {\left(m + 1\right)}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"(b^2*e*x + b^2*d)*(e*x + d)^m*log(c*x + sqrt(c^2*x^2 + 1))^2/(e*(m + 1)) + (e*x + d)^(m + 1)*a^2/(e*(m + 1)) + integrate(-2*((b^2*c^2*d*x - a*b*e*(m + 1) - (a*b*c^2*e*(m + 1) - b^2*c^2*e)*x^2)*sqrt(c^2*x^2 + 1)*(e*x + d)^m + (b^2*c^3*d*x^2 + b^2*c*d - (a*b*c^3*e*(m + 1) - b^2*c^3*e)*x^3 - (a*b*c*e*(m + 1) - b^2*c*e)*x)*(e*x + d)^m)*log(c*x + sqrt(c^2*x^2 + 1))/(c^3*e*(m + 1)*x^3 + c*e*(m + 1)*x + (c^2*e*(m + 1)*x^2 + e*(m + 1))*sqrt(c^2*x^2 + 1)), x)","F",0
31,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","b {\left(\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{e {\left(m + 1\right)}} - \int \frac{{\left(c^{2} e x^{2} + c^{2} d x\right)} {\left(e x + d\right)}^{m}}{c^{2} e {\left(m + 1\right)} x^{2} + e {\left(m + 1\right)}}\,{d x} - \int \frac{{\left(c e x + c d\right)} {\left(e x + d\right)}^{m}}{c^{3} e {\left(m + 1\right)} x^{3} + c e {\left(m + 1\right)} x + {\left(c^{2} e {\left(m + 1\right)} x^{2} + e {\left(m + 1\right)}\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}\right)} + \frac{{\left(e x + d\right)}^{m + 1} a}{e {\left(m + 1\right)}}"," ",0,"b*((e*x + d)*(e*x + d)^m*log(c*x + sqrt(c^2*x^2 + 1))/(e*(m + 1)) - integrate((c^2*e*x^2 + c^2*d*x)*(e*x + d)^m/(c^2*e*(m + 1)*x^2 + e*(m + 1)), x) - integrate((c*e*x + c*d)*(e*x + d)^m/(c^3*e*(m + 1)*x^3 + c*e*(m + 1)*x + (c^2*e*(m + 1)*x^2 + e*(m + 1))*sqrt(c^2*x^2 + 1)), x)) + (e*x + d)^(m + 1)*a/(e*(m + 1))","F",0
32,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arcsinh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{m}}{b \operatorname{arsinh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^m/(b*arcsinh(c*x) + a), x)","F",0
33,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arcsinh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m} + {\left(c^{3} x^{3} + c x\right)} {\left(e x + d\right)}^{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} e {\left(m + 1\right)} x^{3} + c^{3} d x^{2} + c e {\left(m - 1\right)} x - c d\right)} {\left(c^{2} x^{2} + 1\right)} {\left(e x + d\right)}^{m} + {\left(2 \, c^{4} e {\left(m + 1\right)} x^{4} + 2 \, c^{4} d x^{3} + c^{2} e {\left(3 \, m + 1\right)} x^{2} + c^{2} d x + e m\right)} \sqrt{c^{2} x^{2} + 1} {\left(e x + d\right)}^{m} + {\left(c^{5} e {\left(m + 1\right)} x^{5} + c^{5} d x^{4} + 2 \, c^{3} e {\left(m + 1\right)} x^{3} + 2 \, c^{3} d x^{2} + c e {\left(m + 1\right)} x + c d\right)} {\left(e x + d\right)}^{m}}{a b c^{5} e x^{5} + a b c^{5} d x^{4} + 2 \, a b c^{3} e x^{3} + 2 \, a b c^{3} d x^{2} + a b c e x + a b c d + {\left(a b c^{3} e x^{3} + a b c^{3} d x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + {\left(b^{2} c^{5} e x^{5} + b^{2} c^{5} d x^{4} + 2 \, b^{2} c^{3} e x^{3} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c e x + b^{2} c d + {\left(b^{2} c^{3} e x^{3} + b^{2} c^{3} d x^{2}\right)} {\left(c^{2} x^{2} + 1\right)} + 2 \, {\left(b^{2} c^{4} e x^{4} + b^{2} c^{4} d x^{3} + b^{2} c^{2} e x^{2} + 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) + 2 \, {\left(a b c^{4} e x^{4} + a b c^{4} d x^{3} + a b c^{2} e x^{2} + a b c^{2} d x\right)} \sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"-((c^2*x^2 + 1)^(3/2)*(e*x + d)^m + (c^3*x^3 + c*x)*(e*x + d)^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*e*(m + 1)*x^3 + c^3*d*x^2 + c*e*(m - 1)*x - c*d)*(c^2*x^2 + 1)*(e*x + d)^m + (2*c^4*e*(m + 1)*x^4 + 2*c^4*d*x^3 + c^2*e*(3*m + 1)*x^2 + c^2*d*x + e*m)*sqrt(c^2*x^2 + 1)*(e*x + d)^m + (c^5*e*(m + 1)*x^5 + c^5*d*x^4 + 2*c^3*e*(m + 1)*x^3 + 2*c^3*d*x^2 + c*e*(m + 1)*x + c*d)*(e*x + d)^m)/(a*b*c^5*e*x^5 + a*b*c^5*d*x^4 + 2*a*b*c^3*e*x^3 + 2*a*b*c^3*d*x^2 + a*b*c*e*x + a*b*c*d + (a*b*c^3*e*x^3 + a*b*c^3*d*x^2)*(c^2*x^2 + 1) + (b^2*c^5*e*x^5 + b^2*c^5*d*x^4 + 2*b^2*c^3*e*x^3 + 2*b^2*c^3*d*x^2 + b^2*c*e*x + b^2*c*d + (b^2*c^3*e*x^3 + b^2*c^3*d*x^2)*(c^2*x^2 + 1) + 2*(b^2*c^4*e*x^4 + b^2*c^4*d*x^3 + b^2*c^2*e*x^2 + b^2*c^2*d*x)*sqrt(c^2*x^2 + 1))*log(c*x + sqrt(c^2*x^2 + 1)) + 2*(a*b*c^4*e*x^4 + a*b*c^4*d*x^3 + a*b*c^2*e*x^2 + a*b*c^2*d*x)*sqrt(c^2*x^2 + 1)), x)","F",0
34,-2,0,0,0.000000," ","integrate((g*x+f)^3*(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
35,-2,0,0,0.000000," ","integrate((g*x+f)^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
36,-2,0,0,0.000000," ","integrate((g*x+f)*(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
37,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/(g*x+f),x, algorithm=""maxima"")","-{\left(\frac{c \sqrt{d} f \operatorname{arsinh}\left(c x\right)}{g^{2}} - \frac{\sqrt{\frac{c^{2} d f^{2}}{g^{2}} + d} \operatorname{arsinh}\left(\frac{c f x}{{\left| g x + f \right|}} - \frac{g}{c {\left| g x + f \right|}}\right)}{g} - \frac{\sqrt{c^{2} d x^{2} + d}}{g}\right)} a + b \int \frac{\sqrt{c^{2} d x^{2} + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{g x + f}\,{d x}"," ",0,"-(c*sqrt(d)*f*arcsinh(c*x)/g^2 - sqrt(c^2*d*f^2/g^2 + d)*arcsinh(c*f*x/abs(g*x + f) - g/(c*abs(g*x + f)))/g - sqrt(c^2*d*x^2 + d)/g)*a + b*integrate(sqrt(c^2*d*x^2 + d)*log(c*x + sqrt(c^2*x^2 + 1))/(g*x + f), x)","F",0
38,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*(c^2*d*x^2+d)^(1/2)/(g*x+f)^2,x, algorithm=""maxima"")","-{\left(\frac{c^{2} d f \operatorname{arsinh}\left(\frac{c f x}{g {\left| x + \frac{f}{g} \right|}} - \frac{1}{c {\left| x + \frac{f}{g} \right|}}\right)}{\sqrt{\frac{c^{2} d f^{2}}{g^{2}} + d} g^{3}} - \frac{c \sqrt{d} \operatorname{arsinh}\left(c x\right)}{g^{2}} + \frac{\sqrt{c^{2} d x^{2} + d}}{g^{2} x + f g}\right)} a + b \int \frac{\sqrt{c^{2} d x^{2} + d} \log\left(c x + \sqrt{c^{2} x^{2} + 1}\right)}{g^{2} x^{2} + 2 \, f g x + f^{2}}\,{d x}"," ",0,"-(c^2*d*f*arcsinh(c*f*x/(g*abs(x + f/g)) - 1/(c*abs(x + f/g)))/(sqrt(c^2*d*f^2/g^2 + d)*g^3) - c*sqrt(d)*arcsinh(c*x)/g^2 + sqrt(c^2*d*x^2 + d)/(g^2*x + f*g))*a + b*integrate(sqrt(c^2*d*x^2 + d)*log(c*x + sqrt(c^2*x^2 + 1))/(g^2*x^2 + 2*f*g*x + f^2), x)","F",0
39,-2,0,0,0.000000," ","integrate((g*x+f)^3*(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
40,-2,0,0,0.000000," ","integrate((g*x+f)^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
41,-2,0,0,0.000000," ","integrate((g*x+f)*(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
42,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(3/2)*(a+b*arcsinh(c*x))/(g*x+f),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
43,-2,0,0,0.000000," ","integrate((g*x+f)^3*(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
44,-2,0,0,0.000000," ","integrate((g*x+f)^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
45,-2,0,0,0.000000," ","integrate((g*x+f)*(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
46,-2,0,0,0.000000," ","integrate((c^2*d*x^2+d)^(5/2)*(a+b*arcsinh(c*x))/(g*x+f),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
47,-2,0,0,0.000000," ","integrate((g*x+f)^3*(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
48,-2,0,0,0.000000," ","integrate((g*x+f)^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
49,1,87,0,0.418802," ","integrate((g*x+f)*(a+b*arcsinh(c*x))/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b f \operatorname{arsinh}\left(c x\right)^{2}}{2 \, c \sqrt{d}} - \frac{b g x}{c \sqrt{d}} + \frac{a f \operatorname{arsinh}\left(c x\right)}{c \sqrt{d}} + \frac{\sqrt{c^{2} d x^{2} + d} b g \operatorname{arsinh}\left(c x\right)}{c^{2} d} + \frac{\sqrt{c^{2} d x^{2} + d} a g}{c^{2} d}"," ",0,"1/2*b*f*arcsinh(c*x)^2/(c*sqrt(d)) - b*g*x/(c*sqrt(d)) + a*f*arcsinh(c*x)/(c*sqrt(d)) + sqrt(c^2*d*x^2 + d)*b*g*arcsinh(c*x)/(c^2*d) + sqrt(c^2*d*x^2 + d)*a*g/(c^2*d)","A",0
50,1,28,0,0.451625," ","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
51,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(g*x+f)/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{b \operatorname{arsinh}\left(c x\right) + a}{\sqrt{c^{2} d x^{2} + d} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)/(sqrt(c^2*d*x^2 + d)*(g*x + f)), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))/(g*x+f)^2/(c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{b \operatorname{arsinh}\left(c x\right) + a}{\sqrt{c^{2} d x^{2} + d} {\left(g x + f\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)/(sqrt(c^2*d*x^2 + d)*(g*x + f)^2), x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^n*log(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{n} \log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^n*log((g*x + f)^m*h)/sqrt(c^2*x^2 + 1), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))^2*log(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)}^{2} \log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)^2*log((g*x + f)^m*h)/sqrt(c^2*x^2 + 1), x)","F",0
55,0,0,0,0.000000," ","integrate((a+b*arcsinh(c*x))*log(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(c x\right) + a\right)} \log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arcsinh(c*x) + a)*log((g*x + f)^m*h)/sqrt(c^2*x^2 + 1), x)","F",0
56,0,0,0,0.000000," ","integrate(log(h*(g*x+f)^m)/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(log((g*x + f)^m*h)/sqrt(c^2*x^2 + 1), x)","F",0
57,0,0,0,0.000000," ","integrate(log(h*(g*x+f)^m)/(a+b*arcsinh(c*x))/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{c^{2} x^{2} + 1} {\left(b \operatorname{arsinh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(log((g*x + f)^m*h)/(sqrt(c^2*x^2 + 1)*(b*arcsinh(c*x) + a)), x)","F",0
58,1,318,0,0.335588," ","integrate(x^3*arcsinh(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arsinh}\left(b x + a\right) - \frac{1}{96} \, {\left(\frac{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x^{3}}{b^{2}} - \frac{14 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x^{2}}{b^{3}} + \frac{105 \, a^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{5}} + \frac{35 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} x}{b^{4}} - \frac{90 \, {\left(a^{2} + 1\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{5}} - \frac{105 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{b^{5}} - \frac{9 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x}{b^{4}} + \frac{9 \, {\left(a^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{5}} + \frac{55 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a}{b^{5}}\right)} b"," ",0,"1/4*x^4*arcsinh(b*x + a) - 1/96*(6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x^3/b^2 - 14*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x^2/b^3 + 105*a^4*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 35*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*x/b^4 - 90*(a^2 + 1)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 105*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/b^5 - 9*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x/b^4 + 9*(a^2 + 1)^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 55*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a/b^5)*b","B",0
59,1,210,0,0.364737," ","integrate(x^2*arcsinh(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arsinh}\left(b x + a\right) - \frac{1}{18} \, b {\left(\frac{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x^{2}}{b^{2}} - \frac{15 \, a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{4}} - \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{b^{3}} + \frac{9 \, {\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{4}} + \frac{15 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{b^{4}} - \frac{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}}{b^{4}}\right)}"," ",0,"1/3*x^3*arcsinh(b*x + a) - 1/18*b*(2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x^2/b^2 - 15*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 5*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^3 + 9*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + 15*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^4 - 4*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)/b^4)","B",0
60,1,149,0,0.368784," ","integrate(x*arcsinh(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arsinh}\left(b x + a\right) - \frac{1}{4} \, b {\left(\frac{3 \, a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{b^{2}} - \frac{{\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{b^{3}}\right)}"," ",0,"1/2*x^2*arcsinh(b*x + a) - 1/4*b*(3*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^2 - (a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - 3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^3)","B",0
61,1,30,0,0.388403," ","integrate(arcsinh(b*x+a),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \operatorname{arsinh}\left(b x + a\right) - \sqrt{{\left(b x + a\right)}^{2} + 1}}{b}"," ",0,"((b*x + a)*arcsinh(b*x + a) - sqrt((b*x + a)^2 + 1))/b","A",0
62,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arcsinh(b*x + a)/x, x)","F",0
63,1,111,0,0.324830," ","integrate(arcsinh(b*x+a)/x^2,x, algorithm=""maxima"")","-\frac{b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{\sqrt{a^{2} + 1}} - \frac{\operatorname{arsinh}\left(b x + a\right)}{x}"," ",0,"-b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/sqrt(a^2 + 1) - arcsinh(b*x + a)/x","B",0
64,1,146,0,0.409040," ","integrate(arcsinh(b*x+a)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{a b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(a^{2} + 1\right)} x}\right)} b - \frac{\operatorname{arsinh}\left(b x + a\right)}{2 \, x^{2}}"," ",0,"1/2*(a*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/((a^2 + 1)*x))*b - 1/2*arcsinh(b*x + a)/x^2","A",0
65,1,284,0,0.358642," ","integrate(arcsinh(b*x+a)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{3 \, a^{2} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{5}{2}}} - \frac{b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a b}{{\left(a^{2} + 1\right)}^{2} x} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(a^{2} + 1\right)} x^{2}}\right)} b - \frac{\operatorname{arsinh}\left(b x + a\right)}{3 \, x^{3}}"," ",0,"-1/6*(3*a^2*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) - b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*b/((a^2 + 1)^2*x) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/((a^2 + 1)*x^2))*b - 1/3*arcsinh(b*x + a)/x^3","B",0
66,1,357,0,0.363849," ","integrate(arcsinh(b*x+a)/x^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{15 \, a^{3} b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{7}{2}}} - \frac{9 \, a b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{5}{2}}} - \frac{15 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} b^{2}}{{\left(a^{2} + 1\right)}^{3} x} + \frac{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}}{{\left(a^{2} + 1\right)}^{2} x} + \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a b}{{\left(a^{2} + 1\right)}^{2} x^{2}} - \frac{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(a^{2} + 1\right)} x^{3}}\right)} b - \frac{\operatorname{arsinh}\left(b x + a\right)}{4 \, x^{4}}"," ",0,"1/24*(15*a^3*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(7/2) - 9*a*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) - 15*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*b^2/((a^2 + 1)^3*x) + 4*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2/((a^2 + 1)^2*x) + 5*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*b/((a^2 + 1)^2*x^2) - 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/((a^2 + 1)*x^3))*b - 1/4*arcsinh(b*x + a)/x^4","B",0
67,0,0,0,0.000000," ","integrate(x^3*arcsinh(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2} - \int \frac{{\left(b^{3} x^{6} + 2 \, a b^{2} x^{5} + {\left(a^{2} b + b\right)} x^{4} + {\left(b^{2} x^{5} + a b x^{4}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a\right)}}\,{d x}"," ",0,"1/4*x^4*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2 - integrate(1/2*(b^3*x^6 + 2*a*b^2*x^5 + (a^2*b + b)*x^4 + (b^2*x^5 + a*b*x^4)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
68,0,0,0,0.000000," ","integrate(x^2*arcsinh(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2} - \int \frac{2 \, {\left(b^{3} x^{5} + 2 \, a b^{2} x^{4} + {\left(a^{2} b + b\right)} x^{3} + {\left(b^{2} x^{4} + a b x^{3}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{3 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a\right)}}\,{d x}"," ",0,"1/3*x^3*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2 - integrate(2/3*(b^3*x^5 + 2*a*b^2*x^4 + (a^2*b + b)*x^3 + (b^2*x^4 + a*b*x^3)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
69,0,0,0,0.000000," ","integrate(x*arcsinh(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2} - \int \frac{{\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + {\left(a^{2} b + b\right)} x^{2} + {\left(b^{2} x^{3} + a b x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}\,{d x}"," ",0,"1/2*x^2*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2 - integrate((b^3*x^4 + 2*a*b^2*x^3 + (a^2*b + b)*x^2 + (b^2*x^3 + a*b*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
70,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2,x, algorithm=""maxima"")","x \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2} - \int \frac{2 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b + b\right)} x + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x^{2} + a b x\right)}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}\,{d x}"," ",0,"x*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2 - integrate(2*(b^3*x^3 + 2*a*b^2*x^2 + (a^2*b + b)*x + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + a*b*x))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
71,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arcsinh(b*x + a)^2/x, x)","F",0
72,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2/x^2,x, algorithm=""maxima"")","-\frac{\log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{x} + \int \frac{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b + b\right)} x^{2} + {\left(a^{3} + a\right)} x + {\left(b^{2} x^{3} + 2 \, a b x^{2} + {\left(a^{2} + 1\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"-log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/x + integrate(2*(b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b + b)*x^2 + (a^3 + a)*x + (b^2*x^3 + 2*a*b*x^2 + (a^2 + 1)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
73,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2/x^3,x, algorithm=""maxima"")","-\frac{\log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{2 \, x^{2}} + \int \frac{{\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b + b\right)} x^{3} + {\left(a^{3} + a\right)} x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{3} + {\left(a^{2} + 1\right)} x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"-1/2*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/x^2 + integrate((b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b + b)*x^3 + (a^3 + a)*x^2 + (b^2*x^4 + 2*a*b*x^3 + (a^2 + 1)*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
74,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2/x^4,x, algorithm=""maxima"")","-\frac{\log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{3 \, x^{3}} + \int \frac{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{3 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} b + b\right)} x^{4} + {\left(a^{3} + a\right)} x^{3} + {\left(b^{2} x^{5} + 2 \, a b x^{4} + {\left(a^{2} + 1\right)} x^{3}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}}\,{d x}"," ",0,"-1/3*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/x^3 + integrate(2/3*(b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b^3*x^6 + 3*a*b^2*x^5 + (3*a^2*b + b)*x^4 + (a^3 + a)*x^3 + (b^2*x^5 + 2*a*b*x^4 + (a^2 + 1)*x^3)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
75,0,0,0,0.000000," ","integrate(x^2*arcsinh(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{3} - \int \frac{{\left(b^{3} x^{5} + 2 \, a b^{2} x^{4} + {\left(a^{2} b + b\right)} x^{3} + {\left(b^{2} x^{4} + a b x^{3}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}\,{d x}"," ",0,"1/3*x^3*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^3 - integrate((b^3*x^5 + 2*a*b^2*x^4 + (a^2*b + b)*x^3 + (b^2*x^4 + a*b*x^3)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
76,0,0,0,0.000000," ","integrate(x*arcsinh(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{3} - \int \frac{3 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + {\left(a^{2} b + b\right)} x^{2} + {\left(b^{2} x^{3} + a b x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a\right)}}\,{d x}"," ",0,"1/2*x^2*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^3 - integrate(3/2*(b^3*x^4 + 2*a*b^2*x^3 + (a^2*b + b)*x^2 + (b^2*x^3 + a*b*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
77,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^3,x, algorithm=""maxima"")","x \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{3} - \int \frac{3 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b + b\right)} x + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x^{2} + a b x\right)}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}\,{d x}"," ",0,"x*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^3 - integrate(3*(b^3*x^3 + 2*a*b^2*x^2 + (a^2*b + b)*x + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + a*b*x))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a), x)","F",0
78,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(arcsinh(b*x + a)^3/x, x)","F",0
79,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^3/x^2,x, algorithm=""maxima"")","-\frac{\log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{3}}{x} + \int \frac{3 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b + b\right)} x^{2} + {\left(a^{3} + a\right)} x + {\left(b^{2} x^{3} + 2 \, a b x^{2} + {\left(a^{2} + 1\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"-log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^3/x + integrate(3*(b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b + b)*x^2 + (a^3 + a)*x + (b^2*x^3 + 2*a*b*x^2 + (a^2 + 1)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
80,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^3/x^3,x, algorithm=""maxima"")","-\frac{\log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{3}}{2 \, x^{2}} + \int \frac{3 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}}{2 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b + b\right)} x^{3} + {\left(a^{3} + a\right)} x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{3} + {\left(a^{2} + 1\right)} x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^3/x^2 + integrate(3/2*(b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2/(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b + b)*x^3 + (a^3 + a)*x^2 + (b^2*x^4 + 2*a*b*x^3 + (a^2 + 1)*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
81,0,0,0,0.000000," ","integrate(x^2/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{x^{2}}{\operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(x^2/arcsinh(b*x + a), x)","F",0
82,0,0,0,0.000000," ","integrate(x/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{x}{\operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(x/arcsinh(b*x + a), x)","F",0
83,0,0,0,0.000000," ","integrate(1/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{1}{\operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/arcsinh(b*x + a), x)","F",0
84,0,0,0,0.000000," ","integrate(1/x/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{1}{x \operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/(x*arcsinh(b*x + a)), x)","F",0
85,0,0,0,0.000000," ","integrate(x^2/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b + b\right)} x^{3} + {\left(a^{3} + a\right)} x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{3} + {\left(a^{2} + 1\right)} x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} + \int \frac{3 \, b^{5} x^{6} + 14 \, a b^{4} x^{5} + 2 \, {\left(13 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{4} + 8 \, {\left(3 \, a^{3} b^{2} + 2 \, a b^{2}\right)} x^{3} + {\left(11 \, a^{4} b + 14 \, a^{2} b + 3 \, b\right)} x^{2} + {\left(3 \, b^{3} x^{4} + 8 \, a b^{2} x^{3} + {\left(7 \, a^{2} b + b\right)} x^{2} + 2 \, {\left(a^{3} + a\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 2 \, {\left(a^{5} + 2 \, a^{3} + a\right)} x + {\left(6 \, b^{4} x^{5} + 22 \, a b^{3} x^{4} + {\left(30 \, a^{2} b^{2} + 7 \, b^{2}\right)} x^{3} + {\left(18 \, a^{3} b + 13 \, a b\right)} x^{2} + 2 \, {\left(2 \, a^{4} + 3 \, a^{2} + 1\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + a^{4} b + 2 \, a^{2} b + 2 \, {\left(3 \, a^{2} b^{3} + b^{3}\right)} x^{2} + {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, {\left(a^{3} b^{2} + a b^{2}\right)} x + 2 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + a^{3} b + a b + {\left(3 \, a^{2} b^{2} + b^{2}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b + b)*x^3 + (a^3 + a)*x^2 + (b^2*x^4 + 2*a*b*x^3 + (a^2 + 1)*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) + integrate((3*b^5*x^6 + 14*a*b^4*x^5 + 2*(13*a^2*b^3 + 3*b^3)*x^4 + 8*(3*a^3*b^2 + 2*a*b^2)*x^3 + (11*a^4*b + 14*a^2*b + 3*b)*x^2 + (3*b^3*x^4 + 8*a*b^2*x^3 + (7*a^2*b + b)*x^2 + 2*(a^3 + a)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*(a^5 + 2*a^3 + a)*x + (6*b^4*x^5 + 22*a*b^3*x^4 + (30*a^2*b^2 + 7*b^2)*x^3 + (18*a^3*b + 13*a*b)*x^2 + 2*(2*a^4 + 3*a^2 + 1)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^5*x^4 + 4*a*b^4*x^3 + a^4*b + 2*a^2*b + 2*(3*a^2*b^3 + b^3)*x^2 + (b^3*x^2 + 2*a*b^2*x + a^2*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*(a^3*b^2 + a*b^2)*x + 2*(b^4*x^3 + 3*a*b^3*x^2 + a^3*b + a*b + (3*a^2*b^2 + b^2)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
86,0,0,0,0.000000," ","integrate(x/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b + b\right)} x^{2} + {\left(a^{3} + a\right)} x + {\left(b^{2} x^{3} + 2 \, a b x^{2} + {\left(a^{2} + 1\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} + \int \frac{2 \, b^{5} x^{5} + 9 \, a b^{4} x^{4} + a^{5} + 4 \, {\left(4 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 2 \, {\left(7 \, a^{3} b^{2} + 5 \, a b^{2}\right)} x^{2} + {\left(2 \, b^{3} x^{3} + 5 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3} + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 2 \, {\left(3 \, a^{4} b + 4 \, a^{2} b + b\right)} x + {\left(4 \, b^{4} x^{4} + 14 \, a b^{3} x^{3} + 2 \, a^{4} + 2 \, {\left(9 \, a^{2} b^{2} + 2 \, b^{2}\right)} x^{2} + 3 \, a^{2} + {\left(10 \, a^{3} b + 7 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a}{{\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + a^{4} b + 2 \, a^{2} b + 2 \, {\left(3 \, a^{2} b^{3} + b^{3}\right)} x^{2} + {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, {\left(a^{3} b^{2} + a b^{2}\right)} x + 2 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + a^{3} b + a b + {\left(3 \, a^{2} b^{2} + b^{2}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b + b)*x^2 + (a^3 + a)*x + (b^2*x^3 + 2*a*b*x^2 + (a^2 + 1)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) + integrate((2*b^5*x^5 + 9*a*b^4*x^4 + a^5 + 4*(4*a^2*b^3 + b^3)*x^3 + 2*a^3 + 2*(7*a^3*b^2 + 5*a*b^2)*x^2 + (2*b^3*x^3 + 5*a*b^2*x^2 + 4*a^2*b*x + a^3 + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*(3*a^4*b + 4*a^2*b + b)*x + (4*b^4*x^4 + 14*a*b^3*x^3 + 2*a^4 + 2*(9*a^2*b^2 + 2*b^2)*x^2 + 3*a^2 + (10*a^3*b + 7*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + a)/((b^5*x^4 + 4*a*b^4*x^3 + a^4*b + 2*a^2*b + 2*(3*a^2*b^3 + b^3)*x^2 + (b^3*x^2 + 2*a*b^2*x + a^2*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*(a^3*b^2 + a*b^2)*x + 2*(b^4*x^3 + 3*a*b^3*x^2 + a^3*b + a*b + (3*a^2*b^2 + b^2)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
87,0,0,0,0.000000," ","integrate(1/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}{{\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} + \int \frac{b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} + 2 \, a^{2} + 4 \, {\left(a^{3} b + a b\right)} x + {\left(2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 2 \, a^{3} + {\left(6 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1}{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} + 2 \, a^{2} + 4 \, {\left(a^{3} b + a b\right)} x + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a)/((b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) + integrate((b^4*x^4 + 4*a*b^3*x^3 + a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + (b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + 2*a*b*x + a^2 - 1) + 2*a^2 + 4*(a^3*b + a*b)*x + (2*b^3*x^3 + 6*a*b^2*x^2 + 2*a^3 + (6*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)/((b^4*x^4 + 4*a*b^3*x^3 + a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + (b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + 2*a*b*x + a^2) + 2*a^2 + 4*(a^3*b + a*b)*x + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}{{\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b + b\right)} x + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x^{2} + a b x\right)}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} - \int \frac{a b^{4} x^{4} + 4 \, a^{2} b^{3} x^{3} + a^{5} + 2 \, a^{3} + 2 \, {\left(3 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(a b^{2} x^{2} + a^{3} + 2 \, {\left(a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, {\left(a^{4} b + a^{2} b\right)} x + {\left(2 \, a b^{3} x^{3} + 2 \, a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 3 \, a^{2} + {\left(6 \, a^{3} b + 5 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a}{{\left(b^{5} x^{6} + 4 \, a b^{4} x^{5} + 2 \, {\left(3 \, a^{2} b^{3} + b^{3}\right)} x^{4} + 4 \, {\left(a^{3} b^{2} + a b^{2}\right)} x^{3} + {\left(a^{4} b + 2 \, a^{2} b + b\right)} x^{2} + {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + a^{2} b x^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 2 \, {\left(b^{4} x^{5} + 3 \, a b^{3} x^{4} + {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{3} + {\left(a^{3} b + a b\right)} x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a)/((b^3*x^3 + 2*a*b^2*x^2 + (a^2*b + b)*x + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + a*b*x))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) - integrate((a*b^4*x^4 + 4*a^2*b^3*x^3 + a^5 + 2*a^3 + 2*(3*a^3*b^2 + a*b^2)*x^2 + (a*b^2*x^2 + a^3 + 2*(a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*(a^4*b + a^2*b)*x + (2*a*b^3*x^3 + 2*a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + 3*a^2 + (6*a^3*b + 5*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + a)/((b^5*x^6 + 4*a*b^4*x^5 + 2*(3*a^2*b^3 + b^3)*x^4 + 4*(a^3*b^2 + a*b^2)*x^3 + (a^4*b + 2*a^2*b + b)*x^2 + (b^3*x^4 + 2*a*b^2*x^3 + a^2*b*x^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*(b^4*x^5 + 3*a*b^3*x^4 + (3*a^2*b^2 + b^2)*x^3 + (a^3*b + a*b)*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
89,0,0,0,0.000000," ","integrate(x^2/arcsinh(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b^{8} x^{9} + 7 \, a b^{7} x^{8} + 3 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{7} + 5 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{6} + {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{5} + 3 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{4} + {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{3} + {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x^{2} + {\left(b^{5} x^{6} + 4 \, a b^{4} x^{5} + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{4} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{3} + {\left(a^{4} b + a^{2} b\right)} x^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{6} x^{7} + 15 \, a b^{5} x^{6} + 5 \, {\left(6 \, a^{2} b^{4} + b^{4}\right)} x^{5} + 15 \, {\left(2 \, a^{3} b^{3} + a b^{3}\right)} x^{4} + {\left(15 \, a^{4} b^{2} + 15 \, a^{2} b^{2} + 2 \, b^{2}\right)} x^{3} + {\left(3 \, a^{5} b + 5 \, a^{3} b + 2 \, a b\right)} x^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(3 \, b^{8} x^{9} + 23 \, a b^{7} x^{8} + {\left(77 \, a^{2} b^{6} + 9 \, b^{6}\right)} x^{7} + 3 \, {\left(49 \, a^{3} b^{5} + 17 \, a b^{5}\right)} x^{6} + {\left(175 \, a^{4} b^{4} + 120 \, a^{2} b^{4} + 9 \, b^{4}\right)} x^{5} + {\left(133 \, a^{5} b^{3} + 150 \, a^{3} b^{3} + 33 \, a b^{3}\right)} x^{4} + 3 \, {\left(21 \, a^{6} b^{2} + 35 \, a^{4} b^{2} + 15 \, a^{2} b^{2} + b^{2}\right)} x^{3} + {\left(17 \, a^{7} b + 39 \, a^{5} b + 27 \, a^{3} b + 5 \, a b\right)} x^{2} + {\left(3 \, b^{5} x^{6} + 14 \, a b^{4} x^{5} + 2 \, {\left(13 \, a^{2} b^{3} + 2 \, b^{3}\right)} x^{4} + 12 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{3} + {\left(11 \, a^{4} b + 12 \, a^{2} b + b\right)} x^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} + a\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(9 \, b^{6} x^{7} + 51 \, a b^{5} x^{6} + {\left(120 \, a^{2} b^{4} + 17 \, b^{4}\right)} x^{5} + 5 \, {\left(30 \, a^{3} b^{3} + 13 \, a b^{3}\right)} x^{4} + {\left(105 \, a^{4} b^{2} + 93 \, a^{2} b^{2} + 10 \, b^{2}\right)} x^{3} + {\left(39 \, a^{5} b + 59 \, a^{3} b + 20 \, a b\right)} x^{2} + 2 \, {\left(3 \, a^{6} + 7 \, a^{4} + 5 \, a^{2} + 1\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 2 \, {\left(a^{8} + 3 \, a^{6} + 3 \, a^{4} + a^{2}\right)} x + {\left(9 \, b^{7} x^{8} + 60 \, a b^{6} x^{7} + {\left(171 \, a^{2} b^{5} + 22 \, b^{5}\right)} x^{6} + 2 \, {\left(135 \, a^{3} b^{4} + 52 \, a b^{4}\right)} x^{5} + {\left(255 \, a^{4} b^{3} + 196 \, a^{2} b^{3} + 18 \, b^{3}\right)} x^{4} + 2 \, {\left(72 \, a^{5} b^{2} + 92 \, a^{3} b^{2} + 25 \, a b^{2}\right)} x^{3} + {\left(45 \, a^{6} b + 86 \, a^{4} b + 46 \, a^{2} b + 5 \, b\right)} x^{2} + 2 \, {\left(3 \, a^{7} + 8 \, a^{5} + 7 \, a^{3} + 2 \, a\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(3 \, b^{7} x^{8} + 18 \, a b^{6} x^{7} + {\left(45 \, a^{2} b^{5} + 7 \, b^{5}\right)} x^{6} + 4 \, {\left(15 \, a^{3} b^{4} + 7 \, a b^{4}\right)} x^{5} + {\left(45 \, a^{4} b^{3} + 42 \, a^{2} b^{3} + 5 \, b^{3}\right)} x^{4} + 2 \, {\left(9 \, a^{5} b^{2} + 14 \, a^{3} b^{2} + 5 \, a b^{2}\right)} x^{3} + {\left(3 \, a^{6} b + 7 \, a^{4} b + 5 \, a^{2} b + b\right)} x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{8} x^{6} + 6 \, a b^{7} x^{5} + a^{6} b^{2} + 3 \, a^{4} b^{2} + 3 \, {\left(5 \, a^{2} b^{6} + b^{6}\right)} x^{4} + 3 \, a^{2} b^{2} + 4 \, {\left(5 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{3} + 3 \, {\left(5 \, a^{4} b^{4} + 6 \, a^{2} b^{4} + b^{4}\right)} x^{2} + {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + a^{4} b^{2} + a^{2} b^{2} + {\left(6 \, a^{2} b^{4} + b^{4}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{3} + a b^{3}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + b^{2} + 6 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{3} + a b^{3}\right)} x + 3 \, {\left(b^{7} x^{5} + 5 \, a b^{6} x^{4} + a^{5} b^{2} + 2 \, a^{3} b^{2} + 2 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{3} + a b^{2} + 2 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{2} + {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int \frac{9 \, b^{10} x^{10} + 82 \, a b^{9} x^{9} + 2 \, a^{10} + 2 \, {\left(167 \, a^{2} b^{8} + 18 \, b^{8}\right)} x^{8} + 8 \, a^{8} + 32 \, {\left(25 \, a^{3} b^{7} + 8 \, a b^{7}\right)} x^{7} + 2 \, {\left(623 \, a^{4} b^{6} + 394 \, a^{2} b^{6} + 27 \, b^{6}\right)} x^{6} + 12 \, a^{6} + 4 \, {\left(329 \, a^{5} b^{5} + 342 \, a^{3} b^{5} + 69 \, a b^{5}\right)} x^{5} + 4 \, {\left(238 \, a^{6} b^{4} + 365 \, a^{4} b^{4} + 144 \, a^{2} b^{4} + 9 \, b^{4}\right)} x^{4} + 8 \, a^{4} + 16 \, {\left(29 \, a^{7} b^{3} + 61 \, a^{5} b^{3} + 39 \, a^{3} b^{3} + 7 \, a b^{3}\right)} x^{3} + {\left(9 \, b^{6} x^{6} + 46 \, a b^{5} x^{5} + 2 \, a^{6} + 4 \, {\left(24 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 4 \, a^{4} + 8 \, {\left(13 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(61 \, a^{4} b^{2} + 24 \, a^{2} b^{2} - b^{2}\right)} x^{2} + 2 \, a^{2} + 2 \, {\left(9 \, a^{5} b + 8 \, a^{3} b - a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + {\left(145 \, a^{8} b^{2} + 396 \, a^{6} b^{2} + 366 \, a^{4} b^{2} + 124 \, a^{2} b^{2} + 9 \, b^{2}\right)} x^{2} + {\left(36 \, b^{7} x^{7} + 220 \, a b^{6} x^{6} + 8 \, a^{7} + 8 \, {\left(71 \, a^{2} b^{5} + 6 \, b^{5}\right)} x^{5} + 20 \, a^{5} + 16 \, {\left(50 \, a^{3} b^{4} + 13 \, a b^{4}\right)} x^{4} + {\left(660 \, a^{4} b^{3} + 356 \, a^{2} b^{3} + 13 \, b^{3}\right)} x^{3} + 16 \, a^{3} + {\left(316 \, a^{5} b^{2} + 300 \, a^{3} b^{2} + 39 \, a b^{2}\right)} x^{2} + 2 \, {\left(40 \, a^{6} b + 62 \, a^{4} b + 21 \, a^{2} b - b\right)} x + 4 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(54 \, b^{8} x^{8} + 384 \, a b^{7} x^{7} + 12 \, a^{8} + 6 \, {\left(197 \, a^{2} b^{6} + 20 \, b^{6}\right)} x^{6} + 36 \, a^{6} + 12 \, {\left(171 \, a^{3} b^{5} + 52 \, a b^{5}\right)} x^{5} + {\left(2190 \, a^{4} b^{4} + 1332 \, a^{2} b^{4} + 83 \, b^{4}\right)} x^{4} + 38 \, a^{4} + 4 \, {\left(366 \, a^{5} b^{3} + 372 \, a^{3} b^{3} + 71 \, a b^{3}\right)} x^{3} + {\left(594 \, a^{6} b^{2} + 912 \, a^{4} b^{2} + 357 \, a^{2} b^{2} + 19 \, b^{2}\right)} x^{2} + 16 \, a^{2} + 2 \, {\left(66 \, a^{7} b + 144 \, a^{5} b + 97 \, a^{3} b + 19 \, a b\right)} x + 2\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 2 \, a^{2} + 2 \, {\left(13 \, a^{9} b + 44 \, a^{7} b + 54 \, a^{5} b + 28 \, a^{3} b + 5 \, a b\right)} x + {\left(36 \, b^{9} x^{9} + 292 \, a b^{8} x^{8} + 8 \, a^{9} + 4 \, {\left(261 \, a^{2} b^{7} + 28 \, b^{7}\right)} x^{7} + 28 \, a^{7} + 4 \, {\left(539 \, a^{3} b^{6} + 172 \, a b^{6}\right)} x^{6} + {\left(2828 \, a^{4} b^{5} + 1788 \, a^{2} b^{5} + 123 \, b^{5}\right)} x^{5} + 36 \, a^{5} + {\left(2436 \, a^{5} b^{4} + 2540 \, a^{3} b^{4} + 519 \, a b^{4}\right)} x^{4} + {\left(1372 \, a^{6} b^{3} + 2120 \, a^{4} b^{3} + 855 \, a^{2} b^{3} + 57 \, b^{3}\right)} x^{3} + 20 \, a^{3} + {\left(484 \, a^{7} b^{2} + 1032 \, a^{5} b^{2} + 681 \, a^{3} b^{2} + 133 \, a b^{2}\right)} x^{2} + 2 \, {\left(48 \, a^{8} b + 134 \, a^{6} b + 129 \, a^{4} b + 48 \, a^{2} b + 5 \, b\right)} x + 4 \, a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{10} x^{8} + 8 \, a b^{9} x^{7} + a^{8} b^{2} + 4 \, a^{6} b^{2} + 4 \, {\left(7 \, a^{2} b^{8} + b^{8}\right)} x^{6} + 6 \, a^{4} b^{2} + 8 \, {\left(7 \, a^{3} b^{7} + 3 \, a b^{7}\right)} x^{5} + 2 \, {\left(35 \, a^{4} b^{6} + 30 \, a^{2} b^{6} + 3 \, b^{6}\right)} x^{4} + 4 \, a^{2} b^{2} + 8 \, {\left(7 \, a^{5} b^{5} + 10 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{3} + {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, {\left(7 \, a^{6} b^{4} + 15 \, a^{4} b^{4} + 9 \, a^{2} b^{4} + b^{4}\right)} x^{2} + 4 \, {\left(b^{7} x^{5} + 5 \, a b^{6} x^{4} + a^{5} b^{2} + a^{3} b^{2} + {\left(10 \, a^{2} b^{5} + b^{5}\right)} x^{3} + {\left(10 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{2} + {\left(5 \, a^{4} b^{3} + 3 \, a^{2} b^{3}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{8} x^{6} + 6 \, a b^{7} x^{5} + a^{6} b^{2} + 2 \, a^{4} b^{2} + {\left(15 \, a^{2} b^{6} + 2 \, b^{6}\right)} x^{4} + a^{2} b^{2} + 4 \, {\left(5 \, a^{3} b^{5} + 2 \, a b^{5}\right)} x^{3} + {\left(15 \, a^{4} b^{4} + 12 \, a^{2} b^{4} + b^{4}\right)} x^{2} + 2 \, {\left(3 \, a^{5} b^{3} + 4 \, a^{3} b^{3} + a b^{3}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + b^{2} + 8 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{3} + a b^{3}\right)} x + 4 \, {\left(b^{9} x^{7} + 7 \, a b^{8} x^{6} + a^{7} b^{2} + 3 \, a^{5} b^{2} + 3 \, {\left(7 \, a^{2} b^{7} + b^{7}\right)} x^{5} + 3 \, a^{3} b^{2} + 5 \, {\left(7 \, a^{3} b^{6} + 3 \, a b^{6}\right)} x^{4} + {\left(35 \, a^{4} b^{5} + 30 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{3} + a b^{2} + 3 \, {\left(7 \, a^{5} b^{4} + 10 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{2} + {\left(7 \, a^{6} b^{3} + 15 \, a^{4} b^{3} + 9 \, a^{2} b^{3} + b^{3}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*(b^8*x^9 + 7*a*b^7*x^8 + 3*(7*a^2*b^6 + b^6)*x^7 + 5*(7*a^3*b^5 + 3*a*b^5)*x^6 + (35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^5 + 3*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^4 + (7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^3 + (a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x^2 + (b^5*x^6 + 4*a*b^4*x^5 + (6*a^2*b^3 + b^3)*x^4 + 2*(2*a^3*b^2 + a*b^2)*x^3 + (a^4*b + a^2*b)*x^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^6*x^7 + 15*a*b^5*x^6 + 5*(6*a^2*b^4 + b^4)*x^5 + 15*(2*a^3*b^3 + a*b^3)*x^4 + (15*a^4*b^2 + 15*a^2*b^2 + 2*b^2)*x^3 + (3*a^5*b + 5*a^3*b + 2*a*b)*x^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (3*b^8*x^9 + 23*a*b^7*x^8 + (77*a^2*b^6 + 9*b^6)*x^7 + 3*(49*a^3*b^5 + 17*a*b^5)*x^6 + (175*a^4*b^4 + 120*a^2*b^4 + 9*b^4)*x^5 + (133*a^5*b^3 + 150*a^3*b^3 + 33*a*b^3)*x^4 + 3*(21*a^6*b^2 + 35*a^4*b^2 + 15*a^2*b^2 + b^2)*x^3 + (17*a^7*b + 39*a^5*b + 27*a^3*b + 5*a*b)*x^2 + (3*b^5*x^6 + 14*a*b^4*x^5 + 2*(13*a^2*b^3 + 2*b^3)*x^4 + 12*(2*a^3*b^2 + a*b^2)*x^3 + (11*a^4*b + 12*a^2*b + b)*x^2 + 2*(a^5 + 2*a^3 + a)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (9*b^6*x^7 + 51*a*b^5*x^6 + (120*a^2*b^4 + 17*b^4)*x^5 + 5*(30*a^3*b^3 + 13*a*b^3)*x^4 + (105*a^4*b^2 + 93*a^2*b^2 + 10*b^2)*x^3 + (39*a^5*b + 59*a^3*b + 20*a*b)*x^2 + 2*(3*a^6 + 7*a^4 + 5*a^2 + 1)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*(a^8 + 3*a^6 + 3*a^4 + a^2)*x + (9*b^7*x^8 + 60*a*b^6*x^7 + (171*a^2*b^5 + 22*b^5)*x^6 + 2*(135*a^3*b^4 + 52*a*b^4)*x^5 + (255*a^4*b^3 + 196*a^2*b^3 + 18*b^3)*x^4 + 2*(72*a^5*b^2 + 92*a^3*b^2 + 25*a*b^2)*x^3 + (45*a^6*b + 86*a^4*b + 46*a^2*b + 5*b)*x^2 + 2*(3*a^7 + 8*a^5 + 7*a^3 + 2*a)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (3*b^7*x^8 + 18*a*b^6*x^7 + (45*a^2*b^5 + 7*b^5)*x^6 + 4*(15*a^3*b^4 + 7*a*b^4)*x^5 + (45*a^4*b^3 + 42*a^2*b^3 + 5*b^3)*x^4 + 2*(9*a^5*b^2 + 14*a^3*b^2 + 5*a*b^2)*x^3 + (3*a^6*b + 7*a^4*b + 5*a^2*b + b)*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^8*x^6 + 6*a*b^7*x^5 + a^6*b^2 + 3*a^4*b^2 + 3*(5*a^2*b^6 + b^6)*x^4 + 3*a^2*b^2 + 4*(5*a^3*b^5 + 3*a*b^5)*x^3 + 3*(5*a^4*b^4 + 6*a^2*b^4 + b^4)*x^2 + (b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^6*x^4 + 4*a*b^5*x^3 + a^4*b^2 + a^2*b^2 + (6*a^2*b^4 + b^4)*x^2 + 2*(2*a^3*b^3 + a*b^3)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + b^2 + 6*(a^5*b^3 + 2*a^3*b^3 + a*b^3)*x + 3*(b^7*x^5 + 5*a*b^6*x^4 + a^5*b^2 + 2*a^3*b^2 + 2*(5*a^2*b^5 + b^5)*x^3 + a*b^2 + 2*(5*a^3*b^4 + 3*a*b^4)*x^2 + (5*a^4*b^3 + 6*a^2*b^3 + b^3)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(1/2*(9*b^10*x^10 + 82*a*b^9*x^9 + 2*a^10 + 2*(167*a^2*b^8 + 18*b^8)*x^8 + 8*a^8 + 32*(25*a^3*b^7 + 8*a*b^7)*x^7 + 2*(623*a^4*b^6 + 394*a^2*b^6 + 27*b^6)*x^6 + 12*a^6 + 4*(329*a^5*b^5 + 342*a^3*b^5 + 69*a*b^5)*x^5 + 4*(238*a^6*b^4 + 365*a^4*b^4 + 144*a^2*b^4 + 9*b^4)*x^4 + 8*a^4 + 16*(29*a^7*b^3 + 61*a^5*b^3 + 39*a^3*b^3 + 7*a*b^3)*x^3 + (9*b^6*x^6 + 46*a*b^5*x^5 + 2*a^6 + 4*(24*a^2*b^4 + b^4)*x^4 + 4*a^4 + 8*(13*a^3*b^3 + 2*a*b^3)*x^3 + (61*a^4*b^2 + 24*a^2*b^2 - b^2)*x^2 + 2*a^2 + 2*(9*a^5*b + 8*a^3*b - a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + (145*a^8*b^2 + 396*a^6*b^2 + 366*a^4*b^2 + 124*a^2*b^2 + 9*b^2)*x^2 + (36*b^7*x^7 + 220*a*b^6*x^6 + 8*a^7 + 8*(71*a^2*b^5 + 6*b^5)*x^5 + 20*a^5 + 16*(50*a^3*b^4 + 13*a*b^4)*x^4 + (660*a^4*b^3 + 356*a^2*b^3 + 13*b^3)*x^3 + 16*a^3 + (316*a^5*b^2 + 300*a^3*b^2 + 39*a*b^2)*x^2 + 2*(40*a^6*b + 62*a^4*b + 21*a^2*b - b)*x + 4*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (54*b^8*x^8 + 384*a*b^7*x^7 + 12*a^8 + 6*(197*a^2*b^6 + 20*b^6)*x^6 + 36*a^6 + 12*(171*a^3*b^5 + 52*a*b^5)*x^5 + (2190*a^4*b^4 + 1332*a^2*b^4 + 83*b^4)*x^4 + 38*a^4 + 4*(366*a^5*b^3 + 372*a^3*b^3 + 71*a*b^3)*x^3 + (594*a^6*b^2 + 912*a^4*b^2 + 357*a^2*b^2 + 19*b^2)*x^2 + 16*a^2 + 2*(66*a^7*b + 144*a^5*b + 97*a^3*b + 19*a*b)*x + 2)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*a^2 + 2*(13*a^9*b + 44*a^7*b + 54*a^5*b + 28*a^3*b + 5*a*b)*x + (36*b^9*x^9 + 292*a*b^8*x^8 + 8*a^9 + 4*(261*a^2*b^7 + 28*b^7)*x^7 + 28*a^7 + 4*(539*a^3*b^6 + 172*a*b^6)*x^6 + (2828*a^4*b^5 + 1788*a^2*b^5 + 123*b^5)*x^5 + 36*a^5 + (2436*a^5*b^4 + 2540*a^3*b^4 + 519*a*b^4)*x^4 + (1372*a^6*b^3 + 2120*a^4*b^3 + 855*a^2*b^3 + 57*b^3)*x^3 + 20*a^3 + (484*a^7*b^2 + 1032*a^5*b^2 + 681*a^3*b^2 + 133*a*b^2)*x^2 + 2*(48*a^8*b + 134*a^6*b + 129*a^4*b + 48*a^2*b + 5*b)*x + 4*a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^10*x^8 + 8*a*b^9*x^7 + a^8*b^2 + 4*a^6*b^2 + 4*(7*a^2*b^8 + b^8)*x^6 + 6*a^4*b^2 + 8*(7*a^3*b^7 + 3*a*b^7)*x^5 + 2*(35*a^4*b^6 + 30*a^2*b^6 + 3*b^6)*x^4 + 4*a^2*b^2 + 8*(7*a^5*b^5 + 10*a^3*b^5 + 3*a*b^5)*x^3 + (b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*(7*a^6*b^4 + 15*a^4*b^4 + 9*a^2*b^4 + b^4)*x^2 + 4*(b^7*x^5 + 5*a*b^6*x^4 + a^5*b^2 + a^3*b^2 + (10*a^2*b^5 + b^5)*x^3 + (10*a^3*b^4 + 3*a*b^4)*x^2 + (5*a^4*b^3 + 3*a^2*b^3)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 6*(b^8*x^6 + 6*a*b^7*x^5 + a^6*b^2 + 2*a^4*b^2 + (15*a^2*b^6 + 2*b^6)*x^4 + a^2*b^2 + 4*(5*a^3*b^5 + 2*a*b^5)*x^3 + (15*a^4*b^4 + 12*a^2*b^4 + b^4)*x^2 + 2*(3*a^5*b^3 + 4*a^3*b^3 + a*b^3)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + b^2 + 8*(a^7*b^3 + 3*a^5*b^3 + 3*a^3*b^3 + a*b^3)*x + 4*(b^9*x^7 + 7*a*b^8*x^6 + a^7*b^2 + 3*a^5*b^2 + 3*(7*a^2*b^7 + b^7)*x^5 + 3*a^3*b^2 + 5*(7*a^3*b^6 + 3*a*b^6)*x^4 + (35*a^4*b^5 + 30*a^2*b^5 + 3*b^5)*x^3 + a*b^2 + 3*(7*a^5*b^4 + 10*a^3*b^4 + 3*a*b^4)*x^2 + (7*a^6*b^3 + 15*a^4*b^3 + 9*a^2*b^3 + b^3)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
90,0,0,0,0.000000," ","integrate(x/arcsinh(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b^{8} x^{8} + 7 \, a b^{7} x^{7} + 3 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 5 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 3 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{5} x^{5} + 4 \, a b^{4} x^{4} + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(a^{4} b + a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{6} x^{6} + 15 \, a b^{5} x^{5} + 5 \, {\left(6 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 15 \, {\left(2 \, a^{3} b^{3} + a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 15 \, a^{2} b^{2} + 2 \, b^{2}\right)} x^{2} + {\left(3 \, a^{5} b + 5 \, a^{3} b + 2 \, a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + {\left(2 \, b^{8} x^{8} + 15 \, a b^{7} x^{7} + a^{8} + {\left(49 \, a^{2} b^{6} + 6 \, b^{6}\right)} x^{6} + 3 \, a^{6} + {\left(91 \, a^{3} b^{5} + 33 \, a b^{5}\right)} x^{5} + 3 \, {\left(35 \, a^{4} b^{4} + 25 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 3 \, a^{4} + {\left(77 \, a^{5} b^{3} + 90 \, a^{3} b^{3} + 21 \, a b^{3}\right)} x^{3} + {\left(35 \, a^{6} b^{2} + 60 \, a^{4} b^{2} + 27 \, a^{2} b^{2} + 2 \, b^{2}\right)} x^{2} + {\left(2 \, b^{5} x^{5} + 9 \, a b^{4} x^{4} + a^{5} + 2 \, {\left(8 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 2 \, {\left(7 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + 6 \, {\left(a^{4} b + a^{2} b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(6 \, b^{6} x^{6} + 33 \, a b^{5} x^{5} + 3 \, a^{6} + 5 \, {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 7 \, a^{4} + {\left(90 \, a^{3} b^{3} + 37 \, a b^{3}\right)} x^{3} + {\left(60 \, a^{4} b^{2} + 51 \, a^{2} b^{2} + 5 \, b^{2}\right)} x^{2} + 5 \, a^{2} + {\left(21 \, a^{5} b + 31 \, a^{3} b + 10 \, a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + a^{2} + 3 \, {\left(3 \, a^{7} b + 7 \, a^{5} b + 5 \, a^{3} b + a b\right)} x + {\left(6 \, b^{7} x^{7} + 39 \, a b^{6} x^{6} + 3 \, a^{7} + 2 \, {\left(54 \, a^{2} b^{5} + 7 \, b^{5}\right)} x^{5} + 8 \, a^{5} + {\left(165 \, a^{3} b^{4} + 64 \, a b^{4}\right)} x^{4} + {\left(150 \, a^{4} b^{3} + 116 \, a^{2} b^{3} + 11 \, b^{3}\right)} x^{3} + 7 \, a^{3} + {\left(81 \, a^{5} b^{2} + 104 \, a^{3} b^{2} + 29 \, a b^{2}\right)} x^{2} + {\left(24 \, a^{6} b + 46 \, a^{4} b + 25 \, a^{2} b + 3 \, b\right)} x + 2 \, a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(3 \, b^{7} x^{7} + 18 \, a b^{6} x^{6} + {\left(45 \, a^{2} b^{5} + 7 \, b^{5}\right)} x^{5} + 4 \, {\left(15 \, a^{3} b^{4} + 7 \, a b^{4}\right)} x^{4} + {\left(45 \, a^{4} b^{3} + 42 \, a^{2} b^{3} + 5 \, b^{3}\right)} x^{3} + 2 \, {\left(9 \, a^{5} b^{2} + 14 \, a^{3} b^{2} + 5 \, a b^{2}\right)} x^{2} + {\left(3 \, a^{6} b + 7 \, a^{4} b + 5 \, a^{2} b + b\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{8} x^{6} + 6 \, a b^{7} x^{5} + a^{6} b^{2} + 3 \, a^{4} b^{2} + 3 \, {\left(5 \, a^{2} b^{6} + b^{6}\right)} x^{4} + 3 \, a^{2} b^{2} + 4 \, {\left(5 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{3} + 3 \, {\left(5 \, a^{4} b^{4} + 6 \, a^{2} b^{4} + b^{4}\right)} x^{2} + {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + a^{4} b^{2} + a^{2} b^{2} + {\left(6 \, a^{2} b^{4} + b^{4}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{3} + a b^{3}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + b^{2} + 6 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{3} + a b^{3}\right)} x + 3 \, {\left(b^{7} x^{5} + 5 \, a b^{6} x^{4} + a^{5} b^{2} + 2 \, a^{3} b^{2} + 2 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{3} + a b^{2} + 2 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{2} + {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int \frac{4 \, b^{9} x^{9} + 35 \, a b^{8} x^{8} + 3 \, a^{9} + 8 \, {\left(17 \, a^{2} b^{7} + 2 \, b^{7}\right)} x^{7} + 12 \, a^{7} + 4 \, {\left(77 \, a^{3} b^{6} + 27 \, a b^{6}\right)} x^{6} + 8 \, {\left(56 \, a^{4} b^{5} + 39 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{5} + 18 \, a^{5} + 2 \, {\left(217 \, a^{5} b^{4} + 250 \, a^{3} b^{4} + 57 \, a b^{4}\right)} x^{4} + 8 \, {\left(35 \, a^{6} b^{3} + 60 \, a^{4} b^{3} + 27 \, a^{2} b^{3} + 2 \, b^{3}\right)} x^{3} + {\left(4 \, b^{5} x^{5} + 19 \, a b^{4} x^{4} + 36 \, a^{2} b^{3} x^{3} + 34 \, a^{3} b^{2} x^{2} + 16 \, a^{4} b x + 3 \, a^{5} - 3 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 12 \, a^{3} + 4 \, {\left(29 \, a^{7} b^{2} + 69 \, a^{5} b^{2} + 51 \, a^{3} b^{2} + 11 \, a b^{2}\right)} x^{2} + {\left(16 \, b^{6} x^{6} + 92 \, a b^{5} x^{5} + 12 \, a^{6} + 4 \, {\left(55 \, a^{2} b^{4} + 4 \, b^{4}\right)} x^{4} + 12 \, a^{4} + 20 \, {\left(14 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + 4 \, {\left(50 \, a^{4} b^{2} + 21 \, a^{2} b^{2}\right)} x^{2} - 3 \, a^{2} + {\left(76 \, a^{5} b + 52 \, a^{3} b - 3 \, a b\right)} x - 3\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(8 \, b^{7} x^{7} + 54 \, a b^{6} x^{6} + 6 \, a^{7} + 4 \, {\left(39 \, a^{2} b^{5} + 4 \, b^{5}\right)} x^{5} + 12 \, a^{5} + 2 \, {\left(125 \, a^{3} b^{4} + 38 \, a b^{4}\right)} x^{4} + 8 \, {\left(30 \, a^{4} b^{3} + 18 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 7 \, a^{3} + {\left(138 \, a^{5} b^{2} + 136 \, a^{3} b^{2} + 23 \, a b^{2}\right)} x^{2} + 2 \, {\left(22 \, a^{6} b + 32 \, a^{4} b + 11 \, a^{2} b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, {\left(7 \, a^{8} b + 22 \, a^{6} b + 24 \, a^{4} b + 10 \, a^{2} b + b\right)} x + {\left(16 \, b^{8} x^{8} + 124 \, a b^{7} x^{7} + 12 \, a^{8} + 12 \, {\left(35 \, a^{2} b^{6} + 4 \, b^{6}\right)} x^{6} + 36 \, a^{6} + 4 \, {\left(203 \, a^{3} b^{5} + 69 \, a b^{5}\right)} x^{5} + 4 \, {\left(245 \, a^{4} b^{4} + 165 \, a^{2} b^{4} + 12 \, b^{4}\right)} x^{4} + 39 \, a^{4} + 3 \, {\left(252 \, a^{5} b^{3} + 280 \, a^{3} b^{3} + 61 \, a b^{3}\right)} x^{3} + {\left(364 \, a^{6} b^{2} + 600 \, a^{4} b^{2} + 261 \, a^{2} b^{2} + 19 \, b^{2}\right)} x^{2} + 18 \, a^{2} + {\left(100 \, a^{7} b + 228 \, a^{5} b + 165 \, a^{3} b + 37 \, a b\right)} x + 3\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 3 \, a}{2 \, {\left(b^{9} x^{8} + 8 \, a b^{8} x^{7} + a^{8} b + 4 \, a^{6} b + 4 \, {\left(7 \, a^{2} b^{7} + b^{7}\right)} x^{6} + 8 \, {\left(7 \, a^{3} b^{6} + 3 \, a b^{6}\right)} x^{5} + 6 \, a^{4} b + 2 \, {\left(35 \, a^{4} b^{5} + 30 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{4} + 8 \, {\left(7 \, a^{5} b^{4} + 10 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{3} + {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, a^{2} b + 4 \, {\left(7 \, a^{6} b^{3} + 15 \, a^{4} b^{3} + 9 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 4 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + a^{5} b + a^{3} b + {\left(10 \, a^{2} b^{4} + b^{4}\right)} x^{3} + {\left(10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{2} + {\left(5 \, a^{4} b^{2} + 3 \, a^{2} b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{7} x^{6} + 6 \, a b^{6} x^{5} + a^{6} b + 2 \, a^{4} b + {\left(15 \, a^{2} b^{5} + 2 \, b^{5}\right)} x^{4} + 4 \, {\left(5 \, a^{3} b^{4} + 2 \, a b^{4}\right)} x^{3} + a^{2} b + {\left(15 \, a^{4} b^{3} + 12 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 2 \, {\left(3 \, a^{5} b^{2} + 4 \, a^{3} b^{2} + a b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 8 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{2} + a b^{2}\right)} x + 4 \, {\left(b^{8} x^{7} + 7 \, a b^{7} x^{6} + a^{7} b + 3 \, a^{5} b + 3 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{5} + 5 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{4} + 3 \, a^{3} b + {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{3} + 3 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{2} + a b + {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*(b^8*x^8 + 7*a*b^7*x^7 + 3*(7*a^2*b^6 + b^6)*x^6 + 5*(7*a^3*b^5 + 3*a*b^5)*x^5 + (35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 3*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + (7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + (b^5*x^5 + 4*a*b^4*x^4 + (6*a^2*b^3 + b^3)*x^3 + 2*(2*a^3*b^2 + a*b^2)*x^2 + (a^4*b + a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^6*x^6 + 15*a*b^5*x^5 + 5*(6*a^2*b^4 + b^4)*x^4 + 15*(2*a^3*b^3 + a*b^3)*x^3 + (15*a^4*b^2 + 15*a^2*b^2 + 2*b^2)*x^2 + (3*a^5*b + 5*a^3*b + 2*a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x + (2*b^8*x^8 + 15*a*b^7*x^7 + a^8 + (49*a^2*b^6 + 6*b^6)*x^6 + 3*a^6 + (91*a^3*b^5 + 33*a*b^5)*x^5 + 3*(35*a^4*b^4 + 25*a^2*b^4 + 2*b^4)*x^4 + 3*a^4 + (77*a^5*b^3 + 90*a^3*b^3 + 21*a*b^3)*x^3 + (35*a^6*b^2 + 60*a^4*b^2 + 27*a^2*b^2 + 2*b^2)*x^2 + (2*b^5*x^5 + 9*a*b^4*x^4 + a^5 + 2*(8*a^2*b^3 + b^3)*x^3 + 2*a^3 + 2*(7*a^3*b^2 + 3*a*b^2)*x^2 + 6*(a^4*b + a^2*b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (6*b^6*x^6 + 33*a*b^5*x^5 + 3*a^6 + 5*(15*a^2*b^4 + 2*b^4)*x^4 + 7*a^4 + (90*a^3*b^3 + 37*a*b^3)*x^3 + (60*a^4*b^2 + 51*a^2*b^2 + 5*b^2)*x^2 + 5*a^2 + (21*a^5*b + 31*a^3*b + 10*a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + a^2 + 3*(3*a^7*b + 7*a^5*b + 5*a^3*b + a*b)*x + (6*b^7*x^7 + 39*a*b^6*x^6 + 3*a^7 + 2*(54*a^2*b^5 + 7*b^5)*x^5 + 8*a^5 + (165*a^3*b^4 + 64*a*b^4)*x^4 + (150*a^4*b^3 + 116*a^2*b^3 + 11*b^3)*x^3 + 7*a^3 + (81*a^5*b^2 + 104*a^3*b^2 + 29*a*b^2)*x^2 + (24*a^6*b + 46*a^4*b + 25*a^2*b + 3*b)*x + 2*a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (3*b^7*x^7 + 18*a*b^6*x^6 + (45*a^2*b^5 + 7*b^5)*x^5 + 4*(15*a^3*b^4 + 7*a*b^4)*x^4 + (45*a^4*b^3 + 42*a^2*b^3 + 5*b^3)*x^3 + 2*(9*a^5*b^2 + 14*a^3*b^2 + 5*a*b^2)*x^2 + (3*a^6*b + 7*a^4*b + 5*a^2*b + b)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^8*x^6 + 6*a*b^7*x^5 + a^6*b^2 + 3*a^4*b^2 + 3*(5*a^2*b^6 + b^6)*x^4 + 3*a^2*b^2 + 4*(5*a^3*b^5 + 3*a*b^5)*x^3 + 3*(5*a^4*b^4 + 6*a^2*b^4 + b^4)*x^2 + (b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^6*x^4 + 4*a*b^5*x^3 + a^4*b^2 + a^2*b^2 + (6*a^2*b^4 + b^4)*x^2 + 2*(2*a^3*b^3 + a*b^3)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + b^2 + 6*(a^5*b^3 + 2*a^3*b^3 + a*b^3)*x + 3*(b^7*x^5 + 5*a*b^6*x^4 + a^5*b^2 + 2*a^3*b^2 + 2*(5*a^2*b^5 + b^5)*x^3 + a*b^2 + 2*(5*a^3*b^4 + 3*a*b^4)*x^2 + (5*a^4*b^3 + 6*a^2*b^3 + b^3)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(1/2*(4*b^9*x^9 + 35*a*b^8*x^8 + 3*a^9 + 8*(17*a^2*b^7 + 2*b^7)*x^7 + 12*a^7 + 4*(77*a^3*b^6 + 27*a*b^6)*x^6 + 8*(56*a^4*b^5 + 39*a^2*b^5 + 3*b^5)*x^5 + 18*a^5 + 2*(217*a^5*b^4 + 250*a^3*b^4 + 57*a*b^4)*x^4 + 8*(35*a^6*b^3 + 60*a^4*b^3 + 27*a^2*b^3 + 2*b^3)*x^3 + (4*b^5*x^5 + 19*a*b^4*x^4 + 36*a^2*b^3*x^3 + 34*a^3*b^2*x^2 + 16*a^4*b*x + 3*a^5 - 3*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 12*a^3 + 4*(29*a^7*b^2 + 69*a^5*b^2 + 51*a^3*b^2 + 11*a*b^2)*x^2 + (16*b^6*x^6 + 92*a*b^5*x^5 + 12*a^6 + 4*(55*a^2*b^4 + 4*b^4)*x^4 + 12*a^4 + 20*(14*a^3*b^3 + 3*a*b^3)*x^3 + 4*(50*a^4*b^2 + 21*a^2*b^2)*x^2 - 3*a^2 + (76*a^5*b + 52*a^3*b - 3*a*b)*x - 3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(8*b^7*x^7 + 54*a*b^6*x^6 + 6*a^7 + 4*(39*a^2*b^5 + 4*b^5)*x^5 + 12*a^5 + 2*(125*a^3*b^4 + 38*a*b^4)*x^4 + 8*(30*a^4*b^3 + 18*a^2*b^3 + b^3)*x^3 + 7*a^3 + (138*a^5*b^2 + 136*a^3*b^2 + 23*a*b^2)*x^2 + 2*(22*a^6*b + 32*a^4*b + 11*a^2*b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*(7*a^8*b + 22*a^6*b + 24*a^4*b + 10*a^2*b + b)*x + (16*b^8*x^8 + 124*a*b^7*x^7 + 12*a^8 + 12*(35*a^2*b^6 + 4*b^6)*x^6 + 36*a^6 + 4*(203*a^3*b^5 + 69*a*b^5)*x^5 + 4*(245*a^4*b^4 + 165*a^2*b^4 + 12*b^4)*x^4 + 39*a^4 + 3*(252*a^5*b^3 + 280*a^3*b^3 + 61*a*b^3)*x^3 + (364*a^6*b^2 + 600*a^4*b^2 + 261*a^2*b^2 + 19*b^2)*x^2 + 18*a^2 + (100*a^7*b + 228*a^5*b + 165*a^3*b + 37*a*b)*x + 3)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 3*a)/((b^9*x^8 + 8*a*b^8*x^7 + a^8*b + 4*a^6*b + 4*(7*a^2*b^7 + b^7)*x^6 + 8*(7*a^3*b^6 + 3*a*b^6)*x^5 + 6*a^4*b + 2*(35*a^4*b^5 + 30*a^2*b^5 + 3*b^5)*x^4 + 8*(7*a^5*b^4 + 10*a^3*b^4 + 3*a*b^4)*x^3 + (b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*a^2*b + 4*(7*a^6*b^3 + 15*a^4*b^3 + 9*a^2*b^3 + b^3)*x^2 + 4*(b^6*x^5 + 5*a*b^5*x^4 + a^5*b + a^3*b + (10*a^2*b^4 + b^4)*x^3 + (10*a^3*b^3 + 3*a*b^3)*x^2 + (5*a^4*b^2 + 3*a^2*b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 6*(b^7*x^6 + 6*a*b^6*x^5 + a^6*b + 2*a^4*b + (15*a^2*b^5 + 2*b^5)*x^4 + 4*(5*a^3*b^4 + 2*a*b^4)*x^3 + a^2*b + (15*a^4*b^3 + 12*a^2*b^3 + b^3)*x^2 + 2*(3*a^5*b^2 + 4*a^3*b^2 + a*b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 8*(a^7*b^2 + 3*a^5*b^2 + 3*a^3*b^2 + a*b^2)*x + 4*(b^8*x^7 + 7*a*b^7*x^6 + a^7*b + 3*a^5*b + 3*(7*a^2*b^6 + b^6)*x^5 + 5*(7*a^3*b^5 + 3*a*b^5)*x^4 + 3*a^3*b + (35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^3 + 3*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^2 + a*b + (7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
91,0,0,0,0.000000," ","integrate(1/arcsinh(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + {\left(6 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(2 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 3 \, a^{5} + 5 \, {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 5 \, a^{3} + 15 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(15 \, a^{4} b + 15 \, a^{2} b + 2 \, b\right)} x + 2 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4} - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + {\left(10 \, a^{2} b^{3} + b^{3}\right)} x^{3} + a^{3} + {\left(10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 3 \, a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + {\left(3 \, b^{6} x^{6} + 18 \, a b^{5} x^{5} + 3 \, a^{6} + 3 \, {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 6 \, a^{4} + 12 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(45 \, a^{4} b^{2} + 36 \, a^{2} b^{2} + 4 \, b^{2}\right)} x^{2} + 4 \, a^{2} + 2 \, {\left(9 \, a^{5} b + 12 \, a^{3} b + 4 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(3 \, b^{6} x^{6} + 18 \, a b^{5} x^{5} + 3 \, a^{6} + {\left(45 \, a^{2} b^{4} + 7 \, b^{4}\right)} x^{4} + 7 \, a^{4} + 4 \, {\left(15 \, a^{3} b^{3} + 7 \, a b^{3}\right)} x^{3} + {\left(45 \, a^{4} b^{2} + 42 \, a^{2} b^{2} + 5 \, b^{2}\right)} x^{2} + 5 \, a^{2} + 2 \, {\left(9 \, a^{5} b + 14 \, a^{3} b + 5 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a}{2 \, {\left(b^{7} x^{6} + 6 \, a b^{6} x^{5} + a^{6} b + 3 \, a^{4} b + 3 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{4} + 4 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{3} + 3 \, a^{2} b + 3 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + a^{4} b + a^{2} b + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{2} + a b^{2}\right)} x + 3 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + a^{5} b + 2 \, a^{3} b + 2 \, {\left(5 \, a^{2} b^{4} + b^{4}\right)} x^{3} + 2 \, {\left(5 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{2} + a b + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{2} + b^{2}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int \frac{b^{8} x^{8} + 8 \, a b^{7} x^{7} + a^{8} + 4 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 4 \, a^{6} + 8 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 6 \, a^{4} + 8 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4} + 3\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(4 \, b^{5} x^{5} + 20 \, a b^{4} x^{4} + 4 \, a^{5} + 4 \, {\left(10 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 4 \, a^{3} + 4 \, {\left(10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(20 \, a^{4} b + 12 \, a^{2} b + 3 \, b\right)} x + 3 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(2 \, b^{6} x^{6} + 12 \, a b^{5} x^{5} + 2 \, a^{6} + 2 \, {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 4 \, a^{4} + 8 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(30 \, a^{4} b^{2} + 24 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(6 \, a^{5} b + 8 \, a^{3} b + a b\right)} x - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, a^{2} + 8 \, {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + {\left(4 \, b^{7} x^{7} + 28 \, a b^{6} x^{6} + 4 \, a^{7} + 12 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 12 \, a^{5} + 20 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(140 \, a^{4} b^{3} + 120 \, a^{2} b^{3} + 9 \, b^{3}\right)} x^{3} + 9 \, a^{3} + 3 \, {\left(28 \, a^{5} b^{2} + 40 \, a^{3} b^{2} + 9 \, a b^{2}\right)} x^{2} + {\left(28 \, a^{6} b + 60 \, a^{4} b + 27 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1}{2 \, {\left(b^{8} x^{8} + 8 \, a b^{7} x^{7} + a^{8} + 4 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 4 \, a^{6} + 8 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 6 \, a^{4} + 8 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 4 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + {\left(10 \, a^{2} b^{3} + b^{3}\right)} x^{3} + a^{3} + {\left(10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 3 \, a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{6} x^{6} + 6 \, a b^{5} x^{5} + a^{6} + {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 2 \, a^{4} + 4 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(3 \, a^{5} b + 4 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, a^{2} + 8 \, {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + 4 \, {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*(b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (b^4*x^4 + 4*a*b^3*x^3 + a^4 + (6*a^2*b^2 + b^2)*x^2 + a^2 + 2*(2*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^5*x^5 + 15*a*b^4*x^4 + 3*a^5 + 5*(6*a^2*b^3 + b^3)*x^3 + 5*a^3 + 15*(2*a^3*b^2 + a*b^2)*x^2 + (15*a^4*b + 15*a^2*b + 2*b)*x + 2*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + (b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4 - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + (10*a^2*b^3 + b^3)*x^3 + a^3 + (10*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 3*a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + (3*b^6*x^6 + 18*a*b^5*x^5 + 3*a^6 + 3*(15*a^2*b^4 + 2*b^4)*x^4 + 6*a^4 + 12*(5*a^3*b^3 + 2*a*b^3)*x^3 + (45*a^4*b^2 + 36*a^2*b^2 + 4*b^2)*x^2 + 4*a^2 + 2*(9*a^5*b + 12*a^3*b + 4*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + a)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (3*b^6*x^6 + 18*a*b^5*x^5 + 3*a^6 + (45*a^2*b^4 + 7*b^4)*x^4 + 7*a^4 + 4*(15*a^3*b^3 + 7*a*b^3)*x^3 + (45*a^4*b^2 + 42*a^2*b^2 + 5*b^2)*x^2 + 5*a^2 + 2*(9*a^5*b + 14*a^3*b + 5*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + a)/((b^7*x^6 + 6*a*b^6*x^5 + a^6*b + 3*a^4*b + 3*(5*a^2*b^5 + b^5)*x^4 + 4*(5*a^3*b^4 + 3*a*b^4)*x^3 + 3*a^2*b + 3*(5*a^4*b^3 + 6*a^2*b^3 + b^3)*x^2 + (b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^5*x^4 + 4*a*b^4*x^3 + a^4*b + a^2*b + (6*a^2*b^3 + b^3)*x^2 + 2*(2*a^3*b^2 + a*b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 6*(a^5*b^2 + 2*a^3*b^2 + a*b^2)*x + 3*(b^6*x^5 + 5*a*b^5*x^4 + a^5*b + 2*a^3*b + 2*(5*a^2*b^4 + b^4)*x^3 + 2*(5*a^3*b^3 + 3*a*b^3)*x^2 + a*b + (5*a^4*b^2 + 6*a^2*b^2 + b^2)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(1/2*(b^8*x^8 + 8*a*b^7*x^7 + a^8 + 4*(7*a^2*b^6 + b^6)*x^6 + 4*a^6 + 8*(7*a^3*b^5 + 3*a*b^5)*x^5 + 2*(35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 6*a^4 + 8*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + (b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4 + 3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*(7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + (4*b^5*x^5 + 20*a*b^4*x^4 + 4*a^5 + 4*(10*a^2*b^3 + b^3)*x^3 + 4*a^3 + 4*(10*a^3*b^2 + 3*a*b^2)*x^2 + (20*a^4*b + 12*a^2*b + 3*b)*x + 3*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(2*b^6*x^6 + 12*a*b^5*x^5 + 2*a^6 + 2*(15*a^2*b^4 + 2*b^4)*x^4 + 4*a^4 + 8*(5*a^3*b^3 + 2*a*b^3)*x^3 + (30*a^4*b^2 + 24*a^2*b^2 + b^2)*x^2 + a^2 + 2*(6*a^5*b + 8*a^3*b + a*b)*x - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*a^2 + 8*(a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x + (4*b^7*x^7 + 28*a*b^6*x^6 + 4*a^7 + 12*(7*a^2*b^5 + b^5)*x^5 + 12*a^5 + 20*(7*a^3*b^4 + 3*a*b^4)*x^4 + (140*a^4*b^3 + 120*a^2*b^3 + 9*b^3)*x^3 + 9*a^3 + 3*(28*a^5*b^2 + 40*a^3*b^2 + 9*a*b^2)*x^2 + (28*a^6*b + 60*a^4*b + 27*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)/((b^8*x^8 + 8*a*b^7*x^7 + a^8 + 4*(7*a^2*b^6 + b^6)*x^6 + 4*a^6 + 8*(7*a^3*b^5 + 3*a*b^5)*x^5 + 2*(35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 6*a^4 + 8*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + (b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*(7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + 4*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + (10*a^2*b^3 + b^3)*x^3 + a^3 + (10*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 3*a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 6*(b^6*x^6 + 6*a*b^5*x^5 + a^6 + (15*a^2*b^4 + 2*b^4)*x^4 + 2*a^4 + 4*(5*a^3*b^3 + 2*a*b^3)*x^3 + (15*a^4*b^2 + 12*a^2*b^2 + b^2)*x^2 + a^2 + 2*(3*a^5*b + 4*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*a^2 + 8*(a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x + 4*(b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
92,0,0,0,0.000000," ","integrate(1/x/arcsinh(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b^{8} x^{8} + 7 \, a b^{7} x^{7} + 3 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 5 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 3 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{5} x^{5} + 4 \, a b^{4} x^{4} + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(a^{4} b + a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{6} x^{6} + 15 \, a b^{5} x^{5} + 5 \, {\left(6 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 15 \, {\left(2 \, a^{3} b^{3} + a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 15 \, a^{2} b^{2} + 2 \, b^{2}\right)} x^{2} + {\left(3 \, a^{5} b + 5 \, a^{3} b + 2 \, a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x - {\left(a b^{7} x^{7} + 7 \, a^{2} b^{6} x^{6} + a^{8} + 3 \, a^{6} + 3 \, {\left(7 \, a^{3} b^{5} + a b^{5}\right)} x^{5} + 5 \, {\left(7 \, a^{4} b^{4} + 3 \, a^{2} b^{4}\right)} x^{4} + 3 \, a^{4} + {\left(35 \, a^{5} b^{3} + 30 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + 3 \, {\left(7 \, a^{6} b^{2} + 10 \, a^{4} b^{2} + 3 \, a^{2} b^{2}\right)} x^{2} + {\left(a b^{4} x^{4} + a^{5} + 2 \, {\left(2 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 6 \, {\left(a^{3} b^{2} + a b^{2}\right)} x^{2} + 2 \, {\left(2 \, a^{4} b + 3 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, a b^{5} x^{5} + 3 \, a^{6} + {\left(15 \, a^{2} b^{4} + 4 \, b^{4}\right)} x^{4} + 7 \, a^{4} + {\left(30 \, a^{3} b^{3} + 19 \, a b^{3}\right)} x^{3} + {\left(30 \, a^{4} b^{2} + 33 \, a^{2} b^{2} + 5 \, b^{2}\right)} x^{2} + 5 \, a^{2} + 5 \, {\left(3 \, a^{5} b + 5 \, a^{3} b + 2 \, a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + a^{2} + {\left(7 \, a^{7} b + 15 \, a^{5} b + 9 \, a^{3} b + a b\right)} x + {\left(3 \, a b^{6} x^{6} + 3 \, a^{7} + 2 \, {\left(9 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 8 \, a^{5} + {\left(45 \, a^{3} b^{4} + 16 \, a b^{4}\right)} x^{4} + {\left(60 \, a^{4} b^{3} + 44 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 7 \, a^{3} + {\left(45 \, a^{5} b^{2} + 56 \, a^{3} b^{2} + 13 \, a b^{2}\right)} x^{2} + {\left(18 \, a^{6} b + 34 \, a^{4} b + 17 \, a^{2} b + b\right)} x + 2 \, a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(3 \, b^{7} x^{7} + 18 \, a b^{6} x^{6} + {\left(45 \, a^{2} b^{5} + 7 \, b^{5}\right)} x^{5} + 4 \, {\left(15 \, a^{3} b^{4} + 7 \, a b^{4}\right)} x^{4} + {\left(45 \, a^{4} b^{3} + 42 \, a^{2} b^{3} + 5 \, b^{3}\right)} x^{3} + 2 \, {\left(9 \, a^{5} b^{2} + 14 \, a^{3} b^{2} + 5 \, a b^{2}\right)} x^{2} + {\left(3 \, a^{6} b + 7 \, a^{4} b + 5 \, a^{2} b + b\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{8} x^{8} + 6 \, a b^{7} x^{7} + 3 \, {\left(5 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 4 \, {\left(5 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 3 \, {\left(5 \, a^{4} b^{4} + 6 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 6 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{3} + a b^{3}\right)} x^{3} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{5} x^{5} + 3 \, a b^{4} x^{4} + 3 \, a^{2} b^{3} x^{3} + a^{3} b^{2} x^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{6} x^{6} + 4 \, a b^{5} x^{5} + {\left(6 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 2 \, {\left(2 \, a^{3} b^{3} + a b^{3}\right)} x^{3} + {\left(a^{4} b^{2} + a^{2} b^{2}\right)} x^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 3 \, {\left(b^{7} x^{7} + 5 \, a b^{6} x^{6} + 2 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 2 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x^{3} + {\left(a^{5} b^{2} + 2 \, a^{3} b^{2} + a b^{2}\right)} x^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int \frac{a b^{9} x^{9} + 10 \, a^{2} b^{8} x^{8} + 2 \, a^{10} + 8 \, a^{8} + 4 \, {\left(11 \, a^{3} b^{7} + a b^{7}\right)} x^{7} + 16 \, {\left(7 \, a^{4} b^{6} + 2 \, a^{2} b^{6}\right)} x^{6} + 12 \, a^{6} + 2 \, {\left(91 \, a^{5} b^{5} + 54 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 4 \, {\left(49 \, a^{6} b^{4} + 50 \, a^{4} b^{4} + 9 \, a^{2} b^{4}\right)} x^{4} + 8 \, a^{4} + 4 \, {\left(35 \, a^{7} b^{3} + 55 \, a^{5} b^{3} + 21 \, a^{3} b^{3} + a b^{3}\right)} x^{3} + {\left(a b^{5} x^{5} + 2 \, a^{6} + 2 \, {\left(3 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 4 \, a^{4} + 2 \, {\left(7 \, a^{3} b^{3} + 8 \, a b^{3}\right)} x^{3} + 8 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 2 \, a^{2} + {\left(9 \, a^{5} b + 16 \, a^{3} b + 7 \, a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 16 \, {\left(4 \, a^{8} b^{2} + 9 \, a^{6} b^{2} + 6 \, a^{4} b^{2} + a^{2} b^{2}\right)} x^{2} + {\left(4 \, a b^{6} x^{6} + 8 \, a^{7} + 4 \, {\left(7 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{5} + 20 \, a^{5} + 16 \, {\left(5 \, a^{3} b^{4} + 4 \, a b^{4}\right)} x^{4} + 2 \, {\left(60 \, a^{4} b^{3} + 70 \, a^{2} b^{3} + 11 \, b^{3}\right)} x^{3} + 16 \, a^{3} + {\left(100 \, a^{5} b^{2} + 156 \, a^{3} b^{2} + 57 \, a b^{2}\right)} x^{2} + {\left(44 \, a^{6} b + 88 \, a^{4} b + 51 \, a^{2} b + 7 \, b\right)} x + 4 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(6 \, a b^{7} x^{7} + 12 \, a^{8} + 12 \, {\left(4 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 36 \, a^{6} + 6 \, {\left(27 \, a^{3} b^{5} + 14 \, a b^{5}\right)} x^{5} + 4 \, {\left(75 \, a^{4} b^{4} + 63 \, a^{2} b^{4} + 5 \, b^{4}\right)} x^{4} + 38 \, a^{4} + {\left(330 \, a^{5} b^{3} + 408 \, a^{3} b^{3} + 95 \, a b^{3}\right)} x^{3} + 2 \, {\left(108 \, a^{6} b^{2} + 186 \, a^{4} b^{2} + 84 \, a^{2} b^{2} + 5 \, b^{2}\right)} x^{2} + 16 \, a^{2} + {\left(78 \, a^{7} b + 180 \, a^{5} b + 131 \, a^{3} b + 29 \, a b\right)} x + 2\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 2 \, a^{2} + {\left(17 \, a^{9} b + 52 \, a^{7} b + 54 \, a^{5} b + 20 \, a^{3} b + a b\right)} x + {\left(4 \, a b^{8} x^{8} + 8 \, a^{9} + 4 \, {\left(9 \, a^{2} b^{7} + b^{7}\right)} x^{7} + 28 \, a^{7} + 20 \, {\left(7 \, a^{3} b^{6} + 2 \, a b^{6}\right)} x^{6} + 2 \, {\left(154 \, a^{4} b^{5} + 84 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{5} + 36 \, a^{5} + {\left(420 \, a^{5} b^{4} + 380 \, a^{3} b^{4} + 51 \, a b^{4}\right)} x^{4} + {\left(364 \, a^{6} b^{3} + 500 \, a^{4} b^{3} + 153 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 20 \, a^{3} + {\left(196 \, a^{7} b^{2} + 384 \, a^{5} b^{2} + 213 \, a^{3} b^{2} + 25 \, a b^{2}\right)} x^{2} + {\left(60 \, a^{8} b + 160 \, a^{6} b + 141 \, a^{4} b + 42 \, a^{2} b + b\right)} x + 4 \, a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{10} x^{11} + 8 \, a b^{9} x^{10} + 4 \, {\left(7 \, a^{2} b^{8} + b^{8}\right)} x^{9} + 8 \, {\left(7 \, a^{3} b^{7} + 3 \, a b^{7}\right)} x^{8} + 2 \, {\left(35 \, a^{4} b^{6} + 30 \, a^{2} b^{6} + 3 \, b^{6}\right)} x^{7} + 8 \, {\left(7 \, a^{5} b^{5} + 10 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{6} + 4 \, {\left(7 \, a^{6} b^{4} + 15 \, a^{4} b^{4} + 9 \, a^{2} b^{4} + b^{4}\right)} x^{5} + 8 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{3} + a b^{3}\right)} x^{4} + {\left(a^{8} b^{2} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{2} + 4 \, a^{2} b^{2} + b^{2}\right)} x^{3} + {\left(b^{6} x^{7} + 4 \, a b^{5} x^{6} + 6 \, a^{2} b^{4} x^{5} + 4 \, a^{3} b^{3} x^{4} + a^{4} b^{2} x^{3}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, {\left(b^{7} x^{8} + 5 \, a b^{6} x^{7} + {\left(10 \, a^{2} b^{5} + b^{5}\right)} x^{6} + {\left(10 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{5} + {\left(5 \, a^{4} b^{3} + 3 \, a^{2} b^{3}\right)} x^{4} + {\left(a^{5} b^{2} + a^{3} b^{2}\right)} x^{3}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{8} x^{9} + 6 \, a b^{7} x^{8} + {\left(15 \, a^{2} b^{6} + 2 \, b^{6}\right)} x^{7} + 4 \, {\left(5 \, a^{3} b^{5} + 2 \, a b^{5}\right)} x^{6} + {\left(15 \, a^{4} b^{4} + 12 \, a^{2} b^{4} + b^{4}\right)} x^{5} + 2 \, {\left(3 \, a^{5} b^{3} + 4 \, a^{3} b^{3} + a b^{3}\right)} x^{4} + {\left(a^{6} b^{2} + 2 \, a^{4} b^{2} + a^{2} b^{2}\right)} x^{3}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, {\left(b^{9} x^{10} + 7 \, a b^{8} x^{9} + 3 \, {\left(7 \, a^{2} b^{7} + b^{7}\right)} x^{8} + 5 \, {\left(7 \, a^{3} b^{6} + 3 \, a b^{6}\right)} x^{7} + {\left(35 \, a^{4} b^{5} + 30 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{6} + 3 \, {\left(7 \, a^{5} b^{4} + 10 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{5} + {\left(7 \, a^{6} b^{3} + 15 \, a^{4} b^{3} + 9 \, a^{2} b^{3} + b^{3}\right)} x^{4} + {\left(a^{7} b^{2} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{2} + a b^{2}\right)} x^{3}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*(b^8*x^8 + 7*a*b^7*x^7 + 3*(7*a^2*b^6 + b^6)*x^6 + 5*(7*a^3*b^5 + 3*a*b^5)*x^5 + (35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 3*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + (7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + (b^5*x^5 + 4*a*b^4*x^4 + (6*a^2*b^3 + b^3)*x^3 + 2*(2*a^3*b^2 + a*b^2)*x^2 + (a^4*b + a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^6*x^6 + 15*a*b^5*x^5 + 5*(6*a^2*b^4 + b^4)*x^4 + 15*(2*a^3*b^3 + a*b^3)*x^3 + (15*a^4*b^2 + 15*a^2*b^2 + 2*b^2)*x^2 + (3*a^5*b + 5*a^3*b + 2*a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x - (a*b^7*x^7 + 7*a^2*b^6*x^6 + a^8 + 3*a^6 + 3*(7*a^3*b^5 + a*b^5)*x^5 + 5*(7*a^4*b^4 + 3*a^2*b^4)*x^4 + 3*a^4 + (35*a^5*b^3 + 30*a^3*b^3 + 3*a*b^3)*x^3 + 3*(7*a^6*b^2 + 10*a^4*b^2 + 3*a^2*b^2)*x^2 + (a*b^4*x^4 + a^5 + 2*(2*a^2*b^3 + b^3)*x^3 + 2*a^3 + 6*(a^3*b^2 + a*b^2)*x^2 + 2*(2*a^4*b + 3*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*a*b^5*x^5 + 3*a^6 + (15*a^2*b^4 + 4*b^4)*x^4 + 7*a^4 + (30*a^3*b^3 + 19*a*b^3)*x^3 + (30*a^4*b^2 + 33*a^2*b^2 + 5*b^2)*x^2 + 5*a^2 + 5*(3*a^5*b + 5*a^3*b + 2*a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + a^2 + (7*a^7*b + 15*a^5*b + 9*a^3*b + a*b)*x + (3*a*b^6*x^6 + 3*a^7 + 2*(9*a^2*b^5 + b^5)*x^5 + 8*a^5 + (45*a^3*b^4 + 16*a*b^4)*x^4 + (60*a^4*b^3 + 44*a^2*b^3 + 3*b^3)*x^3 + 7*a^3 + (45*a^5*b^2 + 56*a^3*b^2 + 13*a*b^2)*x^2 + (18*a^6*b + 34*a^4*b + 17*a^2*b + b)*x + 2*a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (3*b^7*x^7 + 18*a*b^6*x^6 + (45*a^2*b^5 + 7*b^5)*x^5 + 4*(15*a^3*b^4 + 7*a*b^4)*x^4 + (45*a^4*b^3 + 42*a^2*b^3 + 5*b^3)*x^3 + 2*(9*a^5*b^2 + 14*a^3*b^2 + 5*a*b^2)*x^2 + (3*a^6*b + 7*a^4*b + 5*a^2*b + b)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^8*x^8 + 6*a*b^7*x^7 + 3*(5*a^2*b^6 + b^6)*x^6 + 4*(5*a^3*b^5 + 3*a*b^5)*x^5 + 3*(5*a^4*b^4 + 6*a^2*b^4 + b^4)*x^4 + 6*(a^5*b^3 + 2*a^3*b^3 + a*b^3)*x^3 + (a^6*b^2 + 3*a^4*b^2 + 3*a^2*b^2 + b^2)*x^2 + (b^5*x^5 + 3*a*b^4*x^4 + 3*a^2*b^3*x^3 + a^3*b^2*x^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^6*x^6 + 4*a*b^5*x^5 + (6*a^2*b^4 + b^4)*x^4 + 2*(2*a^3*b^3 + a*b^3)*x^3 + (a^4*b^2 + a^2*b^2)*x^2)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 3*(b^7*x^7 + 5*a*b^6*x^6 + 2*(5*a^2*b^5 + b^5)*x^5 + 2*(5*a^3*b^4 + 3*a*b^4)*x^4 + (5*a^4*b^3 + 6*a^2*b^3 + b^3)*x^3 + (a^5*b^2 + 2*a^3*b^2 + a*b^2)*x^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(1/2*(a*b^9*x^9 + 10*a^2*b^8*x^8 + 2*a^10 + 8*a^8 + 4*(11*a^3*b^7 + a*b^7)*x^7 + 16*(7*a^4*b^6 + 2*a^2*b^6)*x^6 + 12*a^6 + 2*(91*a^5*b^5 + 54*a^3*b^5 + 3*a*b^5)*x^5 + 4*(49*a^6*b^4 + 50*a^4*b^4 + 9*a^2*b^4)*x^4 + 8*a^4 + 4*(35*a^7*b^3 + 55*a^5*b^3 + 21*a^3*b^3 + a*b^3)*x^3 + (a*b^5*x^5 + 2*a^6 + 2*(3*a^2*b^4 + 2*b^4)*x^4 + 4*a^4 + 2*(7*a^3*b^3 + 8*a*b^3)*x^3 + 8*(2*a^4*b^2 + 3*a^2*b^2 + b^2)*x^2 + 2*a^2 + (9*a^5*b + 16*a^3*b + 7*a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 16*(4*a^8*b^2 + 9*a^6*b^2 + 6*a^4*b^2 + a^2*b^2)*x^2 + (4*a*b^6*x^6 + 8*a^7 + 4*(7*a^2*b^5 + 3*b^5)*x^5 + 20*a^5 + 16*(5*a^3*b^4 + 4*a*b^4)*x^4 + 2*(60*a^4*b^3 + 70*a^2*b^3 + 11*b^3)*x^3 + 16*a^3 + (100*a^5*b^2 + 156*a^3*b^2 + 57*a*b^2)*x^2 + (44*a^6*b + 88*a^4*b + 51*a^2*b + 7*b)*x + 4*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (6*a*b^7*x^7 + 12*a^8 + 12*(4*a^2*b^6 + b^6)*x^6 + 36*a^6 + 6*(27*a^3*b^5 + 14*a*b^5)*x^5 + 4*(75*a^4*b^4 + 63*a^2*b^4 + 5*b^4)*x^4 + 38*a^4 + (330*a^5*b^3 + 408*a^3*b^3 + 95*a*b^3)*x^3 + 2*(108*a^6*b^2 + 186*a^4*b^2 + 84*a^2*b^2 + 5*b^2)*x^2 + 16*a^2 + (78*a^7*b + 180*a^5*b + 131*a^3*b + 29*a*b)*x + 2)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*a^2 + (17*a^9*b + 52*a^7*b + 54*a^5*b + 20*a^3*b + a*b)*x + (4*a*b^8*x^8 + 8*a^9 + 4*(9*a^2*b^7 + b^7)*x^7 + 28*a^7 + 20*(7*a^3*b^6 + 2*a*b^6)*x^6 + 2*(154*a^4*b^5 + 84*a^2*b^5 + 3*b^5)*x^5 + 36*a^5 + (420*a^5*b^4 + 380*a^3*b^4 + 51*a*b^4)*x^4 + (364*a^6*b^3 + 500*a^4*b^3 + 153*a^2*b^3 + 3*b^3)*x^3 + 20*a^3 + (196*a^7*b^2 + 384*a^5*b^2 + 213*a^3*b^2 + 25*a*b^2)*x^2 + (60*a^8*b + 160*a^6*b + 141*a^4*b + 42*a^2*b + b)*x + 4*a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^10*x^11 + 8*a*b^9*x^10 + 4*(7*a^2*b^8 + b^8)*x^9 + 8*(7*a^3*b^7 + 3*a*b^7)*x^8 + 2*(35*a^4*b^6 + 30*a^2*b^6 + 3*b^6)*x^7 + 8*(7*a^5*b^5 + 10*a^3*b^5 + 3*a*b^5)*x^6 + 4*(7*a^6*b^4 + 15*a^4*b^4 + 9*a^2*b^4 + b^4)*x^5 + 8*(a^7*b^3 + 3*a^5*b^3 + 3*a^3*b^3 + a*b^3)*x^4 + (a^8*b^2 + 4*a^6*b^2 + 6*a^4*b^2 + 4*a^2*b^2 + b^2)*x^3 + (b^6*x^7 + 4*a*b^5*x^6 + 6*a^2*b^4*x^5 + 4*a^3*b^3*x^4 + a^4*b^2*x^3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*(b^7*x^8 + 5*a*b^6*x^7 + (10*a^2*b^5 + b^5)*x^6 + (10*a^3*b^4 + 3*a*b^4)*x^5 + (5*a^4*b^3 + 3*a^2*b^3)*x^4 + (a^5*b^2 + a^3*b^2)*x^3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 6*(b^8*x^9 + 6*a*b^7*x^8 + (15*a^2*b^6 + 2*b^6)*x^7 + 4*(5*a^3*b^5 + 2*a*b^5)*x^6 + (15*a^4*b^4 + 12*a^2*b^4 + b^4)*x^5 + 2*(3*a^5*b^3 + 4*a^3*b^3 + a*b^3)*x^4 + (a^6*b^2 + 2*a^4*b^2 + a^2*b^2)*x^3)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*(b^9*x^10 + 7*a*b^8*x^9 + 3*(7*a^2*b^7 + b^7)*x^8 + 5*(7*a^3*b^6 + 3*a*b^6)*x^7 + (35*a^4*b^5 + 30*a^2*b^5 + 3*b^5)*x^6 + 3*(7*a^5*b^4 + 10*a^3*b^4 + 3*a*b^4)*x^5 + (7*a^6*b^3 + 15*a^4*b^3 + 9*a^2*b^3 + b^3)*x^4 + (a^7*b^2 + 3*a^5*b^2 + 3*a^3*b^2 + a*b^2)*x^3)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
93,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsinh(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{n} x^{m}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^n*x^m, x)","F",0
94,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^n*x^2, x)","F",0
95,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^n*x, x)","F",0
96,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^n, x)","F",0
97,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^n/x, x)","F",0
98,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x + c) + a)*x^2, x)","F",0
99,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a} x\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x + c) + a)*x, x)","F",0
100,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x + c) + a), x)","F",0
101,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(3/2)*x, x)","F",0
102,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(x*(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}} x\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(5/2)*x, x)","F",0
104,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
105,0,0,0,0.000000," ","integrate(x^2/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
106,0,0,0,0.000000," ","integrate(x/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
108,0,0,0,0.000000," ","integrate(x/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(-3/2), x)","F",0
110,0,0,0,0.000000," ","integrate(x/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
111,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(-5/2), x)","F",0
112,0,0,0,0.000000," ","integrate(x/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x/(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(-7/2), x)","F",0
114,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","b {\left(\frac{{\left(d e^{m} x + c e^{m}\right)} {\left(d x + c\right)}^{m} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d {\left(m + 1\right)}} - \int \frac{{\left(d^{2} e^{m} x^{2} + 2 \, c d e^{m} x + c^{2} e^{m}\right)} {\left(d x + c\right)}^{m}}{d^{2} {\left(m + 1\right)} x^{2} + 2 \, c d {\left(m + 1\right)} x + c^{2} {\left(m + 1\right)} + m + 1}\,{d x} - \int \frac{{\left(d e^{m} x + c e^{m}\right)} {\left(d x + c\right)}^{m}}{d^{3} {\left(m + 1\right)} x^{3} + 3 \, c d^{2} {\left(m + 1\right)} x^{2} + c^{3} {\left(m + 1\right)} + c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} + d {\left(m + 1\right)}\right)} x + {\left(d^{2} {\left(m + 1\right)} x^{2} + 2 \, c d {\left(m + 1\right)} x + c^{2} {\left(m + 1\right)} + m + 1\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}\right)} + \frac{{\left(d e x + c e\right)}^{m + 1} a}{d e {\left(m + 1\right)}}"," ",0,"b*((d*e^m*x + c*e^m)*(d*x + c)^m*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d*(m + 1)) - integrate((d^2*e^m*x^2 + 2*c*d*e^m*x + c^2*e^m)*(d*x + c)^m/(d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) + m + 1), x) - integrate((d*e^m*x + c*e^m)*(d*x + c)^m/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + c*(m + 1) + (3*c^2*d*(m + 1) + d*(m + 1))*x + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) + m + 1)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)) + (d*e*x + c*e)^(m + 1)*a/(d*e*(m + 1))","F",0
115,1,1231,0,0.482812," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{5} \, a d^{4} e^{4} x^{5} + a c d^{3} e^{4} x^{4} + 2 \, a c^{2} d^{2} e^{4} x^{3} + 2 \, a c^{3} d e^{4} x^{2} + {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} b c^{3} d e^{4} + \frac{1}{3} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} b c^{2} d^{2} e^{4} + \frac{1}{24} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} b c d^{3} e^{4} + \frac{1}{600} \, {\left(120 \, x^{5} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{24 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{4}}{d^{2}} - \frac{54 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{3}}{d^{3}} + \frac{126 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x^{2}}{d^{4}} - \frac{945 \, c^{5} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} - \frac{315 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3} x}{d^{5}} - \frac{32 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x^{2}}{d^{4}} + \frac{1050 \, {\left(c^{2} + 1\right)} c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} + \frac{945 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{4}}{d^{6}} + \frac{161 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c x}{d^{5}} - \frac{225 \, {\left(c^{2} + 1\right)}^{2} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} - \frac{735 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c^{2}}{d^{6}} + \frac{64 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}^{2}}{d^{6}}\right)} d\right)} b d^{4} e^{4} + a c^{4} e^{4} x + \frac{{\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} b c^{4} e^{4}}{d}"," ",0,"1/5*a*d^4*e^4*x^5 + a*c*d^3*e^4*x^4 + 2*a*c^2*d^2*e^4*x^3 + 2*a*c^3*d*e^4*x^2 + (2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*b*c^3*d*e^4 + 1/3*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*b*c^2*d^2*e^4 + 1/24*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*b*c*d^3*e^4 + 1/600*(120*x^5*arcsinh(d*x + c) - (24*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^4/d^2 - 54*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^3/d^3 + 126*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x^2/d^4 - 945*c^5*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 - 315*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3*x/d^5 - 32*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x^2/d^4 + 1050*(c^2 + 1)*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 + 945*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^4/d^6 + 161*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c*x/d^5 - 225*(c^2 + 1)^2*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 - 735*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c^2/d^6 + 64*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)^2/d^6)*d)*b*d^4*e^4 + a*c^4*e^4*x + ((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*b*c^4*e^4/d","B",0
116,1,790,0,0.388080," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a d^{3} e^{3} x^{4} + a c d^{2} e^{3} x^{3} + \frac{3}{2} \, a c^{2} d e^{3} x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} b c^{2} d e^{3} + \frac{1}{6} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} b c d^{2} e^{3} + \frac{1}{96} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} b d^{3} e^{3} + a c^{3} e^{3} x + \frac{{\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} b c^{3} e^{3}}{d}"," ",0,"1/4*a*d^3*e^3*x^4 + a*c*d^2*e^3*x^3 + 3/2*a*c^2*d*e^3*x^2 + 3/4*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*b*c^2*d*e^3 + 1/6*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*b*c*d^2*e^3 + 1/96*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*b*d^3*e^3 + a*c^3*e^3*x + ((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*b*c^3*e^3/d","B",0
117,1,445,0,0.356822," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a d^{2} e^{2} x^{3} + a c d e^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} b c d e^{2} + \frac{1}{18} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} b d^{2} e^{2} + a c^{2} e^{2} x + \frac{{\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} b c^{2} e^{2}}{d}"," ",0,"1/3*a*d^2*e^2*x^3 + a*c*d*e^2*x^2 + 1/2*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*b*c*d*e^2 + 1/18*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*b*d^2*e^2 + a*c^2*e^2*x + ((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*b*c^2*e^2/d","B",0
118,1,201,0,0.444450," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a d e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} b d e + a c e x + \frac{{\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} b c e}{d}"," ",0,"1/2*a*d*e*x^2 + 1/4*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*b*d*e + a*c*e*x + ((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*b*c*e/d","B",0
119,1,35,0,0.339944," ","integrate(a+b*arcsinh(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} b}{d}"," ",0,"a*x + ((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*b/d","A",0
120,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e),x, algorithm=""maxima"")","b \int \frac{\log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)}{d e x + c e}\,{d x} + \frac{a \log\left(d e x + c e\right)}{d e}"," ",0,"b*integrate(log(d*x + c + sqrt((d*x + c)^2 + 1))/(d*e*x + c*e), x) + a*log(d*e*x + c*e)/(d*e)","F",0
121,1,80,0,0.366619," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-b {\left(\frac{\operatorname{arsinh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\operatorname{arsinh}\left(\frac{d e^{2}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}}\right)}{d e^{2}}\right)} - \frac{a}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-b*(arcsinh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsinh(d*e^2/abs(d^2*e^2*x + c*d*e^2))/(d*e^2)) - a/(d^2*e^2*x + c*d*e^2)","A",0
122,1,117,0,0.405739," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} - \frac{a}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-1/2*b*(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d/(d^3*e^3*x + c*d^2*e^3) + arcsinh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)) - 1/2*a/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","B",0
123,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{1}{6} \, b {\left(\frac{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}} - \frac{i \, {\left(\log\left(\frac{i \, {\left(d^{2} x + c d\right)}}{d} + 1\right) - \log\left(-\frac{i \, {\left(d^{2} x + c d\right)}}{d} + 1\right)\right)}}{d e^{4}} - 6 \, \int \frac{1}{3 \, {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x + {\left(d^{5} e^{4} x^{5} + 5 \, c d^{4} e^{4} x^{4} + c^{5} e^{4} + c^{3} e^{4} + {\left(10 \, c^{2} d^{3} e^{4} + d^{3} e^{4}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{4} + 3 \, c d^{2} e^{4}\right)} x^{2} + {\left(5 \, c^{4} d e^{4} + 3 \, c^{2} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}\right)} - \frac{a}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}}"," ",0,"-1/6*b*(2*(d^2*x^2 + 2*c*d*x + c^2 + log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - I*(log(I*(d^2*x + c*d)/d + 1) - log(-I*(d^2*x + c*d)/d + 1))/(d*e^4) - 6*integrate(1/3/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x + (d^5*e^4*x^5 + 5*c*d^4*e^4*x^4 + c^5*e^4 + c^3*e^4 + (10*c^2*d^3*e^4 + d^3*e^4)*x^3 + (10*c^3*d^2*e^4 + 3*c*d^2*e^4)*x^2 + (5*c^4*d*e^4 + 3*c^2*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)) - 1/3*a/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4)","F",0
124,1,258,0,0.355738," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^5,x, algorithm=""maxima"")","\frac{1}{12} \, b {\left(\frac{{\left(2 \, d^{4} x^{4} + 8 \, c d^{3} x^{3} + 2 \, c^{4} + {\left(12 \, c^{2} d^{2} + d^{2}\right)} x^{2} + c^{2} + 2 \, {\left(4 \, c^{3} d + c d\right)} x - 1\right)} d}{{\left(d^{5} e^{5} x^{3} + 3 \, c d^{4} e^{5} x^{2} + 3 \, c^{2} d^{3} e^{5} x + c^{3} d^{2} e^{5}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} - \frac{3 \, \operatorname{arsinh}\left(d x + c\right)}{d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}}\right)} - \frac{a}{4 \, {\left(d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}\right)}}"," ",0,"1/12*b*((2*d^4*x^4 + 8*c*d^3*x^3 + 2*c^4 + (12*c^2*d^2 + d^2)*x^2 + c^2 + 2*(4*c^3*d + c*d)*x - 1)*d/((d^5*e^5*x^3 + 3*c*d^4*e^5*x^2 + 3*c^2*d^3*e^5*x + c^3*d^2*e^5)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) - 3*arcsinh(d*x + c)/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5)) - 1/4*a/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5)","B",0
125,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^6,x, algorithm=""maxima"")","\frac{1}{30} \, b {\left(\frac{2 \, {\left(3 \, d^{4} x^{4} + 12 \, c d^{3} x^{3} + 3 \, c^{4} + {\left(18 \, c^{2} d^{2} - d^{2}\right)} x^{2} - c^{2} + 2 \, {\left(6 \, c^{3} d - c d\right)} x - 3 \, \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{d^{6} e^{6} x^{5} + 5 \, c d^{5} e^{6} x^{4} + 10 \, c^{2} d^{4} e^{6} x^{3} + 10 \, c^{3} d^{3} e^{6} x^{2} + 5 \, c^{4} d^{2} e^{6} x + c^{5} d e^{6}} - \frac{3 i \, {\left(\log\left(\frac{i \, {\left(d^{2} x + c d\right)}}{d} + 1\right) - \log\left(-\frac{i \, {\left(d^{2} x + c d\right)}}{d} + 1\right)\right)}}{d e^{6}} + 30 \, \int \frac{1}{5 \, {\left(d^{8} e^{6} x^{8} + 8 \, c d^{7} e^{6} x^{7} + c^{8} e^{6} + c^{6} e^{6} + {\left(28 \, c^{2} d^{6} e^{6} + d^{6} e^{6}\right)} x^{6} + 2 \, {\left(28 \, c^{3} d^{5} e^{6} + 3 \, c d^{5} e^{6}\right)} x^{5} + 5 \, {\left(14 \, c^{4} d^{4} e^{6} + 3 \, c^{2} d^{4} e^{6}\right)} x^{4} + 4 \, {\left(14 \, c^{5} d^{3} e^{6} + 5 \, c^{3} d^{3} e^{6}\right)} x^{3} + {\left(28 \, c^{6} d^{2} e^{6} + 15 \, c^{4} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(4 \, c^{7} d e^{6} + 3 \, c^{5} d e^{6}\right)} x + {\left(d^{7} e^{6} x^{7} + 7 \, c d^{6} e^{6} x^{6} + c^{7} e^{6} + c^{5} e^{6} + {\left(21 \, c^{2} d^{5} e^{6} + d^{5} e^{6}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{6} + c d^{4} e^{6}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{6} + 2 \, c^{2} d^{3} e^{6}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{6} + 10 \, c^{3} d^{2} e^{6}\right)} x^{2} + {\left(7 \, c^{6} d e^{6} + 5 \, c^{4} d e^{6}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}\right)} - \frac{a}{5 \, {\left(d^{6} e^{6} x^{5} + 5 \, c d^{5} e^{6} x^{4} + 10 \, c^{2} d^{4} e^{6} x^{3} + 10 \, c^{3} d^{3} e^{6} x^{2} + 5 \, c^{4} d^{2} e^{6} x + c^{5} d e^{6}\right)}}"," ",0,"1/30*b*(2*(3*d^4*x^4 + 12*c*d^3*x^3 + 3*c^4 + (18*c^2*d^2 - d^2)*x^2 - c^2 + 2*(6*c^3*d - c*d)*x - 3*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^6*e^6*x^5 + 5*c*d^5*e^6*x^4 + 10*c^2*d^4*e^6*x^3 + 10*c^3*d^3*e^6*x^2 + 5*c^4*d^2*e^6*x + c^5*d*e^6) - 3*I*(log(I*(d^2*x + c*d)/d + 1) - log(-I*(d^2*x + c*d)/d + 1))/(d*e^6) + 30*integrate(1/5/(d^8*e^6*x^8 + 8*c*d^7*e^6*x^7 + c^8*e^6 + c^6*e^6 + (28*c^2*d^6*e^6 + d^6*e^6)*x^6 + 2*(28*c^3*d^5*e^6 + 3*c*d^5*e^6)*x^5 + 5*(14*c^4*d^4*e^6 + 3*c^2*d^4*e^6)*x^4 + 4*(14*c^5*d^3*e^6 + 5*c^3*d^3*e^6)*x^3 + (28*c^6*d^2*e^6 + 15*c^4*d^2*e^6)*x^2 + 2*(4*c^7*d*e^6 + 3*c^5*d*e^6)*x + (d^7*e^6*x^7 + 7*c*d^6*e^6*x^6 + c^7*e^6 + c^5*e^6 + (21*c^2*d^5*e^6 + d^5*e^6)*x^5 + 5*(7*c^3*d^4*e^6 + c*d^4*e^6)*x^4 + 5*(7*c^4*d^3*e^6 + 2*c^2*d^3*e^6)*x^3 + (21*c^5*d^2*e^6 + 10*c^3*d^2*e^6)*x^2 + (7*c^6*d*e^6 + 5*c^4*d*e^6)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)) - 1/5*a/(d^6*e^6*x^5 + 5*c*d^5*e^6*x^4 + 10*c^2*d^4*e^6*x^3 + 10*c^3*d^3*e^6*x^2 + 5*c^4*d^2*e^6*x + c^5*d*e^6)","F",0
126,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} d e^{m} x + b^{2} c e^{m}\right)} {\left(d x + c\right)}^{m} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d {\left(m + 1\right)}} + \frac{{\left(d e x + c e\right)}^{m + 1} a^{2}}{d e {\left(m + 1\right)}} + \int -\frac{2 \, {\left({\left(b^{2} c^{2} e^{m} - {\left(c^{2} e^{m} {\left(m + 1\right)} + e^{m} {\left(m + 1\right)}\right)} a b - {\left(a b d^{2} e^{m} {\left(m + 1\right)} - b^{2} d^{2} e^{m}\right)} x^{2} - 2 \, {\left(a b c d e^{m} {\left(m + 1\right)} - b^{2} c d e^{m}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)}^{m} - {\left({\left(a b d^{3} e^{m} {\left(m + 1\right)} - b^{2} d^{3} e^{m}\right)} x^{3} + {\left(c^{3} e^{m} {\left(m + 1\right)} + c e^{m} {\left(m + 1\right)}\right)} a b - {\left(c^{3} e^{m} + c e^{m}\right)} b^{2} + 3 \, {\left(a b c d^{2} e^{m} {\left(m + 1\right)} - b^{2} c d^{2} e^{m}\right)} x^{2} + {\left({\left(3 \, c^{2} d e^{m} {\left(m + 1\right)} + d e^{m} {\left(m + 1\right)}\right)} a b - {\left(3 \, c^{2} d e^{m} + d e^{m}\right)} b^{2}\right)} x\right)} {\left(d x + c\right)}^{m}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{3} {\left(m + 1\right)} x^{3} + 3 \, c d^{2} {\left(m + 1\right)} x^{2} + c^{3} {\left(m + 1\right)} + c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} + d {\left(m + 1\right)}\right)} x + {\left(d^{2} {\left(m + 1\right)} x^{2} + 2 \, c d {\left(m + 1\right)} x + c^{2} {\left(m + 1\right)} + m + 1\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"(b^2*d*e^m*x + b^2*c*e^m)*(d*x + c)^m*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d*(m + 1)) + (d*e*x + c*e)^(m + 1)*a^2/(d*e*(m + 1)) + integrate(-2*((b^2*c^2*e^m - (c^2*e^m*(m + 1) + e^m*(m + 1))*a*b - (a*b*d^2*e^m*(m + 1) - b^2*d^2*e^m)*x^2 - 2*(a*b*c*d*e^m*(m + 1) - b^2*c*d*e^m)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c)^m - ((a*b*d^3*e^m*(m + 1) - b^2*d^3*e^m)*x^3 + (c^3*e^m*(m + 1) + c*e^m*(m + 1))*a*b - (c^3*e^m + c*e^m)*b^2 + 3*(a*b*c*d^2*e^m*(m + 1) - b^2*c*d^2*e^m)*x^2 + ((3*c^2*d*e^m*(m + 1) + d*e^m*(m + 1))*a*b - (3*c^2*d*e^m + d*e^m)*b^2)*x)*(d*x + c)^m)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + c*(m + 1) + (3*c^2*d*(m + 1) + d*(m + 1))*x + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) + m + 1)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
127,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} d^{4} e^{4} x^{5} + a^{2} c d^{3} e^{4} x^{4} + 2 \, a^{2} c^{2} d^{2} e^{4} x^{3} + 2 \, a^{2} c^{3} d e^{4} x^{2} + 2 \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a b c^{3} d e^{4} + \frac{2}{3} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a b c^{2} d^{2} e^{4} + \frac{1}{12} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} a b c d^{3} e^{4} + \frac{1}{300} \, {\left(120 \, x^{5} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{24 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{4}}{d^{2}} - \frac{54 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{3}}{d^{3}} + \frac{126 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x^{2}}{d^{4}} - \frac{945 \, c^{5} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} - \frac{315 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3} x}{d^{5}} - \frac{32 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x^{2}}{d^{4}} + \frac{1050 \, {\left(c^{2} + 1\right)} c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} + \frac{945 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{4}}{d^{6}} + \frac{161 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c x}{d^{5}} - \frac{225 \, {\left(c^{2} + 1\right)}^{2} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} - \frac{735 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c^{2}}{d^{6}} + \frac{64 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}^{2}}{d^{6}}\right)} d\right)} a b d^{4} e^{4} + a^{2} c^{4} e^{4} x + \frac{2 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a b c^{4} e^{4}}{d} + \frac{1}{5} \, {\left(b^{2} d^{4} e^{4} x^{5} + 5 \, b^{2} c d^{3} e^{4} x^{4} + 10 \, b^{2} c^{2} d^{2} e^{4} x^{3} + 10 \, b^{2} c^{3} d e^{4} x^{2} + 5 \, b^{2} c^{4} e^{4} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - \int \frac{2 \, {\left(b^{2} d^{7} e^{4} x^{7} + 7 \, b^{2} c d^{6} e^{4} x^{6} + {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} b^{2} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} b^{2} x^{3} + 10 \, {\left(2 \, c^{5} d^{2} e^{4} + c^{3} d^{2} e^{4}\right)} b^{2} x^{2} + 5 \, {\left(c^{6} d e^{4} + c^{4} d e^{4}\right)} b^{2} x + {\left(b^{2} d^{6} e^{4} x^{6} + 6 \, b^{2} c d^{5} e^{4} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{4} x^{4} + 20 \, b^{2} c^{3} d^{3} e^{4} x^{3} + 15 \, b^{2} c^{4} d^{2} e^{4} x^{2} + 5 \, b^{2} c^{5} d e^{4} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/5*a^2*d^4*e^4*x^5 + a^2*c*d^3*e^4*x^4 + 2*a^2*c^2*d^2*e^4*x^3 + 2*a^2*c^3*d*e^4*x^2 + 2*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a*b*c^3*d*e^4 + 2/3*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a*b*c^2*d^2*e^4 + 1/12*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*a*b*c*d^3*e^4 + 1/300*(120*x^5*arcsinh(d*x + c) - (24*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^4/d^2 - 54*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^3/d^3 + 126*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x^2/d^4 - 945*c^5*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 - 315*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3*x/d^5 - 32*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x^2/d^4 + 1050*(c^2 + 1)*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 + 945*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^4/d^6 + 161*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c*x/d^5 - 225*(c^2 + 1)^2*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 - 735*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c^2/d^6 + 64*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)^2/d^6)*d)*a*b*d^4*e^4 + a^2*c^4*e^4*x + 2*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a*b*c^4*e^4/d + 1/5*(b^2*d^4*e^4*x^5 + 5*b^2*c*d^3*e^4*x^4 + 10*b^2*c^2*d^2*e^4*x^3 + 10*b^2*c^3*d*e^4*x^2 + 5*b^2*c^4*e^4*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - integrate(2/5*(b^2*d^7*e^4*x^7 + 7*b^2*c*d^6*e^4*x^6 + (21*c^2*d^5*e^4 + d^5*e^4)*b^2*x^5 + 5*(7*c^3*d^4*e^4 + c*d^4*e^4)*b^2*x^4 + 5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*b^2*x^3 + 10*(2*c^5*d^2*e^4 + c^3*d^2*e^4)*b^2*x^2 + 5*(c^6*d*e^4 + c^4*d*e^4)*b^2*x + (b^2*d^6*e^4*x^6 + 6*b^2*c*d^5*e^4*x^5 + 15*b^2*c^2*d^4*e^4*x^4 + 20*b^2*c^3*d^3*e^4*x^3 + 15*b^2*c^4*d^2*e^4*x^2 + 5*b^2*c^5*d*e^4*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
128,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} d^{3} e^{3} x^{4} + a^{2} c d^{2} e^{3} x^{3} + \frac{3}{2} \, a^{2} c^{2} d e^{3} x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a b c^{2} d e^{3} + \frac{1}{3} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a b c d^{2} e^{3} + \frac{1}{48} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} a b d^{3} e^{3} + a^{2} c^{3} e^{3} x + \frac{2 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a b c^{3} e^{3}}{d} + \frac{1}{4} \, {\left(b^{2} d^{3} e^{3} x^{4} + 4 \, b^{2} c d^{2} e^{3} x^{3} + 6 \, b^{2} c^{2} d e^{3} x^{2} + 4 \, b^{2} c^{3} e^{3} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - \int \frac{{\left(b^{2} d^{6} e^{3} x^{6} + 6 \, b^{2} c d^{5} e^{3} x^{5} + {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} b^{2} x^{3} + 2 \, {\left(7 \, c^{4} d^{2} e^{3} + 3 \, c^{2} d^{2} e^{3}\right)} b^{2} x^{2} + 4 \, {\left(c^{5} d e^{3} + c^{3} d e^{3}\right)} b^{2} x + {\left(b^{2} d^{5} e^{3} x^{5} + 5 \, b^{2} c d^{4} e^{3} x^{4} + 10 \, b^{2} c^{2} d^{3} e^{3} x^{3} + 10 \, b^{2} c^{3} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{4} d e^{3} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{2 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/4*a^2*d^3*e^3*x^4 + a^2*c*d^2*e^3*x^3 + 3/2*a^2*c^2*d*e^3*x^2 + 3/2*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a*b*c^2*d*e^3 + 1/3*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a*b*c*d^2*e^3 + 1/48*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*a*b*d^3*e^3 + a^2*c^3*e^3*x + 2*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a*b*c^3*e^3/d + 1/4*(b^2*d^3*e^3*x^4 + 4*b^2*c*d^2*e^3*x^3 + 6*b^2*c^2*d*e^3*x^2 + 4*b^2*c^3*e^3*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - integrate(1/2*(b^2*d^6*e^3*x^6 + 6*b^2*c*d^5*e^3*x^5 + (15*c^2*d^4*e^3 + d^4*e^3)*b^2*x^4 + 4*(5*c^3*d^3*e^3 + c*d^3*e^3)*b^2*x^3 + 2*(7*c^4*d^2*e^3 + 3*c^2*d^2*e^3)*b^2*x^2 + 4*(c^5*d*e^3 + c^3*d*e^3)*b^2*x + (b^2*d^5*e^3*x^5 + 5*b^2*c*d^4*e^3*x^4 + 10*b^2*c^2*d^3*e^3*x^3 + 10*b^2*c^3*d^2*e^3*x^2 + 4*b^2*c^4*d*e^3*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
129,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} d^{2} e^{2} x^{3} + a^{2} c d e^{2} x^{2} + {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a b c d e^{2} + \frac{1}{9} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a b d^{2} e^{2} + a^{2} c^{2} e^{2} x + \frac{2 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a b c^{2} e^{2}}{d} + \frac{1}{3} \, {\left(b^{2} d^{2} e^{2} x^{3} + 3 \, b^{2} c d e^{2} x^{2} + 3 \, b^{2} c^{2} e^{2} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - \int \frac{2 \, {\left(b^{2} d^{5} e^{2} x^{5} + 5 \, b^{2} c d^{4} e^{2} x^{4} + {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} b^{2} x^{3} + 3 \, {\left(3 \, c^{3} d^{2} e^{2} + c d^{2} e^{2}\right)} b^{2} x^{2} + 3 \, {\left(c^{4} d e^{2} + c^{2} d e^{2}\right)} b^{2} x + {\left(b^{2} d^{4} e^{2} x^{4} + 4 \, b^{2} c d^{3} e^{2} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{2} x^{2} + 3 \, b^{2} c^{3} d e^{2} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/3*a^2*d^2*e^2*x^3 + a^2*c*d*e^2*x^2 + (2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a*b*c*d*e^2 + 1/9*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a*b*d^2*e^2 + a^2*c^2*e^2*x + 2*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a*b*c^2*e^2/d + 1/3*(b^2*d^2*e^2*x^3 + 3*b^2*c*d*e^2*x^2 + 3*b^2*c^2*e^2*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - integrate(2/3*(b^2*d^5*e^2*x^5 + 5*b^2*c*d^4*e^2*x^4 + (10*c^2*d^3*e^2 + d^3*e^2)*b^2*x^3 + 3*(3*c^3*d^2*e^2 + c*d^2*e^2)*b^2*x^2 + 3*(c^4*d*e^2 + c^2*d*e^2)*b^2*x + (b^2*d^4*e^2*x^4 + 4*b^2*c*d^3*e^2*x^3 + 6*b^2*c^2*d^2*e^2*x^2 + 3*b^2*c^3*d*e^2*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
130,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} d e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a b d e + a^{2} c e x + \frac{2 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a b c e}{d} + \frac{1}{2} \, {\left(b^{2} d e x^{2} + 2 \, b^{2} c e x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - \int \frac{{\left(b^{2} d^{4} e x^{4} + 4 \, b^{2} c d^{3} e x^{3} + {\left(5 \, c^{2} d^{2} e + d^{2} e\right)} b^{2} x^{2} + 2 \, {\left(c^{3} d e + c d e\right)} b^{2} x + {\left(b^{2} d^{3} e x^{3} + 3 \, b^{2} c d^{2} e x^{2} + 2 \, b^{2} c^{2} d e x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"1/2*a^2*d*e*x^2 + 1/2*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a*b*d*e + a^2*c*e*x + 2*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a*b*c*e/d + 1/2*(b^2*d*e*x^2 + 2*b^2*c*e*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - integrate((b^2*d^4*e*x^4 + 4*b^2*c*d^3*e*x^3 + (5*c^2*d^2*e + d^2*e)*b^2*x^2 + 2*(c^3*d*e + c*d*e)*b^2*x + (b^2*d^3*e*x^3 + 3*b^2*c*d^2*e*x^2 + 2*b^2*c^2*d*e*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
131,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","{\left(x \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - \int \frac{2 \, {\left(d^{3} x^{3} + 2 \, c d^{2} x^{2} + {\left(c^{2} d + d\right)} x + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d^{2} x^{2} + c d x\right)}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}\right)} b^{2} + a^{2} x + \frac{2 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a b}{d}"," ",0,"(x*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - integrate(2*(d^3*x^3 + 2*c*d^2*x^2 + (c^2*d + d)*x + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d^2*x^2 + c*d*x))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x))*b^2 + a^2*x + 2*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a*b/d","F",0
132,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(d e x + c e\right)}{d e} + \int \frac{b^{2} \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)^{2}}{d e x + c e} + \frac{2 \, a b \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)}{d e x + c e}\,{d x}"," ",0,"a^2*log(d*e*x + c*e)/(d*e) + integrate(b^2*log(d*x + c + sqrt((d*x + c)^2 + 1))^2/(d*e*x + c*e) + 2*a*b*log(d*x + c + sqrt((d*x + c)^2 + 1))/(d*e*x + c*e), x)","F",0
133,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-b^{2} {\left(\frac{\log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d^{2} e^{2} x + c d e^{2}} - \int \frac{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)} + 1\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + c^{4} e^{2} + c^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} x + {\left(d^{3} e^{2} x^{3} + 3 \, c d^{2} e^{2} x^{2} + c^{3} e^{2} + c e^{2} + {\left(3 \, c^{2} d e^{2} + d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}\right)} - 2 \, a b {\left(\frac{\operatorname{arsinh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\operatorname{arsinh}\left(\frac{d e^{2}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}}\right)}{d e^{2}}\right)} - \frac{a^{2}}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-b^2*(log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^2*e^2*x + c*d*e^2) - integrate(2*(d^2*x^2 + 2*c*d*x + c^2 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c) + 1)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + c^4*e^2 + c^2*e^2 + (6*c^2*d^2*e^2 + d^2*e^2)*x^2 + 2*(2*c^3*d*e^2 + c*d*e^2)*x + (d^3*e^2*x^3 + 3*c*d^2*e^2*x^2 + c^3*e^2 + c*e^2 + (3*c^2*d*e^2 + d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)) - 2*a*b*(arcsinh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsinh(d*e^2/abs(d^2*e^2*x + c*d*e^2))/(d*e^2)) - a^2/(d^2*e^2*x + c*d*e^2)","F",0
134,1,230,0,0.416459," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-{\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d \operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c\right)}{d e^{3}}\right)} b^{2} - a b {\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} - \frac{b^{2} \operatorname{arsinh}\left(d x + c\right)^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{a^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d*arcsinh(d*x + c)/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c)/(d*e^3))*b^2 - a*b*(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d/(d^3*e^3*x + c*d^2*e^3) + arcsinh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)) - 1/2*b^2*arcsinh(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","B",0
135,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \frac{a^{2}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} + \int \frac{2 \, {\left({\left(3 \, a b d^{3} + b^{2} d^{3}\right)} x^{3} + 3 \, {\left(c^{3} + c\right)} a b + {\left(c^{3} + c\right)} b^{2} + 3 \, {\left(3 \, a b c d^{2} + b^{2} c d^{2}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d + d\right)} a b + {\left(3 \, c^{2} d + d\right)} b^{2}\right)} x + {\left(b^{2} c^{2} + 3 \, {\left(c^{2} + 1\right)} a b + {\left(3 \, a b d^{2} + b^{2} d^{2}\right)} x^{2} + 2 \, {\left(3 \, a b c d + b^{2} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{3 \, {\left(d^{7} e^{4} x^{7} + 7 \, c d^{6} e^{4} x^{6} + c^{7} e^{4} + c^{5} e^{4} + {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} x^{2} + {\left(7 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} x + {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/3*b^2*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - 1/3*a^2/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) + integrate(2/3*((3*a*b*d^3 + b^2*d^3)*x^3 + 3*(c^3 + c)*a*b + (c^3 + c)*b^2 + 3*(3*a*b*c*d^2 + b^2*c*d^2)*x^2 + (3*(3*c^2*d + d)*a*b + (3*c^2*d + d)*b^2)*x + (b^2*c^2 + 3*(c^2 + 1)*a*b + (3*a*b*d^2 + b^2*d^2)*x^2 + 2*(3*a*b*c*d + b^2*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^7*e^4*x^7 + 7*c*d^6*e^4*x^6 + c^7*e^4 + c^5*e^4 + (21*c^2*d^5*e^4 + d^5*e^4)*x^5 + 5*(7*c^3*d^4*e^4 + c*d^4*e^4)*x^4 + 5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*x^3 + (21*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*x^2 + (7*c^6*d*e^4 + 5*c^4*d*e^4)*x + (d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
136,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(b^{3} d e^{m} x + b^{3} c e^{m}\right)} {\left(d x + c\right)}^{m} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{d {\left(m + 1\right)}} + \frac{{\left(d e x + c e\right)}^{m + 1} a^{3}}{d e {\left(m + 1\right)}} + \int -\frac{3 \, {\left({\left({\left(b^{3} c^{2} e^{m} - {\left(c^{2} e^{m} {\left(m + 1\right)} + e^{m} {\left(m + 1\right)}\right)} a b^{2} - {\left(a b^{2} d^{2} e^{m} {\left(m + 1\right)} - b^{3} d^{2} e^{m}\right)} x^{2} - 2 \, {\left(a b^{2} c d e^{m} {\left(m + 1\right)} - b^{3} c d e^{m}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)}^{m} - {\left({\left(c^{3} e^{m} {\left(m + 1\right)} + c e^{m} {\left(m + 1\right)}\right)} a b^{2} - {\left(c^{3} e^{m} + c e^{m}\right)} b^{3} + {\left(a b^{2} d^{3} e^{m} {\left(m + 1\right)} - b^{3} d^{3} e^{m}\right)} x^{3} + 3 \, {\left(a b^{2} c d^{2} e^{m} {\left(m + 1\right)} - b^{3} c d^{2} e^{m}\right)} x^{2} + {\left({\left(3 \, c^{2} d e^{m} {\left(m + 1\right)} + d e^{m} {\left(m + 1\right)}\right)} a b^{2} - {\left(3 \, c^{2} d e^{m} + d e^{m}\right)} b^{3}\right)} x\right)} {\left(d x + c\right)}^{m}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - {\left({\left(a^{2} b d^{2} e^{m} {\left(m + 1\right)} x^{2} + 2 \, a^{2} b c d e^{m} {\left(m + 1\right)} x + {\left(c^{2} e^{m} {\left(m + 1\right)} + e^{m} {\left(m + 1\right)}\right)} a^{2} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)}^{m} + {\left(a^{2} b d^{3} e^{m} {\left(m + 1\right)} x^{3} + 3 \, a^{2} b c d^{2} e^{m} {\left(m + 1\right)} x^{2} + {\left(3 \, c^{2} d e^{m} {\left(m + 1\right)} + d e^{m} {\left(m + 1\right)}\right)} a^{2} b x + {\left(c^{3} e^{m} {\left(m + 1\right)} + c e^{m} {\left(m + 1\right)}\right)} a^{2} b\right)} {\left(d x + c\right)}^{m}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{d^{3} {\left(m + 1\right)} x^{3} + 3 \, c d^{2} {\left(m + 1\right)} x^{2} + c^{3} {\left(m + 1\right)} + c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} + d {\left(m + 1\right)}\right)} x + {\left(d^{2} {\left(m + 1\right)} x^{2} + 2 \, c d {\left(m + 1\right)} x + c^{2} {\left(m + 1\right)} + m + 1\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"(b^3*d*e^m*x + b^3*c*e^m)*(d*x + c)^m*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(d*(m + 1)) + (d*e*x + c*e)^(m + 1)*a^3/(d*e*(m + 1)) + integrate(-3*(((b^3*c^2*e^m - (c^2*e^m*(m + 1) + e^m*(m + 1))*a*b^2 - (a*b^2*d^2*e^m*(m + 1) - b^3*d^2*e^m)*x^2 - 2*(a*b^2*c*d*e^m*(m + 1) - b^3*c*d*e^m)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c)^m - ((c^3*e^m*(m + 1) + c*e^m*(m + 1))*a*b^2 - (c^3*e^m + c*e^m)*b^3 + (a*b^2*d^3*e^m*(m + 1) - b^3*d^3*e^m)*x^3 + 3*(a*b^2*c*d^2*e^m*(m + 1) - b^3*c*d^2*e^m)*x^2 + ((3*c^2*d*e^m*(m + 1) + d*e^m*(m + 1))*a*b^2 - (3*c^2*d*e^m + d*e^m)*b^3)*x)*(d*x + c)^m)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - ((a^2*b*d^2*e^m*(m + 1)*x^2 + 2*a^2*b*c*d*e^m*(m + 1)*x + (c^2*e^m*(m + 1) + e^m*(m + 1))*a^2*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c)^m + (a^2*b*d^3*e^m*(m + 1)*x^3 + 3*a^2*b*c*d^2*e^m*(m + 1)*x^2 + (3*c^2*d*e^m*(m + 1) + d*e^m*(m + 1))*a^2*b*x + (c^3*e^m*(m + 1) + c*e^m*(m + 1))*a^2*b)*(d*x + c)^m)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + c*(m + 1) + (3*c^2*d*(m + 1) + d*(m + 1))*x + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) + m + 1)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
137,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{5} \, a^{3} d^{4} e^{4} x^{5} + a^{3} c d^{3} e^{4} x^{4} + 2 \, a^{3} c^{2} d^{2} e^{4} x^{3} + 2 \, a^{3} c^{3} d e^{4} x^{2} + 3 \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b c^{3} d e^{4} + {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a^{2} b c^{2} d^{2} e^{4} + \frac{1}{8} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} a^{2} b c d^{3} e^{4} + \frac{1}{200} \, {\left(120 \, x^{5} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{24 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{4}}{d^{2}} - \frac{54 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{3}}{d^{3}} + \frac{126 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x^{2}}{d^{4}} - \frac{945 \, c^{5} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} - \frac{315 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3} x}{d^{5}} - \frac{32 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x^{2}}{d^{4}} + \frac{1050 \, {\left(c^{2} + 1\right)} c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} + \frac{945 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{4}}{d^{6}} + \frac{161 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c x}{d^{5}} - \frac{225 \, {\left(c^{2} + 1\right)}^{2} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{6}} - \frac{735 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c^{2}}{d^{6}} + \frac{64 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}^{2}}{d^{6}}\right)} d\right)} a^{2} b d^{4} e^{4} + a^{3} c^{4} e^{4} x + \frac{3 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{2} b c^{4} e^{4}}{d} + \frac{1}{5} \, {\left(b^{3} d^{4} e^{4} x^{5} + 5 \, b^{3} c d^{3} e^{4} x^{4} + 10 \, b^{3} c^{2} d^{2} e^{4} x^{3} + 10 \, b^{3} c^{3} d e^{4} x^{2} + 5 \, b^{3} c^{4} e^{4} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + \int \frac{3 \, {\left({\left(5 \, a b^{2} d^{7} e^{4} - b^{3} d^{7} e^{4}\right)} x^{7} + 7 \, {\left(5 \, a b^{2} c d^{6} e^{4} - b^{3} c d^{6} e^{4}\right)} x^{6} + {\left(5 \, {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} a b^{2} - {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} b^{3}\right)} x^{5} + 5 \, {\left(5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} a b^{2} - {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} b^{3}\right)} x^{4} + 5 \, {\left(c^{7} e^{4} + c^{5} e^{4}\right)} a b^{2} + 5 \, {\left(5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} a b^{2} - {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} b^{3}\right)} x^{3} + 5 \, {\left({\left(21 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} a b^{2} - 2 \, {\left(2 \, c^{5} d^{2} e^{4} + c^{3} d^{2} e^{4}\right)} b^{3}\right)} x^{2} + 5 \, {\left({\left(7 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} a b^{2} - {\left(c^{6} d e^{4} + c^{4} d e^{4}\right)} b^{3}\right)} x + {\left({\left(5 \, a b^{2} d^{6} e^{4} - b^{3} d^{6} e^{4}\right)} x^{6} + 6 \, {\left(5 \, a b^{2} c d^{5} e^{4} - b^{3} c d^{5} e^{4}\right)} x^{5} - 5 \, {\left(3 \, b^{3} c^{2} d^{4} e^{4} - {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} a b^{2}\right)} x^{4} + 5 \, {\left(c^{6} e^{4} + c^{4} e^{4}\right)} a b^{2} - 20 \, {\left(b^{3} c^{3} d^{3} e^{4} - {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} a b^{2}\right)} x^{3} - 15 \, {\left(b^{3} c^{4} d^{2} e^{4} - {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} a b^{2}\right)} x^{2} - 5 \, {\left(b^{3} c^{5} d e^{4} - 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/5*a^3*d^4*e^4*x^5 + a^3*c*d^3*e^4*x^4 + 2*a^3*c^2*d^2*e^4*x^3 + 2*a^3*c^3*d*e^4*x^2 + 3*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^2*b*c^3*d*e^4 + (6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a^2*b*c^2*d^2*e^4 + 1/8*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*a^2*b*c*d^3*e^4 + 1/200*(120*x^5*arcsinh(d*x + c) - (24*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^4/d^2 - 54*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^3/d^3 + 126*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x^2/d^4 - 945*c^5*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 - 315*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3*x/d^5 - 32*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x^2/d^4 + 1050*(c^2 + 1)*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 + 945*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^4/d^6 + 161*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c*x/d^5 - 225*(c^2 + 1)^2*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^6 - 735*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c^2/d^6 + 64*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)^2/d^6)*d)*a^2*b*d^4*e^4 + a^3*c^4*e^4*x + 3*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^2*b*c^4*e^4/d + 1/5*(b^3*d^4*e^4*x^5 + 5*b^3*c*d^3*e^4*x^4 + 10*b^3*c^2*d^2*e^4*x^3 + 10*b^3*c^3*d*e^4*x^2 + 5*b^3*c^4*e^4*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + integrate(3/5*((5*a*b^2*d^7*e^4 - b^3*d^7*e^4)*x^7 + 7*(5*a*b^2*c*d^6*e^4 - b^3*c*d^6*e^4)*x^6 + (5*(21*c^2*d^5*e^4 + d^5*e^4)*a*b^2 - (21*c^2*d^5*e^4 + d^5*e^4)*b^3)*x^5 + 5*(5*(7*c^3*d^4*e^4 + c*d^4*e^4)*a*b^2 - (7*c^3*d^4*e^4 + c*d^4*e^4)*b^3)*x^4 + 5*(c^7*e^4 + c^5*e^4)*a*b^2 + 5*(5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*a*b^2 - (7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*b^3)*x^3 + 5*((21*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*a*b^2 - 2*(2*c^5*d^2*e^4 + c^3*d^2*e^4)*b^3)*x^2 + 5*((7*c^6*d*e^4 + 5*c^4*d*e^4)*a*b^2 - (c^6*d*e^4 + c^4*d*e^4)*b^3)*x + ((5*a*b^2*d^6*e^4 - b^3*d^6*e^4)*x^6 + 6*(5*a*b^2*c*d^5*e^4 - b^3*c*d^5*e^4)*x^5 - 5*(3*b^3*c^2*d^4*e^4 - (15*c^2*d^4*e^4 + d^4*e^4)*a*b^2)*x^4 + 5*(c^6*e^4 + c^4*e^4)*a*b^2 - 20*(b^3*c^3*d^3*e^4 - (5*c^3*d^3*e^4 + c*d^3*e^4)*a*b^2)*x^3 - 15*(b^3*c^4*d^2*e^4 - (5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*a*b^2)*x^2 - 5*(b^3*c^5*d*e^4 - 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
138,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} d^{3} e^{3} x^{4} + a^{3} c d^{2} e^{3} x^{3} + \frac{3}{2} \, a^{3} c^{2} d e^{3} x^{2} + \frac{9}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b c^{2} d e^{3} + \frac{1}{2} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a^{2} b c d^{2} e^{3} + \frac{1}{32} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} a^{2} b d^{3} e^{3} + a^{3} c^{3} e^{3} x + \frac{3 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{2} b c^{3} e^{3}}{d} + \frac{1}{4} \, {\left(b^{3} d^{3} e^{3} x^{4} + 4 \, b^{3} c d^{2} e^{3} x^{3} + 6 \, b^{3} c^{2} d e^{3} x^{2} + 4 \, b^{3} c^{3} e^{3} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + \int \frac{3 \, {\left({\left(4 \, a b^{2} d^{6} e^{3} - b^{3} d^{6} e^{3}\right)} x^{6} + 6 \, {\left(4 \, a b^{2} c d^{5} e^{3} - b^{3} c d^{5} e^{3}\right)} x^{5} + {\left(4 \, {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} a b^{2} - {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} b^{3}\right)} x^{4} + 4 \, {\left(c^{6} e^{3} + c^{4} e^{3}\right)} a b^{2} + 4 \, {\left(4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} a b^{2} - {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} b^{3}\right)} x^{3} + 2 \, {\left(6 \, {\left(5 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} a b^{2} - {\left(7 \, c^{4} d^{2} e^{3} + 3 \, c^{2} d^{2} e^{3}\right)} b^{3}\right)} x^{2} + 4 \, {\left(2 \, {\left(3 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} a b^{2} - {\left(c^{5} d e^{3} + c^{3} d e^{3}\right)} b^{3}\right)} x + {\left({\left(4 \, a b^{2} d^{5} e^{3} - b^{3} d^{5} e^{3}\right)} x^{5} + 5 \, {\left(4 \, a b^{2} c d^{4} e^{3} - b^{3} c d^{4} e^{3}\right)} x^{4} + 4 \, {\left(c^{5} e^{3} + c^{3} e^{3}\right)} a b^{2} - 2 \, {\left(5 \, b^{3} c^{2} d^{3} e^{3} - 2 \, {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} a b^{2}\right)} x^{3} - 2 \, {\left(5 \, b^{3} c^{3} d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} a b^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{4} d e^{3} - {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{4 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/4*a^3*d^3*e^3*x^4 + a^3*c*d^2*e^3*x^3 + 3/2*a^3*c^2*d*e^3*x^2 + 9/4*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^2*b*c^2*d*e^3 + 1/2*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a^2*b*c*d^2*e^3 + 1/32*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*a^2*b*d^3*e^3 + a^3*c^3*e^3*x + 3*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^2*b*c^3*e^3/d + 1/4*(b^3*d^3*e^3*x^4 + 4*b^3*c*d^2*e^3*x^3 + 6*b^3*c^2*d*e^3*x^2 + 4*b^3*c^3*e^3*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + integrate(3/4*((4*a*b^2*d^6*e^3 - b^3*d^6*e^3)*x^6 + 6*(4*a*b^2*c*d^5*e^3 - b^3*c*d^5*e^3)*x^5 + (4*(15*c^2*d^4*e^3 + d^4*e^3)*a*b^2 - (15*c^2*d^4*e^3 + d^4*e^3)*b^3)*x^4 + 4*(c^6*e^3 + c^4*e^3)*a*b^2 + 4*(4*(5*c^3*d^3*e^3 + c*d^3*e^3)*a*b^2 - (5*c^3*d^3*e^3 + c*d^3*e^3)*b^3)*x^3 + 2*(6*(5*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*a*b^2 - (7*c^4*d^2*e^3 + 3*c^2*d^2*e^3)*b^3)*x^2 + 4*(2*(3*c^5*d*e^3 + 2*c^3*d*e^3)*a*b^2 - (c^5*d*e^3 + c^3*d*e^3)*b^3)*x + ((4*a*b^2*d^5*e^3 - b^3*d^5*e^3)*x^5 + 5*(4*a*b^2*c*d^4*e^3 - b^3*c*d^4*e^3)*x^4 + 4*(c^5*e^3 + c^3*e^3)*a*b^2 - 2*(5*b^3*c^2*d^3*e^3 - 2*(10*c^2*d^3*e^3 + d^3*e^3)*a*b^2)*x^3 - 2*(5*b^3*c^3*d^2*e^3 - 2*(10*c^3*d^2*e^3 + 3*c*d^2*e^3)*a*b^2)*x^2 - 4*(b^3*c^4*d*e^3 - (5*c^4*d*e^3 + 3*c^2*d*e^3)*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
139,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} d^{2} e^{2} x^{3} + a^{3} c d e^{2} x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b c d e^{2} + \frac{1}{6} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a^{2} b d^{2} e^{2} + a^{3} c^{2} e^{2} x + \frac{3 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{2} b c^{2} e^{2}}{d} + \frac{1}{3} \, {\left(b^{3} d^{2} e^{2} x^{3} + 3 \, b^{3} c d e^{2} x^{2} + 3 \, b^{3} c^{2} e^{2} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + \int \frac{{\left({\left(3 \, a b^{2} d^{5} e^{2} - b^{3} d^{5} e^{2}\right)} x^{5} + 5 \, {\left(3 \, a b^{2} c d^{4} e^{2} - b^{3} c d^{4} e^{2}\right)} x^{4} + 3 \, {\left(c^{5} e^{2} + c^{3} e^{2}\right)} a b^{2} + {\left(3 \, {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} a b^{2} - {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} b^{3}\right)} x^{3} + 3 \, {\left({\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} a b^{2} - {\left(3 \, c^{3} d^{2} e^{2} + c d^{2} e^{2}\right)} b^{3}\right)} x^{2} + 3 \, {\left({\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} a b^{2} - {\left(c^{4} d e^{2} + c^{2} d e^{2}\right)} b^{3}\right)} x + {\left({\left(3 \, a b^{2} d^{4} e^{2} - b^{3} d^{4} e^{2}\right)} x^{4} + 3 \, {\left(c^{4} e^{2} + c^{2} e^{2}\right)} a b^{2} + 4 \, {\left(3 \, a b^{2} c d^{3} e^{2} - b^{3} c d^{3} e^{2}\right)} x^{3} - 3 \, {\left(2 \, b^{3} c^{2} d^{2} e^{2} - {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} a b^{2}\right)} x^{2} - 3 \, {\left(b^{3} c^{3} d e^{2} - 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"1/3*a^3*d^2*e^2*x^3 + a^3*c*d*e^2*x^2 + 3/2*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^2*b*c*d*e^2 + 1/6*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a^2*b*d^2*e^2 + a^3*c^2*e^2*x + 3*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^2*b*c^2*e^2/d + 1/3*(b^3*d^2*e^2*x^3 + 3*b^3*c*d*e^2*x^2 + 3*b^3*c^2*e^2*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + integrate(((3*a*b^2*d^5*e^2 - b^3*d^5*e^2)*x^5 + 5*(3*a*b^2*c*d^4*e^2 - b^3*c*d^4*e^2)*x^4 + 3*(c^5*e^2 + c^3*e^2)*a*b^2 + (3*(10*c^2*d^3*e^2 + d^3*e^2)*a*b^2 - (10*c^2*d^3*e^2 + d^3*e^2)*b^3)*x^3 + 3*((10*c^3*d^2*e^2 + 3*c*d^2*e^2)*a*b^2 - (3*c^3*d^2*e^2 + c*d^2*e^2)*b^3)*x^2 + 3*((5*c^4*d*e^2 + 3*c^2*d*e^2)*a*b^2 - (c^4*d*e^2 + c^2*d*e^2)*b^3)*x + ((3*a*b^2*d^4*e^2 - b^3*d^4*e^2)*x^4 + 3*(c^4*e^2 + c^2*e^2)*a*b^2 + 4*(3*a*b^2*c*d^3*e^2 - b^3*c*d^3*e^2)*x^3 - 3*(2*b^3*c^2*d^2*e^2 - (6*c^2*d^2*e^2 + d^2*e^2)*a*b^2)*x^2 - 3*(b^3*c^3*d*e^2 - 2*(2*c^3*d*e^2 + c*d*e^2)*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
140,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} d e x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b d e + a^{3} c e x + \frac{3 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{2} b c e}{d} + \frac{1}{2} \, {\left(b^{3} d e x^{2} + 2 \, b^{3} c e x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + \int \frac{3 \, {\left({\left(2 \, a b^{2} d^{4} e - b^{3} d^{4} e\right)} x^{4} + 2 \, {\left(c^{4} e + c^{2} e\right)} a b^{2} + 4 \, {\left(2 \, a b^{2} c d^{3} e - b^{3} c d^{3} e\right)} x^{3} + {\left(2 \, {\left(6 \, c^{2} d^{2} e + d^{2} e\right)} a b^{2} - {\left(5 \, c^{2} d^{2} e + d^{2} e\right)} b^{3}\right)} x^{2} + 2 \, {\left(2 \, {\left(2 \, c^{3} d e + c d e\right)} a b^{2} - {\left(c^{3} d e + c d e\right)} b^{3}\right)} x + {\left(2 \, {\left(c^{3} e + c e\right)} a b^{2} + {\left(2 \, a b^{2} d^{3} e - b^{3} d^{3} e\right)} x^{3} + 3 \, {\left(2 \, a b^{2} c d^{2} e - b^{3} c d^{2} e\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d e - {\left(3 \, c^{2} d e + d e\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{2 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/2*a^3*d*e*x^2 + 3/4*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^2*b*d*e + a^3*c*e*x + 3*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^2*b*c*e/d + 1/2*(b^3*d*e*x^2 + 2*b^3*c*e*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + integrate(3/2*((2*a*b^2*d^4*e - b^3*d^4*e)*x^4 + 2*(c^4*e + c^2*e)*a*b^2 + 4*(2*a*b^2*c*d^3*e - b^3*c*d^3*e)*x^3 + (2*(6*c^2*d^2*e + d^2*e)*a*b^2 - (5*c^2*d^2*e + d^2*e)*b^3)*x^2 + 2*(2*(2*c^3*d*e + c*d*e)*a*b^2 - (c^3*d*e + c*d*e)*b^3)*x + (2*(c^3*e + c*e)*a*b^2 + (2*a*b^2*d^3*e - b^3*d^3*e)*x^3 + 3*(2*a*b^2*c*d^2*e - b^3*c*d^2*e)*x^2 - 2*(b^3*c^2*d*e - (3*c^2*d*e + d*e)*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
141,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","b^{3} x \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + a^{3} x + \frac{3 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{2} b}{d} + \int \frac{3 \, {\left({\left(c^{3} + c\right)} a b^{2} + {\left(a b^{2} d^{3} - b^{3} d^{3}\right)} x^{3} + {\left(3 \, a b^{2} c d^{2} - 2 \, b^{3} c d^{2}\right)} x^{2} + {\left({\left(3 \, c^{2} d + d\right)} a b^{2} - {\left(c^{2} d + d\right)} b^{3}\right)} x + {\left({\left(c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{2} - b^{3} d^{2}\right)} x^{2} + {\left(2 \, a b^{2} c d - b^{3} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"b^3*x*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + a^3*x + 3*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^2*b/d + integrate(3*((c^3 + c)*a*b^2 + (a*b^2*d^3 - b^3*d^3)*x^3 + (3*a*b^2*c*d^2 - 2*b^3*c*d^2)*x^2 + ((3*c^2*d + d)*a*b^2 - (c^2*d + d)*b^3)*x + ((c^2 + 1)*a*b^2 + (a*b^2*d^2 - b^3*d^2)*x^2 + (2*a*b^2*c*d - b^3*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
142,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(d e x + c e\right)}{d e} + \int \frac{b^{3} \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)^{3}}{d e x + c e} + \frac{3 \, a b^{2} \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)^{2}}{d e x + c e} + \frac{3 \, a^{2} b \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)}{d e x + c e}\,{d x}"," ",0,"a^3*log(d*e*x + c*e)/(d*e) + integrate(b^3*log(d*x + c + sqrt((d*x + c)^2 + 1))^3/(d*e*x + c*e) + 3*a*b^2*log(d*x + c + sqrt((d*x + c)^2 + 1))^2/(d*e*x + c*e) + 3*a^2*b*log(d*x + c + sqrt((d*x + c)^2 + 1))/(d*e*x + c*e), x)","F",0
143,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{b^{3} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{d^{2} e^{2} x + c d e^{2}} - 3 \, a^{2} b {\left(\frac{\operatorname{arsinh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\operatorname{arsinh}\left(\frac{d e^{2}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}}\right)}{d e^{2}}\right)} - \frac{a^{3}}{d^{2} e^{2} x + c d e^{2}} + \int \frac{3 \, {\left({\left(c^{3} + c\right)} a b^{2} + {\left(c^{3} + c\right)} b^{3} + {\left(a b^{2} d^{3} + b^{3} d^{3}\right)} x^{3} + 3 \, {\left(a b^{2} c d^{2} + b^{3} c d^{2}\right)} x^{2} + {\left({\left(3 \, c^{2} d + d\right)} a b^{2} + {\left(3 \, c^{2} d + d\right)} b^{3}\right)} x + {\left(b^{3} c^{2} + {\left(c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{2} + b^{3} d^{2}\right)} x^{2} + 2 \, {\left(a b^{2} c d + b^{3} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d^{5} e^{2} x^{5} + 5 \, c d^{4} e^{2} x^{4} + c^{5} e^{2} + c^{3} e^{2} + {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} x^{2} + {\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} x + {\left(d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + c^{4} e^{2} + c^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-b^3*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(d^2*e^2*x + c*d*e^2) - 3*a^2*b*(arcsinh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsinh(d*e^2/abs(d^2*e^2*x + c*d*e^2))/(d*e^2)) - a^3/(d^2*e^2*x + c*d*e^2) + integrate(3*((c^3 + c)*a*b^2 + (c^3 + c)*b^3 + (a*b^2*d^3 + b^3*d^3)*x^3 + 3*(a*b^2*c*d^2 + b^3*c*d^2)*x^2 + ((3*c^2*d + d)*a*b^2 + (3*c^2*d + d)*b^3)*x + (b^3*c^2 + (c^2 + 1)*a*b^2 + (a*b^2*d^2 + b^3*d^2)*x^2 + 2*(a*b^2*c*d + b^3*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^5*e^2*x^5 + 5*c*d^4*e^2*x^4 + c^5*e^2 + c^3*e^2 + (10*c^2*d^3*e^2 + d^3*e^2)*x^3 + (10*c^3*d^2*e^2 + 3*c*d^2*e^2)*x^2 + (5*c^4*d*e^2 + 3*c^2*d*e^2)*x + (d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + c^4*e^2 + c^2*e^2 + (6*c^2*d^2*e^2 + d^2*e^2)*x^2 + 2*(2*c^3*d*e^2 + c*d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-3 \, {\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d \operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c\right)}{d e^{3}}\right)} a b^{2} - \frac{1}{2} \, {\left(\frac{\log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}} - 2 \, \int \frac{3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)} + 1\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{2 \, {\left(d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + c^{5} e^{3} + c^{3} e^{3} + {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x + {\left(d^{4} e^{3} x^{4} + 4 \, c d^{3} e^{3} x^{3} + c^{4} e^{3} + c^{2} e^{3} + {\left(6 \, c^{2} d^{2} e^{3} + d^{2} e^{3}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{3} + c d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}\right)} b^{3} - \frac{3}{2} \, a^{2} b {\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} - \frac{3 \, a b^{2} \operatorname{arsinh}\left(d x + c\right)^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{a^{3}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-3*(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d*arcsinh(d*x + c)/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c)/(d*e^3))*a*b^2 - 1/2*(log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 2*integrate(3/2*(d^2*x^2 + 2*c*d*x + c^2 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c) + 1)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + c^5*e^3 + c^3*e^3 + (10*c^2*d^3*e^3 + d^3*e^3)*x^3 + (10*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (5*c^4*d*e^3 + 3*c^2*d*e^3)*x + (d^4*e^3*x^4 + 4*c*d^3*e^3*x^3 + c^4*e^3 + c^2*e^3 + (6*c^2*d^2*e^3 + d^2*e^3)*x^2 + 2*(2*c^3*d*e^3 + c*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x))*b^3 - 3/2*a^2*b*(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d/(d^3*e^3*x + c*d^2*e^3) + arcsinh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)) - 3/2*a*b^2*arcsinh(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^3/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","F",0
145,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{b^{3} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \frac{a^{3}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} + \int \frac{{\left(3 \, {\left(c^{3} + c\right)} a b^{2} + {\left(c^{3} + c\right)} b^{3} + {\left(3 \, a b^{2} d^{3} + b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{2} c d^{2} + b^{3} c d^{2}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d + d\right)} a b^{2} + {\left(3 \, c^{2} d + d\right)} b^{3}\right)} x + {\left(b^{3} c^{2} + 3 \, {\left(c^{2} + 1\right)} a b^{2} + {\left(3 \, a b^{2} d^{2} + b^{3} d^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c d + b^{3} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 3 \, {\left(a^{2} b d^{3} x^{3} + 3 \, a^{2} b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{2} b x + {\left(c^{3} + c\right)} a^{2} b + {\left(a^{2} b d^{2} x^{2} + 2 \, a^{2} b c d x + {\left(c^{2} + 1\right)} a^{2} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{7} e^{4} x^{7} + 7 \, c d^{6} e^{4} x^{6} + c^{7} e^{4} + c^{5} e^{4} + {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} x^{2} + {\left(7 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} x + {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-1/3*b^3*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - 1/3*a^3/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) + integrate(((3*(c^3 + c)*a*b^2 + (c^3 + c)*b^3 + (3*a*b^2*d^3 + b^3*d^3)*x^3 + 3*(3*a*b^2*c*d^2 + b^3*c*d^2)*x^2 + (3*(3*c^2*d + d)*a*b^2 + (3*c^2*d + d)*b^3)*x + (b^3*c^2 + 3*(c^2 + 1)*a*b^2 + (3*a*b^2*d^2 + b^3*d^2)*x^2 + 2*(3*a*b^2*c*d + b^3*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 3*(a^2*b*d^3*x^3 + 3*a^2*b*c*d^2*x^2 + (3*c^2*d + d)*a^2*b*x + (c^3 + c)*a^2*b + (a^2*b*d^2*x^2 + 2*a^2*b*c*d*x + (c^2 + 1)*a^2*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^7*e^4*x^7 + 7*c*d^6*e^4*x^6 + c^7*e^4 + c^5*e^4 + (21*c^2*d^5*e^4 + d^5*e^4)*x^5 + 5*(7*c^3*d^4*e^4 + c*d^4*e^4)*x^4 + 5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*x^3 + (21*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*x^2 + (7*c^6*d*e^4 + 5*c^4*d*e^4)*x + (d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
146,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{{\left(b^{4} d e^{m} x + b^{4} c e^{m}\right)} {\left(d x + c\right)}^{m} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{d {\left(m + 1\right)}} + \frac{{\left(d e x + c e\right)}^{m + 1} a^{4}}{d e {\left(m + 1\right)}} + \int -\frac{2 \, {\left(2 \, {\left({\left(b^{4} c^{2} e^{m} - {\left(c^{2} e^{m} {\left(m + 1\right)} + e^{m} {\left(m + 1\right)}\right)} a b^{3} - {\left(a b^{3} d^{2} e^{m} {\left(m + 1\right)} - b^{4} d^{2} e^{m}\right)} x^{2} - 2 \, {\left(a b^{3} c d e^{m} {\left(m + 1\right)} - b^{4} c d e^{m}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)}^{m} - {\left({\left(c^{3} e^{m} {\left(m + 1\right)} + c e^{m} {\left(m + 1\right)}\right)} a b^{3} - {\left(c^{3} e^{m} + c e^{m}\right)} b^{4} + {\left(a b^{3} d^{3} e^{m} {\left(m + 1\right)} - b^{4} d^{3} e^{m}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{2} e^{m} {\left(m + 1\right)} - b^{4} c d^{2} e^{m}\right)} x^{2} + {\left({\left(3 \, c^{2} d e^{m} {\left(m + 1\right)} + d e^{m} {\left(m + 1\right)}\right)} a b^{3} - {\left(3 \, c^{2} d e^{m} + d e^{m}\right)} b^{4}\right)} x\right)} {\left(d x + c\right)}^{m}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} - 3 \, {\left({\left(a^{2} b^{2} d^{2} e^{m} {\left(m + 1\right)} x^{2} + 2 \, a^{2} b^{2} c d e^{m} {\left(m + 1\right)} x + {\left(c^{2} e^{m} {\left(m + 1\right)} + e^{m} {\left(m + 1\right)}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)}^{m} + {\left(a^{2} b^{2} d^{3} e^{m} {\left(m + 1\right)} x^{3} + 3 \, a^{2} b^{2} c d^{2} e^{m} {\left(m + 1\right)} x^{2} + {\left(3 \, c^{2} d e^{m} {\left(m + 1\right)} + d e^{m} {\left(m + 1\right)}\right)} a^{2} b^{2} x + {\left(c^{3} e^{m} {\left(m + 1\right)} + c e^{m} {\left(m + 1\right)}\right)} a^{2} b^{2}\right)} {\left(d x + c\right)}^{m}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 2 \, {\left({\left(a^{3} b d^{2} e^{m} {\left(m + 1\right)} x^{2} + 2 \, a^{3} b c d e^{m} {\left(m + 1\right)} x + {\left(c^{2} e^{m} {\left(m + 1\right)} + e^{m} {\left(m + 1\right)}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d x + c\right)}^{m} + {\left(a^{3} b d^{3} e^{m} {\left(m + 1\right)} x^{3} + 3 \, a^{3} b c d^{2} e^{m} {\left(m + 1\right)} x^{2} + {\left(3 \, c^{2} d e^{m} {\left(m + 1\right)} + d e^{m} {\left(m + 1\right)}\right)} a^{3} b x + {\left(c^{3} e^{m} {\left(m + 1\right)} + c e^{m} {\left(m + 1\right)}\right)} a^{3} b\right)} {\left(d x + c\right)}^{m}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{d^{3} {\left(m + 1\right)} x^{3} + 3 \, c d^{2} {\left(m + 1\right)} x^{2} + c^{3} {\left(m + 1\right)} + c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} + d {\left(m + 1\right)}\right)} x + {\left(d^{2} {\left(m + 1\right)} x^{2} + 2 \, c d {\left(m + 1\right)} x + c^{2} {\left(m + 1\right)} + m + 1\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"(b^4*d*e^m*x + b^4*c*e^m)*(d*x + c)^m*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d*(m + 1)) + (d*e*x + c*e)^(m + 1)*a^4/(d*e*(m + 1)) + integrate(-2*(2*((b^4*c^2*e^m - (c^2*e^m*(m + 1) + e^m*(m + 1))*a*b^3 - (a*b^3*d^2*e^m*(m + 1) - b^4*d^2*e^m)*x^2 - 2*(a*b^3*c*d*e^m*(m + 1) - b^4*c*d*e^m)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c)^m - ((c^3*e^m*(m + 1) + c*e^m*(m + 1))*a*b^3 - (c^3*e^m + c*e^m)*b^4 + (a*b^3*d^3*e^m*(m + 1) - b^4*d^3*e^m)*x^3 + 3*(a*b^3*c*d^2*e^m*(m + 1) - b^4*c*d^2*e^m)*x^2 + ((3*c^2*d*e^m*(m + 1) + d*e^m*(m + 1))*a*b^3 - (3*c^2*d*e^m + d*e^m)*b^4)*x)*(d*x + c)^m)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 - 3*((a^2*b^2*d^2*e^m*(m + 1)*x^2 + 2*a^2*b^2*c*d*e^m*(m + 1)*x + (c^2*e^m*(m + 1) + e^m*(m + 1))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c)^m + (a^2*b^2*d^3*e^m*(m + 1)*x^3 + 3*a^2*b^2*c*d^2*e^m*(m + 1)*x^2 + (3*c^2*d*e^m*(m + 1) + d*e^m*(m + 1))*a^2*b^2*x + (c^3*e^m*(m + 1) + c*e^m*(m + 1))*a^2*b^2)*(d*x + c)^m)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 2*((a^3*b*d^2*e^m*(m + 1)*x^2 + 2*a^3*b*c*d*e^m*(m + 1)*x + (c^2*e^m*(m + 1) + e^m*(m + 1))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c)^m + (a^3*b*d^3*e^m*(m + 1)*x^3 + 3*a^3*b*c*d^2*e^m*(m + 1)*x^2 + (3*c^2*d*e^m*(m + 1) + d*e^m*(m + 1))*a^3*b*x + (c^3*e^m*(m + 1) + c*e^m*(m + 1))*a^3*b)*(d*x + c)^m)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + c*(m + 1) + (3*c^2*d*(m + 1) + d*(m + 1))*x + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) + m + 1)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
147,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{1}{4} \, a^{4} d^{3} e^{3} x^{4} + a^{4} c d^{2} e^{3} x^{3} + \frac{3}{2} \, a^{4} c^{2} d e^{3} x^{2} + 3 \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{3} b c^{2} d e^{3} + \frac{2}{3} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a^{3} b c d^{2} e^{3} + \frac{1}{24} \, {\left(24 \, x^{4} \operatorname{arsinh}\left(d x + c\right) - {\left(\frac{6 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{3}}{d^{2}} - \frac{14 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x^{2}}{d^{3}} + \frac{105 \, c^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} + 1\right)} c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)} c}{d^{5}}\right)} d\right)} a^{3} b d^{3} e^{3} + a^{4} c^{3} e^{3} x + \frac{4 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{3} b c^{3} e^{3}}{d} + \frac{1}{4} \, {\left(b^{4} d^{3} e^{3} x^{4} + 4 \, b^{4} c d^{2} e^{3} x^{3} + 6 \, b^{4} c^{2} d e^{3} x^{2} + 4 \, b^{4} c^{3} e^{3} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4} + \int \frac{{\left({\left(4 \, a b^{3} d^{6} e^{3} - b^{4} d^{6} e^{3}\right)} x^{6} + 6 \, {\left(4 \, a b^{3} c d^{5} e^{3} - b^{4} c d^{5} e^{3}\right)} x^{5} + 4 \, {\left(c^{6} e^{3} + c^{4} e^{3}\right)} a b^{3} + {\left(4 \, {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} a b^{3} - {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} b^{4}\right)} x^{4} + 4 \, {\left(4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} a b^{3} - {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} b^{4}\right)} x^{3} + 2 \, {\left(6 \, {\left(5 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} a b^{3} - {\left(7 \, c^{4} d^{2} e^{3} + 3 \, c^{2} d^{2} e^{3}\right)} b^{4}\right)} x^{2} + 4 \, {\left(2 \, {\left(3 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} a b^{3} - {\left(c^{5} d e^{3} + c^{3} d e^{3}\right)} b^{4}\right)} x + {\left({\left(4 \, a b^{3} d^{5} e^{3} - b^{4} d^{5} e^{3}\right)} x^{5} + 4 \, {\left(c^{5} e^{3} + c^{3} e^{3}\right)} a b^{3} + 5 \, {\left(4 \, a b^{3} c d^{4} e^{3} - b^{4} c d^{4} e^{3}\right)} x^{4} - 2 \, {\left(5 \, b^{4} c^{2} d^{3} e^{3} - 2 \, {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} a b^{3}\right)} x^{3} - 2 \, {\left(5 \, b^{4} c^{3} d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} a b^{3}\right)} x^{2} - 4 \, {\left(b^{4} c^{4} d e^{3} - {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} a b^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 6 \, {\left(a^{2} b^{2} d^{6} e^{3} x^{6} + 6 \, a^{2} b^{2} c d^{5} e^{3} x^{5} + {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} a^{2} b^{2} x + {\left(c^{6} e^{3} + c^{4} e^{3}\right)} a^{2} b^{2} + {\left(a^{2} b^{2} d^{5} e^{3} x^{5} + 5 \, a^{2} b^{2} c d^{4} e^{3} x^{4} + {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} a^{2} b^{2} x^{3} + {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} a^{2} b^{2} x + {\left(c^{5} e^{3} + c^{3} e^{3}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"1/4*a^4*d^3*e^3*x^4 + a^4*c*d^2*e^3*x^3 + 3/2*a^4*c^2*d*e^3*x^2 + 3*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^3*b*c^2*d*e^3 + 2/3*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a^3*b*c*d^2*e^3 + 1/24*(24*x^4*arcsinh(d*x + c) - (6*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^3/d^2 - 14*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x^2/d^3 + 105*c^4*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 35*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2*x/d^4 - 90*(c^2 + 1)*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 - 105*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^3/d^5 - 9*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*x/d^4 + 9*(c^2 + 1)^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^5 + 55*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)*c/d^5)*d)*a^3*b*d^3*e^3 + a^4*c^3*e^3*x + 4*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^3*b*c^3*e^3/d + 1/4*(b^4*d^3*e^3*x^4 + 4*b^4*c*d^2*e^3*x^3 + 6*b^4*c^2*d*e^3*x^2 + 4*b^4*c^3*e^3*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4 + integrate((((4*a*b^3*d^6*e^3 - b^4*d^6*e^3)*x^6 + 6*(4*a*b^3*c*d^5*e^3 - b^4*c*d^5*e^3)*x^5 + 4*(c^6*e^3 + c^4*e^3)*a*b^3 + (4*(15*c^2*d^4*e^3 + d^4*e^3)*a*b^3 - (15*c^2*d^4*e^3 + d^4*e^3)*b^4)*x^4 + 4*(4*(5*c^3*d^3*e^3 + c*d^3*e^3)*a*b^3 - (5*c^3*d^3*e^3 + c*d^3*e^3)*b^4)*x^3 + 2*(6*(5*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*a*b^3 - (7*c^4*d^2*e^3 + 3*c^2*d^2*e^3)*b^4)*x^2 + 4*(2*(3*c^5*d*e^3 + 2*c^3*d*e^3)*a*b^3 - (c^5*d*e^3 + c^3*d*e^3)*b^4)*x + ((4*a*b^3*d^5*e^3 - b^4*d^5*e^3)*x^5 + 4*(c^5*e^3 + c^3*e^3)*a*b^3 + 5*(4*a*b^3*c*d^4*e^3 - b^4*c*d^4*e^3)*x^4 - 2*(5*b^4*c^2*d^3*e^3 - 2*(10*c^2*d^3*e^3 + d^3*e^3)*a*b^3)*x^3 - 2*(5*b^4*c^3*d^2*e^3 - 2*(10*c^3*d^2*e^3 + 3*c*d^2*e^3)*a*b^3)*x^2 - 4*(b^4*c^4*d*e^3 - (5*c^4*d*e^3 + 3*c^2*d*e^3)*a*b^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 6*(a^2*b^2*d^6*e^3*x^6 + 6*a^2*b^2*c*d^5*e^3*x^5 + (15*c^2*d^4*e^3 + d^4*e^3)*a^2*b^2*x^4 + 4*(5*c^3*d^3*e^3 + c*d^3*e^3)*a^2*b^2*x^3 + 3*(5*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*a^2*b^2*x^2 + 2*(3*c^5*d*e^3 + 2*c^3*d*e^3)*a^2*b^2*x + (c^6*e^3 + c^4*e^3)*a^2*b^2 + (a^2*b^2*d^5*e^3*x^5 + 5*a^2*b^2*c*d^4*e^3*x^4 + (10*c^2*d^3*e^3 + d^3*e^3)*a^2*b^2*x^3 + (10*c^3*d^2*e^3 + 3*c*d^2*e^3)*a^2*b^2*x^2 + (5*c^4*d*e^3 + 3*c^2*d*e^3)*a^2*b^2*x + (c^5*e^3 + c^3*e^3)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
148,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{1}{3} \, a^{4} d^{2} e^{2} x^{3} + a^{4} c d e^{2} x^{2} + 2 \, {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{3} b c d e^{2} + \frac{2}{9} \, {\left(6 \, x^{3} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x^{2}}{d^{2}} - \frac{15 \, c^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} + 1\right)} c \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(c^{2} + 1\right)}}{d^{4}}\right)}\right)} a^{3} b d^{2} e^{2} + a^{4} c^{2} e^{2} x + \frac{4 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{3} b c^{2} e^{2}}{d} + \frac{1}{3} \, {\left(b^{4} d^{2} e^{2} x^{3} + 3 \, b^{4} c d e^{2} x^{2} + 3 \, b^{4} c^{2} e^{2} x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4} + \int \frac{2 \, {\left(2 \, {\left({\left(3 \, a b^{3} d^{5} e^{2} - b^{4} d^{5} e^{2}\right)} x^{5} + 3 \, {\left(c^{5} e^{2} + c^{3} e^{2}\right)} a b^{3} + 5 \, {\left(3 \, a b^{3} c d^{4} e^{2} - b^{4} c d^{4} e^{2}\right)} x^{4} + {\left(3 \, {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} a b^{3} - {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} b^{4}\right)} x^{3} + 3 \, {\left({\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} a b^{3} - {\left(3 \, c^{3} d^{2} e^{2} + c d^{2} e^{2}\right)} b^{4}\right)} x^{2} + 3 \, {\left({\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} a b^{3} - {\left(c^{4} d e^{2} + c^{2} d e^{2}\right)} b^{4}\right)} x + {\left(3 \, {\left(c^{4} e^{2} + c^{2} e^{2}\right)} a b^{3} + {\left(3 \, a b^{3} d^{4} e^{2} - b^{4} d^{4} e^{2}\right)} x^{4} + 4 \, {\left(3 \, a b^{3} c d^{3} e^{2} - b^{4} c d^{3} e^{2}\right)} x^{3} - 3 \, {\left(2 \, b^{4} c^{2} d^{2} e^{2} - {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} a b^{3}\right)} x^{2} - 3 \, {\left(b^{4} c^{3} d e^{2} - 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} a b^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 9 \, {\left(a^{2} b^{2} d^{5} e^{2} x^{5} + 5 \, a^{2} b^{2} c d^{4} e^{2} x^{4} + {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} a^{2} b^{2} x^{3} + {\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} a^{2} b^{2} x + {\left(c^{5} e^{2} + c^{3} e^{2}\right)} a^{2} b^{2} + {\left(a^{2} b^{2} d^{4} e^{2} x^{4} + 4 \, a^{2} b^{2} c d^{3} e^{2} x^{3} + {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} a^{2} b^{2} x + {\left(c^{4} e^{2} + c^{2} e^{2}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}\right)}}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"1/3*a^4*d^2*e^2*x^3 + a^4*c*d*e^2*x^2 + 2*(2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^3*b*c*d*e^2 + 2/9*(6*x^3*arcsinh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x^2/d^2 - 15*c^3*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c*x/d^3 + 9*(c^2 + 1)*c*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^4 + 15*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c^2/d^4 - 4*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(c^2 + 1)/d^4))*a^3*b*d^2*e^2 + a^4*c^2*e^2*x + 4*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^3*b*c^2*e^2/d + 1/3*(b^4*d^2*e^2*x^3 + 3*b^4*c*d*e^2*x^2 + 3*b^4*c^2*e^2*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4 + integrate(2/3*(2*((3*a*b^3*d^5*e^2 - b^4*d^5*e^2)*x^5 + 3*(c^5*e^2 + c^3*e^2)*a*b^3 + 5*(3*a*b^3*c*d^4*e^2 - b^4*c*d^4*e^2)*x^4 + (3*(10*c^2*d^3*e^2 + d^3*e^2)*a*b^3 - (10*c^2*d^3*e^2 + d^3*e^2)*b^4)*x^3 + 3*((10*c^3*d^2*e^2 + 3*c*d^2*e^2)*a*b^3 - (3*c^3*d^2*e^2 + c*d^2*e^2)*b^4)*x^2 + 3*((5*c^4*d*e^2 + 3*c^2*d*e^2)*a*b^3 - (c^4*d*e^2 + c^2*d*e^2)*b^4)*x + (3*(c^4*e^2 + c^2*e^2)*a*b^3 + (3*a*b^3*d^4*e^2 - b^4*d^4*e^2)*x^4 + 4*(3*a*b^3*c*d^3*e^2 - b^4*c*d^3*e^2)*x^3 - 3*(2*b^4*c^2*d^2*e^2 - (6*c^2*d^2*e^2 + d^2*e^2)*a*b^3)*x^2 - 3*(b^4*c^3*d*e^2 - 2*(2*c^3*d*e^2 + c*d*e^2)*a*b^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 9*(a^2*b^2*d^5*e^2*x^5 + 5*a^2*b^2*c*d^4*e^2*x^4 + (10*c^2*d^3*e^2 + d^3*e^2)*a^2*b^2*x^3 + (10*c^3*d^2*e^2 + 3*c*d^2*e^2)*a^2*b^2*x^2 + (5*c^4*d*e^2 + 3*c^2*d*e^2)*a^2*b^2*x + (c^5*e^2 + c^3*e^2)*a^2*b^2 + (a^2*b^2*d^4*e^2*x^4 + 4*a^2*b^2*c*d^3*e^2*x^3 + (6*c^2*d^2*e^2 + d^2*e^2)*a^2*b^2*x^2 + 2*(2*c^3*d*e^2 + c*d*e^2)*a^2*b^2*x + (c^4*e^2 + c^2*e^2)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
149,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{1}{2} \, a^{4} d e x^{2} + {\left(2 \, x^{2} \operatorname{arsinh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(d^{2} x + c d\right)}}{\sqrt{-4 \, c^{2} d^{2} + 4 \, {\left(c^{2} + 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} c}{d^{3}}\right)}\right)} a^{3} b d e + a^{4} c e x + \frac{4 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{3} b c e}{d} + \frac{1}{2} \, {\left(b^{4} d e x^{2} + 2 \, b^{4} c e x\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4} + \int \frac{2 \, {\left({\left(2 \, {\left(c^{4} e + c^{2} e\right)} a b^{3} + {\left(2 \, a b^{3} d^{4} e - b^{4} d^{4} e\right)} x^{4} + 4 \, {\left(2 \, a b^{3} c d^{3} e - b^{4} c d^{3} e\right)} x^{3} + {\left(2 \, {\left(6 \, c^{2} d^{2} e + d^{2} e\right)} a b^{3} - {\left(5 \, c^{2} d^{2} e + d^{2} e\right)} b^{4}\right)} x^{2} + 2 \, {\left(2 \, {\left(2 \, c^{3} d e + c d e\right)} a b^{3} - {\left(c^{3} d e + c d e\right)} b^{4}\right)} x + {\left(2 \, {\left(c^{3} e + c e\right)} a b^{3} + {\left(2 \, a b^{3} d^{3} e - b^{4} d^{3} e\right)} x^{3} + 3 \, {\left(2 \, a b^{3} c d^{2} e - b^{4} c d^{2} e\right)} x^{2} - 2 \, {\left(b^{4} c^{2} d e - {\left(3 \, c^{2} d e + d e\right)} a b^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 3 \, {\left(a^{2} b^{2} d^{4} e x^{4} + 4 \, a^{2} b^{2} c d^{3} e x^{3} + {\left(6 \, c^{2} d^{2} e + d^{2} e\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d e + c d e\right)} a^{2} b^{2} x + {\left(c^{4} e + c^{2} e\right)} a^{2} b^{2} + {\left(a^{2} b^{2} d^{3} e x^{3} + 3 \, a^{2} b^{2} c d^{2} e x^{2} + {\left(3 \, c^{2} d e + d e\right)} a^{2} b^{2} x + {\left(c^{3} e + c e\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}\right)}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"1/2*a^4*d*e*x^2 + (2*x^2*arcsinh(d*x + c) - d*(3*c^2*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*x/d^2 - (c^2 + 1)*arcsinh(2*(d^2*x + c*d)/sqrt(-4*c^2*d^2 + 4*(c^2 + 1)*d^2))/d^3 - 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*c/d^3))*a^3*b*d*e + a^4*c*e*x + 4*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^3*b*c*e/d + 1/2*(b^4*d*e*x^2 + 2*b^4*c*e*x)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4 + integrate(2*((2*(c^4*e + c^2*e)*a*b^3 + (2*a*b^3*d^4*e - b^4*d^4*e)*x^4 + 4*(2*a*b^3*c*d^3*e - b^4*c*d^3*e)*x^3 + (2*(6*c^2*d^2*e + d^2*e)*a*b^3 - (5*c^2*d^2*e + d^2*e)*b^4)*x^2 + 2*(2*(2*c^3*d*e + c*d*e)*a*b^3 - (c^3*d*e + c*d*e)*b^4)*x + (2*(c^3*e + c*e)*a*b^3 + (2*a*b^3*d^3*e - b^4*d^3*e)*x^3 + 3*(2*a*b^3*c*d^2*e - b^4*c*d^2*e)*x^2 - 2*(b^4*c^2*d*e - (3*c^2*d*e + d*e)*a*b^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 3*(a^2*b^2*d^4*e*x^4 + 4*a^2*b^2*c*d^3*e*x^3 + (6*c^2*d^2*e + d^2*e)*a^2*b^2*x^2 + 2*(2*c^3*d*e + c*d*e)*a^2*b^2*x + (c^4*e + c^2*e)*a^2*b^2 + (a^2*b^2*d^3*e*x^3 + 3*a^2*b^2*c*d^2*e*x^2 + (3*c^2*d*e + d*e)*a^2*b^2*x + (c^3*e + c*e)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","b^{4} x \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4} + a^{4} x + \frac{4 \, {\left({\left(d x + c\right)} \operatorname{arsinh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} + 1}\right)} a^{3} b}{d} + \int \frac{2 \, {\left(2 \, {\left({\left(c^{3} + c\right)} a b^{3} + {\left(a b^{3} d^{3} - b^{4} d^{3}\right)} x^{3} + {\left(3 \, a b^{3} c d^{2} - 2 \, b^{4} c d^{2}\right)} x^{2} + {\left({\left(3 \, c^{2} d + d\right)} a b^{3} - {\left(c^{2} d + d\right)} b^{4}\right)} x + {\left({\left(c^{2} + 1\right)} a b^{3} + {\left(a b^{3} d^{2} - b^{4} d^{2}\right)} x^{2} + {\left(2 \, a b^{3} c d - b^{4} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 3 \, {\left(a^{2} b^{2} d^{3} x^{3} + 3 \, a^{2} b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{2} b^{2} x + {\left(c^{3} + c\right)} a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{2} b^{2} c d x + {\left(c^{2} + 1\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}\right)}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"b^4*x*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4 + a^4*x + 4*((d*x + c)*arcsinh(d*x + c) - sqrt((d*x + c)^2 + 1))*a^3*b/d + integrate(2*(2*((c^3 + c)*a*b^3 + (a*b^3*d^3 - b^4*d^3)*x^3 + (3*a*b^3*c*d^2 - 2*b^4*c*d^2)*x^2 + ((3*c^2*d + d)*a*b^3 - (c^2*d + d)*b^4)*x + ((c^2 + 1)*a*b^3 + (a*b^3*d^2 - b^4*d^2)*x^2 + (2*a*b^3*c*d - b^4*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 3*(a^2*b^2*d^3*x^3 + 3*a^2*b^2*c*d^2*x^2 + (3*c^2*d + d)*a^2*b^2*x + (c^3 + c)*a^2*b^2 + (a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + (c^2 + 1)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
151,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{4} \log\left(d e x + c e\right)}{d e} + \int \frac{b^{4} \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)^{4}}{d e x + c e} + \frac{4 \, a b^{3} \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)^{3}}{d e x + c e} + \frac{6 \, a^{2} b^{2} \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)^{2}}{d e x + c e} + \frac{4 \, a^{3} b \log\left(d x + c + \sqrt{{\left(d x + c\right)}^{2} + 1}\right)}{d e x + c e}\,{d x}"," ",0,"a^4*log(d*e*x + c*e)/(d*e) + integrate(b^4*log(d*x + c + sqrt((d*x + c)^2 + 1))^4/(d*e*x + c*e) + 4*a*b^3*log(d*x + c + sqrt((d*x + c)^2 + 1))^3/(d*e*x + c*e) + 6*a^2*b^2*log(d*x + c + sqrt((d*x + c)^2 + 1))^2/(d*e*x + c*e) + 4*a^3*b*log(d*x + c + sqrt((d*x + c)^2 + 1))/(d*e*x + c*e), x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{b^{4} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{d^{2} e^{2} x + c d e^{2}} - 4 \, a^{3} b {\left(\frac{\operatorname{arsinh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\operatorname{arsinh}\left(\frac{d e^{2}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}}\right)}{d e^{2}}\right)} - \frac{a^{4}}{d^{2} e^{2} x + c d e^{2}} + \int \frac{2 \, {\left(2 \, {\left({\left(c^{3} + c\right)} a b^{3} + {\left(c^{3} + c\right)} b^{4} + {\left(a b^{3} d^{3} + b^{4} d^{3}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{2} + b^{4} c d^{2}\right)} x^{2} + {\left({\left(3 \, c^{2} d + d\right)} a b^{3} + {\left(3 \, c^{2} d + d\right)} b^{4}\right)} x + {\left(b^{4} c^{2} + {\left(c^{2} + 1\right)} a b^{3} + {\left(a b^{3} d^{2} + b^{4} d^{2}\right)} x^{2} + 2 \, {\left(a b^{3} c d + b^{4} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 3 \, {\left(a^{2} b^{2} d^{3} x^{3} + 3 \, a^{2} b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{2} b^{2} x + {\left(c^{3} + c\right)} a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{2} b^{2} c d x + {\left(c^{2} + 1\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}\right)}}{d^{5} e^{2} x^{5} + 5 \, c d^{4} e^{2} x^{4} + c^{5} e^{2} + c^{3} e^{2} + {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} x^{2} + {\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} x + {\left(d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + c^{4} e^{2} + c^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-b^4*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d^2*e^2*x + c*d*e^2) - 4*a^3*b*(arcsinh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsinh(d*e^2/abs(d^2*e^2*x + c*d*e^2))/(d*e^2)) - a^4/(d^2*e^2*x + c*d*e^2) + integrate(2*(2*((c^3 + c)*a*b^3 + (c^3 + c)*b^4 + (a*b^3*d^3 + b^4*d^3)*x^3 + 3*(a*b^3*c*d^2 + b^4*c*d^2)*x^2 + ((3*c^2*d + d)*a*b^3 + (3*c^2*d + d)*b^4)*x + (b^4*c^2 + (c^2 + 1)*a*b^3 + (a*b^3*d^2 + b^4*d^2)*x^2 + 2*(a*b^3*c*d + b^4*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 3*(a^2*b^2*d^3*x^3 + 3*a^2*b^2*c*d^2*x^2 + (3*c^2*d + d)*a^2*b^2*x + (c^3 + c)*a^2*b^2 + (a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + (c^2 + 1)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2)/(d^5*e^2*x^5 + 5*c*d^4*e^2*x^4 + c^5*e^2 + c^3*e^2 + (10*c^2*d^3*e^2 + d^3*e^2)*x^3 + (10*c^3*d^2*e^2 + 3*c*d^2*e^2)*x^2 + (5*c^4*d*e^2 + 3*c^2*d*e^2)*x + (d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + c^4*e^2 + c^2*e^2 + (6*c^2*d^2*e^2 + d^2*e^2)*x^2 + 2*(2*c^3*d*e^2 + c*d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{b^{4} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - 6 \, {\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d \operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x + c d^{2} e^{3}} - \frac{\log\left(d x + c\right)}{d e^{3}}\right)} a^{2} b^{2} - 2 \, a^{3} b {\left(\frac{\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} d}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\operatorname{arsinh}\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} - \frac{3 \, a^{2} b^{2} \operatorname{arsinh}\left(d x + c\right)^{2}}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}} - \frac{a^{4}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} + \int \frac{2 \, {\left(2 \, {\left(c^{3} + c\right)} a b^{3} + {\left(c^{3} + c\right)} b^{4} + {\left(2 \, a b^{3} d^{3} + b^{4} d^{3}\right)} x^{3} + 3 \, {\left(2 \, a b^{3} c d^{2} + b^{4} c d^{2}\right)} x^{2} + {\left(2 \, {\left(3 \, c^{2} d + d\right)} a b^{3} + {\left(3 \, c^{2} d + d\right)} b^{4}\right)} x + {\left(b^{4} c^{2} + 2 \, {\left(c^{2} + 1\right)} a b^{3} + {\left(2 \, a b^{3} d^{2} + b^{4} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{3} c d + b^{4} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{d^{6} e^{3} x^{6} + 6 \, c d^{5} e^{3} x^{5} + c^{6} e^{3} + c^{4} e^{3} + {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} x + {\left(d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + c^{5} e^{3} + c^{3} e^{3} + {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-1/2*b^4*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 6*(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d*arcsinh(d*x + c)/(d^3*e^3*x + c*d^2*e^3) - log(d*x + c)/(d*e^3))*a^2*b^2 - 2*a^3*b*(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*d/(d^3*e^3*x + c*d^2*e^3) + arcsinh(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)) - 3*a^2*b^2*arcsinh(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^4/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) + integrate(2*(2*(c^3 + c)*a*b^3 + (c^3 + c)*b^4 + (2*a*b^3*d^3 + b^4*d^3)*x^3 + 3*(2*a*b^3*c*d^2 + b^4*c*d^2)*x^2 + (2*(3*c^2*d + d)*a*b^3 + (3*c^2*d + d)*b^4)*x + (b^4*c^2 + 2*(c^2 + 1)*a*b^3 + (2*a*b^3*d^2 + b^4*d^2)*x^2 + 2*(2*a*b^3*c*d + b^4*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(d^6*e^3*x^6 + 6*c*d^5*e^3*x^5 + c^6*e^3 + c^4*e^3 + (15*c^2*d^4*e^3 + d^4*e^3)*x^4 + 4*(5*c^3*d^3*e^3 + c*d^3*e^3)*x^3 + 3*(5*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*x^2 + 2*(3*c^5*d*e^3 + 2*c^3*d*e^3)*x + (d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + c^5*e^3 + c^3*e^3 + (10*c^2*d^3*e^3 + d^3*e^3)*x^3 + (10*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (5*c^4*d*e^3 + 3*c^2*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{b^{4} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \frac{a^{4}}{3 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} + \int \frac{2 \, {\left(2 \, {\left(3 \, {\left(c^{3} + c\right)} a b^{3} + {\left(c^{3} + c\right)} b^{4} + {\left(3 \, a b^{3} d^{3} + b^{4} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} + b^{4} c d^{2}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d + d\right)} a b^{3} + {\left(3 \, c^{2} d + d\right)} b^{4}\right)} x + {\left(b^{4} c^{2} + 3 \, {\left(c^{2} + 1\right)} a b^{3} + {\left(3 \, a b^{3} d^{2} + b^{4} d^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{3} c d + b^{4} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 9 \, {\left(a^{2} b^{2} d^{3} x^{3} + 3 \, a^{2} b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{2} b^{2} x + {\left(c^{3} + c\right)} a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{2} b^{2} c d x + {\left(c^{2} + 1\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 6 \, {\left(a^{3} b d^{3} x^{3} + 3 \, a^{3} b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{3} b x + {\left(c^{3} + c\right)} a^{3} b + {\left(a^{3} b d^{2} x^{2} + 2 \, a^{3} b c d x + {\left(c^{2} + 1\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{3 \, {\left(d^{7} e^{4} x^{7} + 7 \, c d^{6} e^{4} x^{6} + c^{7} e^{4} + c^{5} e^{4} + {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} x^{2} + {\left(7 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} x + {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/3*b^4*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - 1/3*a^4/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) + integrate(2/3*(2*(3*(c^3 + c)*a*b^3 + (c^3 + c)*b^4 + (3*a*b^3*d^3 + b^4*d^3)*x^3 + 3*(3*a*b^3*c*d^2 + b^4*c*d^2)*x^2 + (3*(3*c^2*d + d)*a*b^3 + (3*c^2*d + d)*b^4)*x + (b^4*c^2 + 3*(c^2 + 1)*a*b^3 + (3*a*b^3*d^2 + b^4*d^2)*x^2 + 2*(3*a*b^3*c*d + b^4*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 9*(a^2*b^2*d^3*x^3 + 3*a^2*b^2*c*d^2*x^2 + (3*c^2*d + d)*a^2*b^2*x + (c^3 + c)*a^2*b^2 + (a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + (c^2 + 1)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 6*(a^3*b*d^3*x^3 + 3*a^3*b*c*d^2*x^2 + (3*c^2*d + d)*a^3*b*x + (c^3 + c)*a^3*b + (a^3*b*d^2*x^2 + 2*a^3*b*c*d*x + (c^2 + 1)*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^7*e^4*x^7 + 7*c*d^6*e^4*x^6 + c^7*e^4 + c^5*e^4 + (21*c^2*d^5*e^4 + d^5*e^4)*x^5 + 5*(7*c^3*d^4*e^4 + c*d^4*e^4)*x^4 + 5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*x^3 + (21*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*x^2 + (7*c^6*d*e^4 + 5*c^4*d*e^4)*x + (d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
155,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{m}}{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^m/(b*arcsinh(d*x + c) + a), x)","F",0
156,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arcsinh(d*x + c) + a), x)","F",0
157,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsinh(d*x + c) + a), x)","F",0
158,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsinh(d*x + c) + a), x)","F",0
159,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{d e x + c e}{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsinh(d*x + c) + a), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsinh(d*x + c) + a), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)), x)","F",0
162,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{7} e^{4} x^{7} + 7 \, c d^{6} e^{4} x^{6} + c^{7} e^{4} + c^{5} e^{4} + {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} x^{2} + {\left(7 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} x + {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d + d\right)} a b + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + {\left(c^{2} d + d\right)} b^{2} + {\left(b^{2} d^{2} x + b^{2} c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(a b d^{2} x + a b c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} + \int \frac{5 \, d^{8} e^{4} x^{8} + 40 \, c d^{7} e^{4} x^{7} + 5 \, c^{8} e^{4} + 10 \, c^{6} e^{4} + 5 \, c^{4} e^{4} + 10 \, {\left(14 \, c^{2} d^{6} e^{4} + d^{6} e^{4}\right)} x^{6} + 20 \, {\left(14 \, c^{3} d^{5} e^{4} + 3 \, c d^{5} e^{4}\right)} x^{5} + 5 \, {\left(70 \, c^{4} d^{4} e^{4} + 30 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 20 \, {\left(14 \, c^{5} d^{3} e^{4} + 10 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 10 \, {\left(14 \, c^{6} d^{2} e^{4} + 15 \, c^{4} d^{2} e^{4} + 3 \, c^{2} d^{2} e^{4}\right)} x^{2} + {\left(5 \, d^{6} e^{4} x^{6} + 30 \, c d^{5} e^{4} x^{5} + 5 \, c^{6} e^{4} + 3 \, c^{4} e^{4} + 3 \, {\left(25 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(25 \, c^{3} d^{3} e^{4} + 3 \, c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(25 \, c^{4} d^{2} e^{4} + 6 \, c^{2} d^{2} e^{4}\right)} x^{2} + 6 \, {\left(5 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 20 \, {\left(2 \, c^{7} d e^{4} + 3 \, c^{5} d e^{4} + c^{3} d e^{4}\right)} x + {\left(10 \, d^{7} e^{4} x^{7} + 70 \, c d^{6} e^{4} x^{6} + 10 \, c^{7} e^{4} + 13 \, c^{5} e^{4} + 4 \, c^{3} e^{4} + {\left(210 \, c^{2} d^{5} e^{4} + 13 \, d^{5} e^{4}\right)} x^{5} + 5 \, {\left(70 \, c^{3} d^{4} e^{4} + 13 \, c d^{4} e^{4}\right)} x^{4} + 2 \, {\left(175 \, c^{4} d^{3} e^{4} + 65 \, c^{2} d^{3} e^{4} + 2 \, d^{3} e^{4}\right)} x^{3} + 2 \, {\left(105 \, c^{5} d^{2} e^{4} + 65 \, c^{3} d^{2} e^{4} + 6 \, c d^{2} e^{4}\right)} x^{2} + {\left(70 \, c^{6} d e^{4} + 65 \, c^{4} d e^{4} + 12 \, c^{2} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{4} x^{4} + 4 \, a b c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} a b x^{2} + 4 \, {\left(c^{3} d + c d\right)} a b x + {\left(c^{4} + 2 \, c^{2} + 1\right)} a b + {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} b^{2} x^{2} + 4 \, {\left(c^{3} d + c d\right)} b^{2} x + {\left(c^{4} + 2 \, c^{2} + 1\right)} b^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} b^{2} x + {\left(c^{3} + c\right)} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 2 \, {\left(a b d^{3} x^{3} + 3 \, a b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a b x + {\left(c^{3} + c\right)} a b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-(d^7*e^4*x^7 + 7*c*d^6*e^4*x^6 + c^7*e^4 + c^5*e^4 + (21*c^2*d^5*e^4 + d^5*e^4)*x^5 + 5*(7*c^3*d^4*e^4 + c*d^4*e^4)*x^4 + 5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*x^3 + (21*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*x^2 + (7*c^6*d*e^4 + 5*c^4*d*e^4)*x + (d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d + d)*a*b + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + (c^2*d + d)*b^2 + (b^2*d^2*x + b^2*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (a*b*d^2*x + a*b*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate((5*d^8*e^4*x^8 + 40*c*d^7*e^4*x^7 + 5*c^8*e^4 + 10*c^6*e^4 + 5*c^4*e^4 + 10*(14*c^2*d^6*e^4 + d^6*e^4)*x^6 + 20*(14*c^3*d^5*e^4 + 3*c*d^5*e^4)*x^5 + 5*(70*c^4*d^4*e^4 + 30*c^2*d^4*e^4 + d^4*e^4)*x^4 + 20*(14*c^5*d^3*e^4 + 10*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 10*(14*c^6*d^2*e^4 + 15*c^4*d^2*e^4 + 3*c^2*d^2*e^4)*x^2 + (5*d^6*e^4*x^6 + 30*c*d^5*e^4*x^5 + 5*c^6*e^4 + 3*c^4*e^4 + 3*(25*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(25*c^3*d^3*e^4 + 3*c*d^3*e^4)*x^3 + 3*(25*c^4*d^2*e^4 + 6*c^2*d^2*e^4)*x^2 + 6*(5*c^5*d*e^4 + 2*c^3*d*e^4)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 20*(2*c^7*d*e^4 + 3*c^5*d*e^4 + c^3*d*e^4)*x + (10*d^7*e^4*x^7 + 70*c*d^6*e^4*x^6 + 10*c^7*e^4 + 13*c^5*e^4 + 4*c^3*e^4 + (210*c^2*d^5*e^4 + 13*d^5*e^4)*x^5 + 5*(70*c^3*d^4*e^4 + 13*c*d^4*e^4)*x^4 + 2*(175*c^4*d^3*e^4 + 65*c^2*d^3*e^4 + 2*d^3*e^4)*x^3 + 2*(105*c^5*d^2*e^4 + 65*c^3*d^2*e^4 + 6*c*d^2*e^4)*x^2 + (70*c^6*d*e^4 + 65*c^4*d*e^4 + 12*c^2*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^4*x^4 + 4*a*b*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*a*b*x^2 + 4*(c^3*d + c*d)*a*b*x + (c^4 + 2*c^2 + 1)*a*b + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*b^2*x^2 + 4*(c^3*d + c*d)*b^2*x + (c^4 + 2*c^2 + 1)*b^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + (3*c^2*d + d)*b^2*x + (c^3 + c)*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 2*(a*b*d^3*x^3 + 3*a*b*c*d^2*x^2 + (3*c^2*d + d)*a*b*x + (c^3 + c)*a*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
163,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{6} e^{3} x^{6} + 6 \, c d^{5} e^{3} x^{5} + c^{6} e^{3} + c^{4} e^{3} + {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} x + {\left(d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + c^{5} e^{3} + c^{3} e^{3} + {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d + d\right)} a b + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + {\left(c^{2} d + d\right)} b^{2} + {\left(b^{2} d^{2} x + b^{2} c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(a b d^{2} x + a b c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} + \int \frac{4 \, d^{7} e^{3} x^{7} + 28 \, c d^{6} e^{3} x^{6} + 4 \, c^{7} e^{3} + 8 \, c^{5} e^{3} + 4 \, c^{3} e^{3} + 4 \, {\left(21 \, c^{2} d^{5} e^{3} + 2 \, d^{5} e^{3}\right)} x^{5} + 20 \, {\left(7 \, c^{3} d^{4} e^{3} + 2 \, c d^{4} e^{3}\right)} x^{4} + 4 \, {\left(35 \, c^{4} d^{3} e^{3} + 20 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + 4 \, {\left(21 \, c^{5} d^{2} e^{3} + 20 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + 2 \, {\left(2 \, d^{5} e^{3} x^{5} + 10 \, c d^{4} e^{3} x^{4} + 2 \, c^{5} e^{3} + c^{3} e^{3} + {\left(20 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + {\left(20 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(10 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(7 \, c^{6} d e^{3} + 10 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x + {\left(8 \, d^{6} e^{3} x^{6} + 48 \, c d^{5} e^{3} x^{5} + 8 \, c^{6} e^{3} + 10 \, c^{4} e^{3} + 3 \, c^{2} e^{3} + 10 \, {\left(12 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} x^{4} + 40 \, {\left(4 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} x^{3} + 3 \, {\left(40 \, c^{4} d^{2} e^{3} + 20 \, c^{2} d^{2} e^{3} + d^{2} e^{3}\right)} x^{2} + 2 \, {\left(24 \, c^{5} d e^{3} + 20 \, c^{3} d e^{3} + 3 \, c d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{4} x^{4} + 4 \, a b c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} a b x^{2} + 4 \, {\left(c^{3} d + c d\right)} a b x + {\left(c^{4} + 2 \, c^{2} + 1\right)} a b + {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} b^{2} x^{2} + 4 \, {\left(c^{3} d + c d\right)} b^{2} x + {\left(c^{4} + 2 \, c^{2} + 1\right)} b^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} b^{2} x + {\left(c^{3} + c\right)} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 2 \, {\left(a b d^{3} x^{3} + 3 \, a b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a b x + {\left(c^{3} + c\right)} a b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-(d^6*e^3*x^6 + 6*c*d^5*e^3*x^5 + c^6*e^3 + c^4*e^3 + (15*c^2*d^4*e^3 + d^4*e^3)*x^4 + 4*(5*c^3*d^3*e^3 + c*d^3*e^3)*x^3 + 3*(5*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*x^2 + 2*(3*c^5*d*e^3 + 2*c^3*d*e^3)*x + (d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + c^5*e^3 + c^3*e^3 + (10*c^2*d^3*e^3 + d^3*e^3)*x^3 + (10*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (5*c^4*d*e^3 + 3*c^2*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d + d)*a*b + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + (c^2*d + d)*b^2 + (b^2*d^2*x + b^2*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (a*b*d^2*x + a*b*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate((4*d^7*e^3*x^7 + 28*c*d^6*e^3*x^6 + 4*c^7*e^3 + 8*c^5*e^3 + 4*c^3*e^3 + 4*(21*c^2*d^5*e^3 + 2*d^5*e^3)*x^5 + 20*(7*c^3*d^4*e^3 + 2*c*d^4*e^3)*x^4 + 4*(35*c^4*d^3*e^3 + 20*c^2*d^3*e^3 + d^3*e^3)*x^3 + 4*(21*c^5*d^2*e^3 + 20*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + 2*(2*d^5*e^3*x^5 + 10*c*d^4*e^3*x^4 + 2*c^5*e^3 + c^3*e^3 + (20*c^2*d^3*e^3 + d^3*e^3)*x^3 + (20*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (10*c^4*d*e^3 + 3*c^2*d*e^3)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(7*c^6*d*e^3 + 10*c^4*d*e^3 + 3*c^2*d*e^3)*x + (8*d^6*e^3*x^6 + 48*c*d^5*e^3*x^5 + 8*c^6*e^3 + 10*c^4*e^3 + 3*c^2*e^3 + 10*(12*c^2*d^4*e^3 + d^4*e^3)*x^4 + 40*(4*c^3*d^3*e^3 + c*d^3*e^3)*x^3 + 3*(40*c^4*d^2*e^3 + 20*c^2*d^2*e^3 + d^2*e^3)*x^2 + 2*(24*c^5*d*e^3 + 20*c^3*d*e^3 + 3*c*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^4*x^4 + 4*a*b*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*a*b*x^2 + 4*(c^3*d + c*d)*a*b*x + (c^4 + 2*c^2 + 1)*a*b + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*b^2*x^2 + 4*(c^3*d + c*d)*b^2*x + (c^4 + 2*c^2 + 1)*b^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + (3*c^2*d + d)*b^2*x + (c^3 + c)*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 2*(a*b*d^3*x^3 + 3*a*b*c*d^2*x^2 + (3*c^2*d + d)*a*b*x + (c^3 + c)*a*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
164,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{5} e^{2} x^{5} + 5 \, c d^{4} e^{2} x^{4} + c^{5} e^{2} + c^{3} e^{2} + {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} x^{2} + {\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} x + {\left(d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + c^{4} e^{2} + c^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d + d\right)} a b + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + {\left(c^{2} d + d\right)} b^{2} + {\left(b^{2} d^{2} x + b^{2} c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(a b d^{2} x + a b c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} + \int \frac{3 \, d^{6} e^{2} x^{6} + 18 \, c d^{5} e^{2} x^{5} + 3 \, c^{6} e^{2} + 6 \, c^{4} e^{2} + 3 \, {\left(15 \, c^{2} d^{4} e^{2} + 2 \, d^{4} e^{2}\right)} x^{4} + 3 \, c^{2} e^{2} + 12 \, {\left(5 \, c^{3} d^{3} e^{2} + 2 \, c d^{3} e^{2}\right)} x^{3} + 3 \, {\left(15 \, c^{4} d^{2} e^{2} + 12 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + {\left(3 \, d^{4} e^{2} x^{4} + 12 \, c d^{3} e^{2} x^{3} + 3 \, c^{4} e^{2} + c^{2} e^{2} + {\left(18 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(6 \, c^{3} d e^{2} + c d e^{2}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 6 \, {\left(3 \, c^{5} d e^{2} + 4 \, c^{3} d e^{2} + c d e^{2}\right)} x + {\left(6 \, d^{5} e^{2} x^{5} + 30 \, c d^{4} e^{2} x^{4} + 6 \, c^{5} e^{2} + 7 \, c^{3} e^{2} + {\left(60 \, c^{2} d^{3} e^{2} + 7 \, d^{3} e^{2}\right)} x^{3} + 2 \, c e^{2} + 3 \, {\left(20 \, c^{3} d^{2} e^{2} + 7 \, c d^{2} e^{2}\right)} x^{2} + {\left(30 \, c^{4} d e^{2} + 21 \, c^{2} d e^{2} + 2 \, d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{4} x^{4} + 4 \, a b c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} a b x^{2} + 4 \, {\left(c^{3} d + c d\right)} a b x + {\left(c^{4} + 2 \, c^{2} + 1\right)} a b + {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} b^{2} x^{2} + 4 \, {\left(c^{3} d + c d\right)} b^{2} x + {\left(c^{4} + 2 \, c^{2} + 1\right)} b^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} b^{2} x + {\left(c^{3} + c\right)} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 2 \, {\left(a b d^{3} x^{3} + 3 \, a b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a b x + {\left(c^{3} + c\right)} a b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-(d^5*e^2*x^5 + 5*c*d^4*e^2*x^4 + c^5*e^2 + c^3*e^2 + (10*c^2*d^3*e^2 + d^3*e^2)*x^3 + (10*c^3*d^2*e^2 + 3*c*d^2*e^2)*x^2 + (5*c^4*d*e^2 + 3*c^2*d*e^2)*x + (d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + c^4*e^2 + c^2*e^2 + (6*c^2*d^2*e^2 + d^2*e^2)*x^2 + 2*(2*c^3*d*e^2 + c*d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d + d)*a*b + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + (c^2*d + d)*b^2 + (b^2*d^2*x + b^2*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (a*b*d^2*x + a*b*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate((3*d^6*e^2*x^6 + 18*c*d^5*e^2*x^5 + 3*c^6*e^2 + 6*c^4*e^2 + 3*(15*c^2*d^4*e^2 + 2*d^4*e^2)*x^4 + 3*c^2*e^2 + 12*(5*c^3*d^3*e^2 + 2*c*d^3*e^2)*x^3 + 3*(15*c^4*d^2*e^2 + 12*c^2*d^2*e^2 + d^2*e^2)*x^2 + (3*d^4*e^2*x^4 + 12*c*d^3*e^2*x^3 + 3*c^4*e^2 + c^2*e^2 + (18*c^2*d^2*e^2 + d^2*e^2)*x^2 + 2*(6*c^3*d*e^2 + c*d*e^2)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 6*(3*c^5*d*e^2 + 4*c^3*d*e^2 + c*d*e^2)*x + (6*d^5*e^2*x^5 + 30*c*d^4*e^2*x^4 + 6*c^5*e^2 + 7*c^3*e^2 + (60*c^2*d^3*e^2 + 7*d^3*e^2)*x^3 + 2*c*e^2 + 3*(20*c^3*d^2*e^2 + 7*c*d^2*e^2)*x^2 + (30*c^4*d*e^2 + 21*c^2*d*e^2 + 2*d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^4*x^4 + 4*a*b*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*a*b*x^2 + 4*(c^3*d + c*d)*a*b*x + (c^4 + 2*c^2 + 1)*a*b + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*b^2*x^2 + 4*(c^3*d + c*d)*b^2*x + (c^4 + 2*c^2 + 1)*b^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + (3*c^2*d + d)*b^2*x + (c^3 + c)*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 2*(a*b*d^3*x^3 + 3*a*b*c*d^2*x^2 + (3*c^2*d + d)*a*b*x + (c^3 + c)*a*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
165,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{4} e x^{4} + 4 \, c d^{3} e x^{3} + c^{4} e + c^{2} e + {\left(6 \, c^{2} d^{2} e + d^{2} e\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e + c d e\right)} x + {\left(d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + c^{3} e + c e + {\left(3 \, c^{2} d e + d e\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d + d\right)} a b + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + {\left(c^{2} d + d\right)} b^{2} + {\left(b^{2} d^{2} x + b^{2} c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(a b d^{2} x + a b c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} + \int \frac{2 \, d^{5} e x^{5} + 10 \, c d^{4} e x^{4} + 2 \, c^{5} e + 4 \, c^{3} e + 4 \, {\left(5 \, c^{2} d^{3} e + d^{3} e\right)} x^{3} + 4 \, {\left(5 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} x^{2} + 2 \, {\left(d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + 3 \, c^{2} d e x + c^{3} e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, c e + 2 \, {\left(5 \, c^{4} d e + 6 \, c^{2} d e + d e\right)} x + {\left(4 \, d^{4} e x^{4} + 16 \, c d^{3} e x^{3} + 4 \, c^{4} e + 4 \, c^{2} e + 4 \, {\left(6 \, c^{2} d^{2} e + d^{2} e\right)} x^{2} + 8 \, {\left(2 \, c^{3} d e + c d e\right)} x + e\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{4} x^{4} + 4 \, a b c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} a b x^{2} + 4 \, {\left(c^{3} d + c d\right)} a b x + {\left(c^{4} + 2 \, c^{2} + 1\right)} a b + {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} b^{2} x^{2} + 4 \, {\left(c^{3} d + c d\right)} b^{2} x + {\left(c^{4} + 2 \, c^{2} + 1\right)} b^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} b^{2} x + {\left(c^{3} + c\right)} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 2 \, {\left(a b d^{3} x^{3} + 3 \, a b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a b x + {\left(c^{3} + c\right)} a b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-(d^4*e*x^4 + 4*c*d^3*e*x^3 + c^4*e + c^2*e + (6*c^2*d^2*e + d^2*e)*x^2 + 2*(2*c^3*d*e + c*d*e)*x + (d^3*e*x^3 + 3*c*d^2*e*x^2 + c^3*e + c*e + (3*c^2*d*e + d*e)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d + d)*a*b + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + (c^2*d + d)*b^2 + (b^2*d^2*x + b^2*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (a*b*d^2*x + a*b*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate((2*d^5*e*x^5 + 10*c*d^4*e*x^4 + 2*c^5*e + 4*c^3*e + 4*(5*c^2*d^3*e + d^3*e)*x^3 + 4*(5*c^3*d^2*e + 3*c*d^2*e)*x^2 + 2*(d^3*e*x^3 + 3*c*d^2*e*x^2 + 3*c^2*d*e*x + c^3*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*c*e + 2*(5*c^4*d*e + 6*c^2*d*e + d*e)*x + (4*d^4*e*x^4 + 16*c*d^3*e*x^3 + 4*c^4*e + 4*c^2*e + 4*(6*c^2*d^2*e + d^2*e)*x^2 + 8*(2*c^3*d*e + c*d*e)*x + e)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^4*x^4 + 4*a*b*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*a*b*x^2 + 4*(c^3*d + c*d)*a*b*x + (c^4 + 2*c^2 + 1)*a*b + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*b^2*x^2 + 4*(c^3*d + c*d)*b^2*x + (c^4 + 2*c^2 + 1)*b^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + (3*c^2*d + d)*b^2*x + (c^3 + c)*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 2*(a*b*d^3*x^3 + 3*a*b*c*d^2*x^2 + (3*c^2*d + d)*a*b*x + (c^3 + c)*a*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
166,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d + d\right)} a b + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + {\left(c^{2} d + d\right)} b^{2} + {\left(b^{2} d^{2} x + b^{2} c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(a b d^{2} x + a b c d\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} + \int \frac{d^{4} x^{4} + 4 \, c d^{3} x^{3} + c^{4} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} x^{2} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} + 2 \, c^{2} + 4 \, {\left(c^{3} d + c d\right)} x + {\left(2 \, d^{3} x^{3} + 6 \, c d^{2} x^{2} + 2 \, c^{3} + {\left(6 \, c^{2} d + d\right)} x + c\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1}{a b d^{4} x^{4} + 4 \, a b c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} a b x^{2} + 4 \, {\left(c^{3} d + c d\right)} a b x + {\left(c^{4} + 2 \, c^{2} + 1\right)} a b + {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} b^{2} x^{2} + 4 \, {\left(c^{3} d + c d\right)} b^{2} x + {\left(c^{4} + 2 \, c^{2} + 1\right)} b^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} b^{2} x + {\left(c^{3} + c\right)} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 2 \, {\left(a b d^{3} x^{3} + 3 \, a b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a b x + {\left(c^{3} + c\right)} a b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c)/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d + d)*a*b + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + (c^2*d + d)*b^2 + (b^2*d^2*x + b^2*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (a*b*d^2*x + a*b*c*d)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate((d^4*x^4 + 4*c*d^3*x^3 + c^4 + 2*(3*c^2*d^2 + d^2)*x^2 + (d^2*x^2 + 2*c*d*x + c^2 + 1)*(d^2*x^2 + 2*c*d*x + c^2 - 1) + 2*c^2 + 4*(c^3*d + c*d)*x + (2*d^3*x^3 + 6*c*d^2*x^2 + 2*c^3 + (6*c^2*d + d)*x + c)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)/(a*b*d^4*x^4 + 4*a*b*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*a*b*x^2 + 4*(c^3*d + c*d)*a*b*x + (c^4 + 2*c^2 + 1)*a*b + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 2*(3*c^2*d^2 + d^2)*b^2*x^2 + 4*(c^3*d + c*d)*b^2*x + (c^4 + 2*c^2 + 1)*b^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + (3*c^2*d + d)*b^2*x + (c^3 + c)*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 2*(a*b*d^3*x^3 + 3*a*b*c*d^2*x^2 + (3*c^2*d + d)*a*b*x + (c^3 + c)*a*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
167,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}{a b d^{4} e x^{3} + 3 \, a b c d^{3} e x^{2} + {\left(3 \, c^{2} d^{2} e + d^{2} e\right)} a b x + {\left(c^{3} d e + c d e\right)} a b + {\left(b^{2} d^{4} e x^{3} + 3 \, b^{2} c d^{3} e x^{2} + {\left(3 \, c^{2} d^{2} e + d^{2} e\right)} b^{2} x + {\left(c^{3} d e + c d e\right)} b^{2} + {\left(b^{2} d^{3} e x^{2} + 2 \, b^{2} c d^{2} e x + b^{2} c^{2} d e\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(a b d^{3} e x^{2} + 2 \, a b c d^{2} e x + a b c^{2} d e\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}} - \int \frac{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} {\left(d x + c\right)} + {\left(2 \, d^{2} x^{2} + 4 \, c d x + 2 \, c^{2} + 1\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{a b d^{6} e x^{6} + 6 \, a b c d^{5} e x^{5} + {\left(15 \, c^{2} d^{4} e + 2 \, d^{4} e\right)} a b x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e + 2 \, c d^{3} e\right)} a b x^{3} + {\left(15 \, c^{4} d^{2} e + 12 \, c^{2} d^{2} e + d^{2} e\right)} a b x^{2} + 2 \, {\left(3 \, c^{5} d e + 4 \, c^{3} d e + c d e\right)} a b x + {\left(c^{6} e + 2 \, c^{4} e + c^{2} e\right)} a b + {\left(a b d^{4} e x^{4} + 4 \, a b c d^{3} e x^{3} + 6 \, a b c^{2} d^{2} e x^{2} + 4 \, a b c^{3} d e x + a b c^{4} e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{2} d^{6} e x^{6} + 6 \, b^{2} c d^{5} e x^{5} + {\left(15 \, c^{2} d^{4} e + 2 \, d^{4} e\right)} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e + 2 \, c d^{3} e\right)} b^{2} x^{3} + {\left(15 \, c^{4} d^{2} e + 12 \, c^{2} d^{2} e + d^{2} e\right)} b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d e + 4 \, c^{3} d e + c d e\right)} b^{2} x + {\left(c^{6} e + 2 \, c^{4} e + c^{2} e\right)} b^{2} + {\left(b^{2} d^{4} e x^{4} + 4 \, b^{2} c d^{3} e x^{3} + 6 \, b^{2} c^{2} d^{2} e x^{2} + 4 \, b^{2} c^{3} d e x + b^{2} c^{4} e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(b^{2} d^{5} e x^{5} + 5 \, b^{2} c d^{4} e x^{4} + {\left(10 \, c^{2} d^{3} e + d^{3} e\right)} b^{2} x^{3} + {\left(10 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} b^{2} x^{2} + {\left(5 \, c^{4} d e + 3 \, c^{2} d e\right)} b^{2} x + {\left(c^{5} e + c^{3} e\right)} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 2 \, {\left(a b d^{5} e x^{5} + 5 \, a b c d^{4} e x^{4} + {\left(10 \, c^{2} d^{3} e + d^{3} e\right)} a b x^{3} + {\left(10 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} a b x^{2} + {\left(5 \, c^{4} d e + 3 \, c^{2} d e\right)} a b x + {\left(c^{5} e + c^{3} e\right)} a b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c)/(a*b*d^4*e*x^3 + 3*a*b*c*d^3*e*x^2 + (3*c^2*d^2*e + d^2*e)*a*b*x + (c^3*d*e + c*d*e)*a*b + (b^2*d^4*e*x^3 + 3*b^2*c*d^3*e*x^2 + (3*c^2*d^2*e + d^2*e)*b^2*x + (c^3*d*e + c*d*e)*b^2 + (b^2*d^3*e*x^2 + 2*b^2*c*d^2*e*x + b^2*c^2*d*e)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (a*b*d^3*e*x^2 + 2*a*b*c*d^2*e*x + a*b*c^2*d*e)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) - integrate((2*(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c) + (2*d^2*x^2 + 4*c*d*x + 2*c^2 + 1)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b*d^6*e*x^6 + 6*a*b*c*d^5*e*x^5 + (15*c^2*d^4*e + 2*d^4*e)*a*b*x^4 + 4*(5*c^3*d^3*e + 2*c*d^3*e)*a*b*x^3 + (15*c^4*d^2*e + 12*c^2*d^2*e + d^2*e)*a*b*x^2 + 2*(3*c^5*d*e + 4*c^3*d*e + c*d*e)*a*b*x + (c^6*e + 2*c^4*e + c^2*e)*a*b + (a*b*d^4*e*x^4 + 4*a*b*c*d^3*e*x^3 + 6*a*b*c^2*d^2*e*x^2 + 4*a*b*c^3*d*e*x + a*b*c^4*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^6*e*x^6 + 6*b^2*c*d^5*e*x^5 + (15*c^2*d^4*e + 2*d^4*e)*b^2*x^4 + 4*(5*c^3*d^3*e + 2*c*d^3*e)*b^2*x^3 + (15*c^4*d^2*e + 12*c^2*d^2*e + d^2*e)*b^2*x^2 + 2*(3*c^5*d*e + 4*c^3*d*e + c*d*e)*b^2*x + (c^6*e + 2*c^4*e + c^2*e)*b^2 + (b^2*d^4*e*x^4 + 4*b^2*c*d^3*e*x^3 + 6*b^2*c^2*d^2*e*x^2 + 4*b^2*c^3*d*e*x + b^2*c^4*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b^2*d^5*e*x^5 + 5*b^2*c*d^4*e*x^4 + (10*c^2*d^3*e + d^3*e)*b^2*x^3 + (10*c^3*d^2*e + 3*c*d^2*e)*b^2*x^2 + (5*c^4*d*e + 3*c^2*d*e)*b^2*x + (c^5*e + c^3*e)*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 2*(a*b*d^5*e*x^5 + 5*a*b*c*d^4*e*x^4 + (10*c^2*d^3*e + d^3*e)*a*b*x^3 + (10*c^3*d^2*e + 3*c*d^2*e)*a*b*x^2 + (5*c^4*d*e + 3*c^2*d*e)*a*b*x + (c^5*e + c^3*e)*a*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
168,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, a d^{11} e^{4} + b d^{11} e^{4}\right)} x^{11} + 11 \, {\left(5 \, a c d^{10} e^{4} + b c d^{10} e^{4}\right)} x^{10} + {\left(5 \, {\left(55 \, c^{2} d^{9} e^{4} + 3 \, d^{9} e^{4}\right)} a + {\left(55 \, c^{2} d^{9} e^{4} + 3 \, d^{9} e^{4}\right)} b\right)} x^{9} + 3 \, {\left(5 \, {\left(55 \, c^{3} d^{8} e^{4} + 9 \, c d^{8} e^{4}\right)} a + {\left(55 \, c^{3} d^{8} e^{4} + 9 \, c d^{8} e^{4}\right)} b\right)} x^{8} + 3 \, {\left(5 \, {\left(110 \, c^{4} d^{7} e^{4} + 36 \, c^{2} d^{7} e^{4} + d^{7} e^{4}\right)} a + {\left(110 \, c^{4} d^{7} e^{4} + 36 \, c^{2} d^{7} e^{4} + d^{7} e^{4}\right)} b\right)} x^{7} + 21 \, {\left(5 \, {\left(22 \, c^{5} d^{6} e^{4} + 12 \, c^{3} d^{6} e^{4} + c d^{6} e^{4}\right)} a + {\left(22 \, c^{5} d^{6} e^{4} + 12 \, c^{3} d^{6} e^{4} + c d^{6} e^{4}\right)} b\right)} x^{6} + {\left(5 \, {\left(462 \, c^{6} d^{5} e^{4} + 378 \, c^{4} d^{5} e^{4} + 63 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} a + {\left(462 \, c^{6} d^{5} e^{4} + 378 \, c^{4} d^{5} e^{4} + 63 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} b\right)} x^{5} + {\left(5 \, {\left(330 \, c^{7} d^{4} e^{4} + 378 \, c^{5} d^{4} e^{4} + 105 \, c^{3} d^{4} e^{4} + 5 \, c d^{4} e^{4}\right)} a + {\left(330 \, c^{7} d^{4} e^{4} + 378 \, c^{5} d^{4} e^{4} + 105 \, c^{3} d^{4} e^{4} + 5 \, c d^{4} e^{4}\right)} b\right)} x^{4} + {\left(5 \, {\left(165 \, c^{8} d^{3} e^{4} + 252 \, c^{6} d^{3} e^{4} + 105 \, c^{4} d^{3} e^{4} + 10 \, c^{2} d^{3} e^{4}\right)} a + {\left(165 \, c^{8} d^{3} e^{4} + 252 \, c^{6} d^{3} e^{4} + 105 \, c^{4} d^{3} e^{4} + 10 \, c^{2} d^{3} e^{4}\right)} b\right)} x^{3} + {\left(5 \, {\left(55 \, c^{9} d^{2} e^{4} + 108 \, c^{7} d^{2} e^{4} + 63 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} a + {\left(55 \, c^{9} d^{2} e^{4} + 108 \, c^{7} d^{2} e^{4} + 63 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} b\right)} x^{2} + {\left({\left(5 \, a d^{8} e^{4} + b d^{8} e^{4}\right)} x^{8} + 8 \, {\left(5 \, a c d^{7} e^{4} + b c d^{7} e^{4}\right)} x^{7} + {\left(4 \, {\left(35 \, c^{2} d^{6} e^{4} + 2 \, d^{6} e^{4}\right)} a + {\left(28 \, c^{2} d^{6} e^{4} + d^{6} e^{4}\right)} b\right)} x^{6} + 2 \, {\left(4 \, {\left(35 \, c^{3} d^{5} e^{4} + 6 \, c d^{5} e^{4}\right)} a + {\left(28 \, c^{3} d^{5} e^{4} + 3 \, c d^{5} e^{4}\right)} b\right)} x^{5} + {\left({\left(350 \, c^{4} d^{4} e^{4} + 120 \, c^{2} d^{4} e^{4} + 3 \, d^{4} e^{4}\right)} a + 5 \, {\left(14 \, c^{4} d^{4} e^{4} + 3 \, c^{2} d^{4} e^{4}\right)} b\right)} x^{4} + 4 \, {\left({\left(70 \, c^{5} d^{3} e^{4} + 40 \, c^{3} d^{3} e^{4} + 3 \, c d^{3} e^{4}\right)} a + {\left(14 \, c^{5} d^{3} e^{4} + 5 \, c^{3} d^{3} e^{4}\right)} b\right)} x^{3} + {\left(2 \, {\left(70 \, c^{6} d^{2} e^{4} + 60 \, c^{4} d^{2} e^{4} + 9 \, c^{2} d^{2} e^{4}\right)} a + {\left(28 \, c^{6} d^{2} e^{4} + 15 \, c^{4} d^{2} e^{4}\right)} b\right)} x^{2} + {\left(5 \, c^{8} e^{4} + 8 \, c^{6} e^{4} + 3 \, c^{4} e^{4}\right)} a + {\left(c^{8} e^{4} + c^{6} e^{4}\right)} b + 2 \, {\left(2 \, {\left(10 \, c^{7} d e^{4} + 12 \, c^{5} d e^{4} + 3 \, c^{3} d e^{4}\right)} a + {\left(4 \, c^{7} d e^{4} + 3 \, c^{5} d e^{4}\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, {\left(5 \, a d^{9} e^{4} + b d^{9} e^{4}\right)} x^{9} + 27 \, {\left(5 \, a c d^{8} e^{4} + b c d^{8} e^{4}\right)} x^{8} + {\left({\left(540 \, c^{2} d^{7} e^{4} + 31 \, d^{7} e^{4}\right)} a + {\left(108 \, c^{2} d^{7} e^{4} + 5 \, d^{7} e^{4}\right)} b\right)} x^{7} + 7 \, {\left({\left(180 \, c^{3} d^{6} e^{4} + 31 \, c d^{6} e^{4}\right)} a + {\left(36 \, c^{3} d^{6} e^{4} + 5 \, c d^{6} e^{4}\right)} b\right)} x^{6} + {\left({\left(1890 \, c^{4} d^{5} e^{4} + 651 \, c^{2} d^{5} e^{4} + 20 \, d^{5} e^{4}\right)} a + {\left(378 \, c^{4} d^{5} e^{4} + 105 \, c^{2} d^{5} e^{4} + 2 \, d^{5} e^{4}\right)} b\right)} x^{5} + {\left(5 \, {\left(378 \, c^{5} d^{4} e^{4} + 217 \, c^{3} d^{4} e^{4} + 20 \, c d^{4} e^{4}\right)} a + {\left(378 \, c^{5} d^{4} e^{4} + 175 \, c^{3} d^{4} e^{4} + 10 \, c d^{4} e^{4}\right)} b\right)} x^{4} + {\left({\left(1260 \, c^{6} d^{3} e^{4} + 1085 \, c^{4} d^{3} e^{4} + 200 \, c^{2} d^{3} e^{4} + 4 \, d^{3} e^{4}\right)} a + {\left(252 \, c^{6} d^{3} e^{4} + 175 \, c^{4} d^{3} e^{4} + 20 \, c^{2} d^{3} e^{4}\right)} b\right)} x^{3} + {\left({\left(540 \, c^{7} d^{2} e^{4} + 651 \, c^{5} d^{2} e^{4} + 200 \, c^{3} d^{2} e^{4} + 12 \, c d^{2} e^{4}\right)} a + {\left(108 \, c^{7} d^{2} e^{4} + 105 \, c^{5} d^{2} e^{4} + 20 \, c^{3} d^{2} e^{4}\right)} b\right)} x^{2} + {\left(15 \, c^{9} e^{4} + 31 \, c^{7} e^{4} + 20 \, c^{5} e^{4} + 4 \, c^{3} e^{4}\right)} a + {\left(3 \, c^{9} e^{4} + 5 \, c^{7} e^{4} + 2 \, c^{5} e^{4}\right)} b + {\left({\left(135 \, c^{8} d e^{4} + 217 \, c^{6} d e^{4} + 100 \, c^{4} d e^{4} + 12 \, c^{2} d e^{4}\right)} a + {\left(27 \, c^{8} d e^{4} + 35 \, c^{6} d e^{4} + 10 \, c^{4} d e^{4}\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 5 \, {\left(c^{11} e^{4} + 3 \, c^{9} e^{4} + 3 \, c^{7} e^{4} + c^{5} e^{4}\right)} a + {\left(c^{11} e^{4} + 3 \, c^{9} e^{4} + 3 \, c^{7} e^{4} + c^{5} e^{4}\right)} b + {\left(5 \, {\left(11 \, c^{10} d e^{4} + 27 \, c^{8} d e^{4} + 21 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} a + {\left(11 \, c^{10} d e^{4} + 27 \, c^{8} d e^{4} + 21 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} b\right)} x + {\left(5 \, b d^{11} e^{4} x^{11} + 55 \, b c d^{10} e^{4} x^{10} + 5 \, {\left(55 \, c^{2} d^{9} e^{4} + 3 \, d^{9} e^{4}\right)} b x^{9} + 15 \, {\left(55 \, c^{3} d^{8} e^{4} + 9 \, c d^{8} e^{4}\right)} b x^{8} + 15 \, {\left(110 \, c^{4} d^{7} e^{4} + 36 \, c^{2} d^{7} e^{4} + d^{7} e^{4}\right)} b x^{7} + 105 \, {\left(22 \, c^{5} d^{6} e^{4} + 12 \, c^{3} d^{6} e^{4} + c d^{6} e^{4}\right)} b x^{6} + 5 \, {\left(462 \, c^{6} d^{5} e^{4} + 378 \, c^{4} d^{5} e^{4} + 63 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} b x^{5} + 5 \, {\left(330 \, c^{7} d^{4} e^{4} + 378 \, c^{5} d^{4} e^{4} + 105 \, c^{3} d^{4} e^{4} + 5 \, c d^{4} e^{4}\right)} b x^{4} + 5 \, {\left(165 \, c^{8} d^{3} e^{4} + 252 \, c^{6} d^{3} e^{4} + 105 \, c^{4} d^{3} e^{4} + 10 \, c^{2} d^{3} e^{4}\right)} b x^{3} + 5 \, {\left(55 \, c^{9} d^{2} e^{4} + 108 \, c^{7} d^{2} e^{4} + 63 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} b x^{2} + 5 \, {\left(11 \, c^{10} d e^{4} + 27 \, c^{8} d e^{4} + 21 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} b x + {\left(5 \, b d^{8} e^{4} x^{8} + 40 \, b c d^{7} e^{4} x^{7} + 4 \, {\left(35 \, c^{2} d^{6} e^{4} + 2 \, d^{6} e^{4}\right)} b x^{6} + 8 \, {\left(35 \, c^{3} d^{5} e^{4} + 6 \, c d^{5} e^{4}\right)} b x^{5} + {\left(350 \, c^{4} d^{4} e^{4} + 120 \, c^{2} d^{4} e^{4} + 3 \, d^{4} e^{4}\right)} b x^{4} + 4 \, {\left(70 \, c^{5} d^{3} e^{4} + 40 \, c^{3} d^{3} e^{4} + 3 \, c d^{3} e^{4}\right)} b x^{3} + 2 \, {\left(70 \, c^{6} d^{2} e^{4} + 60 \, c^{4} d^{2} e^{4} + 9 \, c^{2} d^{2} e^{4}\right)} b x^{2} + 4 \, {\left(10 \, c^{7} d e^{4} + 12 \, c^{5} d e^{4} + 3 \, c^{3} d e^{4}\right)} b x + {\left(5 \, c^{8} e^{4} + 8 \, c^{6} e^{4} + 3 \, c^{4} e^{4}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(15 \, b d^{9} e^{4} x^{9} + 135 \, b c d^{8} e^{4} x^{8} + {\left(540 \, c^{2} d^{7} e^{4} + 31 \, d^{7} e^{4}\right)} b x^{7} + 7 \, {\left(180 \, c^{3} d^{6} e^{4} + 31 \, c d^{6} e^{4}\right)} b x^{6} + {\left(1890 \, c^{4} d^{5} e^{4} + 651 \, c^{2} d^{5} e^{4} + 20 \, d^{5} e^{4}\right)} b x^{5} + 5 \, {\left(378 \, c^{5} d^{4} e^{4} + 217 \, c^{3} d^{4} e^{4} + 20 \, c d^{4} e^{4}\right)} b x^{4} + {\left(1260 \, c^{6} d^{3} e^{4} + 1085 \, c^{4} d^{3} e^{4} + 200 \, c^{2} d^{3} e^{4} + 4 \, d^{3} e^{4}\right)} b x^{3} + {\left(540 \, c^{7} d^{2} e^{4} + 651 \, c^{5} d^{2} e^{4} + 200 \, c^{3} d^{2} e^{4} + 12 \, c d^{2} e^{4}\right)} b x^{2} + {\left(135 \, c^{8} d e^{4} + 217 \, c^{6} d e^{4} + 100 \, c^{4} d e^{4} + 12 \, c^{2} d e^{4}\right)} b x + {\left(15 \, c^{9} e^{4} + 31 \, c^{7} e^{4} + 20 \, c^{5} e^{4} + 4 \, c^{3} e^{4}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 5 \, {\left(c^{11} e^{4} + 3 \, c^{9} e^{4} + 3 \, c^{7} e^{4} + c^{5} e^{4}\right)} b + {\left(15 \, b d^{10} e^{4} x^{10} + 150 \, b c d^{9} e^{4} x^{9} + {\left(675 \, c^{2} d^{8} e^{4} + 38 \, d^{8} e^{4}\right)} b x^{8} + 8 \, {\left(225 \, c^{3} d^{7} e^{4} + 38 \, c d^{7} e^{4}\right)} b x^{7} + 2 \, {\left(1575 \, c^{4} d^{6} e^{4} + 532 \, c^{2} d^{6} e^{4} + 16 \, d^{6} e^{4}\right)} b x^{6} + 4 \, {\left(945 \, c^{5} d^{5} e^{4} + 532 \, c^{3} d^{5} e^{4} + 48 \, c d^{5} e^{4}\right)} b x^{5} + {\left(3150 \, c^{6} d^{4} e^{4} + 2660 \, c^{4} d^{4} e^{4} + 480 \, c^{2} d^{4} e^{4} + 9 \, d^{4} e^{4}\right)} b x^{4} + 4 \, {\left(450 \, c^{7} d^{3} e^{4} + 532 \, c^{5} d^{3} e^{4} + 160 \, c^{3} d^{3} e^{4} + 9 \, c d^{3} e^{4}\right)} b x^{3} + {\left(675 \, c^{8} d^{2} e^{4} + 1064 \, c^{6} d^{2} e^{4} + 480 \, c^{4} d^{2} e^{4} + 54 \, c^{2} d^{2} e^{4}\right)} b x^{2} + 2 \, {\left(75 \, c^{9} d e^{4} + 152 \, c^{7} d e^{4} + 96 \, c^{5} d e^{4} + 18 \, c^{3} d e^{4}\right)} b x + {\left(15 \, c^{10} e^{4} + 38 \, c^{8} e^{4} + 32 \, c^{6} e^{4} + 9 \, c^{4} e^{4}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(3 \, {\left(5 \, a d^{10} e^{4} + b d^{10} e^{4}\right)} x^{10} + 30 \, {\left(5 \, a c d^{9} e^{4} + b c d^{9} e^{4}\right)} x^{9} + {\left({\left(675 \, c^{2} d^{8} e^{4} + 38 \, d^{8} e^{4}\right)} a + {\left(135 \, c^{2} d^{8} e^{4} + 7 \, d^{8} e^{4}\right)} b\right)} x^{8} + 8 \, {\left({\left(225 \, c^{3} d^{7} e^{4} + 38 \, c d^{7} e^{4}\right)} a + {\left(45 \, c^{3} d^{7} e^{4} + 7 \, c d^{7} e^{4}\right)} b\right)} x^{7} + {\left(2 \, {\left(1575 \, c^{4} d^{6} e^{4} + 532 \, c^{2} d^{6} e^{4} + 16 \, d^{6} e^{4}\right)} a + {\left(630 \, c^{4} d^{6} e^{4} + 196 \, c^{2} d^{6} e^{4} + 5 \, d^{6} e^{4}\right)} b\right)} x^{6} + 2 \, {\left(2 \, {\left(945 \, c^{5} d^{5} e^{4} + 532 \, c^{3} d^{5} e^{4} + 48 \, c d^{5} e^{4}\right)} a + {\left(378 \, c^{5} d^{5} e^{4} + 196 \, c^{3} d^{5} e^{4} + 15 \, c d^{5} e^{4}\right)} b\right)} x^{5} + {\left({\left(3150 \, c^{6} d^{4} e^{4} + 2660 \, c^{4} d^{4} e^{4} + 480 \, c^{2} d^{4} e^{4} + 9 \, d^{4} e^{4}\right)} a + {\left(630 \, c^{6} d^{4} e^{4} + 490 \, c^{4} d^{4} e^{4} + 75 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} b\right)} x^{4} + 4 \, {\left({\left(450 \, c^{7} d^{3} e^{4} + 532 \, c^{5} d^{3} e^{4} + 160 \, c^{3} d^{3} e^{4} + 9 \, c d^{3} e^{4}\right)} a + {\left(90 \, c^{7} d^{3} e^{4} + 98 \, c^{5} d^{3} e^{4} + 25 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} b\right)} x^{3} + {\left({\left(675 \, c^{8} d^{2} e^{4} + 1064 \, c^{6} d^{2} e^{4} + 480 \, c^{4} d^{2} e^{4} + 54 \, c^{2} d^{2} e^{4}\right)} a + {\left(135 \, c^{8} d^{2} e^{4} + 196 \, c^{6} d^{2} e^{4} + 75 \, c^{4} d^{2} e^{4} + 6 \, c^{2} d^{2} e^{4}\right)} b\right)} x^{2} + {\left(15 \, c^{10} e^{4} + 38 \, c^{8} e^{4} + 32 \, c^{6} e^{4} + 9 \, c^{4} e^{4}\right)} a + {\left(3 \, c^{10} e^{4} + 7 \, c^{8} e^{4} + 5 \, c^{6} e^{4} + c^{4} e^{4}\right)} b + 2 \, {\left({\left(75 \, c^{9} d e^{4} + 152 \, c^{7} d e^{4} + 96 \, c^{5} d e^{4} + 18 \, c^{3} d e^{4}\right)} a + {\left(15 \, c^{9} d e^{4} + 28 \, c^{7} d e^{4} + 15 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a^{2} b^{2} d^{7} x^{6} + 6 \, a^{2} b^{2} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a^{2} b^{2} + {\left(b^{4} d^{7} x^{6} + 6 \, b^{4} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} b^{4} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{4} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} b^{4} + {\left(b^{4} d^{4} x^{3} + 3 \, b^{4} c d^{3} x^{2} + 3 \, b^{4} c^{2} d^{2} x + b^{4} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{5} x^{4} + 4 \, b^{4} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{4} d + c^{2} d\right)} b^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(b^{4} d^{6} x^{5} + 5 \, b^{4} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} b^{4} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{4} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} b^{4} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} b^{4}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{3} + 3 \, a^{2} b^{2} c d^{3} x^{2} + 3 \, a^{2} b^{2} c^{2} d^{2} x + a^{2} b^{2} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{5} x^{4} + 4 \, a^{2} b^{2} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{4} d + c^{2} d\right)} a^{2} b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(a b^{3} d^{7} x^{6} + 6 \, a b^{3} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{3} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a b^{3} + {\left(a b^{3} d^{4} x^{3} + 3 \, a b^{3} c d^{3} x^{2} + 3 \, a b^{3} c^{2} d^{2} x + a b^{3} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{5} x^{4} + 4 \, a b^{3} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{4} d + c^{2} d\right)} a b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(a b^{3} d^{6} x^{5} + 5 \, a b^{3} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a b^{3} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{3} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a b^{3} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 3 \, {\left(a^{2} b^{2} d^{6} x^{5} + 5 \, a^{2} b^{2} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a^{2} b^{2} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a^{2} b^{2} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}} + \int \frac{25 \, d^{12} e^{4} x^{12} + 300 \, c d^{11} e^{4} x^{11} + 25 \, c^{12} e^{4} + 100 \, c^{10} e^{4} + 150 \, c^{8} e^{4} + 50 \, {\left(33 \, c^{2} d^{10} e^{4} + 2 \, d^{10} e^{4}\right)} x^{10} + 100 \, c^{6} e^{4} + 500 \, {\left(11 \, c^{3} d^{9} e^{4} + 2 \, c d^{9} e^{4}\right)} x^{9} + 75 \, {\left(165 \, c^{4} d^{8} e^{4} + 60 \, c^{2} d^{8} e^{4} + 2 \, d^{8} e^{4}\right)} x^{8} + 25 \, c^{4} e^{4} + 600 \, {\left(33 \, c^{5} d^{7} e^{4} + 20 \, c^{3} d^{7} e^{4} + 2 \, c d^{7} e^{4}\right)} x^{7} + 100 \, {\left(231 \, c^{6} d^{6} e^{4} + 210 \, c^{4} d^{6} e^{4} + 42 \, c^{2} d^{6} e^{4} + d^{6} e^{4}\right)} x^{6} + 600 \, {\left(33 \, c^{7} d^{5} e^{4} + 42 \, c^{5} d^{5} e^{4} + 14 \, c^{3} d^{5} e^{4} + c d^{5} e^{4}\right)} x^{5} + 25 \, {\left(495 \, c^{8} d^{4} e^{4} + 840 \, c^{6} d^{4} e^{4} + 420 \, c^{4} d^{4} e^{4} + 60 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 100 \, {\left(55 \, c^{9} d^{3} e^{4} + 120 \, c^{7} d^{3} e^{4} + 84 \, c^{5} d^{3} e^{4} + 20 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + {\left(25 \, d^{8} e^{4} x^{8} + 200 \, c d^{7} e^{4} x^{7} + 25 \, c^{8} e^{4} + 24 \, c^{6} e^{4} + 3 \, c^{4} e^{4} + 4 \, {\left(175 \, c^{2} d^{6} e^{4} + 6 \, d^{6} e^{4}\right)} x^{6} + 8 \, {\left(175 \, c^{3} d^{5} e^{4} + 18 \, c d^{5} e^{4}\right)} x^{5} + {\left(1750 \, c^{4} d^{4} e^{4} + 360 \, c^{2} d^{4} e^{4} + 3 \, d^{4} e^{4}\right)} x^{4} + 4 \, {\left(350 \, c^{5} d^{3} e^{4} + 120 \, c^{3} d^{3} e^{4} + 3 \, c d^{3} e^{4}\right)} x^{3} + 2 \, {\left(350 \, c^{6} d^{2} e^{4} + 180 \, c^{4} d^{2} e^{4} + 9 \, c^{2} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(50 \, c^{7} d e^{4} + 36 \, c^{5} d e^{4} + 3 \, c^{3} d e^{4}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 150 \, {\left(11 \, c^{10} d^{2} e^{4} + 30 \, c^{8} d^{2} e^{4} + 28 \, c^{6} d^{2} e^{4} + 10 \, c^{4} d^{2} e^{4} + c^{2} d^{2} e^{4}\right)} x^{2} + {\left(100 \, d^{9} e^{4} x^{9} + 900 \, c d^{8} e^{4} x^{8} + 100 \, c^{9} e^{4} + 172 \, c^{7} e^{4} + 87 \, c^{5} e^{4} + 4 \, {\left(900 \, c^{2} d^{7} e^{4} + 43 \, d^{7} e^{4}\right)} x^{7} + 12 \, c^{3} e^{4} + 28 \, {\left(300 \, c^{3} d^{6} e^{4} + 43 \, c d^{6} e^{4}\right)} x^{6} + 3 \, {\left(4200 \, c^{4} d^{5} e^{4} + 1204 \, c^{2} d^{5} e^{4} + 29 \, d^{5} e^{4}\right)} x^{5} + 5 \, {\left(2520 \, c^{5} d^{4} e^{4} + 1204 \, c^{3} d^{4} e^{4} + 87 \, c d^{4} e^{4}\right)} x^{4} + 2 \, {\left(4200 \, c^{6} d^{3} e^{4} + 3010 \, c^{4} d^{3} e^{4} + 435 \, c^{2} d^{3} e^{4} + 6 \, d^{3} e^{4}\right)} x^{3} + 6 \, {\left(600 \, c^{7} d^{2} e^{4} + 602 \, c^{5} d^{2} e^{4} + 145 \, c^{3} d^{2} e^{4} + 6 \, c d^{2} e^{4}\right)} x^{2} + {\left(900 \, c^{8} d e^{4} + 1204 \, c^{6} d e^{4} + 435 \, c^{4} d e^{4} + 36 \, c^{2} d e^{4}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(50 \, d^{10} e^{4} x^{10} + 500 \, c d^{9} e^{4} x^{9} + 50 \, c^{10} e^{4} + 124 \, c^{8} e^{4} + 105 \, c^{6} e^{4} + 2 \, {\left(1125 \, c^{2} d^{8} e^{4} + 62 \, d^{8} e^{4}\right)} x^{8} + 35 \, c^{4} e^{4} + 16 \, {\left(375 \, c^{3} d^{7} e^{4} + 62 \, c d^{7} e^{4}\right)} x^{7} + 7 \, {\left(1500 \, c^{4} d^{6} e^{4} + 496 \, c^{2} d^{6} e^{4} + 15 \, d^{6} e^{4}\right)} x^{6} + 4 \, c^{2} e^{4} + 14 \, {\left(900 \, c^{5} d^{5} e^{4} + 496 \, c^{3} d^{5} e^{4} + 45 \, c d^{5} e^{4}\right)} x^{5} + 35 \, {\left(300 \, c^{6} d^{4} e^{4} + 248 \, c^{4} d^{4} e^{4} + 45 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(1500 \, c^{7} d^{3} e^{4} + 1736 \, c^{5} d^{3} e^{4} + 525 \, c^{3} d^{3} e^{4} + 35 \, c d^{3} e^{4}\right)} x^{3} + {\left(2250 \, c^{8} d^{2} e^{4} + 3472 \, c^{6} d^{2} e^{4} + 1575 \, c^{4} d^{2} e^{4} + 210 \, c^{2} d^{2} e^{4} + 4 \, d^{2} e^{4}\right)} x^{2} + 2 \, {\left(250 \, c^{9} d e^{4} + 496 \, c^{7} d e^{4} + 315 \, c^{5} d e^{4} + 70 \, c^{3} d e^{4} + 4 \, c d e^{4}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 100 \, {\left(3 \, c^{11} d e^{4} + 10 \, c^{9} d e^{4} + 12 \, c^{7} d e^{4} + 6 \, c^{5} d e^{4} + c^{3} d e^{4}\right)} x + {\left(100 \, d^{11} e^{4} x^{11} + 1100 \, c d^{10} e^{4} x^{10} + 100 \, c^{11} e^{4} + 324 \, c^{9} e^{4} + 381 \, c^{7} e^{4} + 4 \, {\left(1375 \, c^{2} d^{9} e^{4} + 81 \, d^{9} e^{4}\right)} x^{9} + 193 \, c^{5} e^{4} + 12 \, {\left(1375 \, c^{3} d^{8} e^{4} + 243 \, c d^{8} e^{4}\right)} x^{8} + 3 \, {\left(11000 \, c^{4} d^{7} e^{4} + 3888 \, c^{2} d^{7} e^{4} + 127 \, d^{7} e^{4}\right)} x^{7} + 36 \, c^{3} e^{4} + 21 \, {\left(2200 \, c^{5} d^{6} e^{4} + 1296 \, c^{3} d^{6} e^{4} + 127 \, c d^{6} e^{4}\right)} x^{6} + {\left(46200 \, c^{6} d^{5} e^{4} + 40824 \, c^{4} d^{5} e^{4} + 8001 \, c^{2} d^{5} e^{4} + 193 \, d^{5} e^{4}\right)} x^{5} + {\left(33000 \, c^{7} d^{4} e^{4} + 40824 \, c^{5} d^{4} e^{4} + 13335 \, c^{3} d^{4} e^{4} + 965 \, c d^{4} e^{4}\right)} x^{4} + {\left(16500 \, c^{8} d^{3} e^{4} + 27216 \, c^{6} d^{3} e^{4} + 13335 \, c^{4} d^{3} e^{4} + 1930 \, c^{2} d^{3} e^{4} + 36 \, d^{3} e^{4}\right)} x^{3} + {\left(5500 \, c^{9} d^{2} e^{4} + 11664 \, c^{7} d^{2} e^{4} + 8001 \, c^{5} d^{2} e^{4} + 1930 \, c^{3} d^{2} e^{4} + 108 \, c d^{2} e^{4}\right)} x^{2} + {\left(1100 \, c^{10} d e^{4} + 2916 \, c^{8} d e^{4} + 2667 \, c^{6} d e^{4} + 965 \, c^{4} d e^{4} + 108 \, c^{2} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a b^{2} d^{8} x^{8} + 8 \, a b^{2} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} a b^{2} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} a b^{2} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} a b^{2} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{2} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{4} x^{4} + 4 \, a b^{2} c d^{3} x^{3} + 6 \, a b^{2} c^{2} d^{2} x^{2} + 4 \, a b^{2} c^{3} d x + a b^{2} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(a b^{2} d^{5} x^{5} + 5 \, a b^{2} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} a b^{2} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} a b^{2} x + {\left(c^{5} + c^{3}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{6} x^{6} + 6 \, a b^{2} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} a b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} a b^{2} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{3} d^{8} x^{8} + 8 \, b^{3} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} b^{3} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} b^{3} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} b^{3} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{3} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} b^{3} + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} b^{3} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b^{3} x + {\left(c^{5} + c^{3}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} b^{3} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(b^{3} d^{7} x^{7} + 7 \, b^{3} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} b^{3} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{3} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b^{3} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b^{3} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 4 \, {\left(a b^{2} d^{7} x^{7} + 7 \, a b^{2} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} a b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{2} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} a b^{2} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} a b^{2} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} a b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*((5*a*d^11*e^4 + b*d^11*e^4)*x^11 + 11*(5*a*c*d^10*e^4 + b*c*d^10*e^4)*x^10 + (5*(55*c^2*d^9*e^4 + 3*d^9*e^4)*a + (55*c^2*d^9*e^4 + 3*d^9*e^4)*b)*x^9 + 3*(5*(55*c^3*d^8*e^4 + 9*c*d^8*e^4)*a + (55*c^3*d^8*e^4 + 9*c*d^8*e^4)*b)*x^8 + 3*(5*(110*c^4*d^7*e^4 + 36*c^2*d^7*e^4 + d^7*e^4)*a + (110*c^4*d^7*e^4 + 36*c^2*d^7*e^4 + d^7*e^4)*b)*x^7 + 21*(5*(22*c^5*d^6*e^4 + 12*c^3*d^6*e^4 + c*d^6*e^4)*a + (22*c^5*d^6*e^4 + 12*c^3*d^6*e^4 + c*d^6*e^4)*b)*x^6 + (5*(462*c^6*d^5*e^4 + 378*c^4*d^5*e^4 + 63*c^2*d^5*e^4 + d^5*e^4)*a + (462*c^6*d^5*e^4 + 378*c^4*d^5*e^4 + 63*c^2*d^5*e^4 + d^5*e^4)*b)*x^5 + (5*(330*c^7*d^4*e^4 + 378*c^5*d^4*e^4 + 105*c^3*d^4*e^4 + 5*c*d^4*e^4)*a + (330*c^7*d^4*e^4 + 378*c^5*d^4*e^4 + 105*c^3*d^4*e^4 + 5*c*d^4*e^4)*b)*x^4 + (5*(165*c^8*d^3*e^4 + 252*c^6*d^3*e^4 + 105*c^4*d^3*e^4 + 10*c^2*d^3*e^4)*a + (165*c^8*d^3*e^4 + 252*c^6*d^3*e^4 + 105*c^4*d^3*e^4 + 10*c^2*d^3*e^4)*b)*x^3 + (5*(55*c^9*d^2*e^4 + 108*c^7*d^2*e^4 + 63*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*a + (55*c^9*d^2*e^4 + 108*c^7*d^2*e^4 + 63*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*b)*x^2 + ((5*a*d^8*e^4 + b*d^8*e^4)*x^8 + 8*(5*a*c*d^7*e^4 + b*c*d^7*e^4)*x^7 + (4*(35*c^2*d^6*e^4 + 2*d^6*e^4)*a + (28*c^2*d^6*e^4 + d^6*e^4)*b)*x^6 + 2*(4*(35*c^3*d^5*e^4 + 6*c*d^5*e^4)*a + (28*c^3*d^5*e^4 + 3*c*d^5*e^4)*b)*x^5 + ((350*c^4*d^4*e^4 + 120*c^2*d^4*e^4 + 3*d^4*e^4)*a + 5*(14*c^4*d^4*e^4 + 3*c^2*d^4*e^4)*b)*x^4 + 4*((70*c^5*d^3*e^4 + 40*c^3*d^3*e^4 + 3*c*d^3*e^4)*a + (14*c^5*d^3*e^4 + 5*c^3*d^3*e^4)*b)*x^3 + (2*(70*c^6*d^2*e^4 + 60*c^4*d^2*e^4 + 9*c^2*d^2*e^4)*a + (28*c^6*d^2*e^4 + 15*c^4*d^2*e^4)*b)*x^2 + (5*c^8*e^4 + 8*c^6*e^4 + 3*c^4*e^4)*a + (c^8*e^4 + c^6*e^4)*b + 2*(2*(10*c^7*d*e^4 + 12*c^5*d*e^4 + 3*c^3*d*e^4)*a + (4*c^7*d*e^4 + 3*c^5*d*e^4)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (3*(5*a*d^9*e^4 + b*d^9*e^4)*x^9 + 27*(5*a*c*d^8*e^4 + b*c*d^8*e^4)*x^8 + ((540*c^2*d^7*e^4 + 31*d^7*e^4)*a + (108*c^2*d^7*e^4 + 5*d^7*e^4)*b)*x^7 + 7*((180*c^3*d^6*e^4 + 31*c*d^6*e^4)*a + (36*c^3*d^6*e^4 + 5*c*d^6*e^4)*b)*x^6 + ((1890*c^4*d^5*e^4 + 651*c^2*d^5*e^4 + 20*d^5*e^4)*a + (378*c^4*d^5*e^4 + 105*c^2*d^5*e^4 + 2*d^5*e^4)*b)*x^5 + (5*(378*c^5*d^4*e^4 + 217*c^3*d^4*e^4 + 20*c*d^4*e^4)*a + (378*c^5*d^4*e^4 + 175*c^3*d^4*e^4 + 10*c*d^4*e^4)*b)*x^4 + ((1260*c^6*d^3*e^4 + 1085*c^4*d^3*e^4 + 200*c^2*d^3*e^4 + 4*d^3*e^4)*a + (252*c^6*d^3*e^4 + 175*c^4*d^3*e^4 + 20*c^2*d^3*e^4)*b)*x^3 + ((540*c^7*d^2*e^4 + 651*c^5*d^2*e^4 + 200*c^3*d^2*e^4 + 12*c*d^2*e^4)*a + (108*c^7*d^2*e^4 + 105*c^5*d^2*e^4 + 20*c^3*d^2*e^4)*b)*x^2 + (15*c^9*e^4 + 31*c^7*e^4 + 20*c^5*e^4 + 4*c^3*e^4)*a + (3*c^9*e^4 + 5*c^7*e^4 + 2*c^5*e^4)*b + ((135*c^8*d*e^4 + 217*c^6*d*e^4 + 100*c^4*d*e^4 + 12*c^2*d*e^4)*a + (27*c^8*d*e^4 + 35*c^6*d*e^4 + 10*c^4*d*e^4)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 5*(c^11*e^4 + 3*c^9*e^4 + 3*c^7*e^4 + c^5*e^4)*a + (c^11*e^4 + 3*c^9*e^4 + 3*c^7*e^4 + c^5*e^4)*b + (5*(11*c^10*d*e^4 + 27*c^8*d*e^4 + 21*c^6*d*e^4 + 5*c^4*d*e^4)*a + (11*c^10*d*e^4 + 27*c^8*d*e^4 + 21*c^6*d*e^4 + 5*c^4*d*e^4)*b)*x + (5*b*d^11*e^4*x^11 + 55*b*c*d^10*e^4*x^10 + 5*(55*c^2*d^9*e^4 + 3*d^9*e^4)*b*x^9 + 15*(55*c^3*d^8*e^4 + 9*c*d^8*e^4)*b*x^8 + 15*(110*c^4*d^7*e^4 + 36*c^2*d^7*e^4 + d^7*e^4)*b*x^7 + 105*(22*c^5*d^6*e^4 + 12*c^3*d^6*e^4 + c*d^6*e^4)*b*x^6 + 5*(462*c^6*d^5*e^4 + 378*c^4*d^5*e^4 + 63*c^2*d^5*e^4 + d^5*e^4)*b*x^5 + 5*(330*c^7*d^4*e^4 + 378*c^5*d^4*e^4 + 105*c^3*d^4*e^4 + 5*c*d^4*e^4)*b*x^4 + 5*(165*c^8*d^3*e^4 + 252*c^6*d^3*e^4 + 105*c^4*d^3*e^4 + 10*c^2*d^3*e^4)*b*x^3 + 5*(55*c^9*d^2*e^4 + 108*c^7*d^2*e^4 + 63*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*b*x^2 + 5*(11*c^10*d*e^4 + 27*c^8*d*e^4 + 21*c^6*d*e^4 + 5*c^4*d*e^4)*b*x + (5*b*d^8*e^4*x^8 + 40*b*c*d^7*e^4*x^7 + 4*(35*c^2*d^6*e^4 + 2*d^6*e^4)*b*x^6 + 8*(35*c^3*d^5*e^4 + 6*c*d^5*e^4)*b*x^5 + (350*c^4*d^4*e^4 + 120*c^2*d^4*e^4 + 3*d^4*e^4)*b*x^4 + 4*(70*c^5*d^3*e^4 + 40*c^3*d^3*e^4 + 3*c*d^3*e^4)*b*x^3 + 2*(70*c^6*d^2*e^4 + 60*c^4*d^2*e^4 + 9*c^2*d^2*e^4)*b*x^2 + 4*(10*c^7*d*e^4 + 12*c^5*d*e^4 + 3*c^3*d*e^4)*b*x + (5*c^8*e^4 + 8*c^6*e^4 + 3*c^4*e^4)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (15*b*d^9*e^4*x^9 + 135*b*c*d^8*e^4*x^8 + (540*c^2*d^7*e^4 + 31*d^7*e^4)*b*x^7 + 7*(180*c^3*d^6*e^4 + 31*c*d^6*e^4)*b*x^6 + (1890*c^4*d^5*e^4 + 651*c^2*d^5*e^4 + 20*d^5*e^4)*b*x^5 + 5*(378*c^5*d^4*e^4 + 217*c^3*d^4*e^4 + 20*c*d^4*e^4)*b*x^4 + (1260*c^6*d^3*e^4 + 1085*c^4*d^3*e^4 + 200*c^2*d^3*e^4 + 4*d^3*e^4)*b*x^3 + (540*c^7*d^2*e^4 + 651*c^5*d^2*e^4 + 200*c^3*d^2*e^4 + 12*c*d^2*e^4)*b*x^2 + (135*c^8*d*e^4 + 217*c^6*d*e^4 + 100*c^4*d*e^4 + 12*c^2*d*e^4)*b*x + (15*c^9*e^4 + 31*c^7*e^4 + 20*c^5*e^4 + 4*c^3*e^4)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 5*(c^11*e^4 + 3*c^9*e^4 + 3*c^7*e^4 + c^5*e^4)*b + (15*b*d^10*e^4*x^10 + 150*b*c*d^9*e^4*x^9 + (675*c^2*d^8*e^4 + 38*d^8*e^4)*b*x^8 + 8*(225*c^3*d^7*e^4 + 38*c*d^7*e^4)*b*x^7 + 2*(1575*c^4*d^6*e^4 + 532*c^2*d^6*e^4 + 16*d^6*e^4)*b*x^6 + 4*(945*c^5*d^5*e^4 + 532*c^3*d^5*e^4 + 48*c*d^5*e^4)*b*x^5 + (3150*c^6*d^4*e^4 + 2660*c^4*d^4*e^4 + 480*c^2*d^4*e^4 + 9*d^4*e^4)*b*x^4 + 4*(450*c^7*d^3*e^4 + 532*c^5*d^3*e^4 + 160*c^3*d^3*e^4 + 9*c*d^3*e^4)*b*x^3 + (675*c^8*d^2*e^4 + 1064*c^6*d^2*e^4 + 480*c^4*d^2*e^4 + 54*c^2*d^2*e^4)*b*x^2 + 2*(75*c^9*d*e^4 + 152*c^7*d*e^4 + 96*c^5*d*e^4 + 18*c^3*d*e^4)*b*x + (15*c^10*e^4 + 38*c^8*e^4 + 32*c^6*e^4 + 9*c^4*e^4)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (3*(5*a*d^10*e^4 + b*d^10*e^4)*x^10 + 30*(5*a*c*d^9*e^4 + b*c*d^9*e^4)*x^9 + ((675*c^2*d^8*e^4 + 38*d^8*e^4)*a + (135*c^2*d^8*e^4 + 7*d^8*e^4)*b)*x^8 + 8*((225*c^3*d^7*e^4 + 38*c*d^7*e^4)*a + (45*c^3*d^7*e^4 + 7*c*d^7*e^4)*b)*x^7 + (2*(1575*c^4*d^6*e^4 + 532*c^2*d^6*e^4 + 16*d^6*e^4)*a + (630*c^4*d^6*e^4 + 196*c^2*d^6*e^4 + 5*d^6*e^4)*b)*x^6 + 2*(2*(945*c^5*d^5*e^4 + 532*c^3*d^5*e^4 + 48*c*d^5*e^4)*a + (378*c^5*d^5*e^4 + 196*c^3*d^5*e^4 + 15*c*d^5*e^4)*b)*x^5 + ((3150*c^6*d^4*e^4 + 2660*c^4*d^4*e^4 + 480*c^2*d^4*e^4 + 9*d^4*e^4)*a + (630*c^6*d^4*e^4 + 490*c^4*d^4*e^4 + 75*c^2*d^4*e^4 + d^4*e^4)*b)*x^4 + 4*((450*c^7*d^3*e^4 + 532*c^5*d^3*e^4 + 160*c^3*d^3*e^4 + 9*c*d^3*e^4)*a + (90*c^7*d^3*e^4 + 98*c^5*d^3*e^4 + 25*c^3*d^3*e^4 + c*d^3*e^4)*b)*x^3 + ((675*c^8*d^2*e^4 + 1064*c^6*d^2*e^4 + 480*c^4*d^2*e^4 + 54*c^2*d^2*e^4)*a + (135*c^8*d^2*e^4 + 196*c^6*d^2*e^4 + 75*c^4*d^2*e^4 + 6*c^2*d^2*e^4)*b)*x^2 + (15*c^10*e^4 + 38*c^8*e^4 + 32*c^6*e^4 + 9*c^4*e^4)*a + (3*c^10*e^4 + 7*c^8*e^4 + 5*c^6*e^4 + c^4*e^4)*b + 2*((75*c^9*d*e^4 + 152*c^7*d*e^4 + 96*c^5*d*e^4 + 18*c^3*d*e^4)*a + (15*c^9*d*e^4 + 28*c^7*d*e^4 + 15*c^5*d*e^4 + 2*c^3*d*e^4)*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a^2*b^2*d^7*x^6 + 6*a^2*b^2*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a^2*b^2*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a^2*b^2*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a^2*b^2 + (b^4*d^7*x^6 + 6*b^4*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*b^4*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*b^4*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*b^4*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*b^4*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*b^4 + (b^4*d^4*x^3 + 3*b^4*c*d^3*x^2 + 3*b^4*c^2*d^2*x + b^4*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b^4*d^5*x^4 + 4*b^4*c*d^4*x^3 + (6*c^2*d^3 + d^3)*b^4*x^2 + 2*(2*c^3*d^2 + c*d^2)*b^4*x + (c^4*d + c^2*d)*b^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^4*d^6*x^5 + 5*b^4*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*b^4*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*b^4*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*b^4*x + (c^5*d + 2*c^3*d + c*d)*b^4)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + (a^2*b^2*d^4*x^3 + 3*a^2*b^2*c*d^3*x^2 + 3*a^2*b^2*c^2*d^2*x + a^2*b^2*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a^2*b^2*d^5*x^4 + 4*a^2*b^2*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 2*(2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^4*d + c^2*d)*a^2*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(a*b^3*d^7*x^6 + 6*a*b^3*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a*b^3*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a*b^3*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a*b^3*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a*b^3*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a*b^3 + (a*b^3*d^4*x^3 + 3*a*b^3*c*d^3*x^2 + 3*a*b^3*c^2*d^2*x + a*b^3*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a*b^3*d^5*x^4 + 4*a*b^3*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a*b^3*x^2 + 2*(2*c^3*d^2 + c*d^2)*a*b^3*x + (c^4*d + c^2*d)*a*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(a*b^3*d^6*x^5 + 5*a*b^3*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a*b^3*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a*b^3*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a*b^3*x + (c^5*d + 2*c^3*d + c*d)*a*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 3*(a^2*b^2*d^6*x^5 + 5*a^2*b^2*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a^2*b^2*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a^2*b^2*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a^2*b^2*x + (c^5*d + 2*c^3*d + c*d)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate(1/2*(25*d^12*e^4*x^12 + 300*c*d^11*e^4*x^11 + 25*c^12*e^4 + 100*c^10*e^4 + 150*c^8*e^4 + 50*(33*c^2*d^10*e^4 + 2*d^10*e^4)*x^10 + 100*c^6*e^4 + 500*(11*c^3*d^9*e^4 + 2*c*d^9*e^4)*x^9 + 75*(165*c^4*d^8*e^4 + 60*c^2*d^8*e^4 + 2*d^8*e^4)*x^8 + 25*c^4*e^4 + 600*(33*c^5*d^7*e^4 + 20*c^3*d^7*e^4 + 2*c*d^7*e^4)*x^7 + 100*(231*c^6*d^6*e^4 + 210*c^4*d^6*e^4 + 42*c^2*d^6*e^4 + d^6*e^4)*x^6 + 600*(33*c^7*d^5*e^4 + 42*c^5*d^5*e^4 + 14*c^3*d^5*e^4 + c*d^5*e^4)*x^5 + 25*(495*c^8*d^4*e^4 + 840*c^6*d^4*e^4 + 420*c^4*d^4*e^4 + 60*c^2*d^4*e^4 + d^4*e^4)*x^4 + 100*(55*c^9*d^3*e^4 + 120*c^7*d^3*e^4 + 84*c^5*d^3*e^4 + 20*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + (25*d^8*e^4*x^8 + 200*c*d^7*e^4*x^7 + 25*c^8*e^4 + 24*c^6*e^4 + 3*c^4*e^4 + 4*(175*c^2*d^6*e^4 + 6*d^6*e^4)*x^6 + 8*(175*c^3*d^5*e^4 + 18*c*d^5*e^4)*x^5 + (1750*c^4*d^4*e^4 + 360*c^2*d^4*e^4 + 3*d^4*e^4)*x^4 + 4*(350*c^5*d^3*e^4 + 120*c^3*d^3*e^4 + 3*c*d^3*e^4)*x^3 + 2*(350*c^6*d^2*e^4 + 180*c^4*d^2*e^4 + 9*c^2*d^2*e^4)*x^2 + 4*(50*c^7*d*e^4 + 36*c^5*d*e^4 + 3*c^3*d*e^4)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 150*(11*c^10*d^2*e^4 + 30*c^8*d^2*e^4 + 28*c^6*d^2*e^4 + 10*c^4*d^2*e^4 + c^2*d^2*e^4)*x^2 + (100*d^9*e^4*x^9 + 900*c*d^8*e^4*x^8 + 100*c^9*e^4 + 172*c^7*e^4 + 87*c^5*e^4 + 4*(900*c^2*d^7*e^4 + 43*d^7*e^4)*x^7 + 12*c^3*e^4 + 28*(300*c^3*d^6*e^4 + 43*c*d^6*e^4)*x^6 + 3*(4200*c^4*d^5*e^4 + 1204*c^2*d^5*e^4 + 29*d^5*e^4)*x^5 + 5*(2520*c^5*d^4*e^4 + 1204*c^3*d^4*e^4 + 87*c*d^4*e^4)*x^4 + 2*(4200*c^6*d^3*e^4 + 3010*c^4*d^3*e^4 + 435*c^2*d^3*e^4 + 6*d^3*e^4)*x^3 + 6*(600*c^7*d^2*e^4 + 602*c^5*d^2*e^4 + 145*c^3*d^2*e^4 + 6*c*d^2*e^4)*x^2 + (900*c^8*d*e^4 + 1204*c^6*d*e^4 + 435*c^4*d*e^4 + 36*c^2*d*e^4)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(50*d^10*e^4*x^10 + 500*c*d^9*e^4*x^9 + 50*c^10*e^4 + 124*c^8*e^4 + 105*c^6*e^4 + 2*(1125*c^2*d^8*e^4 + 62*d^8*e^4)*x^8 + 35*c^4*e^4 + 16*(375*c^3*d^7*e^4 + 62*c*d^7*e^4)*x^7 + 7*(1500*c^4*d^6*e^4 + 496*c^2*d^6*e^4 + 15*d^6*e^4)*x^6 + 4*c^2*e^4 + 14*(900*c^5*d^5*e^4 + 496*c^3*d^5*e^4 + 45*c*d^5*e^4)*x^5 + 35*(300*c^6*d^4*e^4 + 248*c^4*d^4*e^4 + 45*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(1500*c^7*d^3*e^4 + 1736*c^5*d^3*e^4 + 525*c^3*d^3*e^4 + 35*c*d^3*e^4)*x^3 + (2250*c^8*d^2*e^4 + 3472*c^6*d^2*e^4 + 1575*c^4*d^2*e^4 + 210*c^2*d^2*e^4 + 4*d^2*e^4)*x^2 + 2*(250*c^9*d*e^4 + 496*c^7*d*e^4 + 315*c^5*d*e^4 + 70*c^3*d*e^4 + 4*c*d*e^4)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 100*(3*c^11*d*e^4 + 10*c^9*d*e^4 + 12*c^7*d*e^4 + 6*c^5*d*e^4 + c^3*d*e^4)*x + (100*d^11*e^4*x^11 + 1100*c*d^10*e^4*x^10 + 100*c^11*e^4 + 324*c^9*e^4 + 381*c^7*e^4 + 4*(1375*c^2*d^9*e^4 + 81*d^9*e^4)*x^9 + 193*c^5*e^4 + 12*(1375*c^3*d^8*e^4 + 243*c*d^8*e^4)*x^8 + 3*(11000*c^4*d^7*e^4 + 3888*c^2*d^7*e^4 + 127*d^7*e^4)*x^7 + 36*c^3*e^4 + 21*(2200*c^5*d^6*e^4 + 1296*c^3*d^6*e^4 + 127*c*d^6*e^4)*x^6 + (46200*c^6*d^5*e^4 + 40824*c^4*d^5*e^4 + 8001*c^2*d^5*e^4 + 193*d^5*e^4)*x^5 + (33000*c^7*d^4*e^4 + 40824*c^5*d^4*e^4 + 13335*c^3*d^4*e^4 + 965*c*d^4*e^4)*x^4 + (16500*c^8*d^3*e^4 + 27216*c^6*d^3*e^4 + 13335*c^4*d^3*e^4 + 1930*c^2*d^3*e^4 + 36*d^3*e^4)*x^3 + (5500*c^9*d^2*e^4 + 11664*c^7*d^2*e^4 + 8001*c^5*d^2*e^4 + 1930*c^3*d^2*e^4 + 108*c*d^2*e^4)*x^2 + (1100*c^10*d*e^4 + 2916*c^8*d*e^4 + 2667*c^6*d*e^4 + 965*c^4*d*e^4 + 108*c^2*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b^2*d^8*x^8 + 8*a*b^2*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*a*b^2*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*a*b^2*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*a*b^2*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*a*b^2*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*a*b^2*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*a*b^2*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*a*b^2 + (a*b^2*d^4*x^4 + 4*a*b^2*c*d^3*x^3 + 6*a*b^2*c^2*d^2*x^2 + 4*a*b^2*c^3*d*x + a*b^2*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(a*b^2*d^5*x^5 + 5*a*b^2*c*d^4*x^4 + (10*c^2*d^3 + d^3)*a*b^2*x^3 + (10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (5*c^4*d + 3*c^2*d)*a*b^2*x + (c^5 + c^3)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(a*b^2*d^6*x^6 + 6*a*b^2*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*a*b^2*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*a*b^2*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*a*b^2*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*a*b^2*x + (c^6 + 2*c^4 + c^2)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^3*d^8*x^8 + 8*b^3*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*b^3*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*b^3*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*b^3*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*b^3*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*b^3*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*b^3*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*b^3 + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^3*d^5*x^5 + 5*b^3*c*d^4*x^4 + (10*c^2*d^3 + d^3)*b^3*x^3 + (10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (5*c^4*d + 3*c^2*d)*b^3*x + (c^5 + c^3)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(b^3*d^6*x^6 + 6*b^3*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*b^3*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*b^3*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*b^3*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*b^3*x + (c^6 + 2*c^4 + c^2)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(b^3*d^7*x^7 + 7*b^3*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*b^3*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*b^3*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b^3*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b^3*x + (c^7 + 3*c^5 + 3*c^3 + c)*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 4*(a*b^2*d^7*x^7 + 7*a*b^2*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*a*b^2*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*a*b^2*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*a*b^2*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*a*b^2*x + (c^7 + 3*c^5 + 3*c^3 + c)*a*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
169,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, a d^{10} e^{3} + b d^{10} e^{3}\right)} x^{10} + 10 \, {\left(4 \, a c d^{9} e^{3} + b c d^{9} e^{3}\right)} x^{9} + 3 \, {\left(4 \, {\left(15 \, c^{2} d^{8} e^{3} + d^{8} e^{3}\right)} a + {\left(15 \, c^{2} d^{8} e^{3} + d^{8} e^{3}\right)} b\right)} x^{8} + 24 \, {\left(4 \, {\left(5 \, c^{3} d^{7} e^{3} + c d^{7} e^{3}\right)} a + {\left(5 \, c^{3} d^{7} e^{3} + c d^{7} e^{3}\right)} b\right)} x^{7} + 3 \, {\left(4 \, {\left(70 \, c^{4} d^{6} e^{3} + 28 \, c^{2} d^{6} e^{3} + d^{6} e^{3}\right)} a + {\left(70 \, c^{4} d^{6} e^{3} + 28 \, c^{2} d^{6} e^{3} + d^{6} e^{3}\right)} b\right)} x^{6} + 6 \, {\left(4 \, {\left(42 \, c^{5} d^{5} e^{3} + 28 \, c^{3} d^{5} e^{3} + 3 \, c d^{5} e^{3}\right)} a + {\left(42 \, c^{5} d^{5} e^{3} + 28 \, c^{3} d^{5} e^{3} + 3 \, c d^{5} e^{3}\right)} b\right)} x^{5} + {\left(4 \, {\left(210 \, c^{6} d^{4} e^{3} + 210 \, c^{4} d^{4} e^{3} + 45 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} a + {\left(210 \, c^{6} d^{4} e^{3} + 210 \, c^{4} d^{4} e^{3} + 45 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} b\right)} x^{4} + 4 \, {\left(4 \, {\left(30 \, c^{7} d^{3} e^{3} + 42 \, c^{5} d^{3} e^{3} + 15 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} a + {\left(30 \, c^{7} d^{3} e^{3} + 42 \, c^{5} d^{3} e^{3} + 15 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} b\right)} x^{3} + 3 \, {\left(4 \, {\left(15 \, c^{8} d^{2} e^{3} + 28 \, c^{6} d^{2} e^{3} + 15 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} a + {\left(15 \, c^{8} d^{2} e^{3} + 28 \, c^{6} d^{2} e^{3} + 15 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} b\right)} x^{2} + {\left({\left(4 \, a d^{7} e^{3} + b d^{7} e^{3}\right)} x^{7} + 7 \, {\left(4 \, a c d^{6} e^{3} + b c d^{6} e^{3}\right)} x^{6} + {\left(6 \, {\left(14 \, c^{2} d^{5} e^{3} + d^{5} e^{3}\right)} a + {\left(21 \, c^{2} d^{5} e^{3} + d^{5} e^{3}\right)} b\right)} x^{5} + 5 \, {\left(2 \, {\left(14 \, c^{3} d^{4} e^{3} + 3 \, c d^{4} e^{3}\right)} a + {\left(7 \, c^{3} d^{4} e^{3} + c d^{4} e^{3}\right)} b\right)} x^{4} + {\left(2 \, {\left(70 \, c^{4} d^{3} e^{3} + 30 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} a + 5 \, {\left(7 \, c^{4} d^{3} e^{3} + 2 \, c^{2} d^{3} e^{3}\right)} b\right)} x^{3} + {\left(6 \, {\left(14 \, c^{5} d^{2} e^{3} + 10 \, c^{3} d^{2} e^{3} + c d^{2} e^{3}\right)} a + {\left(21 \, c^{5} d^{2} e^{3} + 10 \, c^{3} d^{2} e^{3}\right)} b\right)} x^{2} + 2 \, {\left(2 \, c^{7} e^{3} + 3 \, c^{5} e^{3} + c^{3} e^{3}\right)} a + {\left(c^{7} e^{3} + c^{5} e^{3}\right)} b + {\left(2 \, {\left(14 \, c^{6} d e^{3} + 15 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} a + {\left(7 \, c^{6} d e^{3} + 5 \, c^{4} d e^{3}\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, {\left(4 \, a d^{8} e^{3} + b d^{8} e^{3}\right)} x^{8} + 24 \, {\left(4 \, a c d^{7} e^{3} + b c d^{7} e^{3}\right)} x^{7} + {\left(24 \, {\left(14 \, c^{2} d^{6} e^{3} + d^{6} e^{3}\right)} a + {\left(84 \, c^{2} d^{6} e^{3} + 5 \, d^{6} e^{3}\right)} b\right)} x^{6} + 6 \, {\left(8 \, {\left(14 \, c^{3} d^{5} e^{3} + 3 \, c d^{5} e^{3}\right)} a + {\left(28 \, c^{3} d^{5} e^{3} + 5 \, c d^{5} e^{3}\right)} b\right)} x^{5} + {\left(15 \, {\left(56 \, c^{4} d^{4} e^{3} + 24 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} a + {\left(210 \, c^{4} d^{4} e^{3} + 75 \, c^{2} d^{4} e^{3} + 2 \, d^{4} e^{3}\right)} b\right)} x^{4} + 4 \, {\left(3 \, {\left(56 \, c^{5} d^{3} e^{3} + 40 \, c^{3} d^{3} e^{3} + 5 \, c d^{3} e^{3}\right)} a + {\left(42 \, c^{5} d^{3} e^{3} + 25 \, c^{3} d^{3} e^{3} + 2 \, c d^{3} e^{3}\right)} b\right)} x^{3} + 3 \, {\left({\left(112 \, c^{6} d^{2} e^{3} + 120 \, c^{4} d^{2} e^{3} + 30 \, c^{2} d^{2} e^{3} + d^{2} e^{3}\right)} a + {\left(28 \, c^{6} d^{2} e^{3} + 25 \, c^{4} d^{2} e^{3} + 4 \, c^{2} d^{2} e^{3}\right)} b\right)} x^{2} + 3 \, {\left(4 \, c^{8} e^{3} + 8 \, c^{6} e^{3} + 5 \, c^{4} e^{3} + c^{2} e^{3}\right)} a + {\left(3 \, c^{8} e^{3} + 5 \, c^{6} e^{3} + 2 \, c^{4} e^{3}\right)} b + 2 \, {\left(3 \, {\left(16 \, c^{7} d e^{3} + 24 \, c^{5} d e^{3} + 10 \, c^{3} d e^{3} + c d e^{3}\right)} a + {\left(12 \, c^{7} d e^{3} + 15 \, c^{5} d e^{3} + 4 \, c^{3} d e^{3}\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(c^{10} e^{3} + 3 \, c^{8} e^{3} + 3 \, c^{6} e^{3} + c^{4} e^{3}\right)} a + {\left(c^{10} e^{3} + 3 \, c^{8} e^{3} + 3 \, c^{6} e^{3} + c^{4} e^{3}\right)} b + 2 \, {\left(4 \, {\left(5 \, c^{9} d e^{3} + 12 \, c^{7} d e^{3} + 9 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} a + {\left(5 \, c^{9} d e^{3} + 12 \, c^{7} d e^{3} + 9 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} b\right)} x + {\left(4 \, b d^{10} e^{3} x^{10} + 40 \, b c d^{9} e^{3} x^{9} + 12 \, {\left(15 \, c^{2} d^{8} e^{3} + d^{8} e^{3}\right)} b x^{8} + 96 \, {\left(5 \, c^{3} d^{7} e^{3} + c d^{7} e^{3}\right)} b x^{7} + 12 \, {\left(70 \, c^{4} d^{6} e^{3} + 28 \, c^{2} d^{6} e^{3} + d^{6} e^{3}\right)} b x^{6} + 24 \, {\left(42 \, c^{5} d^{5} e^{3} + 28 \, c^{3} d^{5} e^{3} + 3 \, c d^{5} e^{3}\right)} b x^{5} + 4 \, {\left(210 \, c^{6} d^{4} e^{3} + 210 \, c^{4} d^{4} e^{3} + 45 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} b x^{4} + 16 \, {\left(30 \, c^{7} d^{3} e^{3} + 42 \, c^{5} d^{3} e^{3} + 15 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} b x^{3} + 12 \, {\left(15 \, c^{8} d^{2} e^{3} + 28 \, c^{6} d^{2} e^{3} + 15 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} b x^{2} + 8 \, {\left(5 \, c^{9} d e^{3} + 12 \, c^{7} d e^{3} + 9 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} b x + 2 \, {\left(2 \, b d^{7} e^{3} x^{7} + 14 \, b c d^{6} e^{3} x^{6} + 3 \, {\left(14 \, c^{2} d^{5} e^{3} + d^{5} e^{3}\right)} b x^{5} + 5 \, {\left(14 \, c^{3} d^{4} e^{3} + 3 \, c d^{4} e^{3}\right)} b x^{4} + {\left(70 \, c^{4} d^{3} e^{3} + 30 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} b x^{3} + 3 \, {\left(14 \, c^{5} d^{2} e^{3} + 10 \, c^{3} d^{2} e^{3} + c d^{2} e^{3}\right)} b x^{2} + {\left(14 \, c^{6} d e^{3} + 15 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} b x + {\left(2 \, c^{7} e^{3} + 3 \, c^{5} e^{3} + c^{3} e^{3}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(4 \, b d^{8} e^{3} x^{8} + 32 \, b c d^{7} e^{3} x^{7} + 8 \, {\left(14 \, c^{2} d^{6} e^{3} + d^{6} e^{3}\right)} b x^{6} + 16 \, {\left(14 \, c^{3} d^{5} e^{3} + 3 \, c d^{5} e^{3}\right)} b x^{5} + 5 \, {\left(56 \, c^{4} d^{4} e^{3} + 24 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} b x^{4} + 4 \, {\left(56 \, c^{5} d^{3} e^{3} + 40 \, c^{3} d^{3} e^{3} + 5 \, c d^{3} e^{3}\right)} b x^{3} + {\left(112 \, c^{6} d^{2} e^{3} + 120 \, c^{4} d^{2} e^{3} + 30 \, c^{2} d^{2} e^{3} + d^{2} e^{3}\right)} b x^{2} + 2 \, {\left(16 \, c^{7} d e^{3} + 24 \, c^{5} d e^{3} + 10 \, c^{3} d e^{3} + c d e^{3}\right)} b x + {\left(4 \, c^{8} e^{3} + 8 \, c^{6} e^{3} + 5 \, c^{4} e^{3} + c^{2} e^{3}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(c^{10} e^{3} + 3 \, c^{8} e^{3} + 3 \, c^{6} e^{3} + c^{4} e^{3}\right)} b + {\left(12 \, b d^{9} e^{3} x^{9} + 108 \, b c d^{8} e^{3} x^{8} + 6 \, {\left(72 \, c^{2} d^{7} e^{3} + 5 \, d^{7} e^{3}\right)} b x^{7} + 42 \, {\left(24 \, c^{3} d^{6} e^{3} + 5 \, c d^{6} e^{3}\right)} b x^{6} + {\left(1512 \, c^{4} d^{5} e^{3} + 630 \, c^{2} d^{5} e^{3} + 25 \, d^{5} e^{3}\right)} b x^{5} + {\left(1512 \, c^{5} d^{4} e^{3} + 1050 \, c^{3} d^{4} e^{3} + 125 \, c d^{4} e^{3}\right)} b x^{4} + {\left(1008 \, c^{6} d^{3} e^{3} + 1050 \, c^{4} d^{3} e^{3} + 250 \, c^{2} d^{3} e^{3} + 7 \, d^{3} e^{3}\right)} b x^{3} + {\left(432 \, c^{7} d^{2} e^{3} + 630 \, c^{5} d^{2} e^{3} + 250 \, c^{3} d^{2} e^{3} + 21 \, c d^{2} e^{3}\right)} b x^{2} + {\left(108 \, c^{8} d e^{3} + 210 \, c^{6} d e^{3} + 125 \, c^{4} d e^{3} + 21 \, c^{2} d e^{3}\right)} b x + {\left(12 \, c^{9} e^{3} + 30 \, c^{7} e^{3} + 25 \, c^{5} e^{3} + 7 \, c^{3} e^{3}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(3 \, {\left(4 \, a d^{9} e^{3} + b d^{9} e^{3}\right)} x^{9} + 27 \, {\left(4 \, a c d^{8} e^{3} + b c d^{8} e^{3}\right)} x^{8} + {\left(6 \, {\left(72 \, c^{2} d^{7} e^{3} + 5 \, d^{7} e^{3}\right)} a + {\left(108 \, c^{2} d^{7} e^{3} + 7 \, d^{7} e^{3}\right)} b\right)} x^{7} + 7 \, {\left(6 \, {\left(24 \, c^{3} d^{6} e^{3} + 5 \, c d^{6} e^{3}\right)} a + {\left(36 \, c^{3} d^{6} e^{3} + 7 \, c d^{6} e^{3}\right)} b\right)} x^{6} + {\left({\left(1512 \, c^{4} d^{5} e^{3} + 630 \, c^{2} d^{5} e^{3} + 25 \, d^{5} e^{3}\right)} a + {\left(378 \, c^{4} d^{5} e^{3} + 147 \, c^{2} d^{5} e^{3} + 5 \, d^{5} e^{3}\right)} b\right)} x^{5} + {\left({\left(1512 \, c^{5} d^{4} e^{3} + 1050 \, c^{3} d^{4} e^{3} + 125 \, c d^{4} e^{3}\right)} a + {\left(378 \, c^{5} d^{4} e^{3} + 245 \, c^{3} d^{4} e^{3} + 25 \, c d^{4} e^{3}\right)} b\right)} x^{4} + {\left({\left(1008 \, c^{6} d^{3} e^{3} + 1050 \, c^{4} d^{3} e^{3} + 250 \, c^{2} d^{3} e^{3} + 7 \, d^{3} e^{3}\right)} a + {\left(252 \, c^{6} d^{3} e^{3} + 245 \, c^{4} d^{3} e^{3} + 50 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} b\right)} x^{3} + {\left({\left(432 \, c^{7} d^{2} e^{3} + 630 \, c^{5} d^{2} e^{3} + 250 \, c^{3} d^{2} e^{3} + 21 \, c d^{2} e^{3}\right)} a + {\left(108 \, c^{7} d^{2} e^{3} + 147 \, c^{5} d^{2} e^{3} + 50 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} b\right)} x^{2} + {\left(12 \, c^{9} e^{3} + 30 \, c^{7} e^{3} + 25 \, c^{5} e^{3} + 7 \, c^{3} e^{3}\right)} a + {\left(3 \, c^{9} e^{3} + 7 \, c^{7} e^{3} + 5 \, c^{5} e^{3} + c^{3} e^{3}\right)} b + {\left({\left(108 \, c^{8} d e^{3} + 210 \, c^{6} d e^{3} + 125 \, c^{4} d e^{3} + 21 \, c^{2} d e^{3}\right)} a + {\left(27 \, c^{8} d e^{3} + 49 \, c^{6} d e^{3} + 25 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a^{2} b^{2} d^{7} x^{6} + 6 \, a^{2} b^{2} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a^{2} b^{2} + {\left(b^{4} d^{7} x^{6} + 6 \, b^{4} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} b^{4} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{4} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} b^{4} + {\left(b^{4} d^{4} x^{3} + 3 \, b^{4} c d^{3} x^{2} + 3 \, b^{4} c^{2} d^{2} x + b^{4} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{5} x^{4} + 4 \, b^{4} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{4} d + c^{2} d\right)} b^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(b^{4} d^{6} x^{5} + 5 \, b^{4} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} b^{4} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{4} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} b^{4} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} b^{4}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{3} + 3 \, a^{2} b^{2} c d^{3} x^{2} + 3 \, a^{2} b^{2} c^{2} d^{2} x + a^{2} b^{2} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{5} x^{4} + 4 \, a^{2} b^{2} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{4} d + c^{2} d\right)} a^{2} b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(a b^{3} d^{7} x^{6} + 6 \, a b^{3} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{3} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a b^{3} + {\left(a b^{3} d^{4} x^{3} + 3 \, a b^{3} c d^{3} x^{2} + 3 \, a b^{3} c^{2} d^{2} x + a b^{3} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{5} x^{4} + 4 \, a b^{3} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{4} d + c^{2} d\right)} a b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(a b^{3} d^{6} x^{5} + 5 \, a b^{3} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a b^{3} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{3} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a b^{3} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 3 \, {\left(a^{2} b^{2} d^{6} x^{5} + 5 \, a^{2} b^{2} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a^{2} b^{2} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a^{2} b^{2} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}} + \int \frac{16 \, d^{11} e^{3} x^{11} + 176 \, c d^{10} e^{3} x^{10} + 16 \, c^{11} e^{3} + 64 \, c^{9} e^{3} + 96 \, c^{7} e^{3} + 16 \, {\left(55 \, c^{2} d^{9} e^{3} + 4 \, d^{9} e^{3}\right)} x^{9} + 48 \, {\left(55 \, c^{3} d^{8} e^{3} + 12 \, c d^{8} e^{3}\right)} x^{8} + 64 \, c^{5} e^{3} + 96 \, {\left(55 \, c^{4} d^{7} e^{3} + 24 \, c^{2} d^{7} e^{3} + d^{7} e^{3}\right)} x^{7} + 672 \, {\left(11 \, c^{5} d^{6} e^{3} + 8 \, c^{3} d^{6} e^{3} + c d^{6} e^{3}\right)} x^{6} + 16 \, c^{3} e^{3} + 32 \, {\left(231 \, c^{6} d^{5} e^{3} + 252 \, c^{4} d^{5} e^{3} + 63 \, c^{2} d^{5} e^{3} + 2 \, d^{5} e^{3}\right)} x^{5} + 32 \, {\left(165 \, c^{7} d^{4} e^{3} + 252 \, c^{5} d^{4} e^{3} + 105 \, c^{3} d^{4} e^{3} + 10 \, c d^{4} e^{3}\right)} x^{4} + 16 \, {\left(165 \, c^{8} d^{3} e^{3} + 336 \, c^{6} d^{3} e^{3} + 210 \, c^{4} d^{3} e^{3} + 40 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + 4 \, {\left(4 \, d^{7} e^{3} x^{7} + 28 \, c d^{6} e^{3} x^{6} + 4 \, c^{7} e^{3} + 3 \, c^{5} e^{3} + 3 \, {\left(28 \, c^{2} d^{5} e^{3} + d^{5} e^{3}\right)} x^{5} + 5 \, {\left(28 \, c^{3} d^{4} e^{3} + 3 \, c d^{4} e^{3}\right)} x^{4} + 10 \, {\left(14 \, c^{4} d^{3} e^{3} + 3 \, c^{2} d^{3} e^{3}\right)} x^{3} + 6 \, {\left(14 \, c^{5} d^{2} e^{3} + 5 \, c^{3} d^{2} e^{3}\right)} x^{2} + {\left(28 \, c^{6} d e^{3} + 15 \, c^{4} d e^{3}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 16 \, {\left(55 \, c^{9} d^{2} e^{3} + 144 \, c^{7} d^{2} e^{3} + 126 \, c^{5} d^{2} e^{3} + 40 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(64 \, d^{8} e^{3} x^{8} + 512 \, c d^{7} e^{3} x^{7} + 64 \, c^{8} e^{3} + 100 \, c^{6} e^{3} + 42 \, c^{4} e^{3} + 4 \, {\left(448 \, c^{2} d^{6} e^{3} + 25 \, d^{6} e^{3}\right)} x^{6} + 8 \, {\left(448 \, c^{3} d^{5} e^{3} + 75 \, c d^{5} e^{3}\right)} x^{5} + 3 \, c^{2} e^{3} + 2 \, {\left(2240 \, c^{4} d^{4} e^{3} + 750 \, c^{2} d^{4} e^{3} + 21 \, d^{4} e^{3}\right)} x^{4} + 8 \, {\left(448 \, c^{5} d^{3} e^{3} + 250 \, c^{3} d^{3} e^{3} + 21 \, c d^{3} e^{3}\right)} x^{3} + {\left(1792 \, c^{6} d^{2} e^{3} + 1500 \, c^{4} d^{2} e^{3} + 252 \, c^{2} d^{2} e^{3} + 3 \, d^{2} e^{3}\right)} x^{2} + 2 \, {\left(256 \, c^{7} d e^{3} + 300 \, c^{5} d e^{3} + 84 \, c^{3} d e^{3} + 3 \, c d e^{3}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(16 \, d^{9} e^{3} x^{9} + 144 \, c d^{8} e^{3} x^{8} + 16 \, c^{9} e^{3} + 38 \, c^{7} e^{3} + 30 \, c^{5} e^{3} + 2 \, {\left(288 \, c^{2} d^{7} e^{3} + 19 \, d^{7} e^{3}\right)} x^{7} + 14 \, {\left(96 \, c^{3} d^{6} e^{3} + 19 \, c d^{6} e^{3}\right)} x^{6} + 9 \, c^{3} e^{3} + 6 \, {\left(336 \, c^{4} d^{5} e^{3} + 133 \, c^{2} d^{5} e^{3} + 5 \, d^{5} e^{3}\right)} x^{5} + 2 \, {\left(1008 \, c^{5} d^{4} e^{3} + 665 \, c^{3} d^{4} e^{3} + 75 \, c d^{4} e^{3}\right)} x^{4} + c e^{3} + {\left(1344 \, c^{6} d^{3} e^{3} + 1330 \, c^{4} d^{3} e^{3} + 300 \, c^{2} d^{3} e^{3} + 9 \, d^{3} e^{3}\right)} x^{3} + 3 \, {\left(192 \, c^{7} d^{2} e^{3} + 266 \, c^{5} d^{2} e^{3} + 100 \, c^{3} d^{2} e^{3} + 9 \, c d^{2} e^{3}\right)} x^{2} + {\left(144 \, c^{8} d e^{3} + 266 \, c^{6} d e^{3} + 150 \, c^{4} d e^{3} + 27 \, c^{2} d e^{3} + d e^{3}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 16 \, {\left(11 \, c^{10} d e^{3} + 36 \, c^{8} d e^{3} + 42 \, c^{6} d e^{3} + 20 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x + {\left(64 \, d^{10} e^{3} x^{10} + 640 \, c d^{9} e^{3} x^{9} + 64 \, c^{10} e^{3} + 204 \, c^{8} e^{3} + 234 \, c^{6} e^{3} + 12 \, {\left(240 \, c^{2} d^{8} e^{3} + 17 \, d^{8} e^{3}\right)} x^{8} + 96 \, {\left(80 \, c^{3} d^{7} e^{3} + 17 \, c d^{7} e^{3}\right)} x^{7} + 115 \, c^{4} e^{3} + 6 \, {\left(2240 \, c^{4} d^{6} e^{3} + 952 \, c^{2} d^{6} e^{3} + 39 \, d^{6} e^{3}\right)} x^{6} + 12 \, {\left(1344 \, c^{5} d^{5} e^{3} + 952 \, c^{3} d^{5} e^{3} + 117 \, c d^{5} e^{3}\right)} x^{5} + 21 \, c^{2} e^{3} + 5 \, {\left(2688 \, c^{6} d^{4} e^{3} + 2856 \, c^{4} d^{4} e^{3} + 702 \, c^{2} d^{4} e^{3} + 23 \, d^{4} e^{3}\right)} x^{4} + 4 \, {\left(1920 \, c^{7} d^{3} e^{3} + 2856 \, c^{5} d^{3} e^{3} + 1170 \, c^{3} d^{3} e^{3} + 115 \, c d^{3} e^{3}\right)} x^{3} + 3 \, {\left(960 \, c^{8} d^{2} e^{3} + 1904 \, c^{6} d^{2} e^{3} + 1170 \, c^{4} d^{2} e^{3} + 230 \, c^{2} d^{2} e^{3} + 7 \, d^{2} e^{3}\right)} x^{2} + 2 \, {\left(320 \, c^{9} d e^{3} + 816 \, c^{7} d e^{3} + 702 \, c^{5} d e^{3} + 230 \, c^{3} d e^{3} + 21 \, c d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a b^{2} d^{8} x^{8} + 8 \, a b^{2} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} a b^{2} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} a b^{2} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} a b^{2} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{2} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{4} x^{4} + 4 \, a b^{2} c d^{3} x^{3} + 6 \, a b^{2} c^{2} d^{2} x^{2} + 4 \, a b^{2} c^{3} d x + a b^{2} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(a b^{2} d^{5} x^{5} + 5 \, a b^{2} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} a b^{2} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} a b^{2} x + {\left(c^{5} + c^{3}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{6} x^{6} + 6 \, a b^{2} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} a b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} a b^{2} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{3} d^{8} x^{8} + 8 \, b^{3} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} b^{3} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} b^{3} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} b^{3} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{3} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} b^{3} + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} b^{3} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b^{3} x + {\left(c^{5} + c^{3}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} b^{3} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(b^{3} d^{7} x^{7} + 7 \, b^{3} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} b^{3} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{3} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b^{3} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b^{3} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 4 \, {\left(a b^{2} d^{7} x^{7} + 7 \, a b^{2} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} a b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{2} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} a b^{2} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} a b^{2} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} a b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*((4*a*d^10*e^3 + b*d^10*e^3)*x^10 + 10*(4*a*c*d^9*e^3 + b*c*d^9*e^3)*x^9 + 3*(4*(15*c^2*d^8*e^3 + d^8*e^3)*a + (15*c^2*d^8*e^3 + d^8*e^3)*b)*x^8 + 24*(4*(5*c^3*d^7*e^3 + c*d^7*e^3)*a + (5*c^3*d^7*e^3 + c*d^7*e^3)*b)*x^7 + 3*(4*(70*c^4*d^6*e^3 + 28*c^2*d^6*e^3 + d^6*e^3)*a + (70*c^4*d^6*e^3 + 28*c^2*d^6*e^3 + d^6*e^3)*b)*x^6 + 6*(4*(42*c^5*d^5*e^3 + 28*c^3*d^5*e^3 + 3*c*d^5*e^3)*a + (42*c^5*d^5*e^3 + 28*c^3*d^5*e^3 + 3*c*d^5*e^3)*b)*x^5 + (4*(210*c^6*d^4*e^3 + 210*c^4*d^4*e^3 + 45*c^2*d^4*e^3 + d^4*e^3)*a + (210*c^6*d^4*e^3 + 210*c^4*d^4*e^3 + 45*c^2*d^4*e^3 + d^4*e^3)*b)*x^4 + 4*(4*(30*c^7*d^3*e^3 + 42*c^5*d^3*e^3 + 15*c^3*d^3*e^3 + c*d^3*e^3)*a + (30*c^7*d^3*e^3 + 42*c^5*d^3*e^3 + 15*c^3*d^3*e^3 + c*d^3*e^3)*b)*x^3 + 3*(4*(15*c^8*d^2*e^3 + 28*c^6*d^2*e^3 + 15*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*a + (15*c^8*d^2*e^3 + 28*c^6*d^2*e^3 + 15*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*b)*x^2 + ((4*a*d^7*e^3 + b*d^7*e^3)*x^7 + 7*(4*a*c*d^6*e^3 + b*c*d^6*e^3)*x^6 + (6*(14*c^2*d^5*e^3 + d^5*e^3)*a + (21*c^2*d^5*e^3 + d^5*e^3)*b)*x^5 + 5*(2*(14*c^3*d^4*e^3 + 3*c*d^4*e^3)*a + (7*c^3*d^4*e^3 + c*d^4*e^3)*b)*x^4 + (2*(70*c^4*d^3*e^3 + 30*c^2*d^3*e^3 + d^3*e^3)*a + 5*(7*c^4*d^3*e^3 + 2*c^2*d^3*e^3)*b)*x^3 + (6*(14*c^5*d^2*e^3 + 10*c^3*d^2*e^3 + c*d^2*e^3)*a + (21*c^5*d^2*e^3 + 10*c^3*d^2*e^3)*b)*x^2 + 2*(2*c^7*e^3 + 3*c^5*e^3 + c^3*e^3)*a + (c^7*e^3 + c^5*e^3)*b + (2*(14*c^6*d*e^3 + 15*c^4*d*e^3 + 3*c^2*d*e^3)*a + (7*c^6*d*e^3 + 5*c^4*d*e^3)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (3*(4*a*d^8*e^3 + b*d^8*e^3)*x^8 + 24*(4*a*c*d^7*e^3 + b*c*d^7*e^3)*x^7 + (24*(14*c^2*d^6*e^3 + d^6*e^3)*a + (84*c^2*d^6*e^3 + 5*d^6*e^3)*b)*x^6 + 6*(8*(14*c^3*d^5*e^3 + 3*c*d^5*e^3)*a + (28*c^3*d^5*e^3 + 5*c*d^5*e^3)*b)*x^5 + (15*(56*c^4*d^4*e^3 + 24*c^2*d^4*e^3 + d^4*e^3)*a + (210*c^4*d^4*e^3 + 75*c^2*d^4*e^3 + 2*d^4*e^3)*b)*x^4 + 4*(3*(56*c^5*d^3*e^3 + 40*c^3*d^3*e^3 + 5*c*d^3*e^3)*a + (42*c^5*d^3*e^3 + 25*c^3*d^3*e^3 + 2*c*d^3*e^3)*b)*x^3 + 3*((112*c^6*d^2*e^3 + 120*c^4*d^2*e^3 + 30*c^2*d^2*e^3 + d^2*e^3)*a + (28*c^6*d^2*e^3 + 25*c^4*d^2*e^3 + 4*c^2*d^2*e^3)*b)*x^2 + 3*(4*c^8*e^3 + 8*c^6*e^3 + 5*c^4*e^3 + c^2*e^3)*a + (3*c^8*e^3 + 5*c^6*e^3 + 2*c^4*e^3)*b + 2*(3*(16*c^7*d*e^3 + 24*c^5*d*e^3 + 10*c^3*d*e^3 + c*d*e^3)*a + (12*c^7*d*e^3 + 15*c^5*d*e^3 + 4*c^3*d*e^3)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(c^10*e^3 + 3*c^8*e^3 + 3*c^6*e^3 + c^4*e^3)*a + (c^10*e^3 + 3*c^8*e^3 + 3*c^6*e^3 + c^4*e^3)*b + 2*(4*(5*c^9*d*e^3 + 12*c^7*d*e^3 + 9*c^5*d*e^3 + 2*c^3*d*e^3)*a + (5*c^9*d*e^3 + 12*c^7*d*e^3 + 9*c^5*d*e^3 + 2*c^3*d*e^3)*b)*x + (4*b*d^10*e^3*x^10 + 40*b*c*d^9*e^3*x^9 + 12*(15*c^2*d^8*e^3 + d^8*e^3)*b*x^8 + 96*(5*c^3*d^7*e^3 + c*d^7*e^3)*b*x^7 + 12*(70*c^4*d^6*e^3 + 28*c^2*d^6*e^3 + d^6*e^3)*b*x^6 + 24*(42*c^5*d^5*e^3 + 28*c^3*d^5*e^3 + 3*c*d^5*e^3)*b*x^5 + 4*(210*c^6*d^4*e^3 + 210*c^4*d^4*e^3 + 45*c^2*d^4*e^3 + d^4*e^3)*b*x^4 + 16*(30*c^7*d^3*e^3 + 42*c^5*d^3*e^3 + 15*c^3*d^3*e^3 + c*d^3*e^3)*b*x^3 + 12*(15*c^8*d^2*e^3 + 28*c^6*d^2*e^3 + 15*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*b*x^2 + 8*(5*c^9*d*e^3 + 12*c^7*d*e^3 + 9*c^5*d*e^3 + 2*c^3*d*e^3)*b*x + 2*(2*b*d^7*e^3*x^7 + 14*b*c*d^6*e^3*x^6 + 3*(14*c^2*d^5*e^3 + d^5*e^3)*b*x^5 + 5*(14*c^3*d^4*e^3 + 3*c*d^4*e^3)*b*x^4 + (70*c^4*d^3*e^3 + 30*c^2*d^3*e^3 + d^3*e^3)*b*x^3 + 3*(14*c^5*d^2*e^3 + 10*c^3*d^2*e^3 + c*d^2*e^3)*b*x^2 + (14*c^6*d*e^3 + 15*c^4*d*e^3 + 3*c^2*d*e^3)*b*x + (2*c^7*e^3 + 3*c^5*e^3 + c^3*e^3)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(4*b*d^8*e^3*x^8 + 32*b*c*d^7*e^3*x^7 + 8*(14*c^2*d^6*e^3 + d^6*e^3)*b*x^6 + 16*(14*c^3*d^5*e^3 + 3*c*d^5*e^3)*b*x^5 + 5*(56*c^4*d^4*e^3 + 24*c^2*d^4*e^3 + d^4*e^3)*b*x^4 + 4*(56*c^5*d^3*e^3 + 40*c^3*d^3*e^3 + 5*c*d^3*e^3)*b*x^3 + (112*c^6*d^2*e^3 + 120*c^4*d^2*e^3 + 30*c^2*d^2*e^3 + d^2*e^3)*b*x^2 + 2*(16*c^7*d*e^3 + 24*c^5*d*e^3 + 10*c^3*d*e^3 + c*d*e^3)*b*x + (4*c^8*e^3 + 8*c^6*e^3 + 5*c^4*e^3 + c^2*e^3)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(c^10*e^3 + 3*c^8*e^3 + 3*c^6*e^3 + c^4*e^3)*b + (12*b*d^9*e^3*x^9 + 108*b*c*d^8*e^3*x^8 + 6*(72*c^2*d^7*e^3 + 5*d^7*e^3)*b*x^7 + 42*(24*c^3*d^6*e^3 + 5*c*d^6*e^3)*b*x^6 + (1512*c^4*d^5*e^3 + 630*c^2*d^5*e^3 + 25*d^5*e^3)*b*x^5 + (1512*c^5*d^4*e^3 + 1050*c^3*d^4*e^3 + 125*c*d^4*e^3)*b*x^4 + (1008*c^6*d^3*e^3 + 1050*c^4*d^3*e^3 + 250*c^2*d^3*e^3 + 7*d^3*e^3)*b*x^3 + (432*c^7*d^2*e^3 + 630*c^5*d^2*e^3 + 250*c^3*d^2*e^3 + 21*c*d^2*e^3)*b*x^2 + (108*c^8*d*e^3 + 210*c^6*d*e^3 + 125*c^4*d*e^3 + 21*c^2*d*e^3)*b*x + (12*c^9*e^3 + 30*c^7*e^3 + 25*c^5*e^3 + 7*c^3*e^3)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (3*(4*a*d^9*e^3 + b*d^9*e^3)*x^9 + 27*(4*a*c*d^8*e^3 + b*c*d^8*e^3)*x^8 + (6*(72*c^2*d^7*e^3 + 5*d^7*e^3)*a + (108*c^2*d^7*e^3 + 7*d^7*e^3)*b)*x^7 + 7*(6*(24*c^3*d^6*e^3 + 5*c*d^6*e^3)*a + (36*c^3*d^6*e^3 + 7*c*d^6*e^3)*b)*x^6 + ((1512*c^4*d^5*e^3 + 630*c^2*d^5*e^3 + 25*d^5*e^3)*a + (378*c^4*d^5*e^3 + 147*c^2*d^5*e^3 + 5*d^5*e^3)*b)*x^5 + ((1512*c^5*d^4*e^3 + 1050*c^3*d^4*e^3 + 125*c*d^4*e^3)*a + (378*c^5*d^4*e^3 + 245*c^3*d^4*e^3 + 25*c*d^4*e^3)*b)*x^4 + ((1008*c^6*d^3*e^3 + 1050*c^4*d^3*e^3 + 250*c^2*d^3*e^3 + 7*d^3*e^3)*a + (252*c^6*d^3*e^3 + 245*c^4*d^3*e^3 + 50*c^2*d^3*e^3 + d^3*e^3)*b)*x^3 + ((432*c^7*d^2*e^3 + 630*c^5*d^2*e^3 + 250*c^3*d^2*e^3 + 21*c*d^2*e^3)*a + (108*c^7*d^2*e^3 + 147*c^5*d^2*e^3 + 50*c^3*d^2*e^3 + 3*c*d^2*e^3)*b)*x^2 + (12*c^9*e^3 + 30*c^7*e^3 + 25*c^5*e^3 + 7*c^3*e^3)*a + (3*c^9*e^3 + 7*c^7*e^3 + 5*c^5*e^3 + c^3*e^3)*b + ((108*c^8*d*e^3 + 210*c^6*d*e^3 + 125*c^4*d*e^3 + 21*c^2*d*e^3)*a + (27*c^8*d*e^3 + 49*c^6*d*e^3 + 25*c^4*d*e^3 + 3*c^2*d*e^3)*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a^2*b^2*d^7*x^6 + 6*a^2*b^2*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a^2*b^2*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a^2*b^2*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a^2*b^2 + (b^4*d^7*x^6 + 6*b^4*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*b^4*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*b^4*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*b^4*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*b^4*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*b^4 + (b^4*d^4*x^3 + 3*b^4*c*d^3*x^2 + 3*b^4*c^2*d^2*x + b^4*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b^4*d^5*x^4 + 4*b^4*c*d^4*x^3 + (6*c^2*d^3 + d^3)*b^4*x^2 + 2*(2*c^3*d^2 + c*d^2)*b^4*x + (c^4*d + c^2*d)*b^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^4*d^6*x^5 + 5*b^4*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*b^4*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*b^4*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*b^4*x + (c^5*d + 2*c^3*d + c*d)*b^4)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + (a^2*b^2*d^4*x^3 + 3*a^2*b^2*c*d^3*x^2 + 3*a^2*b^2*c^2*d^2*x + a^2*b^2*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a^2*b^2*d^5*x^4 + 4*a^2*b^2*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 2*(2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^4*d + c^2*d)*a^2*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(a*b^3*d^7*x^6 + 6*a*b^3*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a*b^3*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a*b^3*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a*b^3*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a*b^3*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a*b^3 + (a*b^3*d^4*x^3 + 3*a*b^3*c*d^3*x^2 + 3*a*b^3*c^2*d^2*x + a*b^3*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a*b^3*d^5*x^4 + 4*a*b^3*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a*b^3*x^2 + 2*(2*c^3*d^2 + c*d^2)*a*b^3*x + (c^4*d + c^2*d)*a*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(a*b^3*d^6*x^5 + 5*a*b^3*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a*b^3*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a*b^3*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a*b^3*x + (c^5*d + 2*c^3*d + c*d)*a*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 3*(a^2*b^2*d^6*x^5 + 5*a^2*b^2*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a^2*b^2*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a^2*b^2*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a^2*b^2*x + (c^5*d + 2*c^3*d + c*d)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate(1/2*(16*d^11*e^3*x^11 + 176*c*d^10*e^3*x^10 + 16*c^11*e^3 + 64*c^9*e^3 + 96*c^7*e^3 + 16*(55*c^2*d^9*e^3 + 4*d^9*e^3)*x^9 + 48*(55*c^3*d^8*e^3 + 12*c*d^8*e^3)*x^8 + 64*c^5*e^3 + 96*(55*c^4*d^7*e^3 + 24*c^2*d^7*e^3 + d^7*e^3)*x^7 + 672*(11*c^5*d^6*e^3 + 8*c^3*d^6*e^3 + c*d^6*e^3)*x^6 + 16*c^3*e^3 + 32*(231*c^6*d^5*e^3 + 252*c^4*d^5*e^3 + 63*c^2*d^5*e^3 + 2*d^5*e^3)*x^5 + 32*(165*c^7*d^4*e^3 + 252*c^5*d^4*e^3 + 105*c^3*d^4*e^3 + 10*c*d^4*e^3)*x^4 + 16*(165*c^8*d^3*e^3 + 336*c^6*d^3*e^3 + 210*c^4*d^3*e^3 + 40*c^2*d^3*e^3 + d^3*e^3)*x^3 + 4*(4*d^7*e^3*x^7 + 28*c*d^6*e^3*x^6 + 4*c^7*e^3 + 3*c^5*e^3 + 3*(28*c^2*d^5*e^3 + d^5*e^3)*x^5 + 5*(28*c^3*d^4*e^3 + 3*c*d^4*e^3)*x^4 + 10*(14*c^4*d^3*e^3 + 3*c^2*d^3*e^3)*x^3 + 6*(14*c^5*d^2*e^3 + 5*c^3*d^2*e^3)*x^2 + (28*c^6*d*e^3 + 15*c^4*d*e^3)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 16*(55*c^9*d^2*e^3 + 144*c^7*d^2*e^3 + 126*c^5*d^2*e^3 + 40*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (64*d^8*e^3*x^8 + 512*c*d^7*e^3*x^7 + 64*c^8*e^3 + 100*c^6*e^3 + 42*c^4*e^3 + 4*(448*c^2*d^6*e^3 + 25*d^6*e^3)*x^6 + 8*(448*c^3*d^5*e^3 + 75*c*d^5*e^3)*x^5 + 3*c^2*e^3 + 2*(2240*c^4*d^4*e^3 + 750*c^2*d^4*e^3 + 21*d^4*e^3)*x^4 + 8*(448*c^5*d^3*e^3 + 250*c^3*d^3*e^3 + 21*c*d^3*e^3)*x^3 + (1792*c^6*d^2*e^3 + 1500*c^4*d^2*e^3 + 252*c^2*d^2*e^3 + 3*d^2*e^3)*x^2 + 2*(256*c^7*d*e^3 + 300*c^5*d*e^3 + 84*c^3*d*e^3 + 3*c*d*e^3)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(16*d^9*e^3*x^9 + 144*c*d^8*e^3*x^8 + 16*c^9*e^3 + 38*c^7*e^3 + 30*c^5*e^3 + 2*(288*c^2*d^7*e^3 + 19*d^7*e^3)*x^7 + 14*(96*c^3*d^6*e^3 + 19*c*d^6*e^3)*x^6 + 9*c^3*e^3 + 6*(336*c^4*d^5*e^3 + 133*c^2*d^5*e^3 + 5*d^5*e^3)*x^5 + 2*(1008*c^5*d^4*e^3 + 665*c^3*d^4*e^3 + 75*c*d^4*e^3)*x^4 + c*e^3 + (1344*c^6*d^3*e^3 + 1330*c^4*d^3*e^3 + 300*c^2*d^3*e^3 + 9*d^3*e^3)*x^3 + 3*(192*c^7*d^2*e^3 + 266*c^5*d^2*e^3 + 100*c^3*d^2*e^3 + 9*c*d^2*e^3)*x^2 + (144*c^8*d*e^3 + 266*c^6*d*e^3 + 150*c^4*d*e^3 + 27*c^2*d*e^3 + d*e^3)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 16*(11*c^10*d*e^3 + 36*c^8*d*e^3 + 42*c^6*d*e^3 + 20*c^4*d*e^3 + 3*c^2*d*e^3)*x + (64*d^10*e^3*x^10 + 640*c*d^9*e^3*x^9 + 64*c^10*e^3 + 204*c^8*e^3 + 234*c^6*e^3 + 12*(240*c^2*d^8*e^3 + 17*d^8*e^3)*x^8 + 96*(80*c^3*d^7*e^3 + 17*c*d^7*e^3)*x^7 + 115*c^4*e^3 + 6*(2240*c^4*d^6*e^3 + 952*c^2*d^6*e^3 + 39*d^6*e^3)*x^6 + 12*(1344*c^5*d^5*e^3 + 952*c^3*d^5*e^3 + 117*c*d^5*e^3)*x^5 + 21*c^2*e^3 + 5*(2688*c^6*d^4*e^3 + 2856*c^4*d^4*e^3 + 702*c^2*d^4*e^3 + 23*d^4*e^3)*x^4 + 4*(1920*c^7*d^3*e^3 + 2856*c^5*d^3*e^3 + 1170*c^3*d^3*e^3 + 115*c*d^3*e^3)*x^3 + 3*(960*c^8*d^2*e^3 + 1904*c^6*d^2*e^3 + 1170*c^4*d^2*e^3 + 230*c^2*d^2*e^3 + 7*d^2*e^3)*x^2 + 2*(320*c^9*d*e^3 + 816*c^7*d*e^3 + 702*c^5*d*e^3 + 230*c^3*d*e^3 + 21*c*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b^2*d^8*x^8 + 8*a*b^2*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*a*b^2*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*a*b^2*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*a*b^2*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*a*b^2*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*a*b^2*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*a*b^2*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*a*b^2 + (a*b^2*d^4*x^4 + 4*a*b^2*c*d^3*x^3 + 6*a*b^2*c^2*d^2*x^2 + 4*a*b^2*c^3*d*x + a*b^2*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(a*b^2*d^5*x^5 + 5*a*b^2*c*d^4*x^4 + (10*c^2*d^3 + d^3)*a*b^2*x^3 + (10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (5*c^4*d + 3*c^2*d)*a*b^2*x + (c^5 + c^3)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(a*b^2*d^6*x^6 + 6*a*b^2*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*a*b^2*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*a*b^2*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*a*b^2*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*a*b^2*x + (c^6 + 2*c^4 + c^2)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^3*d^8*x^8 + 8*b^3*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*b^3*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*b^3*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*b^3*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*b^3*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*b^3*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*b^3*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*b^3 + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^3*d^5*x^5 + 5*b^3*c*d^4*x^4 + (10*c^2*d^3 + d^3)*b^3*x^3 + (10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (5*c^4*d + 3*c^2*d)*b^3*x + (c^5 + c^3)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(b^3*d^6*x^6 + 6*b^3*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*b^3*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*b^3*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*b^3*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*b^3*x + (c^6 + 2*c^4 + c^2)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(b^3*d^7*x^7 + 7*b^3*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*b^3*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*b^3*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b^3*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b^3*x + (c^7 + 3*c^5 + 3*c^3 + c)*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 4*(a*b^2*d^7*x^7 + 7*a*b^2*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*a*b^2*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*a*b^2*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*a*b^2*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*a*b^2*x + (c^7 + 3*c^5 + 3*c^3 + c)*a*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
170,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a d^{9} e^{2} + b d^{9} e^{2}\right)} x^{9} + 9 \, {\left(3 \, a c d^{8} e^{2} + b c d^{8} e^{2}\right)} x^{8} + 3 \, {\left(3 \, {\left(12 \, c^{2} d^{7} e^{2} + d^{7} e^{2}\right)} a + {\left(12 \, c^{2} d^{7} e^{2} + d^{7} e^{2}\right)} b\right)} x^{7} + 21 \, {\left(3 \, {\left(4 \, c^{3} d^{6} e^{2} + c d^{6} e^{2}\right)} a + {\left(4 \, c^{3} d^{6} e^{2} + c d^{6} e^{2}\right)} b\right)} x^{6} + 3 \, {\left(3 \, {\left(42 \, c^{4} d^{5} e^{2} + 21 \, c^{2} d^{5} e^{2} + d^{5} e^{2}\right)} a + {\left(42 \, c^{4} d^{5} e^{2} + 21 \, c^{2} d^{5} e^{2} + d^{5} e^{2}\right)} b\right)} x^{5} + 3 \, {\left(3 \, {\left(42 \, c^{5} d^{4} e^{2} + 35 \, c^{3} d^{4} e^{2} + 5 \, c d^{4} e^{2}\right)} a + {\left(42 \, c^{5} d^{4} e^{2} + 35 \, c^{3} d^{4} e^{2} + 5 \, c d^{4} e^{2}\right)} b\right)} x^{4} + {\left(3 \, {\left(84 \, c^{6} d^{3} e^{2} + 105 \, c^{4} d^{3} e^{2} + 30 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} a + {\left(84 \, c^{6} d^{3} e^{2} + 105 \, c^{4} d^{3} e^{2} + 30 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} b\right)} x^{3} + 3 \, {\left(3 \, {\left(12 \, c^{7} d^{2} e^{2} + 21 \, c^{5} d^{2} e^{2} + 10 \, c^{3} d^{2} e^{2} + c d^{2} e^{2}\right)} a + {\left(12 \, c^{7} d^{2} e^{2} + 21 \, c^{5} d^{2} e^{2} + 10 \, c^{3} d^{2} e^{2} + c d^{2} e^{2}\right)} b\right)} x^{2} + {\left({\left(3 \, a d^{6} e^{2} + b d^{6} e^{2}\right)} x^{6} + 6 \, {\left(3 \, a c d^{5} e^{2} + b c d^{5} e^{2}\right)} x^{5} + {\left({\left(45 \, c^{2} d^{4} e^{2} + 4 \, d^{4} e^{2}\right)} a + {\left(15 \, c^{2} d^{4} e^{2} + d^{4} e^{2}\right)} b\right)} x^{4} + 4 \, {\left({\left(15 \, c^{3} d^{3} e^{2} + 4 \, c d^{3} e^{2}\right)} a + {\left(5 \, c^{3} d^{3} e^{2} + c d^{3} e^{2}\right)} b\right)} x^{3} + {\left({\left(45 \, c^{4} d^{2} e^{2} + 24 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} a + 3 \, {\left(5 \, c^{4} d^{2} e^{2} + 2 \, c^{2} d^{2} e^{2}\right)} b\right)} x^{2} + {\left(3 \, c^{6} e^{2} + 4 \, c^{4} e^{2} + c^{2} e^{2}\right)} a + {\left(c^{6} e^{2} + c^{4} e^{2}\right)} b + 2 \, {\left({\left(9 \, c^{5} d e^{2} + 8 \, c^{3} d e^{2} + c d e^{2}\right)} a + {\left(3 \, c^{5} d e^{2} + 2 \, c^{3} d e^{2}\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, {\left(3 \, a d^{7} e^{2} + b d^{7} e^{2}\right)} x^{7} + 21 \, {\left(3 \, a c d^{6} e^{2} + b c d^{6} e^{2}\right)} x^{6} + {\left({\left(189 \, c^{2} d^{5} e^{2} + 17 \, d^{5} e^{2}\right)} a + {\left(63 \, c^{2} d^{5} e^{2} + 5 \, d^{5} e^{2}\right)} b\right)} x^{5} + 5 \, {\left({\left(63 \, c^{3} d^{4} e^{2} + 17 \, c d^{4} e^{2}\right)} a + {\left(21 \, c^{3} d^{4} e^{2} + 5 \, c d^{4} e^{2}\right)} b\right)} x^{4} + {\left(5 \, {\left(63 \, c^{4} d^{3} e^{2} + 34 \, c^{2} d^{3} e^{2} + 2 \, d^{3} e^{2}\right)} a + {\left(105 \, c^{4} d^{3} e^{2} + 50 \, c^{2} d^{3} e^{2} + 2 \, d^{3} e^{2}\right)} b\right)} x^{3} + {\left({\left(189 \, c^{5} d^{2} e^{2} + 170 \, c^{3} d^{2} e^{2} + 30 \, c d^{2} e^{2}\right)} a + {\left(63 \, c^{5} d^{2} e^{2} + 50 \, c^{3} d^{2} e^{2} + 6 \, c d^{2} e^{2}\right)} b\right)} x^{2} + {\left(9 \, c^{7} e^{2} + 17 \, c^{5} e^{2} + 10 \, c^{3} e^{2} + 2 \, c e^{2}\right)} a + {\left(3 \, c^{7} e^{2} + 5 \, c^{5} e^{2} + 2 \, c^{3} e^{2}\right)} b + {\left({\left(63 \, c^{6} d e^{2} + 85 \, c^{4} d e^{2} + 30 \, c^{2} d e^{2} + 2 \, d e^{2}\right)} a + {\left(21 \, c^{6} d e^{2} + 25 \, c^{4} d e^{2} + 6 \, c^{2} d e^{2}\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(c^{9} e^{2} + 3 \, c^{7} e^{2} + 3 \, c^{5} e^{2} + c^{3} e^{2}\right)} a + {\left(c^{9} e^{2} + 3 \, c^{7} e^{2} + 3 \, c^{5} e^{2} + c^{3} e^{2}\right)} b + 3 \, {\left(3 \, {\left(3 \, c^{8} d e^{2} + 7 \, c^{6} d e^{2} + 5 \, c^{4} d e^{2} + c^{2} d e^{2}\right)} a + {\left(3 \, c^{8} d e^{2} + 7 \, c^{6} d e^{2} + 5 \, c^{4} d e^{2} + c^{2} d e^{2}\right)} b\right)} x + {\left(3 \, b d^{9} e^{2} x^{9} + 27 \, b c d^{8} e^{2} x^{8} + 9 \, {\left(12 \, c^{2} d^{7} e^{2} + d^{7} e^{2}\right)} b x^{7} + 63 \, {\left(4 \, c^{3} d^{6} e^{2} + c d^{6} e^{2}\right)} b x^{6} + 9 \, {\left(42 \, c^{4} d^{5} e^{2} + 21 \, c^{2} d^{5} e^{2} + d^{5} e^{2}\right)} b x^{5} + 9 \, {\left(42 \, c^{5} d^{4} e^{2} + 35 \, c^{3} d^{4} e^{2} + 5 \, c d^{4} e^{2}\right)} b x^{4} + 3 \, {\left(84 \, c^{6} d^{3} e^{2} + 105 \, c^{4} d^{3} e^{2} + 30 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} b x^{3} + 9 \, {\left(12 \, c^{7} d^{2} e^{2} + 21 \, c^{5} d^{2} e^{2} + 10 \, c^{3} d^{2} e^{2} + c d^{2} e^{2}\right)} b x^{2} + 9 \, {\left(3 \, c^{8} d e^{2} + 7 \, c^{6} d e^{2} + 5 \, c^{4} d e^{2} + c^{2} d e^{2}\right)} b x + {\left(3 \, b d^{6} e^{2} x^{6} + 18 \, b c d^{5} e^{2} x^{5} + {\left(45 \, c^{2} d^{4} e^{2} + 4 \, d^{4} e^{2}\right)} b x^{4} + 4 \, {\left(15 \, c^{3} d^{3} e^{2} + 4 \, c d^{3} e^{2}\right)} b x^{3} + {\left(45 \, c^{4} d^{2} e^{2} + 24 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} b x^{2} + 2 \, {\left(9 \, c^{5} d e^{2} + 8 \, c^{3} d e^{2} + c d e^{2}\right)} b x + {\left(3 \, c^{6} e^{2} + 4 \, c^{4} e^{2} + c^{2} e^{2}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(9 \, b d^{7} e^{2} x^{7} + 63 \, b c d^{6} e^{2} x^{6} + {\left(189 \, c^{2} d^{5} e^{2} + 17 \, d^{5} e^{2}\right)} b x^{5} + 5 \, {\left(63 \, c^{3} d^{4} e^{2} + 17 \, c d^{4} e^{2}\right)} b x^{4} + 5 \, {\left(63 \, c^{4} d^{3} e^{2} + 34 \, c^{2} d^{3} e^{2} + 2 \, d^{3} e^{2}\right)} b x^{3} + {\left(189 \, c^{5} d^{2} e^{2} + 170 \, c^{3} d^{2} e^{2} + 30 \, c d^{2} e^{2}\right)} b x^{2} + {\left(63 \, c^{6} d e^{2} + 85 \, c^{4} d e^{2} + 30 \, c^{2} d e^{2} + 2 \, d e^{2}\right)} b x + {\left(9 \, c^{7} e^{2} + 17 \, c^{5} e^{2} + 10 \, c^{3} e^{2} + 2 \, c e^{2}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(c^{9} e^{2} + 3 \, c^{7} e^{2} + 3 \, c^{5} e^{2} + c^{3} e^{2}\right)} b + {\left(9 \, b d^{8} e^{2} x^{8} + 72 \, b c d^{7} e^{2} x^{7} + 2 \, {\left(126 \, c^{2} d^{6} e^{2} + 11 \, d^{6} e^{2}\right)} b x^{6} + 12 \, {\left(42 \, c^{3} d^{5} e^{2} + 11 \, c d^{5} e^{2}\right)} b x^{5} + 6 \, {\left(105 \, c^{4} d^{4} e^{2} + 55 \, c^{2} d^{4} e^{2} + 3 \, d^{4} e^{2}\right)} b x^{4} + 8 \, {\left(63 \, c^{5} d^{3} e^{2} + 55 \, c^{3} d^{3} e^{2} + 9 \, c d^{3} e^{2}\right)} b x^{3} + {\left(252 \, c^{6} d^{2} e^{2} + 330 \, c^{4} d^{2} e^{2} + 108 \, c^{2} d^{2} e^{2} + 5 \, d^{2} e^{2}\right)} b x^{2} + 2 \, {\left(36 \, c^{7} d e^{2} + 66 \, c^{5} d e^{2} + 36 \, c^{3} d e^{2} + 5 \, c d e^{2}\right)} b x + {\left(9 \, c^{8} e^{2} + 22 \, c^{6} e^{2} + 18 \, c^{4} e^{2} + 5 \, c^{2} e^{2}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(3 \, {\left(3 \, a d^{8} e^{2} + b d^{8} e^{2}\right)} x^{8} + 24 \, {\left(3 \, a c d^{7} e^{2} + b c d^{7} e^{2}\right)} x^{7} + {\left(2 \, {\left(126 \, c^{2} d^{6} e^{2} + 11 \, d^{6} e^{2}\right)} a + 7 \, {\left(12 \, c^{2} d^{6} e^{2} + d^{6} e^{2}\right)} b\right)} x^{6} + 6 \, {\left(2 \, {\left(42 \, c^{3} d^{5} e^{2} + 11 \, c d^{5} e^{2}\right)} a + 7 \, {\left(4 \, c^{3} d^{5} e^{2} + c d^{5} e^{2}\right)} b\right)} x^{5} + {\left(6 \, {\left(105 \, c^{4} d^{4} e^{2} + 55 \, c^{2} d^{4} e^{2} + 3 \, d^{4} e^{2}\right)} a + 5 \, {\left(42 \, c^{4} d^{4} e^{2} + 21 \, c^{2} d^{4} e^{2} + d^{4} e^{2}\right)} b\right)} x^{4} + 4 \, {\left(2 \, {\left(63 \, c^{5} d^{3} e^{2} + 55 \, c^{3} d^{3} e^{2} + 9 \, c d^{3} e^{2}\right)} a + {\left(42 \, c^{5} d^{3} e^{2} + 35 \, c^{3} d^{3} e^{2} + 5 \, c d^{3} e^{2}\right)} b\right)} x^{3} + {\left({\left(252 \, c^{6} d^{2} e^{2} + 330 \, c^{4} d^{2} e^{2} + 108 \, c^{2} d^{2} e^{2} + 5 \, d^{2} e^{2}\right)} a + {\left(84 \, c^{6} d^{2} e^{2} + 105 \, c^{4} d^{2} e^{2} + 30 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} b\right)} x^{2} + {\left(9 \, c^{8} e^{2} + 22 \, c^{6} e^{2} + 18 \, c^{4} e^{2} + 5 \, c^{2} e^{2}\right)} a + {\left(3 \, c^{8} e^{2} + 7 \, c^{6} e^{2} + 5 \, c^{4} e^{2} + c^{2} e^{2}\right)} b + 2 \, {\left({\left(36 \, c^{7} d e^{2} + 66 \, c^{5} d e^{2} + 36 \, c^{3} d e^{2} + 5 \, c d e^{2}\right)} a + {\left(12 \, c^{7} d e^{2} + 21 \, c^{5} d e^{2} + 10 \, c^{3} d e^{2} + c d e^{2}\right)} b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a^{2} b^{2} d^{7} x^{6} + 6 \, a^{2} b^{2} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a^{2} b^{2} + {\left(b^{4} d^{7} x^{6} + 6 \, b^{4} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} b^{4} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{4} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} b^{4} + {\left(b^{4} d^{4} x^{3} + 3 \, b^{4} c d^{3} x^{2} + 3 \, b^{4} c^{2} d^{2} x + b^{4} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{5} x^{4} + 4 \, b^{4} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{4} d + c^{2} d\right)} b^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(b^{4} d^{6} x^{5} + 5 \, b^{4} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} b^{4} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{4} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} b^{4} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} b^{4}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{3} + 3 \, a^{2} b^{2} c d^{3} x^{2} + 3 \, a^{2} b^{2} c^{2} d^{2} x + a^{2} b^{2} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{5} x^{4} + 4 \, a^{2} b^{2} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{4} d + c^{2} d\right)} a^{2} b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(a b^{3} d^{7} x^{6} + 6 \, a b^{3} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{3} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a b^{3} + {\left(a b^{3} d^{4} x^{3} + 3 \, a b^{3} c d^{3} x^{2} + 3 \, a b^{3} c^{2} d^{2} x + a b^{3} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{5} x^{4} + 4 \, a b^{3} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{4} d + c^{2} d\right)} a b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(a b^{3} d^{6} x^{5} + 5 \, a b^{3} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a b^{3} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{3} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a b^{3} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 3 \, {\left(a^{2} b^{2} d^{6} x^{5} + 5 \, a^{2} b^{2} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a^{2} b^{2} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a^{2} b^{2} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}} + \int \frac{9 \, d^{10} e^{2} x^{10} + 90 \, c d^{9} e^{2} x^{9} + 9 \, c^{10} e^{2} + 36 \, c^{8} e^{2} + 9 \, {\left(45 \, c^{2} d^{8} e^{2} + 4 \, d^{8} e^{2}\right)} x^{8} + 54 \, c^{6} e^{2} + 72 \, {\left(15 \, c^{3} d^{7} e^{2} + 4 \, c d^{7} e^{2}\right)} x^{7} + 18 \, {\left(105 \, c^{4} d^{6} e^{2} + 56 \, c^{2} d^{6} e^{2} + 3 \, d^{6} e^{2}\right)} x^{6} + 36 \, c^{4} e^{2} + 36 \, {\left(63 \, c^{5} d^{5} e^{2} + 56 \, c^{3} d^{5} e^{2} + 9 \, c d^{5} e^{2}\right)} x^{5} + 18 \, {\left(105 \, c^{6} d^{4} e^{2} + 140 \, c^{4} d^{4} e^{2} + 45 \, c^{2} d^{4} e^{2} + 2 \, d^{4} e^{2}\right)} x^{4} + 9 \, c^{2} e^{2} + 72 \, {\left(15 \, c^{7} d^{3} e^{2} + 28 \, c^{5} d^{3} e^{2} + 15 \, c^{3} d^{3} e^{2} + 2 \, c d^{3} e^{2}\right)} x^{3} + {\left(9 \, d^{6} e^{2} x^{6} + 54 \, c d^{5} e^{2} x^{5} + 9 \, c^{6} e^{2} + 4 \, c^{4} e^{2} + {\left(135 \, c^{2} d^{4} e^{2} + 4 \, d^{4} e^{2}\right)} x^{4} - c^{2} e^{2} + 4 \, {\left(45 \, c^{3} d^{3} e^{2} + 4 \, c d^{3} e^{2}\right)} x^{3} + {\left(135 \, c^{4} d^{2} e^{2} + 24 \, c^{2} d^{2} e^{2} - d^{2} e^{2}\right)} x^{2} + 2 \, {\left(27 \, c^{5} d e^{2} + 8 \, c^{3} d e^{2} - c d e^{2}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 9 \, {\left(45 \, c^{8} d^{2} e^{2} + 112 \, c^{6} d^{2} e^{2} + 90 \, c^{4} d^{2} e^{2} + 24 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + {\left(36 \, d^{7} e^{2} x^{7} + 252 \, c d^{6} e^{2} x^{6} + 36 \, c^{7} e^{2} + 48 \, c^{5} e^{2} + 12 \, {\left(63 \, c^{2} d^{5} e^{2} + 4 \, d^{5} e^{2}\right)} x^{5} + 13 \, c^{3} e^{2} + 60 \, {\left(21 \, c^{3} d^{4} e^{2} + 4 \, c d^{4} e^{2}\right)} x^{4} + {\left(1260 \, c^{4} d^{3} e^{2} + 480 \, c^{2} d^{3} e^{2} + 13 \, d^{3} e^{2}\right)} x^{3} - 2 \, c e^{2} + 3 \, {\left(252 \, c^{5} d^{2} e^{2} + 160 \, c^{3} d^{2} e^{2} + 13 \, c d^{2} e^{2}\right)} x^{2} + {\left(252 \, c^{6} d e^{2} + 240 \, c^{4} d e^{2} + 39 \, c^{2} d e^{2} - 2 \, d e^{2}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(54 \, d^{8} e^{2} x^{8} + 432 \, c d^{7} e^{2} x^{7} + 54 \, c^{8} e^{2} + 120 \, c^{6} e^{2} + 24 \, {\left(63 \, c^{2} d^{6} e^{2} + 5 \, d^{6} e^{2}\right)} x^{6} + 83 \, c^{4} e^{2} + 144 \, {\left(21 \, c^{3} d^{5} e^{2} + 5 \, c d^{5} e^{2}\right)} x^{5} + {\left(3780 \, c^{4} d^{4} e^{2} + 1800 \, c^{2} d^{4} e^{2} + 83 \, d^{4} e^{2}\right)} x^{4} + 19 \, c^{2} e^{2} + 4 \, {\left(756 \, c^{5} d^{3} e^{2} + 600 \, c^{3} d^{3} e^{2} + 83 \, c d^{3} e^{2}\right)} x^{3} + {\left(1512 \, c^{6} d^{2} e^{2} + 1800 \, c^{4} d^{2} e^{2} + 498 \, c^{2} d^{2} e^{2} + 19 \, d^{2} e^{2}\right)} x^{2} + 2 \, e^{2} + 2 \, {\left(216 \, c^{7} d e^{2} + 360 \, c^{5} d e^{2} + 166 \, c^{3} d e^{2} + 19 \, c d e^{2}\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 18 \, {\left(5 \, c^{9} d e^{2} + 16 \, c^{7} d e^{2} + 18 \, c^{5} d e^{2} + 8 \, c^{3} d e^{2} + c d e^{2}\right)} x + {\left(36 \, d^{9} e^{2} x^{9} + 324 \, c d^{8} e^{2} x^{8} + 36 \, c^{9} e^{2} + 112 \, c^{7} e^{2} + 16 \, {\left(81 \, c^{2} d^{7} e^{2} + 7 \, d^{7} e^{2}\right)} x^{7} + 123 \, c^{5} e^{2} + 112 \, {\left(27 \, c^{3} d^{6} e^{2} + 7 \, c d^{6} e^{2}\right)} x^{6} + 3 \, {\left(1512 \, c^{4} d^{5} e^{2} + 784 \, c^{2} d^{5} e^{2} + 41 \, d^{5} e^{2}\right)} x^{5} + 57 \, c^{3} e^{2} + {\left(4536 \, c^{5} d^{4} e^{2} + 3920 \, c^{3} d^{4} e^{2} + 615 \, c d^{4} e^{2}\right)} x^{4} + {\left(3024 \, c^{6} d^{3} e^{2} + 3920 \, c^{4} d^{3} e^{2} + 1230 \, c^{2} d^{3} e^{2} + 57 \, d^{3} e^{2}\right)} x^{3} + 10 \, c e^{2} + 3 \, {\left(432 \, c^{7} d^{2} e^{2} + 784 \, c^{5} d^{2} e^{2} + 410 \, c^{3} d^{2} e^{2} + 57 \, c d^{2} e^{2}\right)} x^{2} + {\left(324 \, c^{8} d e^{2} + 784 \, c^{6} d e^{2} + 615 \, c^{4} d e^{2} + 171 \, c^{2} d e^{2} + 10 \, d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a b^{2} d^{8} x^{8} + 8 \, a b^{2} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} a b^{2} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} a b^{2} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} a b^{2} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{2} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{4} x^{4} + 4 \, a b^{2} c d^{3} x^{3} + 6 \, a b^{2} c^{2} d^{2} x^{2} + 4 \, a b^{2} c^{3} d x + a b^{2} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(a b^{2} d^{5} x^{5} + 5 \, a b^{2} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} a b^{2} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} a b^{2} x + {\left(c^{5} + c^{3}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{6} x^{6} + 6 \, a b^{2} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} a b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} a b^{2} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{3} d^{8} x^{8} + 8 \, b^{3} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} b^{3} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} b^{3} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} b^{3} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{3} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} b^{3} + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} b^{3} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b^{3} x + {\left(c^{5} + c^{3}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} b^{3} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(b^{3} d^{7} x^{7} + 7 \, b^{3} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} b^{3} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{3} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b^{3} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b^{3} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 4 \, {\left(a b^{2} d^{7} x^{7} + 7 \, a b^{2} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} a b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{2} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} a b^{2} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} a b^{2} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} a b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*((3*a*d^9*e^2 + b*d^9*e^2)*x^9 + 9*(3*a*c*d^8*e^2 + b*c*d^8*e^2)*x^8 + 3*(3*(12*c^2*d^7*e^2 + d^7*e^2)*a + (12*c^2*d^7*e^2 + d^7*e^2)*b)*x^7 + 21*(3*(4*c^3*d^6*e^2 + c*d^6*e^2)*a + (4*c^3*d^6*e^2 + c*d^6*e^2)*b)*x^6 + 3*(3*(42*c^4*d^5*e^2 + 21*c^2*d^5*e^2 + d^5*e^2)*a + (42*c^4*d^5*e^2 + 21*c^2*d^5*e^2 + d^5*e^2)*b)*x^5 + 3*(3*(42*c^5*d^4*e^2 + 35*c^3*d^4*e^2 + 5*c*d^4*e^2)*a + (42*c^5*d^4*e^2 + 35*c^3*d^4*e^2 + 5*c*d^4*e^2)*b)*x^4 + (3*(84*c^6*d^3*e^2 + 105*c^4*d^3*e^2 + 30*c^2*d^3*e^2 + d^3*e^2)*a + (84*c^6*d^3*e^2 + 105*c^4*d^3*e^2 + 30*c^2*d^3*e^2 + d^3*e^2)*b)*x^3 + 3*(3*(12*c^7*d^2*e^2 + 21*c^5*d^2*e^2 + 10*c^3*d^2*e^2 + c*d^2*e^2)*a + (12*c^7*d^2*e^2 + 21*c^5*d^2*e^2 + 10*c^3*d^2*e^2 + c*d^2*e^2)*b)*x^2 + ((3*a*d^6*e^2 + b*d^6*e^2)*x^6 + 6*(3*a*c*d^5*e^2 + b*c*d^5*e^2)*x^5 + ((45*c^2*d^4*e^2 + 4*d^4*e^2)*a + (15*c^2*d^4*e^2 + d^4*e^2)*b)*x^4 + 4*((15*c^3*d^3*e^2 + 4*c*d^3*e^2)*a + (5*c^3*d^3*e^2 + c*d^3*e^2)*b)*x^3 + ((45*c^4*d^2*e^2 + 24*c^2*d^2*e^2 + d^2*e^2)*a + 3*(5*c^4*d^2*e^2 + 2*c^2*d^2*e^2)*b)*x^2 + (3*c^6*e^2 + 4*c^4*e^2 + c^2*e^2)*a + (c^6*e^2 + c^4*e^2)*b + 2*((9*c^5*d*e^2 + 8*c^3*d*e^2 + c*d*e^2)*a + (3*c^5*d*e^2 + 2*c^3*d*e^2)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (3*(3*a*d^7*e^2 + b*d^7*e^2)*x^7 + 21*(3*a*c*d^6*e^2 + b*c*d^6*e^2)*x^6 + ((189*c^2*d^5*e^2 + 17*d^5*e^2)*a + (63*c^2*d^5*e^2 + 5*d^5*e^2)*b)*x^5 + 5*((63*c^3*d^4*e^2 + 17*c*d^4*e^2)*a + (21*c^3*d^4*e^2 + 5*c*d^4*e^2)*b)*x^4 + (5*(63*c^4*d^3*e^2 + 34*c^2*d^3*e^2 + 2*d^3*e^2)*a + (105*c^4*d^3*e^2 + 50*c^2*d^3*e^2 + 2*d^3*e^2)*b)*x^3 + ((189*c^5*d^2*e^2 + 170*c^3*d^2*e^2 + 30*c*d^2*e^2)*a + (63*c^5*d^2*e^2 + 50*c^3*d^2*e^2 + 6*c*d^2*e^2)*b)*x^2 + (9*c^7*e^2 + 17*c^5*e^2 + 10*c^3*e^2 + 2*c*e^2)*a + (3*c^7*e^2 + 5*c^5*e^2 + 2*c^3*e^2)*b + ((63*c^6*d*e^2 + 85*c^4*d*e^2 + 30*c^2*d*e^2 + 2*d*e^2)*a + (21*c^6*d*e^2 + 25*c^4*d*e^2 + 6*c^2*d*e^2)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(c^9*e^2 + 3*c^7*e^2 + 3*c^5*e^2 + c^3*e^2)*a + (c^9*e^2 + 3*c^7*e^2 + 3*c^5*e^2 + c^3*e^2)*b + 3*(3*(3*c^8*d*e^2 + 7*c^6*d*e^2 + 5*c^4*d*e^2 + c^2*d*e^2)*a + (3*c^8*d*e^2 + 7*c^6*d*e^2 + 5*c^4*d*e^2 + c^2*d*e^2)*b)*x + (3*b*d^9*e^2*x^9 + 27*b*c*d^8*e^2*x^8 + 9*(12*c^2*d^7*e^2 + d^7*e^2)*b*x^7 + 63*(4*c^3*d^6*e^2 + c*d^6*e^2)*b*x^6 + 9*(42*c^4*d^5*e^2 + 21*c^2*d^5*e^2 + d^5*e^2)*b*x^5 + 9*(42*c^5*d^4*e^2 + 35*c^3*d^4*e^2 + 5*c*d^4*e^2)*b*x^4 + 3*(84*c^6*d^3*e^2 + 105*c^4*d^3*e^2 + 30*c^2*d^3*e^2 + d^3*e^2)*b*x^3 + 9*(12*c^7*d^2*e^2 + 21*c^5*d^2*e^2 + 10*c^3*d^2*e^2 + c*d^2*e^2)*b*x^2 + 9*(3*c^8*d*e^2 + 7*c^6*d*e^2 + 5*c^4*d*e^2 + c^2*d*e^2)*b*x + (3*b*d^6*e^2*x^6 + 18*b*c*d^5*e^2*x^5 + (45*c^2*d^4*e^2 + 4*d^4*e^2)*b*x^4 + 4*(15*c^3*d^3*e^2 + 4*c*d^3*e^2)*b*x^3 + (45*c^4*d^2*e^2 + 24*c^2*d^2*e^2 + d^2*e^2)*b*x^2 + 2*(9*c^5*d*e^2 + 8*c^3*d*e^2 + c*d*e^2)*b*x + (3*c^6*e^2 + 4*c^4*e^2 + c^2*e^2)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (9*b*d^7*e^2*x^7 + 63*b*c*d^6*e^2*x^6 + (189*c^2*d^5*e^2 + 17*d^5*e^2)*b*x^5 + 5*(63*c^3*d^4*e^2 + 17*c*d^4*e^2)*b*x^4 + 5*(63*c^4*d^3*e^2 + 34*c^2*d^3*e^2 + 2*d^3*e^2)*b*x^3 + (189*c^5*d^2*e^2 + 170*c^3*d^2*e^2 + 30*c*d^2*e^2)*b*x^2 + (63*c^6*d*e^2 + 85*c^4*d*e^2 + 30*c^2*d*e^2 + 2*d*e^2)*b*x + (9*c^7*e^2 + 17*c^5*e^2 + 10*c^3*e^2 + 2*c*e^2)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(c^9*e^2 + 3*c^7*e^2 + 3*c^5*e^2 + c^3*e^2)*b + (9*b*d^8*e^2*x^8 + 72*b*c*d^7*e^2*x^7 + 2*(126*c^2*d^6*e^2 + 11*d^6*e^2)*b*x^6 + 12*(42*c^3*d^5*e^2 + 11*c*d^5*e^2)*b*x^5 + 6*(105*c^4*d^4*e^2 + 55*c^2*d^4*e^2 + 3*d^4*e^2)*b*x^4 + 8*(63*c^5*d^3*e^2 + 55*c^3*d^3*e^2 + 9*c*d^3*e^2)*b*x^3 + (252*c^6*d^2*e^2 + 330*c^4*d^2*e^2 + 108*c^2*d^2*e^2 + 5*d^2*e^2)*b*x^2 + 2*(36*c^7*d*e^2 + 66*c^5*d*e^2 + 36*c^3*d*e^2 + 5*c*d*e^2)*b*x + (9*c^8*e^2 + 22*c^6*e^2 + 18*c^4*e^2 + 5*c^2*e^2)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (3*(3*a*d^8*e^2 + b*d^8*e^2)*x^8 + 24*(3*a*c*d^7*e^2 + b*c*d^7*e^2)*x^7 + (2*(126*c^2*d^6*e^2 + 11*d^6*e^2)*a + 7*(12*c^2*d^6*e^2 + d^6*e^2)*b)*x^6 + 6*(2*(42*c^3*d^5*e^2 + 11*c*d^5*e^2)*a + 7*(4*c^3*d^5*e^2 + c*d^5*e^2)*b)*x^5 + (6*(105*c^4*d^4*e^2 + 55*c^2*d^4*e^2 + 3*d^4*e^2)*a + 5*(42*c^4*d^4*e^2 + 21*c^2*d^4*e^2 + d^4*e^2)*b)*x^4 + 4*(2*(63*c^5*d^3*e^2 + 55*c^3*d^3*e^2 + 9*c*d^3*e^2)*a + (42*c^5*d^3*e^2 + 35*c^3*d^3*e^2 + 5*c*d^3*e^2)*b)*x^3 + ((252*c^6*d^2*e^2 + 330*c^4*d^2*e^2 + 108*c^2*d^2*e^2 + 5*d^2*e^2)*a + (84*c^6*d^2*e^2 + 105*c^4*d^2*e^2 + 30*c^2*d^2*e^2 + d^2*e^2)*b)*x^2 + (9*c^8*e^2 + 22*c^6*e^2 + 18*c^4*e^2 + 5*c^2*e^2)*a + (3*c^8*e^2 + 7*c^6*e^2 + 5*c^4*e^2 + c^2*e^2)*b + 2*((36*c^7*d*e^2 + 66*c^5*d*e^2 + 36*c^3*d*e^2 + 5*c*d*e^2)*a + (12*c^7*d*e^2 + 21*c^5*d*e^2 + 10*c^3*d*e^2 + c*d*e^2)*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a^2*b^2*d^7*x^6 + 6*a^2*b^2*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a^2*b^2*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a^2*b^2*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a^2*b^2 + (b^4*d^7*x^6 + 6*b^4*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*b^4*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*b^4*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*b^4*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*b^4*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*b^4 + (b^4*d^4*x^3 + 3*b^4*c*d^3*x^2 + 3*b^4*c^2*d^2*x + b^4*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b^4*d^5*x^4 + 4*b^4*c*d^4*x^3 + (6*c^2*d^3 + d^3)*b^4*x^2 + 2*(2*c^3*d^2 + c*d^2)*b^4*x + (c^4*d + c^2*d)*b^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^4*d^6*x^5 + 5*b^4*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*b^4*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*b^4*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*b^4*x + (c^5*d + 2*c^3*d + c*d)*b^4)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + (a^2*b^2*d^4*x^3 + 3*a^2*b^2*c*d^3*x^2 + 3*a^2*b^2*c^2*d^2*x + a^2*b^2*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a^2*b^2*d^5*x^4 + 4*a^2*b^2*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 2*(2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^4*d + c^2*d)*a^2*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(a*b^3*d^7*x^6 + 6*a*b^3*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a*b^3*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a*b^3*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a*b^3*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a*b^3*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a*b^3 + (a*b^3*d^4*x^3 + 3*a*b^3*c*d^3*x^2 + 3*a*b^3*c^2*d^2*x + a*b^3*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a*b^3*d^5*x^4 + 4*a*b^3*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a*b^3*x^2 + 2*(2*c^3*d^2 + c*d^2)*a*b^3*x + (c^4*d + c^2*d)*a*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(a*b^3*d^6*x^5 + 5*a*b^3*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a*b^3*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a*b^3*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a*b^3*x + (c^5*d + 2*c^3*d + c*d)*a*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 3*(a^2*b^2*d^6*x^5 + 5*a^2*b^2*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a^2*b^2*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a^2*b^2*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a^2*b^2*x + (c^5*d + 2*c^3*d + c*d)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate(1/2*(9*d^10*e^2*x^10 + 90*c*d^9*e^2*x^9 + 9*c^10*e^2 + 36*c^8*e^2 + 9*(45*c^2*d^8*e^2 + 4*d^8*e^2)*x^8 + 54*c^6*e^2 + 72*(15*c^3*d^7*e^2 + 4*c*d^7*e^2)*x^7 + 18*(105*c^4*d^6*e^2 + 56*c^2*d^6*e^2 + 3*d^6*e^2)*x^6 + 36*c^4*e^2 + 36*(63*c^5*d^5*e^2 + 56*c^3*d^5*e^2 + 9*c*d^5*e^2)*x^5 + 18*(105*c^6*d^4*e^2 + 140*c^4*d^4*e^2 + 45*c^2*d^4*e^2 + 2*d^4*e^2)*x^4 + 9*c^2*e^2 + 72*(15*c^7*d^3*e^2 + 28*c^5*d^3*e^2 + 15*c^3*d^3*e^2 + 2*c*d^3*e^2)*x^3 + (9*d^6*e^2*x^6 + 54*c*d^5*e^2*x^5 + 9*c^6*e^2 + 4*c^4*e^2 + (135*c^2*d^4*e^2 + 4*d^4*e^2)*x^4 - c^2*e^2 + 4*(45*c^3*d^3*e^2 + 4*c*d^3*e^2)*x^3 + (135*c^4*d^2*e^2 + 24*c^2*d^2*e^2 - d^2*e^2)*x^2 + 2*(27*c^5*d*e^2 + 8*c^3*d*e^2 - c*d*e^2)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 9*(45*c^8*d^2*e^2 + 112*c^6*d^2*e^2 + 90*c^4*d^2*e^2 + 24*c^2*d^2*e^2 + d^2*e^2)*x^2 + (36*d^7*e^2*x^7 + 252*c*d^6*e^2*x^6 + 36*c^7*e^2 + 48*c^5*e^2 + 12*(63*c^2*d^5*e^2 + 4*d^5*e^2)*x^5 + 13*c^3*e^2 + 60*(21*c^3*d^4*e^2 + 4*c*d^4*e^2)*x^4 + (1260*c^4*d^3*e^2 + 480*c^2*d^3*e^2 + 13*d^3*e^2)*x^3 - 2*c*e^2 + 3*(252*c^5*d^2*e^2 + 160*c^3*d^2*e^2 + 13*c*d^2*e^2)*x^2 + (252*c^6*d*e^2 + 240*c^4*d*e^2 + 39*c^2*d*e^2 - 2*d*e^2)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (54*d^8*e^2*x^8 + 432*c*d^7*e^2*x^7 + 54*c^8*e^2 + 120*c^6*e^2 + 24*(63*c^2*d^6*e^2 + 5*d^6*e^2)*x^6 + 83*c^4*e^2 + 144*(21*c^3*d^5*e^2 + 5*c*d^5*e^2)*x^5 + (3780*c^4*d^4*e^2 + 1800*c^2*d^4*e^2 + 83*d^4*e^2)*x^4 + 19*c^2*e^2 + 4*(756*c^5*d^3*e^2 + 600*c^3*d^3*e^2 + 83*c*d^3*e^2)*x^3 + (1512*c^6*d^2*e^2 + 1800*c^4*d^2*e^2 + 498*c^2*d^2*e^2 + 19*d^2*e^2)*x^2 + 2*e^2 + 2*(216*c^7*d*e^2 + 360*c^5*d*e^2 + 166*c^3*d*e^2 + 19*c*d*e^2)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 18*(5*c^9*d*e^2 + 16*c^7*d*e^2 + 18*c^5*d*e^2 + 8*c^3*d*e^2 + c*d*e^2)*x + (36*d^9*e^2*x^9 + 324*c*d^8*e^2*x^8 + 36*c^9*e^2 + 112*c^7*e^2 + 16*(81*c^2*d^7*e^2 + 7*d^7*e^2)*x^7 + 123*c^5*e^2 + 112*(27*c^3*d^6*e^2 + 7*c*d^6*e^2)*x^6 + 3*(1512*c^4*d^5*e^2 + 784*c^2*d^5*e^2 + 41*d^5*e^2)*x^5 + 57*c^3*e^2 + (4536*c^5*d^4*e^2 + 3920*c^3*d^4*e^2 + 615*c*d^4*e^2)*x^4 + (3024*c^6*d^3*e^2 + 3920*c^4*d^3*e^2 + 1230*c^2*d^3*e^2 + 57*d^3*e^2)*x^3 + 10*c*e^2 + 3*(432*c^7*d^2*e^2 + 784*c^5*d^2*e^2 + 410*c^3*d^2*e^2 + 57*c*d^2*e^2)*x^2 + (324*c^8*d*e^2 + 784*c^6*d*e^2 + 615*c^4*d*e^2 + 171*c^2*d*e^2 + 10*d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b^2*d^8*x^8 + 8*a*b^2*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*a*b^2*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*a*b^2*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*a*b^2*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*a*b^2*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*a*b^2*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*a*b^2*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*a*b^2 + (a*b^2*d^4*x^4 + 4*a*b^2*c*d^3*x^3 + 6*a*b^2*c^2*d^2*x^2 + 4*a*b^2*c^3*d*x + a*b^2*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(a*b^2*d^5*x^5 + 5*a*b^2*c*d^4*x^4 + (10*c^2*d^3 + d^3)*a*b^2*x^3 + (10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (5*c^4*d + 3*c^2*d)*a*b^2*x + (c^5 + c^3)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(a*b^2*d^6*x^6 + 6*a*b^2*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*a*b^2*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*a*b^2*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*a*b^2*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*a*b^2*x + (c^6 + 2*c^4 + c^2)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^3*d^8*x^8 + 8*b^3*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*b^3*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*b^3*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*b^3*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*b^3*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*b^3*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*b^3*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*b^3 + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^3*d^5*x^5 + 5*b^3*c*d^4*x^4 + (10*c^2*d^3 + d^3)*b^3*x^3 + (10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (5*c^4*d + 3*c^2*d)*b^3*x + (c^5 + c^3)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(b^3*d^6*x^6 + 6*b^3*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*b^3*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*b^3*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*b^3*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*b^3*x + (c^6 + 2*c^4 + c^2)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(b^3*d^7*x^7 + 7*b^3*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*b^3*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*b^3*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b^3*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b^3*x + (c^7 + 3*c^5 + 3*c^3 + c)*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 4*(a*b^2*d^7*x^7 + 7*a*b^2*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*a*b^2*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*a*b^2*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*a*b^2*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*a*b^2*x + (c^7 + 3*c^5 + 3*c^3 + c)*a*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
171,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, a d^{8} e + b d^{8} e\right)} x^{8} + 8 \, {\left(2 \, a c d^{7} e + b c d^{7} e\right)} x^{7} + {\left(2 \, {\left(28 \, c^{2} d^{6} e + 3 \, d^{6} e\right)} a + {\left(28 \, c^{2} d^{6} e + 3 \, d^{6} e\right)} b\right)} x^{6} + 2 \, {\left(2 \, {\left(28 \, c^{3} d^{5} e + 9 \, c d^{5} e\right)} a + {\left(28 \, c^{3} d^{5} e + 9 \, c d^{5} e\right)} b\right)} x^{5} + {\left(2 \, {\left(70 \, c^{4} d^{4} e + 45 \, c^{2} d^{4} e + 3 \, d^{4} e\right)} a + {\left(70 \, c^{4} d^{4} e + 45 \, c^{2} d^{4} e + 3 \, d^{4} e\right)} b\right)} x^{4} + 4 \, {\left(2 \, {\left(14 \, c^{5} d^{3} e + 15 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} a + {\left(14 \, c^{5} d^{3} e + 15 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} b\right)} x^{3} + {\left(2 \, {\left(28 \, c^{6} d^{2} e + 45 \, c^{4} d^{2} e + 18 \, c^{2} d^{2} e + d^{2} e\right)} a + {\left(28 \, c^{6} d^{2} e + 45 \, c^{4} d^{2} e + 18 \, c^{2} d^{2} e + d^{2} e\right)} b\right)} x^{2} + {\left({\left(2 \, a d^{5} e + b d^{5} e\right)} x^{5} + 5 \, {\left(2 \, a c d^{4} e + b c d^{4} e\right)} x^{4} + {\left(2 \, {\left(10 \, c^{2} d^{3} e + d^{3} e\right)} a + {\left(10 \, c^{2} d^{3} e + d^{3} e\right)} b\right)} x^{3} + {\left(2 \, {\left(10 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} a + {\left(10 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} b\right)} x^{2} + 2 \, {\left(c^{5} e + c^{3} e\right)} a + {\left(c^{5} e + c^{3} e\right)} b + {\left(2 \, {\left(5 \, c^{4} d e + 3 \, c^{2} d e\right)} a + {\left(5 \, c^{4} d e + 3 \, c^{2} d e\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, {\left(2 \, a d^{6} e + b d^{6} e\right)} x^{6} + 18 \, {\left(2 \, a c d^{5} e + b c d^{5} e\right)} x^{5} + 5 \, {\left(2 \, {\left(9 \, c^{2} d^{4} e + d^{4} e\right)} a + {\left(9 \, c^{2} d^{4} e + d^{4} e\right)} b\right)} x^{4} + 20 \, {\left(2 \, {\left(3 \, c^{3} d^{3} e + c d^{3} e\right)} a + {\left(3 \, c^{3} d^{3} e + c d^{3} e\right)} b\right)} x^{3} + {\left(5 \, {\left(18 \, c^{4} d^{2} e + 12 \, c^{2} d^{2} e + d^{2} e\right)} a + {\left(45 \, c^{4} d^{2} e + 30 \, c^{2} d^{2} e + 2 \, d^{2} e\right)} b\right)} x^{2} + {\left(6 \, c^{6} e + 10 \, c^{4} e + 5 \, c^{2} e + e\right)} a + {\left(3 \, c^{6} e + 5 \, c^{4} e + 2 \, c^{2} e\right)} b + 2 \, {\left({\left(18 \, c^{5} d e + 20 \, c^{3} d e + 5 \, c d e\right)} a + {\left(9 \, c^{5} d e + 10 \, c^{3} d e + 2 \, c d e\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(c^{8} e + 3 \, c^{6} e + 3 \, c^{4} e + c^{2} e\right)} a + {\left(c^{8} e + 3 \, c^{6} e + 3 \, c^{4} e + c^{2} e\right)} b + 2 \, {\left(2 \, {\left(4 \, c^{7} d e + 9 \, c^{5} d e + 6 \, c^{3} d e + c d e\right)} a + {\left(4 \, c^{7} d e + 9 \, c^{5} d e + 6 \, c^{3} d e + c d e\right)} b\right)} x + {\left(2 \, b d^{8} e x^{8} + 16 \, b c d^{7} e x^{7} + 2 \, {\left(28 \, c^{2} d^{6} e + 3 \, d^{6} e\right)} b x^{6} + 4 \, {\left(28 \, c^{3} d^{5} e + 9 \, c d^{5} e\right)} b x^{5} + 2 \, {\left(70 \, c^{4} d^{4} e + 45 \, c^{2} d^{4} e + 3 \, d^{4} e\right)} b x^{4} + 8 \, {\left(14 \, c^{5} d^{3} e + 15 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} b x^{3} + 2 \, {\left(28 \, c^{6} d^{2} e + 45 \, c^{4} d^{2} e + 18 \, c^{2} d^{2} e + d^{2} e\right)} b x^{2} + 4 \, {\left(4 \, c^{7} d e + 9 \, c^{5} d e + 6 \, c^{3} d e + c d e\right)} b x + 2 \, {\left(b d^{5} e x^{5} + 5 \, b c d^{4} e x^{4} + {\left(10 \, c^{2} d^{3} e + d^{3} e\right)} b x^{3} + {\left(10 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} b x^{2} + {\left(5 \, c^{4} d e + 3 \, c^{2} d e\right)} b x + {\left(c^{5} e + c^{3} e\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(6 \, b d^{6} e x^{6} + 36 \, b c d^{5} e x^{5} + 10 \, {\left(9 \, c^{2} d^{4} e + d^{4} e\right)} b x^{4} + 40 \, {\left(3 \, c^{3} d^{3} e + c d^{3} e\right)} b x^{3} + 5 \, {\left(18 \, c^{4} d^{2} e + 12 \, c^{2} d^{2} e + d^{2} e\right)} b x^{2} + 2 \, {\left(18 \, c^{5} d e + 20 \, c^{3} d e + 5 \, c d e\right)} b x + {\left(6 \, c^{6} e + 10 \, c^{4} e + 5 \, c^{2} e + e\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(c^{8} e + 3 \, c^{6} e + 3 \, c^{4} e + c^{2} e\right)} b + {\left(6 \, b d^{7} e x^{7} + 42 \, b c d^{6} e x^{6} + 14 \, {\left(9 \, c^{2} d^{5} e + d^{5} e\right)} b x^{5} + 70 \, {\left(3 \, c^{3} d^{4} e + c d^{4} e\right)} b x^{4} + {\left(210 \, c^{4} d^{3} e + 140 \, c^{2} d^{3} e + 11 \, d^{3} e\right)} b x^{3} + {\left(126 \, c^{5} d^{2} e + 140 \, c^{3} d^{2} e + 33 \, c d^{2} e\right)} b x^{2} + {\left(42 \, c^{6} d e + 70 \, c^{4} d e + 33 \, c^{2} d e + 3 \, d e\right)} b x + {\left(6 \, c^{7} e + 14 \, c^{5} e + 11 \, c^{3} e + 3 \, c e\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(3 \, {\left(2 \, a d^{7} e + b d^{7} e\right)} x^{7} + 21 \, {\left(2 \, a c d^{6} e + b c d^{6} e\right)} x^{6} + 7 \, {\left(2 \, {\left(9 \, c^{2} d^{5} e + d^{5} e\right)} a + {\left(9 \, c^{2} d^{5} e + d^{5} e\right)} b\right)} x^{5} + 35 \, {\left(2 \, {\left(3 \, c^{3} d^{4} e + c d^{4} e\right)} a + {\left(3 \, c^{3} d^{4} e + c d^{4} e\right)} b\right)} x^{4} + {\left({\left(210 \, c^{4} d^{3} e + 140 \, c^{2} d^{3} e + 11 \, d^{3} e\right)} a + 5 \, {\left(21 \, c^{4} d^{3} e + 14 \, c^{2} d^{3} e + d^{3} e\right)} b\right)} x^{3} + {\left({\left(126 \, c^{5} d^{2} e + 140 \, c^{3} d^{2} e + 33 \, c d^{2} e\right)} a + {\left(63 \, c^{5} d^{2} e + 70 \, c^{3} d^{2} e + 15 \, c d^{2} e\right)} b\right)} x^{2} + {\left(6 \, c^{7} e + 14 \, c^{5} e + 11 \, c^{3} e + 3 \, c e\right)} a + {\left(3 \, c^{7} e + 7 \, c^{5} e + 5 \, c^{3} e + c e\right)} b + {\left({\left(42 \, c^{6} d e + 70 \, c^{4} d e + 33 \, c^{2} d e + 3 \, d e\right)} a + {\left(21 \, c^{6} d e + 35 \, c^{4} d e + 15 \, c^{2} d e + d e\right)} b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a^{2} b^{2} d^{7} x^{6} + 6 \, a^{2} b^{2} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a^{2} b^{2} + {\left(b^{4} d^{7} x^{6} + 6 \, b^{4} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} b^{4} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{4} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} b^{4} + {\left(b^{4} d^{4} x^{3} + 3 \, b^{4} c d^{3} x^{2} + 3 \, b^{4} c^{2} d^{2} x + b^{4} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{5} x^{4} + 4 \, b^{4} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{4} d + c^{2} d\right)} b^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(b^{4} d^{6} x^{5} + 5 \, b^{4} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} b^{4} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{4} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} b^{4} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} b^{4}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{3} + 3 \, a^{2} b^{2} c d^{3} x^{2} + 3 \, a^{2} b^{2} c^{2} d^{2} x + a^{2} b^{2} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{5} x^{4} + 4 \, a^{2} b^{2} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{4} d + c^{2} d\right)} a^{2} b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(a b^{3} d^{7} x^{6} + 6 \, a b^{3} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{3} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a b^{3} + {\left(a b^{3} d^{4} x^{3} + 3 \, a b^{3} c d^{3} x^{2} + 3 \, a b^{3} c^{2} d^{2} x + a b^{3} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{5} x^{4} + 4 \, a b^{3} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{4} d + c^{2} d\right)} a b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(a b^{3} d^{6} x^{5} + 5 \, a b^{3} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a b^{3} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{3} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a b^{3} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 3 \, {\left(a^{2} b^{2} d^{6} x^{5} + 5 \, a^{2} b^{2} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a^{2} b^{2} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a^{2} b^{2} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}} + \int \frac{4 \, d^{9} e x^{9} + 36 \, c d^{8} e x^{8} + 4 \, c^{9} e + 16 \, c^{7} e + 16 \, {\left(9 \, c^{2} d^{7} e + d^{7} e\right)} x^{7} + 112 \, {\left(3 \, c^{3} d^{6} e + c d^{6} e\right)} x^{6} + 24 \, c^{5} e + 24 \, {\left(21 \, c^{4} d^{5} e + 14 \, c^{2} d^{5} e + d^{5} e\right)} x^{5} + 8 \, {\left(63 \, c^{5} d^{4} e + 70 \, c^{3} d^{4} e + 15 \, c d^{4} e\right)} x^{4} + 16 \, c^{3} e + 16 \, {\left(21 \, c^{6} d^{3} e + 35 \, c^{4} d^{3} e + 15 \, c^{2} d^{3} e + d^{3} e\right)} x^{3} + 4 \, {\left(d^{5} e x^{5} + 5 \, c d^{4} e x^{4} + 10 \, c^{2} d^{3} e x^{3} + 10 \, c^{3} d^{2} e x^{2} + 5 \, c^{4} d e x + c^{5} e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 48 \, {\left(3 \, c^{7} d^{2} e + 7 \, c^{5} d^{2} e + 5 \, c^{3} d^{2} e + c d^{2} e\right)} x^{2} + {\left(16 \, d^{6} e x^{6} + 96 \, c d^{5} e x^{5} + 16 \, c^{6} e + 16 \, c^{4} e + 16 \, {\left(15 \, c^{2} d^{4} e + d^{4} e\right)} x^{4} + 64 \, {\left(5 \, c^{3} d^{3} e + c d^{3} e\right)} x^{3} + 48 \, {\left(5 \, c^{4} d^{2} e + 2 \, c^{2} d^{2} e\right)} x^{2} + 32 \, {\left(3 \, c^{5} d e + 2 \, c^{3} d e\right)} x - 3 \, e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 24 \, {\left(d^{7} e x^{7} + 7 \, c d^{6} e x^{6} + c^{7} e + 2 \, c^{5} e + {\left(21 \, c^{2} d^{5} e + 2 \, d^{5} e\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e + 2 \, c d^{4} e\right)} x^{4} + c^{3} e + {\left(35 \, c^{4} d^{3} e + 20 \, c^{2} d^{3} e + d^{3} e\right)} x^{3} + {\left(21 \, c^{5} d^{2} e + 20 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} x^{2} + {\left(7 \, c^{6} d e + 10 \, c^{4} d e + 3 \, c^{2} d e\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, c e + 4 \, {\left(9 \, c^{8} d e + 28 \, c^{6} d e + 30 \, c^{4} d e + 12 \, c^{2} d e + d e\right)} x + {\left(16 \, d^{8} e x^{8} + 128 \, c d^{7} e x^{7} + 16 \, c^{8} e + 48 \, c^{6} e + 16 \, {\left(28 \, c^{2} d^{6} e + 3 \, d^{6} e\right)} x^{6} + 32 \, {\left(28 \, c^{3} d^{5} e + 9 \, c d^{5} e\right)} x^{5} + 48 \, c^{4} e + 16 \, {\left(70 \, c^{4} d^{4} e + 45 \, c^{2} d^{4} e + 3 \, d^{4} e\right)} x^{4} + 64 \, {\left(14 \, c^{5} d^{3} e + 15 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} x^{3} + 19 \, c^{2} e + {\left(448 \, c^{6} d^{2} e + 720 \, c^{4} d^{2} e + 288 \, c^{2} d^{2} e + 19 \, d^{2} e\right)} x^{2} + 2 \, {\left(64 \, c^{7} d e + 144 \, c^{5} d e + 96 \, c^{3} d e + 19 \, c d e\right)} x + 3 \, e\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a b^{2} d^{8} x^{8} + 8 \, a b^{2} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} a b^{2} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} a b^{2} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} a b^{2} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{2} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{4} x^{4} + 4 \, a b^{2} c d^{3} x^{3} + 6 \, a b^{2} c^{2} d^{2} x^{2} + 4 \, a b^{2} c^{3} d x + a b^{2} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(a b^{2} d^{5} x^{5} + 5 \, a b^{2} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} a b^{2} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} a b^{2} x + {\left(c^{5} + c^{3}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{6} x^{6} + 6 \, a b^{2} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} a b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} a b^{2} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{3} d^{8} x^{8} + 8 \, b^{3} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} b^{3} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} b^{3} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} b^{3} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{3} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} b^{3} + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} b^{3} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b^{3} x + {\left(c^{5} + c^{3}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} b^{3} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(b^{3} d^{7} x^{7} + 7 \, b^{3} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} b^{3} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{3} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b^{3} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b^{3} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 4 \, {\left(a b^{2} d^{7} x^{7} + 7 \, a b^{2} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} a b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{2} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} a b^{2} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} a b^{2} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} a b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*((2*a*d^8*e + b*d^8*e)*x^8 + 8*(2*a*c*d^7*e + b*c*d^7*e)*x^7 + (2*(28*c^2*d^6*e + 3*d^6*e)*a + (28*c^2*d^6*e + 3*d^6*e)*b)*x^6 + 2*(2*(28*c^3*d^5*e + 9*c*d^5*e)*a + (28*c^3*d^5*e + 9*c*d^5*e)*b)*x^5 + (2*(70*c^4*d^4*e + 45*c^2*d^4*e + 3*d^4*e)*a + (70*c^4*d^4*e + 45*c^2*d^4*e + 3*d^4*e)*b)*x^4 + 4*(2*(14*c^5*d^3*e + 15*c^3*d^3*e + 3*c*d^3*e)*a + (14*c^5*d^3*e + 15*c^3*d^3*e + 3*c*d^3*e)*b)*x^3 + (2*(28*c^6*d^2*e + 45*c^4*d^2*e + 18*c^2*d^2*e + d^2*e)*a + (28*c^6*d^2*e + 45*c^4*d^2*e + 18*c^2*d^2*e + d^2*e)*b)*x^2 + ((2*a*d^5*e + b*d^5*e)*x^5 + 5*(2*a*c*d^4*e + b*c*d^4*e)*x^4 + (2*(10*c^2*d^3*e + d^3*e)*a + (10*c^2*d^3*e + d^3*e)*b)*x^3 + (2*(10*c^3*d^2*e + 3*c*d^2*e)*a + (10*c^3*d^2*e + 3*c*d^2*e)*b)*x^2 + 2*(c^5*e + c^3*e)*a + (c^5*e + c^3*e)*b + (2*(5*c^4*d*e + 3*c^2*d*e)*a + (5*c^4*d*e + 3*c^2*d*e)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (3*(2*a*d^6*e + b*d^6*e)*x^6 + 18*(2*a*c*d^5*e + b*c*d^5*e)*x^5 + 5*(2*(9*c^2*d^4*e + d^4*e)*a + (9*c^2*d^4*e + d^4*e)*b)*x^4 + 20*(2*(3*c^3*d^3*e + c*d^3*e)*a + (3*c^3*d^3*e + c*d^3*e)*b)*x^3 + (5*(18*c^4*d^2*e + 12*c^2*d^2*e + d^2*e)*a + (45*c^4*d^2*e + 30*c^2*d^2*e + 2*d^2*e)*b)*x^2 + (6*c^6*e + 10*c^4*e + 5*c^2*e + e)*a + (3*c^6*e + 5*c^4*e + 2*c^2*e)*b + 2*((18*c^5*d*e + 20*c^3*d*e + 5*c*d*e)*a + (9*c^5*d*e + 10*c^3*d*e + 2*c*d*e)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(c^8*e + 3*c^6*e + 3*c^4*e + c^2*e)*a + (c^8*e + 3*c^6*e + 3*c^4*e + c^2*e)*b + 2*(2*(4*c^7*d*e + 9*c^5*d*e + 6*c^3*d*e + c*d*e)*a + (4*c^7*d*e + 9*c^5*d*e + 6*c^3*d*e + c*d*e)*b)*x + (2*b*d^8*e*x^8 + 16*b*c*d^7*e*x^7 + 2*(28*c^2*d^6*e + 3*d^6*e)*b*x^6 + 4*(28*c^3*d^5*e + 9*c*d^5*e)*b*x^5 + 2*(70*c^4*d^4*e + 45*c^2*d^4*e + 3*d^4*e)*b*x^4 + 8*(14*c^5*d^3*e + 15*c^3*d^3*e + 3*c*d^3*e)*b*x^3 + 2*(28*c^6*d^2*e + 45*c^4*d^2*e + 18*c^2*d^2*e + d^2*e)*b*x^2 + 4*(4*c^7*d*e + 9*c^5*d*e + 6*c^3*d*e + c*d*e)*b*x + 2*(b*d^5*e*x^5 + 5*b*c*d^4*e*x^4 + (10*c^2*d^3*e + d^3*e)*b*x^3 + (10*c^3*d^2*e + 3*c*d^2*e)*b*x^2 + (5*c^4*d*e + 3*c^2*d*e)*b*x + (c^5*e + c^3*e)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (6*b*d^6*e*x^6 + 36*b*c*d^5*e*x^5 + 10*(9*c^2*d^4*e + d^4*e)*b*x^4 + 40*(3*c^3*d^3*e + c*d^3*e)*b*x^3 + 5*(18*c^4*d^2*e + 12*c^2*d^2*e + d^2*e)*b*x^2 + 2*(18*c^5*d*e + 20*c^3*d*e + 5*c*d*e)*b*x + (6*c^6*e + 10*c^4*e + 5*c^2*e + e)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(c^8*e + 3*c^6*e + 3*c^4*e + c^2*e)*b + (6*b*d^7*e*x^7 + 42*b*c*d^6*e*x^6 + 14*(9*c^2*d^5*e + d^5*e)*b*x^5 + 70*(3*c^3*d^4*e + c*d^4*e)*b*x^4 + (210*c^4*d^3*e + 140*c^2*d^3*e + 11*d^3*e)*b*x^3 + (126*c^5*d^2*e + 140*c^3*d^2*e + 33*c*d^2*e)*b*x^2 + (42*c^6*d*e + 70*c^4*d*e + 33*c^2*d*e + 3*d*e)*b*x + (6*c^7*e + 14*c^5*e + 11*c^3*e + 3*c*e)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (3*(2*a*d^7*e + b*d^7*e)*x^7 + 21*(2*a*c*d^6*e + b*c*d^6*e)*x^6 + 7*(2*(9*c^2*d^5*e + d^5*e)*a + (9*c^2*d^5*e + d^5*e)*b)*x^5 + 35*(2*(3*c^3*d^4*e + c*d^4*e)*a + (3*c^3*d^4*e + c*d^4*e)*b)*x^4 + ((210*c^4*d^3*e + 140*c^2*d^3*e + 11*d^3*e)*a + 5*(21*c^4*d^3*e + 14*c^2*d^3*e + d^3*e)*b)*x^3 + ((126*c^5*d^2*e + 140*c^3*d^2*e + 33*c*d^2*e)*a + (63*c^5*d^2*e + 70*c^3*d^2*e + 15*c*d^2*e)*b)*x^2 + (6*c^7*e + 14*c^5*e + 11*c^3*e + 3*c*e)*a + (3*c^7*e + 7*c^5*e + 5*c^3*e + c*e)*b + ((42*c^6*d*e + 70*c^4*d*e + 33*c^2*d*e + 3*d*e)*a + (21*c^6*d*e + 35*c^4*d*e + 15*c^2*d*e + d*e)*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a^2*b^2*d^7*x^6 + 6*a^2*b^2*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a^2*b^2*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a^2*b^2*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a^2*b^2 + (b^4*d^7*x^6 + 6*b^4*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*b^4*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*b^4*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*b^4*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*b^4*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*b^4 + (b^4*d^4*x^3 + 3*b^4*c*d^3*x^2 + 3*b^4*c^2*d^2*x + b^4*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b^4*d^5*x^4 + 4*b^4*c*d^4*x^3 + (6*c^2*d^3 + d^3)*b^4*x^2 + 2*(2*c^3*d^2 + c*d^2)*b^4*x + (c^4*d + c^2*d)*b^4)*(d^2*x^2 + 2*c*d*x 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c^2*d)*a*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(a*b^3*d^6*x^5 + 5*a*b^3*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a*b^3*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a*b^3*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a*b^3*x + (c^5*d + 2*c^3*d + c*d)*a*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 3*(a^2*b^2*d^6*x^5 + 5*a^2*b^2*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a^2*b^2*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a^2*b^2*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a^2*b^2*x + (c^5*d + 2*c^3*d + c*d)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate(1/2*(4*d^9*e*x^9 + 36*c*d^8*e*x^8 + 4*c^9*e + 16*c^7*e + 16*(9*c^2*d^7*e + d^7*e)*x^7 + 112*(3*c^3*d^6*e + c*d^6*e)*x^6 + 24*c^5*e + 24*(21*c^4*d^5*e + 14*c^2*d^5*e + d^5*e)*x^5 + 8*(63*c^5*d^4*e + 70*c^3*d^4*e + 15*c*d^4*e)*x^4 + 16*c^3*e + 16*(21*c^6*d^3*e + 35*c^4*d^3*e + 15*c^2*d^3*e + d^3*e)*x^3 + 4*(d^5*e*x^5 + 5*c*d^4*e*x^4 + 10*c^2*d^3*e*x^3 + 10*c^3*d^2*e*x^2 + 5*c^4*d*e*x + c^5*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 48*(3*c^7*d^2*e + 7*c^5*d^2*e + 5*c^3*d^2*e + c*d^2*e)*x^2 + (16*d^6*e*x^6 + 96*c*d^5*e*x^5 + 16*c^6*e + 16*c^4*e + 16*(15*c^2*d^4*e + d^4*e)*x^4 + 64*(5*c^3*d^3*e + c*d^3*e)*x^3 + 48*(5*c^4*d^2*e + 2*c^2*d^2*e)*x^2 + 32*(3*c^5*d*e + 2*c^3*d*e)*x - 3*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 24*(d^7*e*x^7 + 7*c*d^6*e*x^6 + c^7*e + 2*c^5*e + (21*c^2*d^5*e + 2*d^5*e)*x^5 + 5*(7*c^3*d^4*e + 2*c*d^4*e)*x^4 + c^3*e + (35*c^4*d^3*e + 20*c^2*d^3*e + d^3*e)*x^3 + (21*c^5*d^2*e + 20*c^3*d^2*e + 3*c*d^2*e)*x^2 + (7*c^6*d*e + 10*c^4*d*e + 3*c^2*d*e)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*c*e + 4*(9*c^8*d*e + 28*c^6*d*e + 30*c^4*d*e + 12*c^2*d*e + d*e)*x + (16*d^8*e*x^8 + 128*c*d^7*e*x^7 + 16*c^8*e + 48*c^6*e + 16*(28*c^2*d^6*e + 3*d^6*e)*x^6 + 32*(28*c^3*d^5*e + 9*c*d^5*e)*x^5 + 48*c^4*e + 16*(70*c^4*d^4*e + 45*c^2*d^4*e + 3*d^4*e)*x^4 + 64*(14*c^5*d^3*e + 15*c^3*d^3*e + 3*c*d^3*e)*x^3 + 19*c^2*e + (448*c^6*d^2*e + 720*c^4*d^2*e + 288*c^2*d^2*e + 19*d^2*e)*x^2 + 2*(64*c^7*d*e + 144*c^5*d*e + 96*c^3*d*e + 19*c*d*e)*x + 3*e)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b^2*d^8*x^8 + 8*a*b^2*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*a*b^2*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*a*b^2*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*a*b^2*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*a*b^2*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*a*b^2*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*a*b^2*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*a*b^2 + (a*b^2*d^4*x^4 + 4*a*b^2*c*d^3*x^3 + 6*a*b^2*c^2*d^2*x^2 + 4*a*b^2*c^3*d*x + a*b^2*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(a*b^2*d^5*x^5 + 5*a*b^2*c*d^4*x^4 + (10*c^2*d^3 + d^3)*a*b^2*x^3 + (10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (5*c^4*d + 3*c^2*d)*a*b^2*x + (c^5 + c^3)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(a*b^2*d^6*x^6 + 6*a*b^2*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*a*b^2*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*a*b^2*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*a*b^2*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*a*b^2*x + (c^6 + 2*c^4 + c^2)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^3*d^8*x^8 + 8*b^3*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*b^3*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*b^3*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*b^3*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*b^3*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*b^3*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*b^3*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*b^3 + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^3*d^5*x^5 + 5*b^3*c*d^4*x^4 + (10*c^2*d^3 + d^3)*b^3*x^3 + (10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (5*c^4*d + 3*c^2*d)*b^3*x + (c^5 + c^3)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(b^3*d^6*x^6 + 6*b^3*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*b^3*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*b^3*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*b^3*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*b^3*x + (c^6 + 2*c^4 + c^2)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(b^3*d^7*x^7 + 7*b^3*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*b^3*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*b^3*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b^3*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b^3*x + (c^7 + 3*c^5 + 3*c^3 + c)*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 4*(a*b^2*d^7*x^7 + 7*a*b^2*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*a*b^2*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*a*b^2*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*a*b^2*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*a*b^2*x + (c^7 + 3*c^5 + 3*c^3 + c)*a*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
172,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(a d^{7} + b d^{7}\right)} x^{7} + 7 \, {\left(a c d^{6} + b c d^{6}\right)} x^{6} + 3 \, {\left({\left(7 \, c^{2} d^{5} + d^{5}\right)} a + {\left(7 \, c^{2} d^{5} + d^{5}\right)} b\right)} x^{5} + 5 \, {\left({\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a + {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b\right)} x^{4} + {\left({\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} a + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b\right)} x^{3} + 3 \, {\left({\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a + {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b\right)} x^{2} + {\left({\left(a d^{4} + b d^{4}\right)} x^{4} + 4 \, {\left(a c d^{3} + b c d^{3}\right)} x^{3} + {\left(6 \, a c^{2} d^{2} + {\left(6 \, c^{2} d^{2} + d^{2}\right)} b\right)} x^{2} + {\left(c^{4} - 1\right)} a + {\left(c^{4} + c^{2}\right)} b + 2 \, {\left(2 \, a c^{3} d + {\left(2 \, c^{3} d + c d\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, {\left(a d^{5} + b d^{5}\right)} x^{5} + 15 \, {\left(a c d^{4} + b c d^{4}\right)} x^{4} + {\left(3 \, {\left(10 \, c^{2} d^{3} + d^{3}\right)} a + 5 \, {\left(6 \, c^{2} d^{3} + d^{3}\right)} b\right)} x^{3} + 3 \, {\left({\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a + 5 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} b\right)} x^{2} + 3 \, {\left(c^{5} + c^{3}\right)} a + {\left(3 \, c^{5} + 5 \, c^{3} + 2 \, c\right)} b + {\left(3 \, {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} a + {\left(15 \, c^{4} d + 15 \, c^{2} d + 2 \, d\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} a + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b + {\left({\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} a + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b\right)} x + {\left(b d^{7} x^{7} + 7 \, b c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} b x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b x + {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + {\left(c^{4} - 1\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} b x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b x + {\left(c^{5} + c^{3}\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b + {\left(3 \, b d^{6} x^{6} + 18 \, b c d^{5} x^{5} + 3 \, {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} b x^{4} + 12 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} b x^{3} + {\left(45 \, c^{4} d^{2} + 36 \, c^{2} d^{2} + 4 \, d^{2}\right)} b x^{2} + 2 \, {\left(9 \, c^{5} d + 12 \, c^{3} d + 4 \, c d\right)} b x + {\left(3 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(3 \, {\left(a d^{6} + b d^{6}\right)} x^{6} + 18 \, {\left(a c d^{5} + b c d^{5}\right)} x^{5} + {\left(3 \, {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} a + {\left(45 \, c^{2} d^{4} + 7 \, d^{4}\right)} b\right)} x^{4} + 4 \, {\left(3 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} a + {\left(15 \, c^{3} d^{3} + 7 \, c d^{3}\right)} b\right)} x^{3} + {\left({\left(45 \, c^{4} d^{2} + 36 \, c^{2} d^{2} + 4 \, d^{2}\right)} a + {\left(45 \, c^{4} d^{2} + 42 \, c^{2} d^{2} + 5 \, d^{2}\right)} b\right)} x^{2} + {\left(3 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} a + {\left(3 \, c^{6} + 7 \, c^{4} + 5 \, c^{2} + 1\right)} b + 2 \, {\left({\left(9 \, c^{5} d + 12 \, c^{3} d + 4 \, c d\right)} a + {\left(9 \, c^{5} d + 14 \, c^{3} d + 5 \, c d\right)} b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a^{2} b^{2} d^{7} x^{6} + 6 \, a^{2} b^{2} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a^{2} b^{2} + {\left(b^{4} d^{7} x^{6} + 6 \, b^{4} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} b^{4} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{4} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} b^{4} + {\left(b^{4} d^{4} x^{3} + 3 \, b^{4} c d^{3} x^{2} + 3 \, b^{4} c^{2} d^{2} x + b^{4} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{5} x^{4} + 4 \, b^{4} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} b^{4} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} b^{4} x + {\left(c^{4} d + c^{2} d\right)} b^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(b^{4} d^{6} x^{5} + 5 \, b^{4} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} b^{4} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{4} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} b^{4} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} b^{4}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{3} + 3 \, a^{2} b^{2} c d^{3} x^{2} + 3 \, a^{2} b^{2} c^{2} d^{2} x + a^{2} b^{2} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{5} x^{4} + 4 \, a^{2} b^{2} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a^{2} b^{2} x + {\left(c^{4} d + c^{2} d\right)} a^{2} b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(a b^{3} d^{7} x^{6} + 6 \, a b^{3} c d^{6} x^{5} + 3 \, {\left(5 \, c^{2} d^{5} + d^{5}\right)} a b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{3} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} + 6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 6 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{6} d + 3 \, c^{4} d + 3 \, c^{2} d + d\right)} a b^{3} + {\left(a b^{3} d^{4} x^{3} + 3 \, a b^{3} c d^{3} x^{2} + 3 \, a b^{3} c^{2} d^{2} x + a b^{3} c^{3} d\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{5} x^{4} + 4 \, a b^{3} c d^{4} x^{3} + {\left(6 \, c^{2} d^{3} + d^{3}\right)} a b^{3} x^{2} + 2 \, {\left(2 \, c^{3} d^{2} + c d^{2}\right)} a b^{3} x + {\left(c^{4} d + c^{2} d\right)} a b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(a b^{3} d^{6} x^{5} + 5 \, a b^{3} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a b^{3} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{3} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a b^{3} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 3 \, {\left(a^{2} b^{2} d^{6} x^{5} + 5 \, a^{2} b^{2} c d^{5} x^{4} + 2 \, {\left(5 \, c^{2} d^{4} + d^{4}\right)} a^{2} b^{2} x^{3} + 2 \, {\left(5 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d^{2} + 6 \, c^{2} d^{2} + d^{2}\right)} a^{2} b^{2} x + {\left(c^{5} d + 2 \, c^{3} d + c d\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}} + \int \frac{d^{8} x^{8} + 8 \, c d^{7} x^{7} + c^{8} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} x^{6} + 4 \, c^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} x^{4} + 6 \, c^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} x^{3} + {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4} + 3\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} x^{2} + {\left(4 \, d^{5} x^{5} + 20 \, c d^{4} x^{4} + 4 \, c^{5} + 4 \, {\left(10 \, c^{2} d^{3} + d^{3}\right)} x^{3} + 4 \, c^{3} + 4 \, {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} x^{2} + {\left(20 \, c^{4} d + 12 \, c^{2} d + 3 \, d\right)} x + 3 \, c\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(2 \, d^{6} x^{6} + 12 \, c d^{5} x^{5} + 2 \, c^{6} + 2 \, {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} x^{4} + 4 \, c^{4} + 8 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} x^{3} + {\left(30 \, c^{4} d^{2} + 24 \, c^{2} d^{2} + d^{2}\right)} x^{2} + c^{2} + 2 \, {\left(6 \, c^{5} d + 8 \, c^{3} d + c d\right)} x - 1\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, c^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} x + {\left(4 \, d^{7} x^{7} + 28 \, c d^{6} x^{6} + 4 \, c^{7} + 12 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} x^{5} + 12 \, c^{5} + 20 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} x^{4} + {\left(140 \, c^{4} d^{3} + 120 \, c^{2} d^{3} + 9 \, d^{3}\right)} x^{3} + 9 \, c^{3} + 3 \, {\left(28 \, c^{5} d^{2} + 40 \, c^{3} d^{2} + 9 \, c d^{2}\right)} x^{2} + {\left(28 \, c^{6} d + 60 \, c^{4} d + 27 \, c^{2} d + d\right)} x + c\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1}{2 \, {\left(a b^{2} d^{8} x^{8} + 8 \, a b^{2} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} a b^{2} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} a b^{2} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} a b^{2} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} a b^{2} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} a b^{2} + {\left(a b^{2} d^{4} x^{4} + 4 \, a b^{2} c d^{3} x^{3} + 6 \, a b^{2} c^{2} d^{2} x^{2} + 4 \, a b^{2} c^{3} d x + a b^{2} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(a b^{2} d^{5} x^{5} + 5 \, a b^{2} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} a b^{2} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} a b^{2} x + {\left(c^{5} + c^{3}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{6} x^{6} + 6 \, a b^{2} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} a b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} a b^{2} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} a b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} a b^{2} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{3} d^{8} x^{8} + 8 \, b^{3} c d^{7} x^{7} + 4 \, {\left(7 \, c^{2} d^{6} + d^{6}\right)} b^{3} x^{6} + 8 \, {\left(7 \, c^{3} d^{5} + 3 \, c d^{5}\right)} b^{3} x^{5} + 2 \, {\left(35 \, c^{4} d^{4} + 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} b^{3} x^{4} + 8 \, {\left(7 \, c^{5} d^{3} + 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b^{3} x^{3} + 4 \, {\left(7 \, c^{6} d^{2} + 15 \, c^{4} d^{2} + 9 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 8 \, {\left(c^{7} d + 3 \, c^{5} d + 3 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{8} + 4 \, c^{6} + 6 \, c^{4} + 4 \, c^{2} + 1\right)} b^{3} + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(b^{3} d^{5} x^{5} + 5 \, b^{3} c d^{4} x^{4} + {\left(10 \, c^{2} d^{3} + d^{3}\right)} b^{3} x^{3} + {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b^{3} x + {\left(c^{5} + c^{3}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + {\left(15 \, c^{2} d^{4} + 2 \, d^{4}\right)} b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} + 2 \, c d^{3}\right)} b^{3} x^{3} + {\left(15 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} b^{3} x^{2} + 2 \, {\left(3 \, c^{5} d + 4 \, c^{3} d + c d\right)} b^{3} x + {\left(c^{6} + 2 \, c^{4} + c^{2}\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(b^{3} d^{7} x^{7} + 7 \, b^{3} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} b^{3} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} b^{3} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} b^{3} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b^{3} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} b^{3} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 4 \, {\left(a b^{2} d^{7} x^{7} + 7 \, a b^{2} c d^{6} x^{6} + 3 \, {\left(7 \, c^{2} d^{5} + d^{5}\right)} a b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} + 3 \, c d^{4}\right)} a b^{2} x^{4} + {\left(35 \, c^{4} d^{3} + 30 \, c^{2} d^{3} + 3 \, d^{3}\right)} a b^{2} x^{3} + 3 \, {\left(7 \, c^{5} d^{2} + 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} a b^{2} x^{2} + {\left(7 \, c^{6} d + 15 \, c^{4} d + 9 \, c^{2} d + d\right)} a b^{2} x + {\left(c^{7} + 3 \, c^{5} + 3 \, c^{3} + c\right)} a b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*((a*d^7 + b*d^7)*x^7 + 7*(a*c*d^6 + b*c*d^6)*x^6 + 3*((7*c^2*d^5 + d^5)*a + (7*c^2*d^5 + d^5)*b)*x^5 + 5*((7*c^3*d^4 + 3*c*d^4)*a + (7*c^3*d^4 + 3*c*d^4)*b)*x^4 + ((35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*a + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b)*x^3 + 3*((7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*a + (7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b)*x^2 + ((a*d^4 + b*d^4)*x^4 + 4*(a*c*d^3 + b*c*d^3)*x^3 + (6*a*c^2*d^2 + (6*c^2*d^2 + d^2)*b)*x^2 + (c^4 - 1)*a + (c^4 + c^2)*b + 2*(2*a*c^3*d + (2*c^3*d + c*d)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (3*(a*d^5 + b*d^5)*x^5 + 15*(a*c*d^4 + b*c*d^4)*x^4 + (3*(10*c^2*d^3 + d^3)*a + 5*(6*c^2*d^3 + d^3)*b)*x^3 + 3*((10*c^3*d^2 + 3*c*d^2)*a + 5*(2*c^3*d^2 + c*d^2)*b)*x^2 + 3*(c^5 + c^3)*a + (3*c^5 + 5*c^3 + 2*c)*b + (3*(5*c^4*d + 3*c^2*d)*a + (15*c^4*d + 15*c^2*d + 2*d)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (c^7 + 3*c^5 + 3*c^3 + c)*a + (c^7 + 3*c^5 + 3*c^3 + c)*b + ((7*c^6*d + 15*c^4*d + 9*c^2*d + d)*a + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b)*x + (b*d^7*x^7 + 7*b*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*b*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*b*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b*x + (b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + (c^4 - 1)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b*d^5*x^5 + 5*b*c*d^4*x^4 + (10*c^2*d^3 + d^3)*b*x^3 + (10*c^3*d^2 + 3*c*d^2)*b*x^2 + (5*c^4*d + 3*c^2*d)*b*x + (c^5 + c^3)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (c^7 + 3*c^5 + 3*c^3 + c)*b + (3*b*d^6*x^6 + 18*b*c*d^5*x^5 + 3*(15*c^2*d^4 + 2*d^4)*b*x^4 + 12*(5*c^3*d^3 + 2*c*d^3)*b*x^3 + (45*c^4*d^2 + 36*c^2*d^2 + 4*d^2)*b*x^2 + 2*(9*c^5*d + 12*c^3*d + 4*c*d)*b*x + (3*c^6 + 6*c^4 + 4*c^2 + 1)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (3*(a*d^6 + b*d^6)*x^6 + 18*(a*c*d^5 + b*c*d^5)*x^5 + (3*(15*c^2*d^4 + 2*d^4)*a + (45*c^2*d^4 + 7*d^4)*b)*x^4 + 4*(3*(5*c^3*d^3 + 2*c*d^3)*a + (15*c^3*d^3 + 7*c*d^3)*b)*x^3 + ((45*c^4*d^2 + 36*c^2*d^2 + 4*d^2)*a + (45*c^4*d^2 + 42*c^2*d^2 + 5*d^2)*b)*x^2 + (3*c^6 + 6*c^4 + 4*c^2 + 1)*a + (3*c^6 + 7*c^4 + 5*c^2 + 1)*b + 2*((9*c^5*d + 12*c^3*d + 4*c*d)*a + (9*c^5*d + 14*c^3*d + 5*c*d)*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a^2*b^2*d^7*x^6 + 6*a^2*b^2*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a^2*b^2*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a^2*b^2*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a^2*b^2 + (b^4*d^7*x^6 + 6*b^4*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*b^4*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*b^4*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*b^4*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*b^4*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*b^4 + (b^4*d^4*x^3 + 3*b^4*c*d^3*x^2 + 3*b^4*c^2*d^2*x + b^4*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b^4*d^5*x^4 + 4*b^4*c*d^4*x^3 + (6*c^2*d^3 + d^3)*b^4*x^2 + 2*(2*c^3*d^2 + c*d^2)*b^4*x + (c^4*d + c^2*d)*b^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^4*d^6*x^5 + 5*b^4*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*b^4*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*b^4*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*b^4*x + (c^5*d + 2*c^3*d + c*d)*b^4)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + (a^2*b^2*d^4*x^3 + 3*a^2*b^2*c*d^3*x^2 + 3*a^2*b^2*c^2*d^2*x + a^2*b^2*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a^2*b^2*d^5*x^4 + 4*a^2*b^2*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a^2*b^2*x^2 + 2*(2*c^3*d^2 + c*d^2)*a^2*b^2*x + (c^4*d + c^2*d)*a^2*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(a*b^3*d^7*x^6 + 6*a*b^3*c*d^6*x^5 + 3*(5*c^2*d^5 + d^5)*a*b^3*x^4 + 4*(5*c^3*d^4 + 3*c*d^4)*a*b^3*x^3 + 3*(5*c^4*d^3 + 6*c^2*d^3 + d^3)*a*b^3*x^2 + 6*(c^5*d^2 + 2*c^3*d^2 + c*d^2)*a*b^3*x + (c^6*d + 3*c^4*d + 3*c^2*d + d)*a*b^3 + (a*b^3*d^4*x^3 + 3*a*b^3*c*d^3*x^2 + 3*a*b^3*c^2*d^2*x + a*b^3*c^3*d)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a*b^3*d^5*x^4 + 4*a*b^3*c*d^4*x^3 + (6*c^2*d^3 + d^3)*a*b^3*x^2 + 2*(2*c^3*d^2 + c*d^2)*a*b^3*x + (c^4*d + c^2*d)*a*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(a*b^3*d^6*x^5 + 5*a*b^3*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a*b^3*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a*b^3*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a*b^3*x + (c^5*d + 2*c^3*d + c*d)*a*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 3*(a^2*b^2*d^6*x^5 + 5*a^2*b^2*c*d^5*x^4 + 2*(5*c^2*d^4 + d^4)*a^2*b^2*x^3 + 2*(5*c^3*d^3 + 3*c*d^3)*a^2*b^2*x^2 + (5*c^4*d^2 + 6*c^2*d^2 + d^2)*a^2*b^2*x + (c^5*d + 2*c^3*d + c*d)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate(1/2*(d^8*x^8 + 8*c*d^7*x^7 + c^8 + 4*(7*c^2*d^6 + d^6)*x^6 + 4*c^6 + 8*(7*c^3*d^5 + 3*c*d^5)*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*x^4 + 6*c^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*x^3 + (d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4 + 3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*x^2 + (4*d^5*x^5 + 20*c*d^4*x^4 + 4*c^5 + 4*(10*c^2*d^3 + d^3)*x^3 + 4*c^3 + 4*(10*c^3*d^2 + 3*c*d^2)*x^2 + (20*c^4*d + 12*c^2*d + 3*d)*x + 3*c)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(2*d^6*x^6 + 12*c*d^5*x^5 + 2*c^6 + 2*(15*c^2*d^4 + 2*d^4)*x^4 + 4*c^4 + 8*(5*c^3*d^3 + 2*c*d^3)*x^3 + (30*c^4*d^2 + 24*c^2*d^2 + d^2)*x^2 + c^2 + 2*(6*c^5*d + 8*c^3*d + c*d)*x - 1)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*c^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*x + (4*d^7*x^7 + 28*c*d^6*x^6 + 4*c^7 + 12*(7*c^2*d^5 + d^5)*x^5 + 12*c^5 + 20*(7*c^3*d^4 + 3*c*d^4)*x^4 + (140*c^4*d^3 + 120*c^2*d^3 + 9*d^3)*x^3 + 9*c^3 + 3*(28*c^5*d^2 + 40*c^3*d^2 + 9*c*d^2)*x^2 + (28*c^6*d + 60*c^4*d + 27*c^2*d + d)*x + c)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)/(a*b^2*d^8*x^8 + 8*a*b^2*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*a*b^2*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*a*b^2*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*a*b^2*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*a*b^2*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*a*b^2*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*a*b^2*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*a*b^2 + (a*b^2*d^4*x^4 + 4*a*b^2*c*d^3*x^3 + 6*a*b^2*c^2*d^2*x^2 + 4*a*b^2*c^3*d*x + a*b^2*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(a*b^2*d^5*x^5 + 5*a*b^2*c*d^4*x^4 + (10*c^2*d^3 + d^3)*a*b^2*x^3 + (10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (5*c^4*d + 3*c^2*d)*a*b^2*x + (c^5 + c^3)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(a*b^2*d^6*x^6 + 6*a*b^2*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*a*b^2*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*a*b^2*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*a*b^2*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*a*b^2*x + (c^6 + 2*c^4 + c^2)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^3*d^8*x^8 + 8*b^3*c*d^7*x^7 + 4*(7*c^2*d^6 + d^6)*b^3*x^6 + 8*(7*c^3*d^5 + 3*c*d^5)*b^3*x^5 + 2*(35*c^4*d^4 + 30*c^2*d^4 + 3*d^4)*b^3*x^4 + 8*(7*c^5*d^3 + 10*c^3*d^3 + 3*c*d^3)*b^3*x^3 + 4*(7*c^6*d^2 + 15*c^4*d^2 + 9*c^2*d^2 + d^2)*b^3*x^2 + 8*(c^7*d + 3*c^5*d + 3*c^3*d + c*d)*b^3*x + (c^8 + 4*c^6 + 6*c^4 + 4*c^2 + 1)*b^3 + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^3*d^5*x^5 + 5*b^3*c*d^4*x^4 + (10*c^2*d^3 + d^3)*b^3*x^3 + (10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (5*c^4*d + 3*c^2*d)*b^3*x + (c^5 + c^3)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(b^3*d^6*x^6 + 6*b^3*c*d^5*x^5 + (15*c^2*d^4 + 2*d^4)*b^3*x^4 + 4*(5*c^3*d^3 + 2*c*d^3)*b^3*x^3 + (15*c^4*d^2 + 12*c^2*d^2 + d^2)*b^3*x^2 + 2*(3*c^5*d + 4*c^3*d + c*d)*b^3*x + (c^6 + 2*c^4 + c^2)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(b^3*d^7*x^7 + 7*b^3*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*b^3*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*b^3*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*b^3*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*b^3*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*b^3*x + (c^7 + 3*c^5 + 3*c^3 + c)*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 4*(a*b^2*d^7*x^7 + 7*a*b^2*c*d^6*x^6 + 3*(7*c^2*d^5 + d^5)*a*b^2*x^5 + 5*(7*c^3*d^4 + 3*c*d^4)*a*b^2*x^4 + (35*c^4*d^3 + 30*c^2*d^3 + 3*d^3)*a*b^2*x^3 + 3*(7*c^5*d^2 + 10*c^3*d^2 + 3*c*d^2)*a*b^2*x^2 + (7*c^6*d + 15*c^4*d + 9*c^2*d + d)*a*b^2*x + (c^7 + 3*c^5 + 3*c^3 + c)*a*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
173,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b d^{8} x^{8} + 8 \, b c d^{7} x^{7} + {\left(28 \, c^{2} d^{6} + 3 \, d^{6}\right)} b x^{6} + 2 \, {\left(28 \, c^{3} d^{5} + 9 \, c d^{5}\right)} b x^{5} + {\left(70 \, c^{4} d^{4} + 45 \, c^{2} d^{4} + 3 \, d^{4}\right)} b x^{4} + 4 \, {\left(14 \, c^{5} d^{3} + 15 \, c^{3} d^{3} + 3 \, c d^{3}\right)} b x^{3} + {\left(28 \, c^{6} d^{2} + 45 \, c^{4} d^{2} + 18 \, c^{2} d^{2} + d^{2}\right)} b x^{2} + 2 \, {\left(4 \, c^{7} d + 9 \, c^{5} d + 6 \, c^{3} d + c d\right)} b x + {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} - {\left(2 \, a d^{3} - {\left(10 \, c^{2} d^{3} + d^{3}\right)} b\right)} x^{3} - {\left(6 \, a c d^{2} - {\left(10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b\right)} x^{2} - 2 \, {\left(c^{3} + c\right)} a + {\left(c^{5} + c^{3}\right)} b - {\left(2 \, {\left(3 \, c^{2} d + d\right)} a - {\left(5 \, c^{4} d + 3 \, c^{2} d\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b d^{6} x^{6} + 18 \, b c d^{5} x^{5} - {\left(4 \, a d^{4} - 5 \, {\left(9 \, c^{2} d^{4} + d^{4}\right)} b\right)} x^{4} - 4 \, {\left(4 \, a c d^{3} - 5 \, {\left(3 \, c^{3} d^{3} + c d^{3}\right)} b\right)} x^{3} - {\left({\left(24 \, c^{2} d^{2} + 5 \, d^{2}\right)} a - {\left(45 \, c^{4} d^{2} + 30 \, c^{2} d^{2} + 2 \, d^{2}\right)} b\right)} x^{2} - {\left(4 \, c^{4} + 5 \, c^{2} + 1\right)} a + {\left(3 \, c^{6} + 5 \, c^{4} + 2 \, c^{2}\right)} b - 2 \, {\left({\left(8 \, c^{3} d + 5 \, c d\right)} a - {\left(9 \, c^{5} d + 10 \, c^{3} d + 2 \, c d\right)} b\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(c^{8} + 3 \, c^{6} + 3 \, c^{4} + c^{2}\right)} b - {\left(2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} b x + {\left(c^{3} + c\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + {\left(4 \, b d^{4} x^{4} + 16 \, b c d^{3} x^{3} + {\left(24 \, c^{2} d^{2} + 5 \, d^{2}\right)} b x^{2} + 2 \, {\left(8 \, c^{3} d + 5 \, c d\right)} b x + {\left(4 \, c^{4} + 5 \, c^{2} + 1\right)} b\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(2 \, b d^{5} x^{5} + 10 \, b c d^{4} x^{4} + {\left(20 \, c^{2} d^{3} + 3 \, d^{3}\right)} b x^{3} + {\left(20 \, c^{3} d^{2} + 9 \, c d^{2}\right)} b x^{2} + {\left(10 \, c^{4} d + 9 \, c^{2} d + d\right)} b x + {\left(2 \, c^{5} + 3 \, c^{3} + c\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + {\left(3 \, b d^{7} x^{7} + 21 \, b c d^{6} x^{6} - {\left(2 \, a d^{5} - 7 \, {\left(9 \, c^{2} d^{5} + d^{5}\right)} b\right)} x^{5} - 5 \, {\left(2 \, a c d^{4} - 7 \, {\left(3 \, c^{3} d^{4} + c d^{4}\right)} b\right)} x^{4} - {\left({\left(20 \, c^{2} d^{3} + 3 \, d^{3}\right)} a - 5 \, {\left(21 \, c^{4} d^{3} + 14 \, c^{2} d^{3} + d^{3}\right)} b\right)} x^{3} - {\left({\left(20 \, c^{3} d^{2} + 9 \, c d^{2}\right)} a - {\left(63 \, c^{5} d^{2} + 70 \, c^{3} d^{2} + 15 \, c d^{2}\right)} b\right)} x^{2} - {\left(2 \, c^{5} + 3 \, c^{3} + c\right)} a + {\left(3 \, c^{7} + 7 \, c^{5} + 5 \, c^{3} + c\right)} b - {\left({\left(10 \, c^{4} d + 9 \, c^{2} d + d\right)} a - {\left(21 \, c^{6} d + 35 \, c^{4} d + 15 \, c^{2} d + d\right)} b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a^{2} b^{2} d^{9} e x^{8} + 8 \, a^{2} b^{2} c d^{8} e x^{7} + {\left(28 \, c^{2} d^{7} e + 3 \, d^{7} e\right)} a^{2} b^{2} x^{6} + 2 \, {\left(28 \, c^{3} d^{6} e + 9 \, c d^{6} e\right)} a^{2} b^{2} x^{5} + {\left(70 \, c^{4} d^{5} e + 45 \, c^{2} d^{5} e + 3 \, d^{5} e\right)} a^{2} b^{2} x^{4} + 4 \, {\left(14 \, c^{5} d^{4} e + 15 \, c^{3} d^{4} e + 3 \, c d^{4} e\right)} a^{2} b^{2} x^{3} + {\left(28 \, c^{6} d^{3} e + 45 \, c^{4} d^{3} e + 18 \, c^{2} d^{3} e + d^{3} e\right)} a^{2} b^{2} x^{2} + 2 \, {\left(4 \, c^{7} d^{2} e + 9 \, c^{5} d^{2} e + 6 \, c^{3} d^{2} e + c d^{2} e\right)} a^{2} b^{2} x + {\left(c^{8} d e + 3 \, c^{6} d e + 3 \, c^{4} d e + c^{2} d e\right)} a^{2} b^{2} + {\left(b^{4} d^{9} e x^{8} + 8 \, b^{4} c d^{8} e x^{7} + {\left(28 \, c^{2} d^{7} e + 3 \, d^{7} e\right)} b^{4} x^{6} + 2 \, {\left(28 \, c^{3} d^{6} e + 9 \, c d^{6} e\right)} b^{4} x^{5} + {\left(70 \, c^{4} d^{5} e + 45 \, c^{2} d^{5} e + 3 \, d^{5} e\right)} b^{4} x^{4} + 4 \, {\left(14 \, c^{5} d^{4} e + 15 \, c^{3} d^{4} e + 3 \, c d^{4} e\right)} b^{4} x^{3} + {\left(28 \, c^{6} d^{3} e + 45 \, c^{4} d^{3} e + 18 \, c^{2} d^{3} e + d^{3} e\right)} b^{4} x^{2} + 2 \, {\left(4 \, c^{7} d^{2} e + 9 \, c^{5} d^{2} e + 6 \, c^{3} d^{2} e + c d^{2} e\right)} b^{4} x + {\left(c^{8} d e + 3 \, c^{6} d e + 3 \, c^{4} d e + c^{2} d e\right)} b^{4} + {\left(b^{4} d^{6} e x^{5} + 5 \, b^{4} c d^{5} e x^{4} + 10 \, b^{4} c^{2} d^{4} e x^{3} + 10 \, b^{4} c^{3} d^{3} e x^{2} + 5 \, b^{4} c^{4} d^{2} e x + b^{4} c^{5} d e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{7} e x^{6} + 6 \, b^{4} c d^{6} e x^{5} + {\left(15 \, c^{2} d^{5} e + d^{5} e\right)} b^{4} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} e + c d^{4} e\right)} b^{4} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} e + 2 \, c^{2} d^{3} e\right)} b^{4} x^{2} + 2 \, {\left(3 \, c^{5} d^{2} e + 2 \, c^{3} d^{2} e\right)} b^{4} x + {\left(c^{6} d e + c^{4} d e\right)} b^{4}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(b^{4} d^{8} e x^{7} + 7 \, b^{4} c d^{7} e x^{6} + {\left(21 \, c^{2} d^{6} e + 2 \, d^{6} e\right)} b^{4} x^{5} + 5 \, {\left(7 \, c^{3} d^{5} e + 2 \, c d^{5} e\right)} b^{4} x^{4} + {\left(35 \, c^{4} d^{4} e + 20 \, c^{2} d^{4} e + d^{4} e\right)} b^{4} x^{3} + {\left(21 \, c^{5} d^{3} e + 20 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} b^{4} x^{2} + {\left(7 \, c^{6} d^{2} e + 10 \, c^{4} d^{2} e + 3 \, c^{2} d^{2} e\right)} b^{4} x + {\left(c^{7} d e + 2 \, c^{5} d e + c^{3} d e\right)} b^{4}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b^{2} d^{6} e x^{5} + 5 \, a^{2} b^{2} c d^{5} e x^{4} + 10 \, a^{2} b^{2} c^{2} d^{4} e x^{3} + 10 \, a^{2} b^{2} c^{3} d^{3} e x^{2} + 5 \, a^{2} b^{2} c^{4} d^{2} e x + a^{2} b^{2} c^{5} d e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{7} e x^{6} + 6 \, a^{2} b^{2} c d^{6} e x^{5} + {\left(15 \, c^{2} d^{5} e + d^{5} e\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} e + c d^{4} e\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} e + 2 \, c^{2} d^{3} e\right)} a^{2} b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d^{2} e + 2 \, c^{3} d^{2} e\right)} a^{2} b^{2} x + {\left(c^{6} d e + c^{4} d e\right)} a^{2} b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 2 \, {\left(a b^{3} d^{9} e x^{8} + 8 \, a b^{3} c d^{8} e x^{7} + {\left(28 \, c^{2} d^{7} e + 3 \, d^{7} e\right)} a b^{3} x^{6} + 2 \, {\left(28 \, c^{3} d^{6} e + 9 \, c d^{6} e\right)} a b^{3} x^{5} + {\left(70 \, c^{4} d^{5} e + 45 \, c^{2} d^{5} e + 3 \, d^{5} e\right)} a b^{3} x^{4} + 4 \, {\left(14 \, c^{5} d^{4} e + 15 \, c^{3} d^{4} e + 3 \, c d^{4} e\right)} a b^{3} x^{3} + {\left(28 \, c^{6} d^{3} e + 45 \, c^{4} d^{3} e + 18 \, c^{2} d^{3} e + d^{3} e\right)} a b^{3} x^{2} + 2 \, {\left(4 \, c^{7} d^{2} e + 9 \, c^{5} d^{2} e + 6 \, c^{3} d^{2} e + c d^{2} e\right)} a b^{3} x + {\left(c^{8} d e + 3 \, c^{6} d e + 3 \, c^{4} d e + c^{2} d e\right)} a b^{3} + {\left(a b^{3} d^{6} e x^{5} + 5 \, a b^{3} c d^{5} e x^{4} + 10 \, a b^{3} c^{2} d^{4} e x^{3} + 10 \, a b^{3} c^{3} d^{3} e x^{2} + 5 \, a b^{3} c^{4} d^{2} e x + a b^{3} c^{5} d e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{7} e x^{6} + 6 \, a b^{3} c d^{6} e x^{5} + {\left(15 \, c^{2} d^{5} e + d^{5} e\right)} a b^{3} x^{4} + 4 \, {\left(5 \, c^{3} d^{4} e + c d^{4} e\right)} a b^{3} x^{3} + 3 \, {\left(5 \, c^{4} d^{3} e + 2 \, c^{2} d^{3} e\right)} a b^{3} x^{2} + 2 \, {\left(3 \, c^{5} d^{2} e + 2 \, c^{3} d^{2} e\right)} a b^{3} x + {\left(c^{6} d e + c^{4} d e\right)} a b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 3 \, {\left(a b^{3} d^{8} e x^{7} + 7 \, a b^{3} c d^{7} e x^{6} + {\left(21 \, c^{2} d^{6} e + 2 \, d^{6} e\right)} a b^{3} x^{5} + 5 \, {\left(7 \, c^{3} d^{5} e + 2 \, c d^{5} e\right)} a b^{3} x^{4} + {\left(35 \, c^{4} d^{4} e + 20 \, c^{2} d^{4} e + d^{4} e\right)} a b^{3} x^{3} + {\left(21 \, c^{5} d^{3} e + 20 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} a b^{3} x^{2} + {\left(7 \, c^{6} d^{2} e + 10 \, c^{4} d^{2} e + 3 \, c^{2} d^{2} e\right)} a b^{3} x + {\left(c^{7} d e + 2 \, c^{5} d e + c^{3} d e\right)} a b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 3 \, {\left(a^{2} b^{2} d^{8} e x^{7} + 7 \, a^{2} b^{2} c d^{7} e x^{6} + {\left(21 \, c^{2} d^{6} e + 2 \, d^{6} e\right)} a^{2} b^{2} x^{5} + 5 \, {\left(7 \, c^{3} d^{5} e + 2 \, c d^{5} e\right)} a^{2} b^{2} x^{4} + {\left(35 \, c^{4} d^{4} e + 20 \, c^{2} d^{4} e + d^{4} e\right)} a^{2} b^{2} x^{3} + {\left(21 \, c^{5} d^{3} e + 20 \, c^{3} d^{3} e + 3 \, c d^{3} e\right)} a^{2} b^{2} x^{2} + {\left(7 \, c^{6} d^{2} e + 10 \, c^{4} d^{2} e + 3 \, c^{2} d^{2} e\right)} a^{2} b^{2} x + {\left(c^{7} d e + 2 \, c^{5} d e + c^{3} d e\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}} + \int \frac{4 \, {\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + c^{4} + 2 \, {\left(3 \, c^{2} d^{2} + d^{2}\right)} x^{2} + 2 \, c^{2} + 4 \, {\left(c^{3} d + c d\right)} x\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + {\left(12 \, d^{5} x^{5} + 60 \, c d^{4} x^{4} + 12 \, c^{5} + 2 \, {\left(60 \, c^{2} d^{3} + 11 \, d^{3}\right)} x^{3} + 22 \, c^{3} + 6 \, {\left(20 \, c^{3} d^{2} + 11 \, c d^{2}\right)} x^{2} + {\left(60 \, c^{4} d + 66 \, c^{2} d + 7 \, d\right)} x + 7 \, c\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(6 \, d^{6} x^{6} + 36 \, c d^{5} x^{5} + 6 \, c^{6} + 10 \, {\left(9 \, c^{2} d^{4} + d^{4}\right)} x^{4} + 10 \, c^{4} + 40 \, {\left(3 \, c^{3} d^{3} + c d^{3}\right)} x^{3} + 5 \, {\left(18 \, c^{4} d^{2} + 12 \, c^{2} d^{2} + d^{2}\right)} x^{2} + 5 \, c^{2} + 2 \, {\left(18 \, c^{5} d + 20 \, c^{3} d + 5 \, c d\right)} x + 1\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(4 \, d^{7} x^{7} + 28 \, c d^{6} x^{6} + 4 \, c^{7} + 6 \, {\left(14 \, c^{2} d^{5} + d^{5}\right)} x^{5} + 6 \, c^{5} + 10 \, {\left(14 \, c^{3} d^{4} + 3 \, c d^{4}\right)} x^{4} + {\left(140 \, c^{4} d^{3} + 60 \, c^{2} d^{3} + 3 \, d^{3}\right)} x^{3} + 3 \, c^{3} + 3 \, {\left(28 \, c^{5} d^{2} + 20 \, c^{3} d^{2} + 3 \, c d^{2}\right)} x^{2} + {\left(28 \, c^{6} d + 30 \, c^{4} d + 9 \, c^{2} d + d\right)} x + c\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}{2 \, {\left(a b^{2} d^{11} e x^{11} + 11 \, a b^{2} c d^{10} e x^{10} + {\left(55 \, c^{2} d^{9} e + 4 \, d^{9} e\right)} a b^{2} x^{9} + 3 \, {\left(55 \, c^{3} d^{8} e + 12 \, c d^{8} e\right)} a b^{2} x^{8} + 6 \, {\left(55 \, c^{4} d^{7} e + 24 \, c^{2} d^{7} e + d^{7} e\right)} a b^{2} x^{7} + 42 \, {\left(11 \, c^{5} d^{6} e + 8 \, c^{3} d^{6} e + c d^{6} e\right)} a b^{2} x^{6} + 2 \, {\left(231 \, c^{6} d^{5} e + 252 \, c^{4} d^{5} e + 63 \, c^{2} d^{5} e + 2 \, d^{5} e\right)} a b^{2} x^{5} + 2 \, {\left(165 \, c^{7} d^{4} e + 252 \, c^{5} d^{4} e + 105 \, c^{3} d^{4} e + 10 \, c d^{4} e\right)} a b^{2} x^{4} + {\left(165 \, c^{8} d^{3} e + 336 \, c^{6} d^{3} e + 210 \, c^{4} d^{3} e + 40 \, c^{2} d^{3} e + d^{3} e\right)} a b^{2} x^{3} + {\left(55 \, c^{9} d^{2} e + 144 \, c^{7} d^{2} e + 126 \, c^{5} d^{2} e + 40 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} a b^{2} x^{2} + {\left(11 \, c^{10} d e + 36 \, c^{8} d e + 42 \, c^{6} d e + 20 \, c^{4} d e + 3 \, c^{2} d e\right)} a b^{2} x + {\left(c^{11} e + 4 \, c^{9} e + 6 \, c^{7} e + 4 \, c^{5} e + c^{3} e\right)} a b^{2} + {\left(a b^{2} d^{7} e x^{7} + 7 \, a b^{2} c d^{6} e x^{6} + 21 \, a b^{2} c^{2} d^{5} e x^{5} + 35 \, a b^{2} c^{3} d^{4} e x^{4} + 35 \, a b^{2} c^{4} d^{3} e x^{3} + 21 \, a b^{2} c^{5} d^{2} e x^{2} + 7 \, a b^{2} c^{6} d e x + a b^{2} c^{7} e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(a b^{2} d^{8} e x^{8} + 8 \, a b^{2} c d^{7} e x^{7} + {\left(28 \, c^{2} d^{6} e + d^{6} e\right)} a b^{2} x^{6} + 2 \, {\left(28 \, c^{3} d^{5} e + 3 \, c d^{5} e\right)} a b^{2} x^{5} + 5 \, {\left(14 \, c^{4} d^{4} e + 3 \, c^{2} d^{4} e\right)} a b^{2} x^{4} + 4 \, {\left(14 \, c^{5} d^{3} e + 5 \, c^{3} d^{3} e\right)} a b^{2} x^{3} + {\left(28 \, c^{6} d^{2} e + 15 \, c^{4} d^{2} e\right)} a b^{2} x^{2} + 2 \, {\left(4 \, c^{7} d e + 3 \, c^{5} d e\right)} a b^{2} x + {\left(c^{8} e + c^{6} e\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{9} e x^{9} + 9 \, a b^{2} c d^{8} e x^{8} + 2 \, {\left(18 \, c^{2} d^{7} e + d^{7} e\right)} a b^{2} x^{7} + 14 \, {\left(6 \, c^{3} d^{6} e + c d^{6} e\right)} a b^{2} x^{6} + {\left(126 \, c^{4} d^{5} e + 42 \, c^{2} d^{5} e + d^{5} e\right)} a b^{2} x^{5} + {\left(126 \, c^{5} d^{4} e + 70 \, c^{3} d^{4} e + 5 \, c d^{4} e\right)} a b^{2} x^{4} + 2 \, {\left(42 \, c^{6} d^{3} e + 35 \, c^{4} d^{3} e + 5 \, c^{2} d^{3} e\right)} a b^{2} x^{3} + 2 \, {\left(18 \, c^{7} d^{2} e + 21 \, c^{5} d^{2} e + 5 \, c^{3} d^{2} e\right)} a b^{2} x^{2} + {\left(9 \, c^{8} d e + 14 \, c^{6} d e + 5 \, c^{4} d e\right)} a b^{2} x + {\left(c^{9} e + 2 \, c^{7} e + c^{5} e\right)} a b^{2}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + {\left(b^{3} d^{11} e x^{11} + 11 \, b^{3} c d^{10} e x^{10} + {\left(55 \, c^{2} d^{9} e + 4 \, d^{9} e\right)} b^{3} x^{9} + 3 \, {\left(55 \, c^{3} d^{8} e + 12 \, c d^{8} e\right)} b^{3} x^{8} + 6 \, {\left(55 \, c^{4} d^{7} e + 24 \, c^{2} d^{7} e + d^{7} e\right)} b^{3} x^{7} + 42 \, {\left(11 \, c^{5} d^{6} e + 8 \, c^{3} d^{6} e + c d^{6} e\right)} b^{3} x^{6} + 2 \, {\left(231 \, c^{6} d^{5} e + 252 \, c^{4} d^{5} e + 63 \, c^{2} d^{5} e + 2 \, d^{5} e\right)} b^{3} x^{5} + 2 \, {\left(165 \, c^{7} d^{4} e + 252 \, c^{5} d^{4} e + 105 \, c^{3} d^{4} e + 10 \, c d^{4} e\right)} b^{3} x^{4} + {\left(165 \, c^{8} d^{3} e + 336 \, c^{6} d^{3} e + 210 \, c^{4} d^{3} e + 40 \, c^{2} d^{3} e + d^{3} e\right)} b^{3} x^{3} + {\left(55 \, c^{9} d^{2} e + 144 \, c^{7} d^{2} e + 126 \, c^{5} d^{2} e + 40 \, c^{3} d^{2} e + 3 \, c d^{2} e\right)} b^{3} x^{2} + {\left(11 \, c^{10} d e + 36 \, c^{8} d e + 42 \, c^{6} d e + 20 \, c^{4} d e + 3 \, c^{2} d e\right)} b^{3} x + {\left(c^{11} e + 4 \, c^{9} e + 6 \, c^{7} e + 4 \, c^{5} e + c^{3} e\right)} b^{3} + {\left(b^{3} d^{7} e x^{7} + 7 \, b^{3} c d^{6} e x^{6} + 21 \, b^{3} c^{2} d^{5} e x^{5} + 35 \, b^{3} c^{3} d^{4} e x^{4} + 35 \, b^{3} c^{4} d^{3} e x^{3} + 21 \, b^{3} c^{5} d^{2} e x^{2} + 7 \, b^{3} c^{6} d e x + b^{3} c^{7} e\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{2} + 4 \, {\left(b^{3} d^{8} e x^{8} + 8 \, b^{3} c d^{7} e x^{7} + {\left(28 \, c^{2} d^{6} e + d^{6} e\right)} b^{3} x^{6} + 2 \, {\left(28 \, c^{3} d^{5} e + 3 \, c d^{5} e\right)} b^{3} x^{5} + 5 \, {\left(14 \, c^{4} d^{4} e + 3 \, c^{2} d^{4} e\right)} b^{3} x^{4} + 4 \, {\left(14 \, c^{5} d^{3} e + 5 \, c^{3} d^{3} e\right)} b^{3} x^{3} + {\left(28 \, c^{6} d^{2} e + 15 \, c^{4} d^{2} e\right)} b^{3} x^{2} + 2 \, {\left(4 \, c^{7} d e + 3 \, c^{5} d e\right)} b^{3} x + {\left(c^{8} e + c^{6} e\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{9} e x^{9} + 9 \, b^{3} c d^{8} e x^{8} + 2 \, {\left(18 \, c^{2} d^{7} e + d^{7} e\right)} b^{3} x^{7} + 14 \, {\left(6 \, c^{3} d^{6} e + c d^{6} e\right)} b^{3} x^{6} + {\left(126 \, c^{4} d^{5} e + 42 \, c^{2} d^{5} e + d^{5} e\right)} b^{3} x^{5} + {\left(126 \, c^{5} d^{4} e + 70 \, c^{3} d^{4} e + 5 \, c d^{4} e\right)} b^{3} x^{4} + 2 \, {\left(42 \, c^{6} d^{3} e + 35 \, c^{4} d^{3} e + 5 \, c^{2} d^{3} e\right)} b^{3} x^{3} + 2 \, {\left(18 \, c^{7} d^{2} e + 21 \, c^{5} d^{2} e + 5 \, c^{3} d^{2} e\right)} b^{3} x^{2} + {\left(9 \, c^{8} d e + 14 \, c^{6} d e + 5 \, c^{4} d e\right)} b^{3} x + {\left(c^{9} e + 2 \, c^{7} e + c^{5} e\right)} b^{3}\right)} {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} + 4 \, {\left(b^{3} d^{10} e x^{10} + 10 \, b^{3} c d^{9} e x^{9} + 3 \, {\left(15 \, c^{2} d^{8} e + d^{8} e\right)} b^{3} x^{8} + 24 \, {\left(5 \, c^{3} d^{7} e + c d^{7} e\right)} b^{3} x^{7} + 3 \, {\left(70 \, c^{4} d^{6} e + 28 \, c^{2} d^{6} e + d^{6} e\right)} b^{3} x^{6} + 6 \, {\left(42 \, c^{5} d^{5} e + 28 \, c^{3} d^{5} e + 3 \, c d^{5} e\right)} b^{3} x^{5} + {\left(210 \, c^{6} d^{4} e + 210 \, c^{4} d^{4} e + 45 \, c^{2} d^{4} e + d^{4} e\right)} b^{3} x^{4} + 4 \, {\left(30 \, c^{7} d^{3} e + 42 \, c^{5} d^{3} e + 15 \, c^{3} d^{3} e + c d^{3} e\right)} b^{3} x^{3} + 3 \, {\left(15 \, c^{8} d^{2} e + 28 \, c^{6} d^{2} e + 15 \, c^{4} d^{2} e + 2 \, c^{2} d^{2} e\right)} b^{3} x^{2} + 2 \, {\left(5 \, c^{9} d e + 12 \, c^{7} d e + 9 \, c^{5} d e + 2 \, c^{3} d e\right)} b^{3} x + {\left(c^{10} e + 3 \, c^{8} e + 3 \, c^{6} e + c^{4} e\right)} b^{3}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right) + 4 \, {\left(a b^{2} d^{10} e x^{10} + 10 \, a b^{2} c d^{9} e x^{9} + 3 \, {\left(15 \, c^{2} d^{8} e + d^{8} e\right)} a b^{2} x^{8} + 24 \, {\left(5 \, c^{3} d^{7} e + c d^{7} e\right)} a b^{2} x^{7} + 3 \, {\left(70 \, c^{4} d^{6} e + 28 \, c^{2} d^{6} e + d^{6} e\right)} a b^{2} x^{6} + 6 \, {\left(42 \, c^{5} d^{5} e + 28 \, c^{3} d^{5} e + 3 \, c d^{5} e\right)} a b^{2} x^{5} + {\left(210 \, c^{6} d^{4} e + 210 \, c^{4} d^{4} e + 45 \, c^{2} d^{4} e + d^{4} e\right)} a b^{2} x^{4} + 4 \, {\left(30 \, c^{7} d^{3} e + 42 \, c^{5} d^{3} e + 15 \, c^{3} d^{3} e + c d^{3} e\right)} a b^{2} x^{3} + 3 \, {\left(15 \, c^{8} d^{2} e + 28 \, c^{6} d^{2} e + 15 \, c^{4} d^{2} e + 2 \, c^{2} d^{2} e\right)} a b^{2} x^{2} + 2 \, {\left(5 \, c^{9} d e + 12 \, c^{7} d e + 9 \, c^{5} d e + 2 \, c^{3} d e\right)} a b^{2} x + {\left(c^{10} e + 3 \, c^{8} e + 3 \, c^{6} e + c^{4} e\right)} a b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-1/2*(b*d^8*x^8 + 8*b*c*d^7*x^7 + (28*c^2*d^6 + 3*d^6)*b*x^6 + 2*(28*c^3*d^5 + 9*c*d^5)*b*x^5 + (70*c^4*d^4 + 45*c^2*d^4 + 3*d^4)*b*x^4 + 4*(14*c^5*d^3 + 15*c^3*d^3 + 3*c*d^3)*b*x^3 + (28*c^6*d^2 + 45*c^4*d^2 + 18*c^2*d^2 + d^2)*b*x^2 + 2*(4*c^7*d + 9*c^5*d + 6*c^3*d + c*d)*b*x + (b*d^5*x^5 + 5*b*c*d^4*x^4 - (2*a*d^3 - (10*c^2*d^3 + d^3)*b)*x^3 - (6*a*c*d^2 - (10*c^3*d^2 + 3*c*d^2)*b)*x^2 - 2*(c^3 + c)*a + (c^5 + c^3)*b - (2*(3*c^2*d + d)*a - (5*c^4*d + 3*c^2*d)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (3*b*d^6*x^6 + 18*b*c*d^5*x^5 - (4*a*d^4 - 5*(9*c^2*d^4 + d^4)*b)*x^4 - 4*(4*a*c*d^3 - 5*(3*c^3*d^3 + c*d^3)*b)*x^3 - ((24*c^2*d^2 + 5*d^2)*a - (45*c^4*d^2 + 30*c^2*d^2 + 2*d^2)*b)*x^2 - (4*c^4 + 5*c^2 + 1)*a + (3*c^6 + 5*c^4 + 2*c^2)*b - 2*((8*c^3*d + 5*c*d)*a - (9*c^5*d + 10*c^3*d + 2*c*d)*b)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (c^8 + 3*c^6 + 3*c^4 + c^2)*b - (2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + (3*c^2*d + d)*b*x + (c^3 + c)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + (4*b*d^4*x^4 + 16*b*c*d^3*x^3 + (24*c^2*d^2 + 5*d^2)*b*x^2 + 2*(8*c^3*d + 5*c*d)*b*x + (4*c^4 + 5*c^2 + 1)*b)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (2*b*d^5*x^5 + 10*b*c*d^4*x^4 + (20*c^2*d^3 + 3*d^3)*b*x^3 + (20*c^3*d^2 + 9*c*d^2)*b*x^2 + (10*c^4*d + 9*c^2*d + d)*b*x + (2*c^5 + 3*c^3 + c)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + (3*b*d^7*x^7 + 21*b*c*d^6*x^6 - (2*a*d^5 - 7*(9*c^2*d^5 + d^5)*b)*x^5 - 5*(2*a*c*d^4 - 7*(3*c^3*d^4 + c*d^4)*b)*x^4 - ((20*c^2*d^3 + 3*d^3)*a - 5*(21*c^4*d^3 + 14*c^2*d^3 + d^3)*b)*x^3 - ((20*c^3*d^2 + 9*c*d^2)*a - (63*c^5*d^2 + 70*c^3*d^2 + 15*c*d^2)*b)*x^2 - (2*c^5 + 3*c^3 + c)*a + (3*c^7 + 7*c^5 + 5*c^3 + c)*b - ((10*c^4*d + 9*c^2*d + d)*a - (21*c^6*d + 35*c^4*d + 15*c^2*d + d)*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a^2*b^2*d^9*e*x^8 + 8*a^2*b^2*c*d^8*e*x^7 + (28*c^2*d^7*e + 3*d^7*e)*a^2*b^2*x^6 + 2*(28*c^3*d^6*e + 9*c*d^6*e)*a^2*b^2*x^5 + (70*c^4*d^5*e + 45*c^2*d^5*e + 3*d^5*e)*a^2*b^2*x^4 + 4*(14*c^5*d^4*e + 15*c^3*d^4*e + 3*c*d^4*e)*a^2*b^2*x^3 + (28*c^6*d^3*e + 45*c^4*d^3*e + 18*c^2*d^3*e + d^3*e)*a^2*b^2*x^2 + 2*(4*c^7*d^2*e + 9*c^5*d^2*e + 6*c^3*d^2*e + c*d^2*e)*a^2*b^2*x + (c^8*d*e + 3*c^6*d*e + 3*c^4*d*e + c^2*d*e)*a^2*b^2 + (b^4*d^9*e*x^8 + 8*b^4*c*d^8*e*x^7 + (28*c^2*d^7*e + 3*d^7*e)*b^4*x^6 + 2*(28*c^3*d^6*e + 9*c*d^6*e)*b^4*x^5 + (70*c^4*d^5*e + 45*c^2*d^5*e + 3*d^5*e)*b^4*x^4 + 4*(14*c^5*d^4*e + 15*c^3*d^4*e + 3*c*d^4*e)*b^4*x^3 + (28*c^6*d^3*e + 45*c^4*d^3*e + 18*c^2*d^3*e + d^3*e)*b^4*x^2 + 2*(4*c^7*d^2*e + 9*c^5*d^2*e + 6*c^3*d^2*e + c*d^2*e)*b^4*x + (c^8*d*e + 3*c^6*d*e + 3*c^4*d*e + c^2*d*e)*b^4 + (b^4*d^6*e*x^5 + 5*b^4*c*d^5*e*x^4 + 10*b^4*c^2*d^4*e*x^3 + 10*b^4*c^3*d^3*e*x^2 + 5*b^4*c^4*d^2*e*x + b^4*c^5*d*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(b^4*d^7*e*x^6 + 6*b^4*c*d^6*e*x^5 + (15*c^2*d^5*e + d^5*e)*b^4*x^4 + 4*(5*c^3*d^4*e + c*d^4*e)*b^4*x^3 + 3*(5*c^4*d^3*e + 2*c^2*d^3*e)*b^4*x^2 + 2*(3*c^5*d^2*e + 2*c^3*d^2*e)*b^4*x + (c^6*d*e + c^4*d*e)*b^4)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^4*d^8*e*x^7 + 7*b^4*c*d^7*e*x^6 + (21*c^2*d^6*e + 2*d^6*e)*b^4*x^5 + 5*(7*c^3*d^5*e + 2*c*d^5*e)*b^4*x^4 + (35*c^4*d^4*e + 20*c^2*d^4*e + d^4*e)*b^4*x^3 + (21*c^5*d^3*e + 20*c^3*d^3*e + 3*c*d^3*e)*b^4*x^2 + (7*c^6*d^2*e + 10*c^4*d^2*e + 3*c^2*d^2*e)*b^4*x + (c^7*d*e + 2*c^5*d*e + c^3*d*e)*b^4)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + (a^2*b^2*d^6*e*x^5 + 5*a^2*b^2*c*d^5*e*x^4 + 10*a^2*b^2*c^2*d^4*e*x^3 + 10*a^2*b^2*c^3*d^3*e*x^2 + 5*a^2*b^2*c^4*d^2*e*x + a^2*b^2*c^5*d*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a^2*b^2*d^7*e*x^6 + 6*a^2*b^2*c*d^6*e*x^5 + (15*c^2*d^5*e + d^5*e)*a^2*b^2*x^4 + 4*(5*c^3*d^4*e + c*d^4*e)*a^2*b^2*x^3 + 3*(5*c^4*d^3*e + 2*c^2*d^3*e)*a^2*b^2*x^2 + 2*(3*c^5*d^2*e + 2*c^3*d^2*e)*a^2*b^2*x + (c^6*d*e + c^4*d*e)*a^2*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(a*b^3*d^9*e*x^8 + 8*a*b^3*c*d^8*e*x^7 + (28*c^2*d^7*e + 3*d^7*e)*a*b^3*x^6 + 2*(28*c^3*d^6*e + 9*c*d^6*e)*a*b^3*x^5 + (70*c^4*d^5*e + 45*c^2*d^5*e + 3*d^5*e)*a*b^3*x^4 + 4*(14*c^5*d^4*e + 15*c^3*d^4*e + 3*c*d^4*e)*a*b^3*x^3 + (28*c^6*d^3*e + 45*c^4*d^3*e + 18*c^2*d^3*e + d^3*e)*a*b^3*x^2 + 2*(4*c^7*d^2*e + 9*c^5*d^2*e + 6*c^3*d^2*e + c*d^2*e)*a*b^3*x + (c^8*d*e + 3*c^6*d*e + 3*c^4*d*e + c^2*d*e)*a*b^3 + (a*b^3*d^6*e*x^5 + 5*a*b^3*c*d^5*e*x^4 + 10*a*b^3*c^2*d^4*e*x^3 + 10*a*b^3*c^3*d^3*e*x^2 + 5*a*b^3*c^4*d^2*e*x + a*b^3*c^5*d*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 3*(a*b^3*d^7*e*x^6 + 6*a*b^3*c*d^6*e*x^5 + (15*c^2*d^5*e + d^5*e)*a*b^3*x^4 + 4*(5*c^3*d^4*e + c*d^4*e)*a*b^3*x^3 + 3*(5*c^4*d^3*e + 2*c^2*d^3*e)*a*b^3*x^2 + 2*(3*c^5*d^2*e + 2*c^3*d^2*e)*a*b^3*x + (c^6*d*e + c^4*d*e)*a*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(a*b^3*d^8*e*x^7 + 7*a*b^3*c*d^7*e*x^6 + (21*c^2*d^6*e + 2*d^6*e)*a*b^3*x^5 + 5*(7*c^3*d^5*e + 2*c*d^5*e)*a*b^3*x^4 + (35*c^4*d^4*e + 20*c^2*d^4*e + d^4*e)*a*b^3*x^3 + (21*c^5*d^3*e + 20*c^3*d^3*e + 3*c*d^3*e)*a*b^3*x^2 + (7*c^6*d^2*e + 10*c^4*d^2*e + 3*c^2*d^2*e)*a*b^3*x + (c^7*d*e + 2*c^5*d*e + c^3*d*e)*a*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 3*(a^2*b^2*d^8*e*x^7 + 7*a^2*b^2*c*d^7*e*x^6 + (21*c^2*d^6*e + 2*d^6*e)*a^2*b^2*x^5 + 5*(7*c^3*d^5*e + 2*c*d^5*e)*a^2*b^2*x^4 + (35*c^4*d^4*e + 20*c^2*d^4*e + d^4*e)*a^2*b^2*x^3 + (21*c^5*d^3*e + 20*c^3*d^3*e + 3*c*d^3*e)*a^2*b^2*x^2 + (7*c^6*d^2*e + 10*c^4*d^2*e + 3*c^2*d^2*e)*a^2*b^2*x + (c^7*d*e + 2*c^5*d*e + c^3*d*e)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + integrate(1/2*(4*(d^4*x^4 + 4*c*d^3*x^3 + c^4 + 2*(3*c^2*d^2 + d^2)*x^2 + 2*c^2 + 4*(c^3*d + c*d)*x)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + (12*d^5*x^5 + 60*c*d^4*x^4 + 12*c^5 + 2*(60*c^2*d^3 + 11*d^3)*x^3 + 22*c^3 + 6*(20*c^3*d^2 + 11*c*d^2)*x^2 + (60*c^4*d + 66*c^2*d + 7*d)*x + 7*c)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 2*(6*d^6*x^6 + 36*c*d^5*x^5 + 6*c^6 + 10*(9*c^2*d^4 + d^4)*x^4 + 10*c^4 + 40*(3*c^3*d^3 + c*d^3)*x^3 + 5*(18*c^4*d^2 + 12*c^2*d^2 + d^2)*x^2 + 5*c^2 + 2*(18*c^5*d + 20*c^3*d + 5*c*d)*x + 1)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (4*d^7*x^7 + 28*c*d^6*x^6 + 4*c^7 + 6*(14*c^2*d^5 + d^5)*x^5 + 6*c^5 + 10*(14*c^3*d^4 + 3*c*d^4)*x^4 + (140*c^4*d^3 + 60*c^2*d^3 + 3*d^3)*x^3 + 3*c^3 + 3*(28*c^5*d^2 + 20*c^3*d^2 + 3*c*d^2)*x^2 + (28*c^6*d + 30*c^4*d + 9*c^2*d + d)*x + c)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(a*b^2*d^11*e*x^11 + 11*a*b^2*c*d^10*e*x^10 + (55*c^2*d^9*e + 4*d^9*e)*a*b^2*x^9 + 3*(55*c^3*d^8*e + 12*c*d^8*e)*a*b^2*x^8 + 6*(55*c^4*d^7*e + 24*c^2*d^7*e + d^7*e)*a*b^2*x^7 + 42*(11*c^5*d^6*e + 8*c^3*d^6*e + c*d^6*e)*a*b^2*x^6 + 2*(231*c^6*d^5*e + 252*c^4*d^5*e + 63*c^2*d^5*e + 2*d^5*e)*a*b^2*x^5 + 2*(165*c^7*d^4*e + 252*c^5*d^4*e + 105*c^3*d^4*e + 10*c*d^4*e)*a*b^2*x^4 + (165*c^8*d^3*e + 336*c^6*d^3*e + 210*c^4*d^3*e + 40*c^2*d^3*e + d^3*e)*a*b^2*x^3 + (55*c^9*d^2*e + 144*c^7*d^2*e + 126*c^5*d^2*e + 40*c^3*d^2*e + 3*c*d^2*e)*a*b^2*x^2 + (11*c^10*d*e + 36*c^8*d*e + 42*c^6*d*e + 20*c^4*d*e + 3*c^2*d*e)*a*b^2*x + (c^11*e + 4*c^9*e + 6*c^7*e + 4*c^5*e + c^3*e)*a*b^2 + (a*b^2*d^7*e*x^7 + 7*a*b^2*c*d^6*e*x^6 + 21*a*b^2*c^2*d^5*e*x^5 + 35*a*b^2*c^3*d^4*e*x^4 + 35*a*b^2*c^4*d^3*e*x^3 + 21*a*b^2*c^5*d^2*e*x^2 + 7*a*b^2*c^6*d*e*x + a*b^2*c^7*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(a*b^2*d^8*e*x^8 + 8*a*b^2*c*d^7*e*x^7 + (28*c^2*d^6*e + d^6*e)*a*b^2*x^6 + 2*(28*c^3*d^5*e + 3*c*d^5*e)*a*b^2*x^5 + 5*(14*c^4*d^4*e + 3*c^2*d^4*e)*a*b^2*x^4 + 4*(14*c^5*d^3*e + 5*c^3*d^3*e)*a*b^2*x^3 + (28*c^6*d^2*e + 15*c^4*d^2*e)*a*b^2*x^2 + 2*(4*c^7*d*e + 3*c^5*d*e)*a*b^2*x + (c^8*e + c^6*e)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(a*b^2*d^9*e*x^9 + 9*a*b^2*c*d^8*e*x^8 + 2*(18*c^2*d^7*e + d^7*e)*a*b^2*x^7 + 14*(6*c^3*d^6*e + c*d^6*e)*a*b^2*x^6 + (126*c^4*d^5*e + 42*c^2*d^5*e + d^5*e)*a*b^2*x^5 + (126*c^5*d^4*e + 70*c^3*d^4*e + 5*c*d^4*e)*a*b^2*x^4 + 2*(42*c^6*d^3*e + 35*c^4*d^3*e + 5*c^2*d^3*e)*a*b^2*x^3 + 2*(18*c^7*d^2*e + 21*c^5*d^2*e + 5*c^3*d^2*e)*a*b^2*x^2 + (9*c^8*d*e + 14*c^6*d*e + 5*c^4*d*e)*a*b^2*x + (c^9*e + 2*c^7*e + c^5*e)*a*b^2)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^3*d^11*e*x^11 + 11*b^3*c*d^10*e*x^10 + (55*c^2*d^9*e + 4*d^9*e)*b^3*x^9 + 3*(55*c^3*d^8*e + 12*c*d^8*e)*b^3*x^8 + 6*(55*c^4*d^7*e + 24*c^2*d^7*e + d^7*e)*b^3*x^7 + 42*(11*c^5*d^6*e + 8*c^3*d^6*e + c*d^6*e)*b^3*x^6 + 2*(231*c^6*d^5*e + 252*c^4*d^5*e + 63*c^2*d^5*e + 2*d^5*e)*b^3*x^5 + 2*(165*c^7*d^4*e + 252*c^5*d^4*e + 105*c^3*d^4*e + 10*c*d^4*e)*b^3*x^4 + (165*c^8*d^3*e + 336*c^6*d^3*e + 210*c^4*d^3*e + 40*c^2*d^3*e + d^3*e)*b^3*x^3 + (55*c^9*d^2*e + 144*c^7*d^2*e + 126*c^5*d^2*e + 40*c^3*d^2*e + 3*c*d^2*e)*b^3*x^2 + (11*c^10*d*e + 36*c^8*d*e + 42*c^6*d*e + 20*c^4*d*e + 3*c^2*d*e)*b^3*x + (c^11*e + 4*c^9*e + 6*c^7*e + 4*c^5*e + c^3*e)*b^3 + (b^3*d^7*e*x^7 + 7*b^3*c*d^6*e*x^6 + 21*b^3*c^2*d^5*e*x^5 + 35*b^3*c^3*d^4*e*x^4 + 35*b^3*c^4*d^3*e*x^3 + 21*b^3*c^5*d^2*e*x^2 + 7*b^3*c^6*d*e*x + b^3*c^7*e)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^3*d^8*e*x^8 + 8*b^3*c*d^7*e*x^7 + (28*c^2*d^6*e + d^6*e)*b^3*x^6 + 2*(28*c^3*d^5*e + 3*c*d^5*e)*b^3*x^5 + 5*(14*c^4*d^4*e + 3*c^2*d^4*e)*b^3*x^4 + 4*(14*c^5*d^3*e + 5*c^3*d^3*e)*b^3*x^3 + (28*c^6*d^2*e + 15*c^4*d^2*e)*b^3*x^2 + 2*(4*c^7*d*e + 3*c^5*d*e)*b^3*x + (c^8*e + c^6*e)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 6*(b^3*d^9*e*x^9 + 9*b^3*c*d^8*e*x^8 + 2*(18*c^2*d^7*e + d^7*e)*b^3*x^7 + 14*(6*c^3*d^6*e + c*d^6*e)*b^3*x^6 + (126*c^4*d^5*e + 42*c^2*d^5*e + d^5*e)*b^3*x^5 + (126*c^5*d^4*e + 70*c^3*d^4*e + 5*c*d^4*e)*b^3*x^4 + 2*(42*c^6*d^3*e + 35*c^4*d^3*e + 5*c^2*d^3*e)*b^3*x^3 + 2*(18*c^7*d^2*e + 21*c^5*d^2*e + 5*c^3*d^2*e)*b^3*x^2 + (9*c^8*d*e + 14*c^6*d*e + 5*c^4*d*e)*b^3*x + (c^9*e + 2*c^7*e + c^5*e)*b^3)*(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(b^3*d^10*e*x^10 + 10*b^3*c*d^9*e*x^9 + 3*(15*c^2*d^8*e + d^8*e)*b^3*x^8 + 24*(5*c^3*d^7*e + c*d^7*e)*b^3*x^7 + 3*(70*c^4*d^6*e + 28*c^2*d^6*e + d^6*e)*b^3*x^6 + 6*(42*c^5*d^5*e + 28*c^3*d^5*e + 3*c*d^5*e)*b^3*x^5 + (210*c^6*d^4*e + 210*c^4*d^4*e + 45*c^2*d^4*e + d^4*e)*b^3*x^4 + 4*(30*c^7*d^3*e + 42*c^5*d^3*e + 15*c^3*d^3*e + c*d^3*e)*b^3*x^3 + 3*(15*c^8*d^2*e + 28*c^6*d^2*e + 15*c^4*d^2*e + 2*c^2*d^2*e)*b^3*x^2 + 2*(5*c^9*d*e + 12*c^7*d*e + 9*c^5*d*e + 2*c^3*d*e)*b^3*x + (c^10*e + 3*c^8*e + 3*c^6*e + c^4*e)*b^3)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)) + 4*(a*b^2*d^10*e*x^10 + 10*a*b^2*c*d^9*e*x^9 + 3*(15*c^2*d^8*e + d^8*e)*a*b^2*x^8 + 24*(5*c^3*d^7*e + c*d^7*e)*a*b^2*x^7 + 3*(70*c^4*d^6*e + 28*c^2*d^6*e + d^6*e)*a*b^2*x^6 + 6*(42*c^5*d^5*e + 28*c^3*d^5*e + 3*c*d^5*e)*a*b^2*x^5 + (210*c^6*d^4*e + 210*c^4*d^4*e + 45*c^2*d^4*e + d^4*e)*a*b^2*x^4 + 4*(30*c^7*d^3*e + 42*c^5*d^3*e + 15*c^3*d^3*e + c*d^3*e)*a*b^2*x^3 + 3*(15*c^8*d^2*e + 28*c^6*d^2*e + 15*c^4*d^2*e + 2*c^2*d^2*e)*a*b^2*x^2 + 2*(5*c^9*d*e + 12*c^7*d*e + 9*c^5*d*e + 2*c^3*d*e)*a*b^2*x + (c^10*e + 3*c^8*e + 3*c^6*e + c^4*e)*a*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
174,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{4} \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4*sqrt(b*arcsinh(d*x + c) + a), x)","F",0
181,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*sqrt(b*arcsinh(d*x + c) + a), x)","F",0
182,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*sqrt(b*arcsinh(d*x + c) + a), x)","F",0
183,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)*sqrt(b*arcsinh(d*x + c) + a), x)","F",0
184,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x + c) + a), x)","F",0
185,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(1/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}{d e x + c e}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x + c) + a)/(d*e*x + c*e), x)","F",0
186,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{4} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4*(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
187,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
188,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
189,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
190,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(3/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(3/2)/(d*e*x + c*e), x)","F",0
192,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{4} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4*(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
193,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
194,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
195,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
196,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
197,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(5/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(5/2)/(d*e*x + c*e), x)","F",0
198,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{4} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4*(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
199,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
200,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
201,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
202,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
203,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^(7/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(7/2)/(d*e*x + c*e), x)","F",0
204,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
205,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
206,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
207,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsinh(d*x + c) + a), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} \sqrt{b \operatorname{arsinh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*sqrt(b*arcsinh(d*x + c) + a)), x)","F",0
210,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
211,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
212,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
213,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsinh(d*x + c) + a)^(3/2), x)","F",0
214,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(-3/2), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)^(3/2)), x)","F",0
216,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
217,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
218,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsinh(d*x + c) + a)^(5/2), x)","F",0
220,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(-5/2), x)","F",0
221,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)^(5/2)), x)","F",0
222,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
223,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
224,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
225,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsinh(d*x + c) + a)^(7/2), x)","F",0
226,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x + c) + a)^(-7/2), x)","F",0
227,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsinh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arsinh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsinh(d*x + c) + a)^(7/2)), x)","F",0
228,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{9}{2}} a}{9 \, d e} + \frac{1}{810} \, {\left(\frac{180 \, {\left(d^{4} e^{\frac{7}{2}} x^{4} + 4 \, c d^{3} e^{\frac{7}{2}} x^{3} + 6 \, c^{2} d^{2} e^{\frac{7}{2}} x^{2} + 4 \, c^{3} d e^{\frac{7}{2}} x + c^{4} e^{\frac{7}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d} - \frac{40 \, {\left(d x + c\right)}^{\frac{9}{2}} e^{\frac{7}{2}} - 72 \, {\left(d x + c\right)}^{\frac{5}{2}} e^{\frac{7}{2}} + 360 \, \sqrt{d x + c} e^{\frac{7}{2}} + 45 \, {\left(i \, \sqrt{2} e^{3} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - i \, \sqrt{2} e^{3} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - \sqrt{2} e^{3} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right) + \sqrt{2} e^{3} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)\right)} \sqrt{e}}{d} - 810 \, \int \frac{2 \, {\left(d^{4} e^{\frac{7}{2}} x^{4} + 4 \, c d^{3} e^{\frac{7}{2}} x^{3} + 6 \, c^{2} d^{2} e^{\frac{7}{2}} x^{2} + 4 \, c^{3} d e^{\frac{7}{2}} x + c^{4} e^{\frac{7}{2}}\right)} \sqrt{d x + c}}{9 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}\right)} b"," ",0,"2/9*(d*e*x + c*e)^(9/2)*a/(d*e) + 1/810*(180*(d^4*e^(7/2)*x^4 + 4*c*d^3*e^(7/2)*x^3 + 6*c^2*d^2*e^(7/2)*x^2 + 4*c^3*d*e^(7/2)*x + c^4*e^(7/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/d - (40*(d*x + c)^(9/2)*e^(7/2) - 72*(d*x + c)^(5/2)*e^(7/2) + 360*sqrt(d*x + c)*e^(7/2) + 45*(I*sqrt(2)*e^3*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1)) - I*sqrt(2)*e^3*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1)) - sqrt(2)*e^3*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1) + sqrt(2)*e^3*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1))*sqrt(e))/d - 810*integrate(2/9*(d^4*e^(7/2)*x^4 + 4*c*d^3*e^(7/2)*x^3 + 6*c^2*d^2*e^(7/2)*x^2 + 4*c^3*d*e^(7/2)*x + c^4*e^(7/2))*sqrt(d*x + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x))*b","F",0
229,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{7}{2}} a}{7 \, d e} + \frac{1}{294} \, {\left(\frac{84 \, {\left(d^{3} e^{\frac{5}{2}} x^{3} + 3 \, c d^{2} e^{\frac{5}{2}} x^{2} + 3 \, c^{2} d e^{\frac{5}{2}} x + c^{3} e^{\frac{5}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d} - \frac{24 \, {\left(d x + c\right)}^{\frac{7}{2}} e^{\frac{5}{2}} - 56 \, {\left(d x + c\right)}^{\frac{3}{2}} e^{\frac{5}{2}} - 21 \, {\left(i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} + \sqrt{2} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right) - \sqrt{2} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)\right)} e^{\frac{5}{2}}}{d} - 294 \, \int \frac{2 \, {\left(d^{3} e^{\frac{5}{2}} x^{3} + 3 \, c d^{2} e^{\frac{5}{2}} x^{2} + 3 \, c^{2} d e^{\frac{5}{2}} x + c^{3} e^{\frac{5}{2}}\right)} \sqrt{d x + c}}{7 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}\right)} b"," ",0,"2/7*(d*e*x + c*e)^(7/2)*a/(d*e) + 1/294*(84*(d^3*e^(5/2)*x^3 + 3*c*d^2*e^(5/2)*x^2 + 3*c^2*d*e^(5/2)*x + c^3*e^(5/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/d - (24*(d*x + c)^(7/2)*e^(5/2) - 56*(d*x + c)^(3/2)*e^(5/2) - 21*(I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1)) - I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1)) + sqrt(2)*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1) - sqrt(2)*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1))*e^(5/2))/d - 294*integrate(2/7*(d^3*e^(5/2)*x^3 + 3*c*d^2*e^(5/2)*x^2 + 3*c^2*d*e^(5/2)*x + c^3*e^(5/2))*sqrt(d*x + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x))*b","F",0
230,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{50} \, {\left(\frac{20 \, {\left(d^{2} e^{\frac{3}{2}} x^{2} + 2 \, c d e^{\frac{3}{2}} x + c^{2} e^{\frac{3}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d} - \frac{8 \, {\left(d x + c\right)}^{\frac{5}{2}} e^{\frac{3}{2}} - 40 \, \sqrt{d x + c} e^{\frac{3}{2}} - 5 \, {\left(i \, \sqrt{2} e {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - i \, \sqrt{2} e {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - \sqrt{2} e \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right) + \sqrt{2} e \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)\right)} \sqrt{e}}{d} - 50 \, \int \frac{2 \, {\left(d^{2} e^{\frac{3}{2}} x^{2} + 2 \, c d e^{\frac{3}{2}} x + c^{2} e^{\frac{3}{2}}\right)} \sqrt{d x + c}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}\right)} b + \frac{2 \, {\left(d e x + c e\right)}^{\frac{5}{2}} a}{5 \, d e}"," ",0,"1/50*(20*(d^2*e^(3/2)*x^2 + 2*c*d*e^(3/2)*x + c^2*e^(3/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/d - (8*(d*x + c)^(5/2)*e^(3/2) - 40*sqrt(d*x + c)*e^(3/2) - 5*(I*sqrt(2)*e*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1)) - I*sqrt(2)*e*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1)) - sqrt(2)*e*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1) + sqrt(2)*e*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1))*sqrt(e))/d - 50*integrate(2/5*(d^2*e^(3/2)*x^2 + 2*c*d*e^(3/2)*x + c^2*e^(3/2))*sqrt(d*x + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x))*b + 2/5*(d*e*x + c*e)^(5/2)*a/(d*e)","F",0
231,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))*(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{1}{18} \, {\left(\frac{12 \, {\left(d \sqrt{e} x + c \sqrt{e}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d} - \frac{8 \, {\left(d x + c\right)}^{\frac{3}{2}} \sqrt{e} + 3 \, {\left(i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} + \sqrt{2} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right) - \sqrt{2} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)\right)} \sqrt{e}}{d} - 18 \, \int \frac{2 \, {\left(d \sqrt{e} x + c \sqrt{e}\right)} \sqrt{d x + c}}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}\right)} b + \frac{2 \, {\left(d e x + c e\right)}^{\frac{3}{2}} a}{3 \, d e}"," ",0,"1/18*(12*(d*sqrt(e)*x + c*sqrt(e))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/d - (8*(d*x + c)^(3/2)*sqrt(e) + 3*(I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1)) - I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1)) + sqrt(2)*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1) - sqrt(2)*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1))*sqrt(e))/d - 18*integrate(2/3*(d*sqrt(e)*x + c*sqrt(e))*sqrt(d*x + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x))*b + 2/3*(d*e*x + c*e)^(3/2)*a/(d*e)","F",0
232,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\frac{i \, \sqrt{2} \sqrt{e} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - i \, \sqrt{2} \sqrt{e} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - \sqrt{2} \sqrt{e} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right) + \sqrt{2} \sqrt{e} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)}{e} + \frac{8 \, \sqrt{d x + c}}{\sqrt{e}}}{d} - \frac{4 \, {\left(d \sqrt{e} x + c \sqrt{e}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{\sqrt{d x + c} d e} + 2 \, \int \frac{2 \, {\left(d \sqrt{e} x + c \sqrt{e}\right)}}{{\left(d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + c^{3} e + c e + {\left(3 \, c^{2} d e + d e\right)} x + {\left(d^{2} e x^{2} + 2 \, c d e x + c^{2} e + e\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \sqrt{d x + c}}\,{d x}\right)} + \frac{2 \, \sqrt{d e x + c e} a}{d e}"," ",0,"-1/2*b*(((I*sqrt(2)*sqrt(e)*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1)) - I*sqrt(2)*sqrt(e)*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1)) - sqrt(2)*sqrt(e)*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1) + sqrt(2)*sqrt(e)*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1))/e + 8*sqrt(d*x + c)/sqrt(e))/d - 4*(d*sqrt(e)*x + c*sqrt(e))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(sqrt(d*x + c)*d*e) + 2*integrate(2*(d*sqrt(e)*x + c*sqrt(e))/((d^3*e*x^3 + 3*c*d^2*e*x^2 + c^3*e + c*e + (3*c^2*d*e + d*e)*x + (d^2*e*x^2 + 2*c*d*e*x + c^2*e + e)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*sqrt(d*x + c)), x)) + 2*sqrt(d*e*x + c*e)*a/(d*e)","F",0
233,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\frac{i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)}}{e^{\frac{3}{2}}} - \frac{i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)}}{e^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right)}{e^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)}{e^{\frac{3}{2}}}}{d} + \frac{4 \, \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{\sqrt{d x + c} d e^{\frac{3}{2}}} - 4 \, \int \frac{1}{{\left(d^{2} e^{\frac{3}{2}} x^{2} + 2 \, c d e^{\frac{3}{2}} x + c^{2} e^{\frac{3}{2}} + e^{\frac{3}{2}}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(d^{3} e^{\frac{3}{2}} x^{3} + 3 \, c d^{2} e^{\frac{3}{2}} x^{2} + c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}} + {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} x\right)} \sqrt{d x + c}}\,{d x}\right)} - \frac{2 \, a}{\sqrt{d e x + c e} d e}"," ",0,"-1/2*b*((I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1))/e^(3/2) - I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1))/e^(3/2) + sqrt(2)*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1)/e^(3/2) - sqrt(2)*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1)/e^(3/2))/d + 4*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(sqrt(d*x + c)*d*e^(3/2)) - 4*integrate(1/((d^2*e^(3/2)*x^2 + 2*c*d*e^(3/2)*x + c^2*e^(3/2) + e^(3/2))*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (d^3*e^(3/2)*x^3 + 3*c*d^2*e^(3/2)*x^2 + c^3*e^(3/2) + c*e^(3/2) + (3*c^2*d*e^(3/2) + d*e^(3/2))*x)*sqrt(d*x + c)), x)) - 2*a/(sqrt(d*e*x + c*e)*d*e)","F",0
234,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(12 \, \sqrt{e} \int \frac{1}{3 \, {\left(d^{4} e^{3} x^{4} + 4 \, c d^{3} e^{3} x^{3} + c^{4} e^{3} + c^{2} e^{3} + {\left(6 \, c^{2} d^{2} e^{3} + d^{2} e^{3}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{3} + c d e^{3}\right)} x + {\left(d^{3} e^{3} x^{3} + 3 \, c d^{2} e^{3} x^{2} + c^{3} e^{3} + c e^{3} + {\left(3 \, c^{2} d e^{3} + d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \sqrt{d x + c}}\,{d x} - \frac{\sqrt{e} {\left(\frac{i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)}}{e^{3}} - \frac{i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)}}{e^{3}} - \frac{\sqrt{2} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right)}{e^{3}} + \frac{\sqrt{2} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)}{e^{3}}\right)}}{d} - \frac{4 \, \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{{\left(d^{2} e^{3} x + c d e^{3}\right)} \sqrt{d x + c}}\right)} b - \frac{2 \, a}{3 \, {\left(d e x + c e\right)}^{\frac{3}{2}} d e}"," ",0,"1/6*(12*sqrt(e)*integrate(1/3/((d^4*e^3*x^4 + 4*c*d^3*e^3*x^3 + c^4*e^3 + c^2*e^3 + (6*c^2*d^2*e^3 + d^2*e^3)*x^2 + 2*(2*c^3*d*e^3 + c*d*e^3)*x + (d^3*e^3*x^3 + 3*c*d^2*e^3*x^2 + c^3*e^3 + c*e^3 + (3*c^2*d*e^3 + d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*sqrt(d*x + c)), x) - sqrt(e)*(I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1))/e^3 - I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1))/e^3 - sqrt(2)*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1)/e^3 + sqrt(2)*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1)/e^3)/d - 4*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/((d^2*e^3*x + c*d*e^3)*sqrt(d*x + c)))*b - 2/3*a/((d*e*x + c*e)^(3/2)*d*e)","F",0
235,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","\frac{1}{10} \, {\left(20 \, \sqrt{e} \int \frac{1}{5 \, {\left(d^{5} e^{4} x^{5} + 5 \, c d^{4} e^{4} x^{4} + c^{5} e^{4} + c^{3} e^{4} + {\left(10 \, c^{2} d^{3} e^{4} + d^{3} e^{4}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{4} + 3 \, c d^{2} e^{4}\right)} x^{2} + {\left(5 \, c^{4} d e^{4} + 3 \, c^{2} d e^{4}\right)} x + {\left(d^{4} e^{4} x^{4} + 4 \, c d^{3} e^{4} x^{3} + c^{4} e^{4} + c^{2} e^{4} + {\left(6 \, c^{2} d^{2} e^{4} + d^{2} e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{4} + c d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \sqrt{d x + c}}\,{d x} + \frac{\sqrt{e} {\left(\frac{i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} - i \, \sqrt{2} {\left(\log\left(\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right) - \log\left(-\frac{1}{2} i \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{d x + c}\right)} + 1\right)\right)} + \sqrt{2} \log\left(d x + \sqrt{2} \sqrt{d x + c} + c + 1\right) - \sqrt{2} \log\left(d x - \sqrt{2} \sqrt{d x + c} + c + 1\right)}{e^{4}} - \frac{8}{\sqrt{d x + c} e^{4}}\right)}}{d} - \frac{4 \, \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{{\left(d^{3} e^{4} x^{2} + 2 \, c d^{2} e^{4} x + c^{2} d e^{4}\right)} \sqrt{d x + c}}\right)} b - \frac{2 \, a}{5 \, {\left(d e x + c e\right)}^{\frac{5}{2}} d e}"," ",0,"1/10*(20*sqrt(e)*integrate(1/5/((d^5*e^4*x^5 + 5*c*d^4*e^4*x^4 + c^5*e^4 + c^3*e^4 + (10*c^2*d^3*e^4 + d^3*e^4)*x^3 + (10*c^3*d^2*e^4 + 3*c*d^2*e^4)*x^2 + (5*c^4*d*e^4 + 3*c^2*d*e^4)*x + (d^4*e^4*x^4 + 4*c*d^3*e^4*x^3 + c^4*e^4 + c^2*e^4 + (6*c^2*d^2*e^4 + d^2*e^4)*x^2 + 2*(2*c^3*d*e^4 + c*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*sqrt(d*x + c)), x) + sqrt(e)*((I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) + 2*sqrt(d*x + c)) + 1)) - I*sqrt(2)*(log(1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1) - log(-1/2*I*sqrt(2)*(sqrt(2) - 2*sqrt(d*x + c)) + 1)) + sqrt(2)*log(d*x + sqrt(2)*sqrt(d*x + c) + c + 1) - sqrt(2)*log(d*x - sqrt(2)*sqrt(d*x + c) + c + 1))/e^4 - 8/(sqrt(d*x + c)*e^4))/d - 4*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/((d^3*e^4*x^2 + 2*c*d^2*e^4*x + c^2*d*e^4)*sqrt(d*x + c)))*b - 2/5*a/((d*e*x + c*e)^(5/2)*d*e)","F",0
236,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{9}{2}} a^{2}}{9 \, d e} + \frac{2 \, {\left(b^{2} d^{4} e^{\frac{7}{2}} x^{4} + 4 \, b^{2} c d^{3} e^{\frac{7}{2}} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{\frac{7}{2}} x^{2} + 4 \, b^{2} c^{3} d e^{\frac{7}{2}} x + b^{2} c^{4} e^{\frac{7}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{9 \, d} + \int -\frac{2 \, {\left({\left(2 \, b^{2} c^{5} e^{\frac{7}{2}} - {\left(9 \, a b d^{5} e^{\frac{7}{2}} - 2 \, b^{2} d^{5} e^{\frac{7}{2}}\right)} x^{5} - 5 \, {\left(9 \, a b c d^{4} e^{\frac{7}{2}} - 2 \, b^{2} c d^{4} e^{\frac{7}{2}}\right)} x^{4} + {\left(20 \, b^{2} c^{2} d^{3} e^{\frac{7}{2}} - 9 \, {\left(10 \, c^{2} d^{3} e^{\frac{7}{2}} + d^{3} e^{\frac{7}{2}}\right)} a b\right)} x^{3} - 9 \, {\left(c^{5} e^{\frac{7}{2}} + c^{3} e^{\frac{7}{2}}\right)} a b + {\left(20 \, b^{2} c^{3} d^{2} e^{\frac{7}{2}} - 9 \, {\left(10 \, c^{3} d^{2} e^{\frac{7}{2}} + 3 \, c d^{2} e^{\frac{7}{2}}\right)} a b\right)} x^{2} + {\left(10 \, b^{2} c^{4} d e^{\frac{7}{2}} - 9 \, {\left(5 \, c^{4} d e^{\frac{7}{2}} + 3 \, c^{2} d e^{\frac{7}{2}}\right)} a b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(9 \, a b d^{6} e^{\frac{7}{2}} - 2 \, b^{2} d^{6} e^{\frac{7}{2}}\right)} x^{6} + 6 \, {\left(9 \, a b c d^{5} e^{\frac{7}{2}} - 2 \, b^{2} c d^{5} e^{\frac{7}{2}}\right)} x^{5} + {\left(9 \, {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} a b - 2 \, {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} b^{2}\right)} x^{4} + 4 \, {\left(9 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} a b - 2 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} b^{2}\right)} x^{3} + 9 \, {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} a b - 2 \, {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} b^{2} + 3 \, {\left(9 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} a b - 2 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} b^{2}\right)} x^{2} + 2 \, {\left(9 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} a b - 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{9 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/9*(d*e*x + c*e)^(9/2)*a^2/(d*e) + 2/9*(b^2*d^4*e^(7/2)*x^4 + 4*b^2*c*d^3*e^(7/2)*x^3 + 6*b^2*c^2*d^2*e^(7/2)*x^2 + 4*b^2*c^3*d*e^(7/2)*x + b^2*c^4*e^(7/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/d + integrate(-2/9*((2*b^2*c^5*e^(7/2) - (9*a*b*d^5*e^(7/2) - 2*b^2*d^5*e^(7/2))*x^5 - 5*(9*a*b*c*d^4*e^(7/2) - 2*b^2*c*d^4*e^(7/2))*x^4 + (20*b^2*c^2*d^3*e^(7/2) - 9*(10*c^2*d^3*e^(7/2) + d^3*e^(7/2))*a*b)*x^3 - 9*(c^5*e^(7/2) + c^3*e^(7/2))*a*b + (20*b^2*c^3*d^2*e^(7/2) - 9*(10*c^3*d^2*e^(7/2) + 3*c*d^2*e^(7/2))*a*b)*x^2 + (10*b^2*c^4*d*e^(7/2) - 9*(5*c^4*d*e^(7/2) + 3*c^2*d*e^(7/2))*a*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((9*a*b*d^6*e^(7/2) - 2*b^2*d^6*e^(7/2))*x^6 + 6*(9*a*b*c*d^5*e^(7/2) - 2*b^2*c*d^5*e^(7/2))*x^5 + (9*(15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*a*b - 2*(15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*b^2)*x^4 + 4*(9*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*a*b - 2*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*b^2)*x^3 + 9*(c^6*e^(7/2) + c^4*e^(7/2))*a*b - 2*(c^6*e^(7/2) + c^4*e^(7/2))*b^2 + 3*(9*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*a*b - 2*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*b^2)*x^2 + 2*(9*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*a*b - 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
237,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{7}{2}} a^{2}}{7 \, d e} + \frac{2 \, {\left(b^{2} d^{3} e^{\frac{5}{2}} x^{3} + 3 \, b^{2} c d^{2} e^{\frac{5}{2}} x^{2} + 3 \, b^{2} c^{2} d e^{\frac{5}{2}} x + b^{2} c^{3} e^{\frac{5}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{7 \, d} + \int -\frac{2 \, {\left({\left(2 \, b^{2} c^{4} e^{\frac{5}{2}} - {\left(7 \, a b d^{4} e^{\frac{5}{2}} - 2 \, b^{2} d^{4} e^{\frac{5}{2}}\right)} x^{4} - 4 \, {\left(7 \, a b c d^{3} e^{\frac{5}{2}} - 2 \, b^{2} c d^{3} e^{\frac{5}{2}}\right)} x^{3} - 7 \, {\left(c^{4} e^{\frac{5}{2}} + c^{2} e^{\frac{5}{2}}\right)} a b + {\left(12 \, b^{2} c^{2} d^{2} e^{\frac{5}{2}} - 7 \, {\left(6 \, c^{2} d^{2} e^{\frac{5}{2}} + d^{2} e^{\frac{5}{2}}\right)} a b\right)} x^{2} + 2 \, {\left(4 \, b^{2} c^{3} d e^{\frac{5}{2}} - 7 \, {\left(2 \, c^{3} d e^{\frac{5}{2}} + c d e^{\frac{5}{2}}\right)} a b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(7 \, a b d^{5} e^{\frac{5}{2}} - 2 \, b^{2} d^{5} e^{\frac{5}{2}}\right)} x^{5} + 5 \, {\left(7 \, a b c d^{4} e^{\frac{5}{2}} - 2 \, b^{2} c d^{4} e^{\frac{5}{2}}\right)} x^{4} + {\left(7 \, {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} a b - 2 \, {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} b^{2}\right)} x^{3} + 7 \, {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} a b - 2 \, {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} b^{2} + {\left(7 \, {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} a b - 2 \, {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} b^{2}\right)} x^{2} + {\left(7 \, {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} a b - 2 \, {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{7 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/7*(d*e*x + c*e)^(7/2)*a^2/(d*e) + 2/7*(b^2*d^3*e^(5/2)*x^3 + 3*b^2*c*d^2*e^(5/2)*x^2 + 3*b^2*c^2*d*e^(5/2)*x + b^2*c^3*e^(5/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/d + integrate(-2/7*((2*b^2*c^4*e^(5/2) - (7*a*b*d^4*e^(5/2) - 2*b^2*d^4*e^(5/2))*x^4 - 4*(7*a*b*c*d^3*e^(5/2) - 2*b^2*c*d^3*e^(5/2))*x^3 - 7*(c^4*e^(5/2) + c^2*e^(5/2))*a*b + (12*b^2*c^2*d^2*e^(5/2) - 7*(6*c^2*d^2*e^(5/2) + d^2*e^(5/2))*a*b)*x^2 + 2*(4*b^2*c^3*d*e^(5/2) - 7*(2*c^3*d*e^(5/2) + c*d*e^(5/2))*a*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((7*a*b*d^5*e^(5/2) - 2*b^2*d^5*e^(5/2))*x^5 + 5*(7*a*b*c*d^4*e^(5/2) - 2*b^2*c*d^4*e^(5/2))*x^4 + (7*(10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*a*b - 2*(10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*b^2)*x^3 + 7*(c^5*e^(5/2) + c^3*e^(5/2))*a*b - 2*(c^5*e^(5/2) + c^3*e^(5/2))*b^2 + (7*(10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*a*b - 2*(10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*b^2)*x^2 + (7*(5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*a*b - 2*(5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
238,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{5}{2}} a^{2}}{5 \, d e} + \frac{2 \, {\left(b^{2} d^{2} e^{\frac{3}{2}} x^{2} + 2 \, b^{2} c d e^{\frac{3}{2}} x + b^{2} c^{2} e^{\frac{3}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{5 \, d} + \int -\frac{2 \, {\left({\left(2 \, b^{2} c^{3} e^{\frac{3}{2}} - {\left(5 \, a b d^{3} e^{\frac{3}{2}} - 2 \, b^{2} d^{3} e^{\frac{3}{2}}\right)} x^{3} - 5 \, {\left(c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}}\right)} a b - 3 \, {\left(5 \, a b c d^{2} e^{\frac{3}{2}} - 2 \, b^{2} c d^{2} e^{\frac{3}{2}}\right)} x^{2} + {\left(6 \, b^{2} c^{2} d e^{\frac{3}{2}} - 5 \, {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} a b\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(5 \, a b d^{4} e^{\frac{3}{2}} - 2 \, b^{2} d^{4} e^{\frac{3}{2}}\right)} x^{4} + 4 \, {\left(5 \, a b c d^{3} e^{\frac{3}{2}} - 2 \, b^{2} c d^{3} e^{\frac{3}{2}}\right)} x^{3} + 5 \, {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} a b - 2 \, {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} b^{2} + {\left(5 \, {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} a b - 2 \, {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} b^{2}\right)} x^{2} + 2 \, {\left(5 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} a b - 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/5*(d*e*x + c*e)^(5/2)*a^2/(d*e) + 2/5*(b^2*d^2*e^(3/2)*x^2 + 2*b^2*c*d*e^(3/2)*x + b^2*c^2*e^(3/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/d + integrate(-2/5*((2*b^2*c^3*e^(3/2) - (5*a*b*d^3*e^(3/2) - 2*b^2*d^3*e^(3/2))*x^3 - 5*(c^3*e^(3/2) + c*e^(3/2))*a*b - 3*(5*a*b*c*d^2*e^(3/2) - 2*b^2*c*d^2*e^(3/2))*x^2 + (6*b^2*c^2*d*e^(3/2) - 5*(3*c^2*d*e^(3/2) + d*e^(3/2))*a*b)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((5*a*b*d^4*e^(3/2) - 2*b^2*d^4*e^(3/2))*x^4 + 4*(5*a*b*c*d^3*e^(3/2) - 2*b^2*c*d^3*e^(3/2))*x^3 + 5*(c^4*e^(3/2) + c^2*e^(3/2))*a*b - 2*(c^4*e^(3/2) + c^2*e^(3/2))*b^2 + (5*(6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*a*b - 2*(6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*b^2)*x^2 + 2*(5*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*a*b - 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
239,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2*(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b^{2} d \sqrt{e} x + b^{2} c \sqrt{e}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{3 \, d} + \frac{2 \, {\left(d e x + c e\right)}^{\frac{3}{2}} a^{2}}{3 \, d e} + \int -\frac{2 \, {\left({\left(2 \, b^{2} c^{2} \sqrt{e} - 3 \, {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b - {\left(3 \, a b d^{2} \sqrt{e} - 2 \, b^{2} d^{2} \sqrt{e}\right)} x^{2} - 2 \, {\left(3 \, a b c d \sqrt{e} - 2 \, b^{2} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(3 \, a b d^{3} \sqrt{e} - 2 \, b^{2} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b - 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{2} + 3 \, {\left(3 \, a b c d^{2} \sqrt{e} - 2 \, b^{2} c d^{2} \sqrt{e}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b - 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/3*(b^2*d*sqrt(e)*x + b^2*c*sqrt(e))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/d + 2/3*(d*e*x + c*e)^(3/2)*a^2/(d*e) + integrate(-2/3*((2*b^2*c^2*sqrt(e) - 3*(c^2*sqrt(e) + sqrt(e))*a*b - (3*a*b*d^2*sqrt(e) - 2*b^2*d^2*sqrt(e))*x^2 - 2*(3*a*b*c*d*sqrt(e) - 2*b^2*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((3*a*b*d^3*sqrt(e) - 2*b^2*d^3*sqrt(e))*x^3 + 3*(c^3*sqrt(e) + c*sqrt(e))*a*b - 2*(c^3*sqrt(e) + c*sqrt(e))*b^2 + 3*(3*a*b*c*d^2*sqrt(e) - 2*b^2*c*d^2*sqrt(e))*x^2 + (3*(3*c^2*d*sqrt(e) + d*sqrt(e))*a*b - 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
240,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{d x + c} b^{2} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d \sqrt{e}} + \frac{2 \, \sqrt{d e x + c e} a^{2}}{d e} + \int -\frac{2 \, {\left({\left(2 \, b^{2} c^{2} \sqrt{e} - {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b - {\left(a b d^{2} \sqrt{e} - 2 \, b^{2} d^{2} \sqrt{e}\right)} x^{2} - 2 \, {\left(a b c d \sqrt{e} - 2 \, b^{2} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(a b d^{3} \sqrt{e} - 2 \, b^{2} d^{3} \sqrt{e}\right)} x^{3} + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b - 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{2} + 3 \, {\left(a b c d^{2} \sqrt{e} - 2 \, b^{2} c d^{2} \sqrt{e}\right)} x^{2} + {\left({\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b - 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{4} e x^{4} + 4 \, c d^{3} e x^{3} + c^{4} e + c^{2} e + {\left(6 \, c^{2} d^{2} e + d^{2} e\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e + c d e\right)} x + {\left(d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + c^{3} e + c e + {\left(3 \, c^{2} d e + d e\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"2*sqrt(d*x + c)*b^2*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d*sqrt(e)) + 2*sqrt(d*e*x + c*e)*a^2/(d*e) + integrate(-2*((2*b^2*c^2*sqrt(e) - (c^2*sqrt(e) + sqrt(e))*a*b - (a*b*d^2*sqrt(e) - 2*b^2*d^2*sqrt(e))*x^2 - 2*(a*b*c*d*sqrt(e) - 2*b^2*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((a*b*d^3*sqrt(e) - 2*b^2*d^3*sqrt(e))*x^3 + (c^3*sqrt(e) + c*sqrt(e))*a*b - 2*(c^3*sqrt(e) + c*sqrt(e))*b^2 + 3*(a*b*c*d^2*sqrt(e) - 2*b^2*c*d^2*sqrt(e))*x^2 + ((3*c^2*d*sqrt(e) + d*sqrt(e))*a*b - 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^4*e*x^4 + 4*c*d^3*e*x^3 + c^4*e + c^2*e + (6*c^2*d^2*e + d^2*e)*x^2 + 2*(2*c^3*d*e + c*d*e)*x + (d^3*e*x^3 + 3*c*d^2*e*x^2 + c^3*e + c*e + (3*c^2*d*e + d*e)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
241,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{d x + c} b^{2} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{d^{2} e^{2} x + c d e^{2}} - \frac{2 \, a^{2}}{\sqrt{d e x + c e} d e} + \int \frac{2 \, {\left({\left(2 \, b^{2} c^{2} + {\left(c^{2} + 1\right)} a b + {\left(a b d^{2} + 2 \, b^{2} d^{2}\right)} x^{2} + 2 \, {\left(a b c d + 2 \, b^{2} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left({\left(a b d^{3} + 2 \, b^{2} d^{3}\right)} x^{3} + {\left(c^{3} + c\right)} a b + 2 \, {\left(c^{3} + c\right)} b^{2} + 3 \, {\left(a b c d^{2} + 2 \, b^{2} c d^{2}\right)} x^{2} + {\left({\left(3 \, c^{2} d + d\right)} a b + 2 \, {\left(3 \, c^{2} d + d\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{5} e^{\frac{3}{2}} x^{5} + 5 \, c d^{4} e^{\frac{3}{2}} x^{4} + c^{5} e^{\frac{3}{2}} + c^{3} e^{\frac{3}{2}} + {\left(10 \, c^{2} d^{3} e^{\frac{3}{2}} + d^{3} e^{\frac{3}{2}}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{3}{2}} + 3 \, c d^{2} e^{\frac{3}{2}}\right)} x^{2} + {\left(5 \, c^{4} d e^{\frac{3}{2}} + 3 \, c^{2} d e^{\frac{3}{2}}\right)} x + {\left(d^{4} e^{\frac{3}{2}} x^{4} + 4 \, c d^{3} e^{\frac{3}{2}} x^{3} + c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}} + {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-2*sqrt(d*x + c)*b^2*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^2*e^2*x + c*d*e^2) - 2*a^2/(sqrt(d*e*x + c*e)*d*e) + integrate(2*((2*b^2*c^2 + (c^2 + 1)*a*b + (a*b*d^2 + 2*b^2*d^2)*x^2 + 2*(a*b*c*d + 2*b^2*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + ((a*b*d^3 + 2*b^2*d^3)*x^3 + (c^3 + c)*a*b + 2*(c^3 + c)*b^2 + 3*(a*b*c*d^2 + 2*b^2*c*d^2)*x^2 + ((3*c^2*d + d)*a*b + 2*(3*c^2*d + d)*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^5*e^(3/2)*x^5 + 5*c*d^4*e^(3/2)*x^4 + c^5*e^(3/2) + c^3*e^(3/2) + (10*c^2*d^3*e^(3/2) + d^3*e^(3/2))*x^3 + (10*c^3*d^2*e^(3/2) + 3*c*d^2*e^(3/2))*x^2 + (5*c^4*d*e^(3/2) + 3*c^2*d*e^(3/2))*x + (d^4*e^(3/2)*x^4 + 4*c*d^3*e^(3/2)*x^3 + c^4*e^(3/2) + c^2*e^(3/2) + (6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*x^2 + 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
242,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{d x + c} b^{2} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{3 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{2 \, a^{2}}{3 \, {\left(d e x + c e\right)}^{\frac{3}{2}} d e} + \int \frac{2 \, {\left({\left(2 \, b^{2} c^{2} + 3 \, {\left(c^{2} + 1\right)} a b + {\left(3 \, a b d^{2} + 2 \, b^{2} d^{2}\right)} x^{2} + 2 \, {\left(3 \, a b c d + 2 \, b^{2} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left({\left(3 \, a b d^{3} + 2 \, b^{2} d^{3}\right)} x^{3} + 3 \, {\left(c^{3} + c\right)} a b + 2 \, {\left(c^{3} + c\right)} b^{2} + 3 \, {\left(3 \, a b c d^{2} + 2 \, b^{2} c d^{2}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d + d\right)} a b + 2 \, {\left(3 \, c^{2} d + d\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{3 \, {\left(d^{6} e^{\frac{5}{2}} x^{6} + 6 \, c d^{5} e^{\frac{5}{2}} x^{5} + c^{6} e^{\frac{5}{2}} + c^{4} e^{\frac{5}{2}} + {\left(15 \, c^{2} d^{4} e^{\frac{5}{2}} + d^{4} e^{\frac{5}{2}}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{\frac{5}{2}} + c d^{3} e^{\frac{5}{2}}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{\frac{5}{2}} + 2 \, c^{2} d^{2} e^{\frac{5}{2}}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{\frac{5}{2}} + 2 \, c^{3} d e^{\frac{5}{2}}\right)} x + {\left(d^{5} e^{\frac{5}{2}} x^{5} + 5 \, c d^{4} e^{\frac{5}{2}} x^{4} + c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}} + {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} x^{2} + {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-2/3*sqrt(d*x + c)*b^2*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 2/3*a^2/((d*e*x + c*e)^(3/2)*d*e) + integrate(2/3*((2*b^2*c^2 + 3*(c^2 + 1)*a*b + (3*a*b*d^2 + 2*b^2*d^2)*x^2 + 2*(3*a*b*c*d + 2*b^2*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + ((3*a*b*d^3 + 2*b^2*d^3)*x^3 + 3*(c^3 + c)*a*b + 2*(c^3 + c)*b^2 + 3*(3*a*b*c*d^2 + 2*b^2*c*d^2)*x^2 + (3*(3*c^2*d + d)*a*b + 2*(3*c^2*d + d)*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^6*e^(5/2)*x^6 + 6*c*d^5*e^(5/2)*x^5 + c^6*e^(5/2) + c^4*e^(5/2) + (15*c^2*d^4*e^(5/2) + d^4*e^(5/2))*x^4 + 4*(5*c^3*d^3*e^(5/2) + c*d^3*e^(5/2))*x^3 + 3*(5*c^4*d^2*e^(5/2) + 2*c^2*d^2*e^(5/2))*x^2 + 2*(3*c^5*d*e^(5/2) + 2*c^3*d*e^(5/2))*x + (d^5*e^(5/2)*x^5 + 5*c*d^4*e^(5/2)*x^4 + c^5*e^(5/2) + c^3*e^(5/2) + (10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*x^3 + (10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*x^2 + (5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
243,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^2/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{d x + c} b^{2} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2}}{5 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \frac{2 \, a^{2}}{5 \, {\left(d e x + c e\right)}^{\frac{5}{2}} d e} + \int \frac{2 \, {\left({\left(2 \, b^{2} c^{2} + 5 \, {\left(c^{2} + 1\right)} a b + {\left(5 \, a b d^{2} + 2 \, b^{2} d^{2}\right)} x^{2} + 2 \, {\left(5 \, a b c d + 2 \, b^{2} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left({\left(5 \, a b d^{3} + 2 \, b^{2} d^{3}\right)} x^{3} + 5 \, {\left(c^{3} + c\right)} a b + 2 \, {\left(c^{3} + c\right)} b^{2} + 3 \, {\left(5 \, a b c d^{2} + 2 \, b^{2} c d^{2}\right)} x^{2} + {\left(5 \, {\left(3 \, c^{2} d + d\right)} a b + 2 \, {\left(3 \, c^{2} d + d\right)} b^{2}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{5 \, {\left(d^{7} e^{\frac{7}{2}} x^{7} + 7 \, c d^{6} e^{\frac{7}{2}} x^{6} + c^{7} e^{\frac{7}{2}} + c^{5} e^{\frac{7}{2}} + {\left(21 \, c^{2} d^{5} e^{\frac{7}{2}} + d^{5} e^{\frac{7}{2}}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{\frac{7}{2}} + c d^{4} e^{\frac{7}{2}}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{\frac{7}{2}} + 2 \, c^{2} d^{3} e^{\frac{7}{2}}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{\frac{7}{2}} + 10 \, c^{3} d^{2} e^{\frac{7}{2}}\right)} x^{2} + {\left(7 \, c^{6} d e^{\frac{7}{2}} + 5 \, c^{4} d e^{\frac{7}{2}}\right)} x + {\left(d^{6} e^{\frac{7}{2}} x^{6} + 6 \, c d^{5} e^{\frac{7}{2}} x^{5} + c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}} + {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-2/5*sqrt(d*x + c)*b^2*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - 2/5*a^2/((d*e*x + c*e)^(5/2)*d*e) + integrate(2/5*((2*b^2*c^2 + 5*(c^2 + 1)*a*b + (5*a*b*d^2 + 2*b^2*d^2)*x^2 + 2*(5*a*b*c*d + 2*b^2*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + ((5*a*b*d^3 + 2*b^2*d^3)*x^3 + 5*(c^3 + c)*a*b + 2*(c^3 + c)*b^2 + 3*(5*a*b*c*d^2 + 2*b^2*c*d^2)*x^2 + (5*(3*c^2*d + d)*a*b + 2*(3*c^2*d + d)*b^2)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^7*e^(7/2)*x^7 + 7*c*d^6*e^(7/2)*x^6 + c^7*e^(7/2) + c^5*e^(7/2) + (21*c^2*d^5*e^(7/2) + d^5*e^(7/2))*x^5 + 5*(7*c^3*d^4*e^(7/2) + c*d^4*e^(7/2))*x^4 + 5*(7*c^4*d^3*e^(7/2) + 2*c^2*d^3*e^(7/2))*x^3 + (21*c^5*d^2*e^(7/2) + 10*c^3*d^2*e^(7/2))*x^2 + (7*c^6*d*e^(7/2) + 5*c^4*d*e^(7/2))*x + (d^6*e^(7/2)*x^6 + 6*c*d^5*e^(7/2)*x^5 + c^6*e^(7/2) + c^4*e^(7/2) + (15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*x^4 + 4*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*x^3 + 3*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*x^2 + 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
244,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{9}{2}} a^{3}}{9 \, d e} + \frac{2 \, {\left(b^{3} d^{4} e^{\frac{7}{2}} x^{4} + 4 \, b^{3} c d^{3} e^{\frac{7}{2}} x^{3} + 6 \, b^{3} c^{2} d^{2} e^{\frac{7}{2}} x^{2} + 4 \, b^{3} c^{3} d e^{\frac{7}{2}} x + b^{3} c^{4} e^{\frac{7}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{9 \, d} + \int -\frac{{\left({\left(2 \, b^{3} c^{5} e^{\frac{7}{2}} - {\left(9 \, a b^{2} d^{5} e^{\frac{7}{2}} - 2 \, b^{3} d^{5} e^{\frac{7}{2}}\right)} x^{5} - 5 \, {\left(9 \, a b^{2} c d^{4} e^{\frac{7}{2}} - 2 \, b^{3} c d^{4} e^{\frac{7}{2}}\right)} x^{4} - 9 \, {\left(c^{5} e^{\frac{7}{2}} + c^{3} e^{\frac{7}{2}}\right)} a b^{2} + {\left(20 \, b^{3} c^{2} d^{3} e^{\frac{7}{2}} - 9 \, {\left(10 \, c^{2} d^{3} e^{\frac{7}{2}} + d^{3} e^{\frac{7}{2}}\right)} a b^{2}\right)} x^{3} + {\left(20 \, b^{3} c^{3} d^{2} e^{\frac{7}{2}} - 9 \, {\left(10 \, c^{3} d^{2} e^{\frac{7}{2}} + 3 \, c d^{2} e^{\frac{7}{2}}\right)} a b^{2}\right)} x^{2} + {\left(10 \, b^{3} c^{4} d e^{\frac{7}{2}} - 9 \, {\left(5 \, c^{4} d e^{\frac{7}{2}} + 3 \, c^{2} d e^{\frac{7}{2}}\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(9 \, a b^{2} d^{6} e^{\frac{7}{2}} - 2 \, b^{3} d^{6} e^{\frac{7}{2}}\right)} x^{6} + 6 \, {\left(9 \, a b^{2} c d^{5} e^{\frac{7}{2}} - 2 \, b^{3} c d^{5} e^{\frac{7}{2}}\right)} x^{5} + {\left(9 \, {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} a b^{2} - 2 \, {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} b^{3}\right)} x^{4} + 9 \, {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} a b^{2} - 2 \, {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} b^{3} + 4 \, {\left(9 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} a b^{2} - 2 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} b^{3}\right)} x^{3} + 3 \, {\left(9 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} a b^{2} - 2 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} b^{3}\right)} x^{2} + 2 \, {\left(9 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} a b^{2} - 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} b^{3}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 9 \, {\left({\left(a^{2} b d^{5} e^{\frac{7}{2}} x^{5} + 5 \, a^{2} b c d^{4} e^{\frac{7}{2}} x^{4} + {\left(10 \, c^{2} d^{3} e^{\frac{7}{2}} + d^{3} e^{\frac{7}{2}}\right)} a^{2} b x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{7}{2}} + 3 \, c d^{2} e^{\frac{7}{2}}\right)} a^{2} b x^{2} + {\left(5 \, c^{4} d e^{\frac{7}{2}} + 3 \, c^{2} d e^{\frac{7}{2}}\right)} a^{2} b x + {\left(c^{5} e^{\frac{7}{2}} + c^{3} e^{\frac{7}{2}}\right)} a^{2} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b d^{6} e^{\frac{7}{2}} x^{6} + 6 \, a^{2} b c d^{5} e^{\frac{7}{2}} x^{5} + {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} a^{2} b x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} a^{2} b x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} a^{2} b x^{2} + 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} a^{2} b x + {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} a^{2} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/9*(d*e*x + c*e)^(9/2)*a^3/(d*e) + 2/9*(b^3*d^4*e^(7/2)*x^4 + 4*b^3*c*d^3*e^(7/2)*x^3 + 6*b^3*c^2*d^2*e^(7/2)*x^2 + 4*b^3*c^3*d*e^(7/2)*x + b^3*c^4*e^(7/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/d + integrate(-1/3*(((2*b^3*c^5*e^(7/2) - (9*a*b^2*d^5*e^(7/2) - 2*b^3*d^5*e^(7/2))*x^5 - 5*(9*a*b^2*c*d^4*e^(7/2) - 2*b^3*c*d^4*e^(7/2))*x^4 - 9*(c^5*e^(7/2) + c^3*e^(7/2))*a*b^2 + (20*b^3*c^2*d^3*e^(7/2) - 9*(10*c^2*d^3*e^(7/2) + d^3*e^(7/2))*a*b^2)*x^3 + (20*b^3*c^3*d^2*e^(7/2) - 9*(10*c^3*d^2*e^(7/2) + 3*c*d^2*e^(7/2))*a*b^2)*x^2 + (10*b^3*c^4*d*e^(7/2) - 9*(5*c^4*d*e^(7/2) + 3*c^2*d*e^(7/2))*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((9*a*b^2*d^6*e^(7/2) - 2*b^3*d^6*e^(7/2))*x^6 + 6*(9*a*b^2*c*d^5*e^(7/2) - 2*b^3*c*d^5*e^(7/2))*x^5 + (9*(15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*a*b^2 - 2*(15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*b^3)*x^4 + 9*(c^6*e^(7/2) + c^4*e^(7/2))*a*b^2 - 2*(c^6*e^(7/2) + c^4*e^(7/2))*b^3 + 4*(9*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*a*b^2 - 2*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*b^3)*x^3 + 3*(9*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*a*b^2 - 2*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*b^3)*x^2 + 2*(9*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*a*b^2 - 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*b^3)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 9*((a^2*b*d^5*e^(7/2)*x^5 + 5*a^2*b*c*d^4*e^(7/2)*x^4 + (10*c^2*d^3*e^(7/2) + d^3*e^(7/2))*a^2*b*x^3 + (10*c^3*d^2*e^(7/2) + 3*c*d^2*e^(7/2))*a^2*b*x^2 + (5*c^4*d*e^(7/2) + 3*c^2*d*e^(7/2))*a^2*b*x + (c^5*e^(7/2) + c^3*e^(7/2))*a^2*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b*d^6*e^(7/2)*x^6 + 6*a^2*b*c*d^5*e^(7/2)*x^5 + (15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*a^2*b*x^4 + 4*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*a^2*b*x^3 + 3*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*a^2*b*x^2 + 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*a^2*b*x + (c^6*e^(7/2) + c^4*e^(7/2))*a^2*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
245,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{7}{2}} a^{3}}{7 \, d e} + \frac{2 \, {\left(b^{3} d^{3} e^{\frac{5}{2}} x^{3} + 3 \, b^{3} c d^{2} e^{\frac{5}{2}} x^{2} + 3 \, b^{3} c^{2} d e^{\frac{5}{2}} x + b^{3} c^{3} e^{\frac{5}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{7 \, d} + \int -\frac{3 \, {\left({\left({\left(2 \, b^{3} c^{4} e^{\frac{5}{2}} - {\left(7 \, a b^{2} d^{4} e^{\frac{5}{2}} - 2 \, b^{3} d^{4} e^{\frac{5}{2}}\right)} x^{4} - 7 \, {\left(c^{4} e^{\frac{5}{2}} + c^{2} e^{\frac{5}{2}}\right)} a b^{2} - 4 \, {\left(7 \, a b^{2} c d^{3} e^{\frac{5}{2}} - 2 \, b^{3} c d^{3} e^{\frac{5}{2}}\right)} x^{3} + {\left(12 \, b^{3} c^{2} d^{2} e^{\frac{5}{2}} - 7 \, {\left(6 \, c^{2} d^{2} e^{\frac{5}{2}} + d^{2} e^{\frac{5}{2}}\right)} a b^{2}\right)} x^{2} + 2 \, {\left(4 \, b^{3} c^{3} d e^{\frac{5}{2}} - 7 \, {\left(2 \, c^{3} d e^{\frac{5}{2}} + c d e^{\frac{5}{2}}\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(7 \, a b^{2} d^{5} e^{\frac{5}{2}} - 2 \, b^{3} d^{5} e^{\frac{5}{2}}\right)} x^{5} + 5 \, {\left(7 \, a b^{2} c d^{4} e^{\frac{5}{2}} - 2 \, b^{3} c d^{4} e^{\frac{5}{2}}\right)} x^{4} + 7 \, {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} a b^{2} - 2 \, {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} b^{3} + {\left(7 \, {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} a b^{2} - 2 \, {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} b^{3}\right)} x^{3} + {\left(7 \, {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} a b^{2} - 2 \, {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} b^{3}\right)} x^{2} + {\left(7 \, {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} a b^{2} - 2 \, {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} b^{3}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 7 \, {\left({\left(a^{2} b d^{4} e^{\frac{5}{2}} x^{4} + 4 \, a^{2} b c d^{3} e^{\frac{5}{2}} x^{3} + {\left(6 \, c^{2} d^{2} e^{\frac{5}{2}} + d^{2} e^{\frac{5}{2}}\right)} a^{2} b x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{5}{2}} + c d e^{\frac{5}{2}}\right)} a^{2} b x + {\left(c^{4} e^{\frac{5}{2}} + c^{2} e^{\frac{5}{2}}\right)} a^{2} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b d^{5} e^{\frac{5}{2}} x^{5} + 5 \, a^{2} b c d^{4} e^{\frac{5}{2}} x^{4} + {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} a^{2} b x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} a^{2} b x^{2} + {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} a^{2} b x + {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} a^{2} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{7 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/7*(d*e*x + c*e)^(7/2)*a^3/(d*e) + 2/7*(b^3*d^3*e^(5/2)*x^3 + 3*b^3*c*d^2*e^(5/2)*x^2 + 3*b^3*c^2*d*e^(5/2)*x + b^3*c^3*e^(5/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/d + integrate(-3/7*(((2*b^3*c^4*e^(5/2) - (7*a*b^2*d^4*e^(5/2) - 2*b^3*d^4*e^(5/2))*x^4 - 7*(c^4*e^(5/2) + c^2*e^(5/2))*a*b^2 - 4*(7*a*b^2*c*d^3*e^(5/2) - 2*b^3*c*d^3*e^(5/2))*x^3 + (12*b^3*c^2*d^2*e^(5/2) - 7*(6*c^2*d^2*e^(5/2) + d^2*e^(5/2))*a*b^2)*x^2 + 2*(4*b^3*c^3*d*e^(5/2) - 7*(2*c^3*d*e^(5/2) + c*d*e^(5/2))*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((7*a*b^2*d^5*e^(5/2) - 2*b^3*d^5*e^(5/2))*x^5 + 5*(7*a*b^2*c*d^4*e^(5/2) - 2*b^3*c*d^4*e^(5/2))*x^4 + 7*(c^5*e^(5/2) + c^3*e^(5/2))*a*b^2 - 2*(c^5*e^(5/2) + c^3*e^(5/2))*b^3 + (7*(10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*a*b^2 - 2*(10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*b^3)*x^3 + (7*(10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*a*b^2 - 2*(10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*b^3)*x^2 + (7*(5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*a*b^2 - 2*(5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*b^3)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 7*((a^2*b*d^4*e^(5/2)*x^4 + 4*a^2*b*c*d^3*e^(5/2)*x^3 + (6*c^2*d^2*e^(5/2) + d^2*e^(5/2))*a^2*b*x^2 + 2*(2*c^3*d*e^(5/2) + c*d*e^(5/2))*a^2*b*x + (c^4*e^(5/2) + c^2*e^(5/2))*a^2*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b*d^5*e^(5/2)*x^5 + 5*a^2*b*c*d^4*e^(5/2)*x^4 + (10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*a^2*b*x^3 + (10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*a^2*b*x^2 + (5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*a^2*b*x + (c^5*e^(5/2) + c^3*e^(5/2))*a^2*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
246,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{5}{2}} a^{3}}{5 \, d e} + \frac{2 \, {\left(b^{3} d^{2} e^{\frac{3}{2}} x^{2} + 2 \, b^{3} c d e^{\frac{3}{2}} x + b^{3} c^{2} e^{\frac{3}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{5 \, d} + \int -\frac{3 \, {\left({\left({\left(2 \, b^{3} c^{3} e^{\frac{3}{2}} - 5 \, {\left(c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}}\right)} a b^{2} - {\left(5 \, a b^{2} d^{3} e^{\frac{3}{2}} - 2 \, b^{3} d^{3} e^{\frac{3}{2}}\right)} x^{3} - 3 \, {\left(5 \, a b^{2} c d^{2} e^{\frac{3}{2}} - 2 \, b^{3} c d^{2} e^{\frac{3}{2}}\right)} x^{2} + {\left(6 \, b^{3} c^{2} d e^{\frac{3}{2}} - 5 \, {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} a b^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(5 \, a b^{2} d^{4} e^{\frac{3}{2}} - 2 \, b^{3} d^{4} e^{\frac{3}{2}}\right)} x^{4} + 5 \, {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} a b^{2} - 2 \, {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} b^{3} + 4 \, {\left(5 \, a b^{2} c d^{3} e^{\frac{3}{2}} - 2 \, b^{3} c d^{3} e^{\frac{3}{2}}\right)} x^{3} + {\left(5 \, {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} a b^{2} - 2 \, {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} b^{3}\right)} x^{2} + 2 \, {\left(5 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} a b^{2} - 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} b^{3}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 5 \, {\left({\left(a^{2} b d^{3} e^{\frac{3}{2}} x^{3} + 3 \, a^{2} b c d^{2} e^{\frac{3}{2}} x^{2} + {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} a^{2} b x + {\left(c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}}\right)} a^{2} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b d^{4} e^{\frac{3}{2}} x^{4} + 4 \, a^{2} b c d^{3} e^{\frac{3}{2}} x^{3} + {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} a^{2} b x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} a^{2} b x + {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} a^{2} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/5*(d*e*x + c*e)^(5/2)*a^3/(d*e) + 2/5*(b^3*d^2*e^(3/2)*x^2 + 2*b^3*c*d*e^(3/2)*x + b^3*c^2*e^(3/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/d + integrate(-3/5*(((2*b^3*c^3*e^(3/2) - 5*(c^3*e^(3/2) + c*e^(3/2))*a*b^2 - (5*a*b^2*d^3*e^(3/2) - 2*b^3*d^3*e^(3/2))*x^3 - 3*(5*a*b^2*c*d^2*e^(3/2) - 2*b^3*c*d^2*e^(3/2))*x^2 + (6*b^3*c^2*d*e^(3/2) - 5*(3*c^2*d*e^(3/2) + d*e^(3/2))*a*b^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((5*a*b^2*d^4*e^(3/2) - 2*b^3*d^4*e^(3/2))*x^4 + 5*(c^4*e^(3/2) + c^2*e^(3/2))*a*b^2 - 2*(c^4*e^(3/2) + c^2*e^(3/2))*b^3 + 4*(5*a*b^2*c*d^3*e^(3/2) - 2*b^3*c*d^3*e^(3/2))*x^3 + (5*(6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*a*b^2 - 2*(6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*b^3)*x^2 + 2*(5*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*a*b^2 - 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*b^3)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 5*((a^2*b*d^3*e^(3/2)*x^3 + 3*a^2*b*c*d^2*e^(3/2)*x^2 + (3*c^2*d*e^(3/2) + d*e^(3/2))*a^2*b*x + (c^3*e^(3/2) + c*e^(3/2))*a^2*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b*d^4*e^(3/2)*x^4 + 4*a^2*b*c*d^3*e^(3/2)*x^3 + (6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*a^2*b*x^2 + 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*a^2*b*x + (c^4*e^(3/2) + c^2*e^(3/2))*a^2*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
247,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3*(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b^{3} d \sqrt{e} x + b^{3} c \sqrt{e}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{3 \, d} + \frac{2 \, {\left(d e x + c e\right)}^{\frac{3}{2}} a^{3}}{3 \, d e} + \int -\frac{{\left({\left(2 \, b^{3} c^{2} \sqrt{e} - 3 \, {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b^{2} - {\left(3 \, a b^{2} d^{2} \sqrt{e} - 2 \, b^{3} d^{2} \sqrt{e}\right)} x^{2} - 2 \, {\left(3 \, a b^{2} c d \sqrt{e} - 2 \, b^{3} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left(3 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b^{2} - 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{3} + {\left(3 \, a b^{2} d^{3} \sqrt{e} - 2 \, b^{3} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(3 \, a b^{2} c d^{2} \sqrt{e} - 2 \, b^{3} c d^{2} \sqrt{e}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b^{2} - 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{3}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 3 \, {\left({\left(a^{2} b d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{2} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{2} b x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{2} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c}\,{d x}"," ",0,"2/3*(b^3*d*sqrt(e)*x + b^3*c*sqrt(e))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/d + 2/3*(d*e*x + c*e)^(3/2)*a^3/(d*e) + integrate(-(((2*b^3*c^2*sqrt(e) - 3*(c^2*sqrt(e) + sqrt(e))*a*b^2 - (3*a*b^2*d^2*sqrt(e) - 2*b^3*d^2*sqrt(e))*x^2 - 2*(3*a*b^2*c*d*sqrt(e) - 2*b^3*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - (3*(c^3*sqrt(e) + c*sqrt(e))*a*b^2 - 2*(c^3*sqrt(e) + c*sqrt(e))*b^3 + (3*a*b^2*d^3*sqrt(e) - 2*b^3*d^3*sqrt(e))*x^3 + 3*(3*a*b^2*c*d^2*sqrt(e) - 2*b^3*c*d^2*sqrt(e))*x^2 + (3*(3*c^2*d*sqrt(e) + d*sqrt(e))*a*b^2 - 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^3)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 3*((a^2*b*d^2*sqrt(e)*x^2 + 2*a^2*b*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^2*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b*d^3*sqrt(e)*x^3 + 3*a^2*b*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^2*b*x + (c^3*sqrt(e) + c*sqrt(e))*a^2*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{d e x + c e} a^{3}}{d e} + \frac{2 \, {\left(b^{3} d \sqrt{e} x + b^{3} c \sqrt{e}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{\sqrt{d x + c} d e} - \int \frac{3 \, {\left({\left(2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{3} - {\left(a b^{2} d^{3} \sqrt{e} - 2 \, b^{3} d^{3} \sqrt{e}\right)} x^{3} - {\left(a c^{3} \sqrt{e} + a c \sqrt{e}\right)} b^{2} - 3 \, {\left(a b^{2} c d^{2} \sqrt{e} - 2 \, b^{3} c d^{2} \sqrt{e}\right)} x^{2} + {\left(2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{3} - {\left(3 \, a c^{2} d \sqrt{e} + a d \sqrt{e}\right)} b^{2}\right)} x + {\left(2 \, b^{3} c^{2} \sqrt{e} - {\left(a c^{2} \sqrt{e} + a \sqrt{e}\right)} b^{2} - {\left(a b^{2} d^{2} \sqrt{e} - 2 \, b^{3} d^{2} \sqrt{e}\right)} x^{2} - 2 \, {\left(a b^{2} c d \sqrt{e} - 2 \, b^{3} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - {\left(a^{2} b d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, a^{2} c^{2} d \sqrt{e} + a^{2} d \sqrt{e}\right)} b x + {\left(a^{2} c^{3} \sqrt{e} + a^{2} c \sqrt{e}\right)} b + {\left(a^{2} b d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b c d \sqrt{e} x + {\left(a^{2} c^{2} \sqrt{e} + a^{2} \sqrt{e}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{{\left(d^{2} e x^{2} + 2 \, c d e x + c^{2} e + e\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + c^{3} e + c e + {\left(3 \, c^{2} d e + d e\right)} x\right)} \sqrt{d x + c}}\,{d x}"," ",0,"2*sqrt(d*e*x + c*e)*a^3/(d*e) + 2*(b^3*d*sqrt(e)*x + b^3*c*sqrt(e))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(sqrt(d*x + c)*d*e) - integrate(3*((2*(c^3*sqrt(e) + c*sqrt(e))*b^3 - (a*b^2*d^3*sqrt(e) - 2*b^3*d^3*sqrt(e))*x^3 - (a*c^3*sqrt(e) + a*c*sqrt(e))*b^2 - 3*(a*b^2*c*d^2*sqrt(e) - 2*b^3*c*d^2*sqrt(e))*x^2 + (2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^3 - (3*a*c^2*d*sqrt(e) + a*d*sqrt(e))*b^2)*x + (2*b^3*c^2*sqrt(e) - (a*c^2*sqrt(e) + a*sqrt(e))*b^2 - (a*b^2*d^2*sqrt(e) - 2*b^3*d^2*sqrt(e))*x^2 - 2*(a*b^2*c*d*sqrt(e) - 2*b^3*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - (a^2*b*d^3*sqrt(e)*x^3 + 3*a^2*b*c*d^2*sqrt(e)*x^2 + (3*a^2*c^2*d*sqrt(e) + a^2*d*sqrt(e))*b*x + (a^2*c^3*sqrt(e) + a^2*c*sqrt(e))*b + (a^2*b*d^2*sqrt(e)*x^2 + 2*a^2*b*c*d*sqrt(e)*x + (a^2*c^2*sqrt(e) + a^2*sqrt(e))*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/((d^2*e*x^2 + 2*c*d*e*x + c^2*e + e)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (d^3*e*x^3 + 3*c*d^2*e*x^2 + c^3*e + c*e + (3*c^2*d*e + d*e)*x)*sqrt(d*x + c)), x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{\sqrt{d x + c} d e^{\frac{3}{2}}} - \frac{2 \, a^{3}}{\sqrt{d e x + c e} d e} + \int \frac{3 \, {\left({\left(2 \, {\left(c^{3} + c\right)} b^{3} + {\left(a b^{2} d^{3} + 2 \, b^{3} d^{3}\right)} x^{3} + {\left(a c^{3} + a c\right)} b^{2} + 3 \, {\left(a b^{2} c d^{2} + 2 \, b^{3} c d^{2}\right)} x^{2} + {\left(2 \, {\left(3 \, c^{2} d + d\right)} b^{3} + {\left(3 \, a c^{2} d + a d\right)} b^{2}\right)} x + {\left(2 \, b^{3} c^{2} + {\left(a c^{2} + a\right)} b^{2} + {\left(a b^{2} d^{2} + 2 \, b^{3} d^{2}\right)} x^{2} + 2 \, {\left(a b^{2} c d + 2 \, b^{3} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + {\left(a^{2} b d^{3} x^{3} + 3 \, a^{2} b c d^{2} x^{2} + {\left(3 \, a^{2} c^{2} d + a^{2} d\right)} b x + {\left(a^{2} c^{3} + a^{2} c\right)} b + {\left(a^{2} b d^{2} x^{2} + 2 \, a^{2} b c d x + {\left(a^{2} c^{2} + a^{2}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{{\left(d^{3} e^{\frac{3}{2}} x^{3} + 3 \, c d^{2} e^{\frac{3}{2}} x^{2} + c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}} + {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(d^{4} e^{\frac{3}{2}} x^{4} + 4 \, c d^{3} e^{\frac{3}{2}} x^{3} + c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}} + {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} x\right)} \sqrt{d x + c}}\,{d x}"," ",0,"-2*b^3*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/(sqrt(d*x + c)*d*e^(3/2)) - 2*a^3/(sqrt(d*e*x + c*e)*d*e) + integrate(3*((2*(c^3 + c)*b^3 + (a*b^2*d^3 + 2*b^3*d^3)*x^3 + (a*c^3 + a*c)*b^2 + 3*(a*b^2*c*d^2 + 2*b^3*c*d^2)*x^2 + (2*(3*c^2*d + d)*b^3 + (3*a*c^2*d + a*d)*b^2)*x + (2*b^3*c^2 + (a*c^2 + a)*b^2 + (a*b^2*d^2 + 2*b^3*d^2)*x^2 + 2*(a*b^2*c*d + 2*b^3*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + (a^2*b*d^3*x^3 + 3*a^2*b*c*d^2*x^2 + (3*a^2*c^2*d + a^2*d)*b*x + (a^2*c^3 + a^2*c)*b + (a^2*b*d^2*x^2 + 2*a^2*b*c*d*x + (a^2*c^2 + a^2)*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/((d^3*e^(3/2)*x^3 + 3*c*d^2*e^(3/2)*x^2 + c^3*e^(3/2) + c*e^(3/2) + (3*c^2*d*e^(3/2) + d*e^(3/2))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (d^4*e^(3/2)*x^4 + 4*c*d^3*e^(3/2)*x^3 + c^4*e^(3/2) + c^2*e^(3/2) + (6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*x^2 + 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*x)*sqrt(d*x + c)), x)","F",0
250,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{3 \, {\left(d^{2} e^{3} x + c d e^{3}\right)} \sqrt{d x + c}} - \frac{2 \, a^{3}}{3 \, {\left(d e x + c e\right)}^{\frac{3}{2}} d e} + \int \frac{{\left(2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{3} + {\left(3 \, a b^{2} d^{3} \sqrt{e} + 2 \, b^{3} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(a c^{3} \sqrt{e} + a c \sqrt{e}\right)} b^{2} + 3 \, {\left(3 \, a b^{2} c d^{2} \sqrt{e} + 2 \, b^{3} c d^{2} \sqrt{e}\right)} x^{2} + {\left(2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{3} + 3 \, {\left(3 \, a c^{2} d \sqrt{e} + a d \sqrt{e}\right)} b^{2}\right)} x + {\left(2 \, b^{3} c^{2} \sqrt{e} + 3 \, {\left(a c^{2} \sqrt{e} + a \sqrt{e}\right)} b^{2} + {\left(3 \, a b^{2} d^{2} \sqrt{e} + 2 \, b^{3} d^{2} \sqrt{e}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c d \sqrt{e} + 2 \, b^{3} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 3 \, {\left(a^{2} b d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, a^{2} c^{2} d \sqrt{e} + a^{2} d \sqrt{e}\right)} b x + {\left(a^{2} c^{3} \sqrt{e} + a^{2} c \sqrt{e}\right)} b + {\left(a^{2} b d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b c d \sqrt{e} x + {\left(a^{2} c^{2} \sqrt{e} + a^{2} \sqrt{e}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}{{\left(d^{4} e^{3} x^{4} + 4 \, c d^{3} e^{3} x^{3} + c^{4} e^{3} + c^{2} e^{3} + {\left(6 \, c^{2} d^{2} e^{3} + d^{2} e^{3}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{3} + c d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + c^{5} e^{3} + c^{3} e^{3} + {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x\right)} \sqrt{d x + c}}\,{d x}"," ",0,"-2/3*b^3*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/((d^2*e^3*x + c*d*e^3)*sqrt(d*x + c)) - 2/3*a^3/((d*e*x + c*e)^(3/2)*d*e) + integrate(((2*(c^3*sqrt(e) + c*sqrt(e))*b^3 + (3*a*b^2*d^3*sqrt(e) + 2*b^3*d^3*sqrt(e))*x^3 + 3*(a*c^3*sqrt(e) + a*c*sqrt(e))*b^2 + 3*(3*a*b^2*c*d^2*sqrt(e) + 2*b^3*c*d^2*sqrt(e))*x^2 + (2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^3 + 3*(3*a*c^2*d*sqrt(e) + a*d*sqrt(e))*b^2)*x + (2*b^3*c^2*sqrt(e) + 3*(a*c^2*sqrt(e) + a*sqrt(e))*b^2 + (3*a*b^2*d^2*sqrt(e) + 2*b^3*d^2*sqrt(e))*x^2 + 2*(3*a*b^2*c*d*sqrt(e) + 2*b^3*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 3*(a^2*b*d^3*sqrt(e)*x^3 + 3*a^2*b*c*d^2*sqrt(e)*x^2 + (3*a^2*c^2*d*sqrt(e) + a^2*d*sqrt(e))*b*x + (a^2*c^3*sqrt(e) + a^2*c*sqrt(e))*b + (a^2*b*d^2*sqrt(e)*x^2 + 2*a^2*b*c*d*sqrt(e)*x + (a^2*c^2*sqrt(e) + a^2*sqrt(e))*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/((d^4*e^3*x^4 + 4*c*d^3*e^3*x^3 + c^4*e^3 + c^2*e^3 + (6*c^2*d^2*e^3 + d^2*e^3)*x^2 + 2*(2*c^3*d*e^3 + c*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + c^5*e^3 + c^3*e^3 + (10*c^2*d^3*e^3 + d^3*e^3)*x^3 + (10*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (5*c^4*d*e^3 + 3*c^2*d*e^3)*x)*sqrt(d*x + c)), x)","F",0
251,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^3/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3}}{5 \, {\left(d^{3} e^{4} x^{2} + 2 \, c d^{2} e^{4} x + c^{2} d e^{4}\right)} \sqrt{d x + c}} - \frac{2 \, a^{3}}{5 \, {\left(d e x + c e\right)}^{\frac{5}{2}} d e} + \int \frac{3 \, {\left({\left(2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{3} + {\left(5 \, a b^{2} d^{3} \sqrt{e} + 2 \, b^{3} d^{3} \sqrt{e}\right)} x^{3} + 5 \, {\left(a c^{3} \sqrt{e} + a c \sqrt{e}\right)} b^{2} + 3 \, {\left(5 \, a b^{2} c d^{2} \sqrt{e} + 2 \, b^{3} c d^{2} \sqrt{e}\right)} x^{2} + {\left(2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{3} + 5 \, {\left(3 \, a c^{2} d \sqrt{e} + a d \sqrt{e}\right)} b^{2}\right)} x + {\left(2 \, b^{3} c^{2} \sqrt{e} + 5 \, {\left(a c^{2} \sqrt{e} + a \sqrt{e}\right)} b^{2} + {\left(5 \, a b^{2} d^{2} \sqrt{e} + 2 \, b^{3} d^{2} \sqrt{e}\right)} x^{2} + 2 \, {\left(5 \, a b^{2} c d \sqrt{e} + 2 \, b^{3} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 5 \, {\left(a^{2} b d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, a^{2} c^{2} d \sqrt{e} + a^{2} d \sqrt{e}\right)} b x + {\left(a^{2} c^{3} \sqrt{e} + a^{2} c \sqrt{e}\right)} b + {\left(a^{2} b d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b c d \sqrt{e} x + {\left(a^{2} c^{2} \sqrt{e} + a^{2} \sqrt{e}\right)} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{5 \, {\left({\left(d^{5} e^{4} x^{5} + 5 \, c d^{4} e^{4} x^{4} + c^{5} e^{4} + c^{3} e^{4} + {\left(10 \, c^{2} d^{3} e^{4} + d^{3} e^{4}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{4} + 3 \, c d^{2} e^{4}\right)} x^{2} + {\left(5 \, c^{4} d e^{4} + 3 \, c^{2} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} \sqrt{d x + c}\right)}}\,{d x}"," ",0,"-2/5*b^3*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3/((d^3*e^4*x^2 + 2*c*d^2*e^4*x + c^2*d*e^4)*sqrt(d*x + c)) - 2/5*a^3/((d*e*x + c*e)^(5/2)*d*e) + integrate(3/5*((2*(c^3*sqrt(e) + c*sqrt(e))*b^3 + (5*a*b^2*d^3*sqrt(e) + 2*b^3*d^3*sqrt(e))*x^3 + 5*(a*c^3*sqrt(e) + a*c*sqrt(e))*b^2 + 3*(5*a*b^2*c*d^2*sqrt(e) + 2*b^3*c*d^2*sqrt(e))*x^2 + (2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^3 + 5*(3*a*c^2*d*sqrt(e) + a*d*sqrt(e))*b^2)*x + (2*b^3*c^2*sqrt(e) + 5*(a*c^2*sqrt(e) + a*sqrt(e))*b^2 + (5*a*b^2*d^2*sqrt(e) + 2*b^3*d^2*sqrt(e))*x^2 + 2*(5*a*b^2*c*d*sqrt(e) + 2*b^3*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 5*(a^2*b*d^3*sqrt(e)*x^3 + 3*a^2*b*c*d^2*sqrt(e)*x^2 + (3*a^2*c^2*d*sqrt(e) + a^2*d*sqrt(e))*b*x + (a^2*c^3*sqrt(e) + a^2*c*sqrt(e))*b + (a^2*b*d^2*sqrt(e)*x^2 + 2*a^2*b*c*d*sqrt(e)*x + (a^2*c^2*sqrt(e) + a^2*sqrt(e))*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/((d^5*e^4*x^5 + 5*c*d^4*e^4*x^4 + c^5*e^4 + c^3*e^4 + (10*c^2*d^3*e^4 + d^3*e^4)*x^3 + (10*c^3*d^2*e^4 + 3*c*d^2*e^4)*x^2 + (5*c^4*d*e^4 + 3*c^2*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x)*sqrt(d*x + c)), x)","F",0
252,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{9}{2}} a^{4}}{9 \, d e} + \frac{2 \, {\left(b^{4} d^{4} e^{\frac{7}{2}} x^{4} + 4 \, b^{4} c d^{3} e^{\frac{7}{2}} x^{3} + 6 \, b^{4} c^{2} d^{2} e^{\frac{7}{2}} x^{2} + 4 \, b^{4} c^{3} d e^{\frac{7}{2}} x + b^{4} c^{4} e^{\frac{7}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{9 \, d} + \int -\frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{5} e^{\frac{7}{2}} - {\left(9 \, a b^{3} d^{5} e^{\frac{7}{2}} - 2 \, b^{4} d^{5} e^{\frac{7}{2}}\right)} x^{5} - 9 \, {\left(c^{5} e^{\frac{7}{2}} + c^{3} e^{\frac{7}{2}}\right)} a b^{3} - 5 \, {\left(9 \, a b^{3} c d^{4} e^{\frac{7}{2}} - 2 \, b^{4} c d^{4} e^{\frac{7}{2}}\right)} x^{4} + {\left(20 \, b^{4} c^{2} d^{3} e^{\frac{7}{2}} - 9 \, {\left(10 \, c^{2} d^{3} e^{\frac{7}{2}} + d^{3} e^{\frac{7}{2}}\right)} a b^{3}\right)} x^{3} + {\left(20 \, b^{4} c^{3} d^{2} e^{\frac{7}{2}} - 9 \, {\left(10 \, c^{3} d^{2} e^{\frac{7}{2}} + 3 \, c d^{2} e^{\frac{7}{2}}\right)} a b^{3}\right)} x^{2} + {\left(10 \, b^{4} c^{4} d e^{\frac{7}{2}} - 9 \, {\left(5 \, c^{4} d e^{\frac{7}{2}} + 3 \, c^{2} d e^{\frac{7}{2}}\right)} a b^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(9 \, a b^{3} d^{6} e^{\frac{7}{2}} - 2 \, b^{4} d^{6} e^{\frac{7}{2}}\right)} x^{6} + 6 \, {\left(9 \, a b^{3} c d^{5} e^{\frac{7}{2}} - 2 \, b^{4} c d^{5} e^{\frac{7}{2}}\right)} x^{5} + 9 \, {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} a b^{3} - 2 \, {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} b^{4} + {\left(9 \, {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} a b^{3} - 2 \, {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} b^{4}\right)} x^{4} + 4 \, {\left(9 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} a b^{3} - 2 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} b^{4}\right)} x^{3} + 3 \, {\left(9 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} a b^{3} - 2 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} b^{4}\right)} x^{2} + 2 \, {\left(9 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} a b^{3} - 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} - 27 \, {\left({\left(a^{2} b^{2} d^{5} e^{\frac{7}{2}} x^{5} + 5 \, a^{2} b^{2} c d^{4} e^{\frac{7}{2}} x^{4} + {\left(10 \, c^{2} d^{3} e^{\frac{7}{2}} + d^{3} e^{\frac{7}{2}}\right)} a^{2} b^{2} x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{7}{2}} + 3 \, c d^{2} e^{\frac{7}{2}}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d e^{\frac{7}{2}} + 3 \, c^{2} d e^{\frac{7}{2}}\right)} a^{2} b^{2} x + {\left(c^{5} e^{\frac{7}{2}} + c^{3} e^{\frac{7}{2}}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{6} e^{\frac{7}{2}} x^{6} + 6 \, a^{2} b^{2} c d^{5} e^{\frac{7}{2}} x^{5} + {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} a^{2} b^{2} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} a^{2} b^{2} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} a^{2} b^{2} x + {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 18 \, {\left({\left(a^{3} b d^{5} e^{\frac{7}{2}} x^{5} + 5 \, a^{3} b c d^{4} e^{\frac{7}{2}} x^{4} + {\left(10 \, c^{2} d^{3} e^{\frac{7}{2}} + d^{3} e^{\frac{7}{2}}\right)} a^{3} b x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{7}{2}} + 3 \, c d^{2} e^{\frac{7}{2}}\right)} a^{3} b x^{2} + {\left(5 \, c^{4} d e^{\frac{7}{2}} + 3 \, c^{2} d e^{\frac{7}{2}}\right)} a^{3} b x + {\left(c^{5} e^{\frac{7}{2}} + c^{3} e^{\frac{7}{2}}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{6} e^{\frac{7}{2}} x^{6} + 6 \, a^{3} b c d^{5} e^{\frac{7}{2}} x^{5} + {\left(15 \, c^{2} d^{4} e^{\frac{7}{2}} + d^{4} e^{\frac{7}{2}}\right)} a^{3} b x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{\frac{7}{2}} + c d^{3} e^{\frac{7}{2}}\right)} a^{3} b x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{\frac{7}{2}} + 2 \, c^{2} d^{2} e^{\frac{7}{2}}\right)} a^{3} b x^{2} + 2 \, {\left(3 \, c^{5} d e^{\frac{7}{2}} + 2 \, c^{3} d e^{\frac{7}{2}}\right)} a^{3} b x + {\left(c^{6} e^{\frac{7}{2}} + c^{4} e^{\frac{7}{2}}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{9 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/9*(d*e*x + c*e)^(9/2)*a^4/(d*e) + 2/9*(b^4*d^4*e^(7/2)*x^4 + 4*b^4*c*d^3*e^(7/2)*x^3 + 6*b^4*c^2*d^2*e^(7/2)*x^2 + 4*b^4*c^3*d*e^(7/2)*x + b^4*c^4*e^(7/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/d + integrate(-2/9*(2*((2*b^4*c^5*e^(7/2) - (9*a*b^3*d^5*e^(7/2) - 2*b^4*d^5*e^(7/2))*x^5 - 9*(c^5*e^(7/2) + c^3*e^(7/2))*a*b^3 - 5*(9*a*b^3*c*d^4*e^(7/2) - 2*b^4*c*d^4*e^(7/2))*x^4 + (20*b^4*c^2*d^3*e^(7/2) - 9*(10*c^2*d^3*e^(7/2) + d^3*e^(7/2))*a*b^3)*x^3 + (20*b^4*c^3*d^2*e^(7/2) - 9*(10*c^3*d^2*e^(7/2) + 3*c*d^2*e^(7/2))*a*b^3)*x^2 + (10*b^4*c^4*d*e^(7/2) - 9*(5*c^4*d*e^(7/2) + 3*c^2*d*e^(7/2))*a*b^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((9*a*b^3*d^6*e^(7/2) - 2*b^4*d^6*e^(7/2))*x^6 + 6*(9*a*b^3*c*d^5*e^(7/2) - 2*b^4*c*d^5*e^(7/2))*x^5 + 9*(c^6*e^(7/2) + c^4*e^(7/2))*a*b^3 - 2*(c^6*e^(7/2) + c^4*e^(7/2))*b^4 + (9*(15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*a*b^3 - 2*(15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*b^4)*x^4 + 4*(9*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*a*b^3 - 2*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*b^4)*x^3 + 3*(9*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*a*b^3 - 2*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*b^4)*x^2 + 2*(9*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*a*b^3 - 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 - 27*((a^2*b^2*d^5*e^(7/2)*x^5 + 5*a^2*b^2*c*d^4*e^(7/2)*x^4 + (10*c^2*d^3*e^(7/2) + d^3*e^(7/2))*a^2*b^2*x^3 + (10*c^3*d^2*e^(7/2) + 3*c*d^2*e^(7/2))*a^2*b^2*x^2 + (5*c^4*d*e^(7/2) + 3*c^2*d*e^(7/2))*a^2*b^2*x + (c^5*e^(7/2) + c^3*e^(7/2))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^6*e^(7/2)*x^6 + 6*a^2*b^2*c*d^5*e^(7/2)*x^5 + (15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*a^2*b^2*x^4 + 4*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*a^2*b^2*x^3 + 3*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*a^2*b^2*x^2 + 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*a^2*b^2*x + (c^6*e^(7/2) + c^4*e^(7/2))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 18*((a^3*b*d^5*e^(7/2)*x^5 + 5*a^3*b*c*d^4*e^(7/2)*x^4 + (10*c^2*d^3*e^(7/2) + d^3*e^(7/2))*a^3*b*x^3 + (10*c^3*d^2*e^(7/2) + 3*c*d^2*e^(7/2))*a^3*b*x^2 + (5*c^4*d*e^(7/2) + 3*c^2*d*e^(7/2))*a^3*b*x + (c^5*e^(7/2) + c^3*e^(7/2))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^6*e^(7/2)*x^6 + 6*a^3*b*c*d^5*e^(7/2)*x^5 + (15*c^2*d^4*e^(7/2) + d^4*e^(7/2))*a^3*b*x^4 + 4*(5*c^3*d^3*e^(7/2) + c*d^3*e^(7/2))*a^3*b*x^3 + 3*(5*c^4*d^2*e^(7/2) + 2*c^2*d^2*e^(7/2))*a^3*b*x^2 + 2*(3*c^5*d*e^(7/2) + 2*c^3*d*e^(7/2))*a^3*b*x + (c^6*e^(7/2) + c^4*e^(7/2))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
253,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{7}{2}} a^{4}}{7 \, d e} + \frac{2 \, {\left(b^{4} d^{3} e^{\frac{5}{2}} x^{3} + 3 \, b^{4} c d^{2} e^{\frac{5}{2}} x^{2} + 3 \, b^{4} c^{2} d e^{\frac{5}{2}} x + b^{4} c^{3} e^{\frac{5}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{7 \, d} + \int -\frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{4} e^{\frac{5}{2}} - 7 \, {\left(c^{4} e^{\frac{5}{2}} + c^{2} e^{\frac{5}{2}}\right)} a b^{3} - {\left(7 \, a b^{3} d^{4} e^{\frac{5}{2}} - 2 \, b^{4} d^{4} e^{\frac{5}{2}}\right)} x^{4} - 4 \, {\left(7 \, a b^{3} c d^{3} e^{\frac{5}{2}} - 2 \, b^{4} c d^{3} e^{\frac{5}{2}}\right)} x^{3} + {\left(12 \, b^{4} c^{2} d^{2} e^{\frac{5}{2}} - 7 \, {\left(6 \, c^{2} d^{2} e^{\frac{5}{2}} + d^{2} e^{\frac{5}{2}}\right)} a b^{3}\right)} x^{2} + 2 \, {\left(4 \, b^{4} c^{3} d e^{\frac{5}{2}} - 7 \, {\left(2 \, c^{3} d e^{\frac{5}{2}} + c d e^{\frac{5}{2}}\right)} a b^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(7 \, a b^{3} d^{5} e^{\frac{5}{2}} - 2 \, b^{4} d^{5} e^{\frac{5}{2}}\right)} x^{5} + 7 \, {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} a b^{3} - 2 \, {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} b^{4} + 5 \, {\left(7 \, a b^{3} c d^{4} e^{\frac{5}{2}} - 2 \, b^{4} c d^{4} e^{\frac{5}{2}}\right)} x^{4} + {\left(7 \, {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} a b^{3} - 2 \, {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} b^{4}\right)} x^{3} + {\left(7 \, {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} a b^{3} - 2 \, {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} b^{4}\right)} x^{2} + {\left(7 \, {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} a b^{3} - 2 \, {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} - 21 \, {\left({\left(a^{2} b^{2} d^{4} e^{\frac{5}{2}} x^{4} + 4 \, a^{2} b^{2} c d^{3} e^{\frac{5}{2}} x^{3} + {\left(6 \, c^{2} d^{2} e^{\frac{5}{2}} + d^{2} e^{\frac{5}{2}}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{5}{2}} + c d e^{\frac{5}{2}}\right)} a^{2} b^{2} x + {\left(c^{4} e^{\frac{5}{2}} + c^{2} e^{\frac{5}{2}}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{5} e^{\frac{5}{2}} x^{5} + 5 \, a^{2} b^{2} c d^{4} e^{\frac{5}{2}} x^{4} + {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} a^{2} b^{2} x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} a^{2} b^{2} x^{2} + {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} a^{2} b^{2} x + {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 14 \, {\left({\left(a^{3} b d^{4} e^{\frac{5}{2}} x^{4} + 4 \, a^{3} b c d^{3} e^{\frac{5}{2}} x^{3} + {\left(6 \, c^{2} d^{2} e^{\frac{5}{2}} + d^{2} e^{\frac{5}{2}}\right)} a^{3} b x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{5}{2}} + c d e^{\frac{5}{2}}\right)} a^{3} b x + {\left(c^{4} e^{\frac{5}{2}} + c^{2} e^{\frac{5}{2}}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{5} e^{\frac{5}{2}} x^{5} + 5 \, a^{3} b c d^{4} e^{\frac{5}{2}} x^{4} + {\left(10 \, c^{2} d^{3} e^{\frac{5}{2}} + d^{3} e^{\frac{5}{2}}\right)} a^{3} b x^{3} + {\left(10 \, c^{3} d^{2} e^{\frac{5}{2}} + 3 \, c d^{2} e^{\frac{5}{2}}\right)} a^{3} b x^{2} + {\left(5 \, c^{4} d e^{\frac{5}{2}} + 3 \, c^{2} d e^{\frac{5}{2}}\right)} a^{3} b x + {\left(c^{5} e^{\frac{5}{2}} + c^{3} e^{\frac{5}{2}}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{7 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/7*(d*e*x + c*e)^(7/2)*a^4/(d*e) + 2/7*(b^4*d^3*e^(5/2)*x^3 + 3*b^4*c*d^2*e^(5/2)*x^2 + 3*b^4*c^2*d*e^(5/2)*x + b^4*c^3*e^(5/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/d + integrate(-2/7*(2*((2*b^4*c^4*e^(5/2) - 7*(c^4*e^(5/2) + c^2*e^(5/2))*a*b^3 - (7*a*b^3*d^4*e^(5/2) - 2*b^4*d^4*e^(5/2))*x^4 - 4*(7*a*b^3*c*d^3*e^(5/2) - 2*b^4*c*d^3*e^(5/2))*x^3 + (12*b^4*c^2*d^2*e^(5/2) - 7*(6*c^2*d^2*e^(5/2) + d^2*e^(5/2))*a*b^3)*x^2 + 2*(4*b^4*c^3*d*e^(5/2) - 7*(2*c^3*d*e^(5/2) + c*d*e^(5/2))*a*b^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((7*a*b^3*d^5*e^(5/2) - 2*b^4*d^5*e^(5/2))*x^5 + 7*(c^5*e^(5/2) + c^3*e^(5/2))*a*b^3 - 2*(c^5*e^(5/2) + c^3*e^(5/2))*b^4 + 5*(7*a*b^3*c*d^4*e^(5/2) - 2*b^4*c*d^4*e^(5/2))*x^4 + (7*(10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*a*b^3 - 2*(10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*b^4)*x^3 + (7*(10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*a*b^3 - 2*(10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*b^4)*x^2 + (7*(5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*a*b^3 - 2*(5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 - 21*((a^2*b^2*d^4*e^(5/2)*x^4 + 4*a^2*b^2*c*d^3*e^(5/2)*x^3 + (6*c^2*d^2*e^(5/2) + d^2*e^(5/2))*a^2*b^2*x^2 + 2*(2*c^3*d*e^(5/2) + c*d*e^(5/2))*a^2*b^2*x + (c^4*e^(5/2) + c^2*e^(5/2))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^5*e^(5/2)*x^5 + 5*a^2*b^2*c*d^4*e^(5/2)*x^4 + (10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*a^2*b^2*x^3 + (10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*a^2*b^2*x^2 + (5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*a^2*b^2*x + (c^5*e^(5/2) + c^3*e^(5/2))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 14*((a^3*b*d^4*e^(5/2)*x^4 + 4*a^3*b*c*d^3*e^(5/2)*x^3 + (6*c^2*d^2*e^(5/2) + d^2*e^(5/2))*a^3*b*x^2 + 2*(2*c^3*d*e^(5/2) + c*d*e^(5/2))*a^3*b*x + (c^4*e^(5/2) + c^2*e^(5/2))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^5*e^(5/2)*x^5 + 5*a^3*b*c*d^4*e^(5/2)*x^4 + (10*c^2*d^3*e^(5/2) + d^3*e^(5/2))*a^3*b*x^3 + (10*c^3*d^2*e^(5/2) + 3*c*d^2*e^(5/2))*a^3*b*x^2 + (5*c^4*d*e^(5/2) + 3*c^2*d*e^(5/2))*a^3*b*x + (c^5*e^(5/2) + c^3*e^(5/2))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
254,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsinh(d*x+c))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{5}{2}} a^{4}}{5 \, d e} + \frac{2 \, {\left(b^{4} d^{2} e^{\frac{3}{2}} x^{2} + 2 \, b^{4} c d e^{\frac{3}{2}} x + b^{4} c^{2} e^{\frac{3}{2}}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{5 \, d} + \int -\frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{3} e^{\frac{3}{2}} - 5 \, {\left(c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}}\right)} a b^{3} - {\left(5 \, a b^{3} d^{3} e^{\frac{3}{2}} - 2 \, b^{4} d^{3} e^{\frac{3}{2}}\right)} x^{3} - 3 \, {\left(5 \, a b^{3} c d^{2} e^{\frac{3}{2}} - 2 \, b^{4} c d^{2} e^{\frac{3}{2}}\right)} x^{2} + {\left(6 \, b^{4} c^{2} d e^{\frac{3}{2}} - 5 \, {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} a b^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left(5 \, {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} a b^{3} - 2 \, {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} b^{4} + {\left(5 \, a b^{3} d^{4} e^{\frac{3}{2}} - 2 \, b^{4} d^{4} e^{\frac{3}{2}}\right)} x^{4} + 4 \, {\left(5 \, a b^{3} c d^{3} e^{\frac{3}{2}} - 2 \, b^{4} c d^{3} e^{\frac{3}{2}}\right)} x^{3} + {\left(5 \, {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} a b^{3} - 2 \, {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} b^{4}\right)} x^{2} + 2 \, {\left(5 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} a b^{3} - 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} - 15 \, {\left({\left(a^{2} b^{2} d^{3} e^{\frac{3}{2}} x^{3} + 3 \, a^{2} b^{2} c d^{2} e^{\frac{3}{2}} x^{2} + {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} a^{2} b^{2} x + {\left(c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{4} e^{\frac{3}{2}} x^{4} + 4 \, a^{2} b^{2} c d^{3} e^{\frac{3}{2}} x^{3} + {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} a^{2} b^{2} x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} a^{2} b^{2} x + {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 10 \, {\left({\left(a^{3} b d^{3} e^{\frac{3}{2}} x^{3} + 3 \, a^{3} b c d^{2} e^{\frac{3}{2}} x^{2} + {\left(3 \, c^{2} d e^{\frac{3}{2}} + d e^{\frac{3}{2}}\right)} a^{3} b x + {\left(c^{3} e^{\frac{3}{2}} + c e^{\frac{3}{2}}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{4} e^{\frac{3}{2}} x^{4} + 4 \, a^{3} b c d^{3} e^{\frac{3}{2}} x^{3} + {\left(6 \, c^{2} d^{2} e^{\frac{3}{2}} + d^{2} e^{\frac{3}{2}}\right)} a^{3} b x^{2} + 2 \, {\left(2 \, c^{3} d e^{\frac{3}{2}} + c d e^{\frac{3}{2}}\right)} a^{3} b x + {\left(c^{4} e^{\frac{3}{2}} + c^{2} e^{\frac{3}{2}}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/5*(d*e*x + c*e)^(5/2)*a^4/(d*e) + 2/5*(b^4*d^2*e^(3/2)*x^2 + 2*b^4*c*d*e^(3/2)*x + b^4*c^2*e^(3/2))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/d + integrate(-2/5*(2*((2*b^4*c^3*e^(3/2) - 5*(c^3*e^(3/2) + c*e^(3/2))*a*b^3 - (5*a*b^3*d^3*e^(3/2) - 2*b^4*d^3*e^(3/2))*x^3 - 3*(5*a*b^3*c*d^2*e^(3/2) - 2*b^4*c*d^2*e^(3/2))*x^2 + (6*b^4*c^2*d*e^(3/2) - 5*(3*c^2*d*e^(3/2) + d*e^(3/2))*a*b^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - (5*(c^4*e^(3/2) + c^2*e^(3/2))*a*b^3 - 2*(c^4*e^(3/2) + c^2*e^(3/2))*b^4 + (5*a*b^3*d^4*e^(3/2) - 2*b^4*d^4*e^(3/2))*x^4 + 4*(5*a*b^3*c*d^3*e^(3/2) - 2*b^4*c*d^3*e^(3/2))*x^3 + (5*(6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*a*b^3 - 2*(6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*b^4)*x^2 + 2*(5*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*a*b^3 - 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 - 15*((a^2*b^2*d^3*e^(3/2)*x^3 + 3*a^2*b^2*c*d^2*e^(3/2)*x^2 + (3*c^2*d*e^(3/2) + d*e^(3/2))*a^2*b^2*x + (c^3*e^(3/2) + c*e^(3/2))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^4*e^(3/2)*x^4 + 4*a^2*b^2*c*d^3*e^(3/2)*x^3 + (6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*a^2*b^2*x^2 + 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*a^2*b^2*x + (c^4*e^(3/2) + c^2*e^(3/2))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 10*((a^3*b*d^3*e^(3/2)*x^3 + 3*a^3*b*c*d^2*e^(3/2)*x^2 + (3*c^2*d*e^(3/2) + d*e^(3/2))*a^3*b*x + (c^3*e^(3/2) + c*e^(3/2))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^4*e^(3/2)*x^4 + 4*a^3*b*c*d^3*e^(3/2)*x^3 + (6*c^2*d^2*e^(3/2) + d^2*e^(3/2))*a^3*b*x^2 + 2*(2*c^3*d*e^(3/2) + c*d*e^(3/2))*a^3*b*x + (c^4*e^(3/2) + c^2*e^(3/2))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
255,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4*(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b^{4} d \sqrt{e} x + b^{4} c \sqrt{e}\right)} \sqrt{d x + c} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{3 \, d} + \frac{2 \, {\left(d e x + c e\right)}^{\frac{3}{2}} a^{4}}{3 \, d e} + \int -\frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{2} \sqrt{e} - 3 \, {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b^{3} - {\left(3 \, a b^{3} d^{2} \sqrt{e} - 2 \, b^{4} d^{2} \sqrt{e}\right)} x^{2} - 2 \, {\left(3 \, a b^{3} c d \sqrt{e} - 2 \, b^{4} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left(3 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b^{3} - 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{4} + {\left(3 \, a b^{3} d^{3} \sqrt{e} - 2 \, b^{4} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} \sqrt{e} - 2 \, b^{4} c d^{2} \sqrt{e}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b^{3} - 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} - 9 \, {\left({\left(a^{2} b^{2} d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b^{2} c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b^{2} c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{2} b^{2} x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 6 \, {\left({\left(a^{3} b d^{2} \sqrt{e} x^{2} + 2 \, a^{3} b c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{3} \sqrt{e} x^{3} + 3 \, a^{3} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{3} b x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} d + d\right)} x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + c\right)}}\,{d x}"," ",0,"2/3*(b^4*d*sqrt(e)*x + b^4*c*sqrt(e))*sqrt(d*x + c)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/d + 2/3*(d*e*x + c*e)^(3/2)*a^4/(d*e) + integrate(-2/3*(2*((2*b^4*c^2*sqrt(e) - 3*(c^2*sqrt(e) + sqrt(e))*a*b^3 - (3*a*b^3*d^2*sqrt(e) - 2*b^4*d^2*sqrt(e))*x^2 - 2*(3*a*b^3*c*d*sqrt(e) - 2*b^4*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - (3*(c^3*sqrt(e) + c*sqrt(e))*a*b^3 - 2*(c^3*sqrt(e) + c*sqrt(e))*b^4 + (3*a*b^3*d^3*sqrt(e) - 2*b^4*d^3*sqrt(e))*x^3 + 3*(3*a*b^3*c*d^2*sqrt(e) - 2*b^4*c*d^2*sqrt(e))*x^2 + (3*(3*c^2*d*sqrt(e) + d*sqrt(e))*a*b^3 - 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 - 9*((a^2*b^2*d^2*sqrt(e)*x^2 + 2*a^2*b^2*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^3*sqrt(e)*x^3 + 3*a^2*b^2*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^2*b^2*x + (c^3*sqrt(e) + c*sqrt(e))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 6*((a^3*b*d^2*sqrt(e)*x^2 + 2*a^3*b*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^3*sqrt(e)*x^3 + 3*a^3*b*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^3*b*x + (c^3*sqrt(e) + c*sqrt(e))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2*d + d)*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + c), x)","F",0
256,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{d x + c} b^{4} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{d \sqrt{e}} + \frac{2 \, \sqrt{d e x + c e} a^{4}}{d e} + \int -\frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{2} - {\left(c^{2} + 1\right)} a b^{3} - {\left(a b^{3} d^{2} - 2 \, b^{4} d^{2}\right)} x^{2} - 2 \, {\left(a b^{3} c d - 2 \, b^{4} c d\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} - {\left({\left(c^{3} + c\right)} a b^{3} - 2 \, {\left(c^{3} + c\right)} b^{4} + {\left(a b^{3} d^{3} - 2 \, b^{4} d^{3}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{2} - 2 \, b^{4} c d^{2}\right)} x^{2} + {\left({\left(3 \, c^{2} d + d\right)} a b^{3} - 2 \, {\left(3 \, c^{2} d + d\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} - 3 \, {\left({\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{2} b^{2} c d x + {\left(c^{2} + 1\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{3} x^{3} + 3 \, a^{2} b^{2} c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{2} b^{2} x + {\left(c^{3} + c\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} - 2 \, {\left({\left(a^{3} b d^{2} x^{2} + 2 \, a^{3} b c d x + {\left(c^{2} + 1\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{3} x^{3} + 3 \, a^{3} b c d^{2} x^{2} + {\left(3 \, c^{2} d + d\right)} a^{3} b x + {\left(c^{3} + c\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{d^{4} \sqrt{e} x^{4} + 4 \, c d^{3} \sqrt{e} x^{3} + c^{4} \sqrt{e} + {\left(6 \, c^{2} d^{2} \sqrt{e} + d^{2} \sqrt{e}\right)} x^{2} + c^{2} \sqrt{e} + 2 \, {\left(2 \, c^{3} d \sqrt{e} + c d \sqrt{e}\right)} x + {\left(d^{3} \sqrt{e} x^{3} + 3 \, c d^{2} \sqrt{e} x^{2} + c^{3} \sqrt{e} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} x + c \sqrt{e}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"2*sqrt(d*x + c)*b^4*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d*sqrt(e)) + 2*sqrt(d*e*x + c*e)*a^4/(d*e) + integrate(-2*(2*((2*b^4*c^2 - (c^2 + 1)*a*b^3 - (a*b^3*d^2 - 2*b^4*d^2)*x^2 - 2*(a*b^3*c*d - 2*b^4*c*d)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) - ((c^3 + c)*a*b^3 - 2*(c^3 + c)*b^4 + (a*b^3*d^3 - 2*b^4*d^3)*x^3 + 3*(a*b^3*c*d^2 - 2*b^4*c*d^2)*x^2 + ((3*c^2*d + d)*a*b^3 - 2*(3*c^2*d + d)*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 - 3*((a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + (c^2 + 1)*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^3*x^3 + 3*a^2*b^2*c*d^2*x^2 + (3*c^2*d + d)*a^2*b^2*x + (c^3 + c)*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 - 2*((a^3*b*d^2*x^2 + 2*a^3*b*c*d*x + (c^2 + 1)*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^3*x^3 + 3*a^3*b*c*d^2*x^2 + (3*c^2*d + d)*a^3*b*x + (c^3 + c)*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^4*sqrt(e)*x^4 + 4*c*d^3*sqrt(e)*x^3 + c^4*sqrt(e) + (6*c^2*d^2*sqrt(e) + d^2*sqrt(e))*x^2 + c^2*sqrt(e) + 2*(2*c^3*d*sqrt(e) + c*d*sqrt(e))*x + (d^3*sqrt(e)*x^3 + 3*c*d^2*sqrt(e)*x^2 + c^3*sqrt(e) + (3*c^2*d*sqrt(e) + d*sqrt(e))*x + c*sqrt(e))*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
257,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{d x + c} b^{4} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{d^{2} e^{2} x + c d e^{2}} - \frac{2 \, a^{4}}{\sqrt{d e x + c e} d e} + \int \frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{2} \sqrt{e} + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b^{3} + {\left(a b^{3} d^{2} \sqrt{e} + 2 \, b^{4} d^{2} \sqrt{e}\right)} x^{2} + 2 \, {\left(a b^{3} c d \sqrt{e} + 2 \, b^{4} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left({\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b^{3} + 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{4} + {\left(a b^{3} d^{3} \sqrt{e} + 2 \, b^{4} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{2} \sqrt{e} + 2 \, b^{4} c d^{2} \sqrt{e}\right)} x^{2} + {\left({\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b^{3} + 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 3 \, {\left({\left(a^{2} b^{2} d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b^{2} c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b^{2} c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{2} b^{2} x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 2 \, {\left({\left(a^{3} b d^{2} \sqrt{e} x^{2} + 2 \, a^{3} b c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{3} \sqrt{e} x^{3} + 3 \, a^{3} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{3} b x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{d^{5} e^{2} x^{5} + 5 \, c d^{4} e^{2} x^{4} + c^{5} e^{2} + c^{3} e^{2} + {\left(10 \, c^{2} d^{3} e^{2} + d^{3} e^{2}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{2} + 3 \, c d^{2} e^{2}\right)} x^{2} + {\left(5 \, c^{4} d e^{2} + 3 \, c^{2} d e^{2}\right)} x + {\left(d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + c^{4} e^{2} + c^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d e^{2} + c d e^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-2*sqrt(d*x + c)*b^4*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d^2*e^2*x + c*d*e^2) - 2*a^4/(sqrt(d*e*x + c*e)*d*e) + integrate(2*(2*((2*b^4*c^2*sqrt(e) + (c^2*sqrt(e) + sqrt(e))*a*b^3 + (a*b^3*d^2*sqrt(e) + 2*b^4*d^2*sqrt(e))*x^2 + 2*(a*b^3*c*d*sqrt(e) + 2*b^4*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + ((c^3*sqrt(e) + c*sqrt(e))*a*b^3 + 2*(c^3*sqrt(e) + c*sqrt(e))*b^4 + (a*b^3*d^3*sqrt(e) + 2*b^4*d^3*sqrt(e))*x^3 + 3*(a*b^3*c*d^2*sqrt(e) + 2*b^4*c*d^2*sqrt(e))*x^2 + ((3*c^2*d*sqrt(e) + d*sqrt(e))*a*b^3 + 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 3*((a^2*b^2*d^2*sqrt(e)*x^2 + 2*a^2*b^2*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^3*sqrt(e)*x^3 + 3*a^2*b^2*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^2*b^2*x + (c^3*sqrt(e) + c*sqrt(e))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 2*((a^3*b*d^2*sqrt(e)*x^2 + 2*a^3*b*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^3*sqrt(e)*x^3 + 3*a^3*b*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^3*b*x + (c^3*sqrt(e) + c*sqrt(e))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^5*e^2*x^5 + 5*c*d^4*e^2*x^4 + c^5*e^2 + c^3*e^2 + (10*c^2*d^3*e^2 + d^3*e^2)*x^3 + (10*c^3*d^2*e^2 + 3*c*d^2*e^2)*x^2 + (5*c^4*d*e^2 + 3*c^2*d*e^2)*x + (d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + c^4*e^2 + c^2*e^2 + (6*c^2*d^2*e^2 + d^2*e^2)*x^2 + 2*(2*c^3*d*e^2 + c*d*e^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
258,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{d x + c} b^{4} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{3 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{2 \, a^{4}}{3 \, {\left(d e x + c e\right)}^{\frac{3}{2}} d e} + \int \frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{2} \sqrt{e} + 3 \, {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b^{3} + {\left(3 \, a b^{3} d^{2} \sqrt{e} + 2 \, b^{4} d^{2} \sqrt{e}\right)} x^{2} + 2 \, {\left(3 \, a b^{3} c d \sqrt{e} + 2 \, b^{4} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(3 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b^{3} + 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{4} + {\left(3 \, a b^{3} d^{3} \sqrt{e} + 2 \, b^{4} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} \sqrt{e} + 2 \, b^{4} c d^{2} \sqrt{e}\right)} x^{2} + {\left(3 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b^{3} + 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 9 \, {\left({\left(a^{2} b^{2} d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b^{2} c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b^{2} c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{2} b^{2} x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 6 \, {\left({\left(a^{3} b d^{2} \sqrt{e} x^{2} + 2 \, a^{3} b c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{3} \sqrt{e} x^{3} + 3 \, a^{3} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{3} b x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{3 \, {\left(d^{6} e^{3} x^{6} + 6 \, c d^{5} e^{3} x^{5} + c^{6} e^{3} + c^{4} e^{3} + {\left(15 \, c^{2} d^{4} e^{3} + d^{4} e^{3}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} + c d^{3} e^{3}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{3} + 2 \, c^{2} d^{2} e^{3}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{3} + 2 \, c^{3} d e^{3}\right)} x + {\left(d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + c^{5} e^{3} + c^{3} e^{3} + {\left(10 \, c^{2} d^{3} e^{3} + d^{3} e^{3}\right)} x^{3} + {\left(10 \, c^{3} d^{2} e^{3} + 3 \, c d^{2} e^{3}\right)} x^{2} + {\left(5 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-2/3*sqrt(d*x + c)*b^4*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 2/3*a^4/((d*e*x + c*e)^(3/2)*d*e) + integrate(2/3*(2*((2*b^4*c^2*sqrt(e) + 3*(c^2*sqrt(e) + sqrt(e))*a*b^3 + (3*a*b^3*d^2*sqrt(e) + 2*b^4*d^2*sqrt(e))*x^2 + 2*(3*a*b^3*c*d*sqrt(e) + 2*b^4*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (3*(c^3*sqrt(e) + c*sqrt(e))*a*b^3 + 2*(c^3*sqrt(e) + c*sqrt(e))*b^4 + (3*a*b^3*d^3*sqrt(e) + 2*b^4*d^3*sqrt(e))*x^3 + 3*(3*a*b^3*c*d^2*sqrt(e) + 2*b^4*c*d^2*sqrt(e))*x^2 + (3*(3*c^2*d*sqrt(e) + d*sqrt(e))*a*b^3 + 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 9*((a^2*b^2*d^2*sqrt(e)*x^2 + 2*a^2*b^2*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^3*sqrt(e)*x^3 + 3*a^2*b^2*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^2*b^2*x + (c^3*sqrt(e) + c*sqrt(e))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 6*((a^3*b*d^2*sqrt(e)*x^2 + 2*a^3*b*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^3*sqrt(e)*x^3 + 3*a^3*b*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^3*b*x + (c^3*sqrt(e) + c*sqrt(e))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^6*e^3*x^6 + 6*c*d^5*e^3*x^5 + c^6*e^3 + c^4*e^3 + (15*c^2*d^4*e^3 + d^4*e^3)*x^4 + 4*(5*c^3*d^3*e^3 + c*d^3*e^3)*x^3 + 3*(5*c^4*d^2*e^3 + 2*c^2*d^2*e^3)*x^2 + 2*(3*c^5*d*e^3 + 2*c^3*d*e^3)*x + (d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + c^5*e^3 + c^3*e^3 + (10*c^2*d^3*e^3 + d^3*e^3)*x^3 + (10*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (5*c^4*d*e^3 + 3*c^2*d*e^3)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
259,0,0,0,0.000000," ","integrate((a+b*arcsinh(d*x+c))^4/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{d x + c} b^{4} \sqrt{e} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{4}}{5 \, {\left(d^{4} e^{4} x^{3} + 3 \, c d^{3} e^{4} x^{2} + 3 \, c^{2} d^{2} e^{4} x + c^{3} d e^{4}\right)}} - \frac{2 \, a^{4}}{5 \, {\left(d e x + c e\right)}^{\frac{5}{2}} d e} + \int \frac{2 \, {\left(2 \, {\left({\left(2 \, b^{4} c^{2} \sqrt{e} + 5 \, {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a b^{3} + {\left(5 \, a b^{3} d^{2} \sqrt{e} + 2 \, b^{4} d^{2} \sqrt{e}\right)} x^{2} + 2 \, {\left(5 \, a b^{3} c d \sqrt{e} + 2 \, b^{4} c d \sqrt{e}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(5 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a b^{3} + 2 \, {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} b^{4} + {\left(5 \, a b^{3} d^{3} \sqrt{e} + 2 \, b^{4} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(5 \, a b^{3} c d^{2} \sqrt{e} + 2 \, b^{4} c d^{2} \sqrt{e}\right)} x^{2} + {\left(5 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a b^{3} + 2 \, {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} b^{4}\right)} x\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{3} + 15 \, {\left({\left(a^{2} b^{2} d^{2} \sqrt{e} x^{2} + 2 \, a^{2} b^{2} c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{2} b^{2} d^{3} \sqrt{e} x^{3} + 3 \, a^{2} b^{2} c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{2} b^{2} x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{2} b^{2}\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)^{2} + 10 \, {\left({\left(a^{3} b d^{2} \sqrt{e} x^{2} + 2 \, a^{3} b c d \sqrt{e} x + {\left(c^{2} \sqrt{e} + \sqrt{e}\right)} a^{3} b\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} \sqrt{d x + c} + {\left(a^{3} b d^{3} \sqrt{e} x^{3} + 3 \, a^{3} b c d^{2} \sqrt{e} x^{2} + {\left(3 \, c^{2} d \sqrt{e} + d \sqrt{e}\right)} a^{3} b x + {\left(c^{3} \sqrt{e} + c \sqrt{e}\right)} a^{3} b\right)} \sqrt{d x + c}\right)} \log\left(d x + c + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)\right)}}{5 \, {\left(d^{7} e^{4} x^{7} + 7 \, c d^{6} e^{4} x^{6} + c^{7} e^{4} + c^{5} e^{4} + {\left(21 \, c^{2} d^{5} e^{4} + d^{5} e^{4}\right)} x^{5} + 5 \, {\left(7 \, c^{3} d^{4} e^{4} + c d^{4} e^{4}\right)} x^{4} + 5 \, {\left(7 \, c^{4} d^{3} e^{4} + 2 \, c^{2} d^{3} e^{4}\right)} x^{3} + {\left(21 \, c^{5} d^{2} e^{4} + 10 \, c^{3} d^{2} e^{4}\right)} x^{2} + {\left(7 \, c^{6} d e^{4} + 5 \, c^{4} d e^{4}\right)} x + {\left(d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + c^{6} e^{4} + c^{4} e^{4} + {\left(15 \, c^{2} d^{4} e^{4} + d^{4} e^{4}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{4} + c d^{3} e^{4}\right)} x^{3} + 3 \, {\left(5 \, c^{4} d^{2} e^{4} + 2 \, c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{5} d e^{4} + 2 \, c^{3} d e^{4}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)}}\,{d x}"," ",0,"-2/5*sqrt(d*x + c)*b^4*sqrt(e)*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^4/(d^4*e^4*x^3 + 3*c*d^3*e^4*x^2 + 3*c^2*d^2*e^4*x + c^3*d*e^4) - 2/5*a^4/((d*e*x + c*e)^(5/2)*d*e) + integrate(2/5*(2*((2*b^4*c^2*sqrt(e) + 5*(c^2*sqrt(e) + sqrt(e))*a*b^3 + (5*a*b^3*d^2*sqrt(e) + 2*b^4*d^2*sqrt(e))*x^2 + 2*(5*a*b^3*c*d*sqrt(e) + 2*b^4*c*d*sqrt(e))*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (5*(c^3*sqrt(e) + c*sqrt(e))*a*b^3 + 2*(c^3*sqrt(e) + c*sqrt(e))*b^4 + (5*a*b^3*d^3*sqrt(e) + 2*b^4*d^3*sqrt(e))*x^3 + 3*(5*a*b^3*c*d^2*sqrt(e) + 2*b^4*c*d^2*sqrt(e))*x^2 + (5*(3*c^2*d*sqrt(e) + d*sqrt(e))*a*b^3 + 2*(3*c^2*d*sqrt(e) + d*sqrt(e))*b^4)*x)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^3 + 15*((a^2*b^2*d^2*sqrt(e)*x^2 + 2*a^2*b^2*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^2*b^2)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^2*b^2*d^3*sqrt(e)*x^3 + 3*a^2*b^2*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^2*b^2*x + (c^3*sqrt(e) + c*sqrt(e))*a^2*b^2)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))^2 + 10*((a^3*b*d^2*sqrt(e)*x^2 + 2*a^3*b*c*d*sqrt(e)*x + (c^2*sqrt(e) + sqrt(e))*a^3*b)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*sqrt(d*x + c) + (a^3*b*d^3*sqrt(e)*x^3 + 3*a^3*b*c*d^2*sqrt(e)*x^2 + (3*c^2*d*sqrt(e) + d*sqrt(e))*a^3*b*x + (c^3*sqrt(e) + c*sqrt(e))*a^3*b)*sqrt(d*x + c))*log(d*x + c + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)))/(d^7*e^4*x^7 + 7*c*d^6*e^4*x^6 + c^7*e^4 + c^5*e^4 + (21*c^2*d^5*e^4 + d^5*e^4)*x^5 + 5*(7*c^3*d^4*e^4 + c*d^4*e^4)*x^4 + 5*(7*c^4*d^3*e^4 + 2*c^2*d^3*e^4)*x^3 + (21*c^5*d^2*e^4 + 10*c^3*d^2*e^4)*x^2 + (7*c^6*d*e^4 + 5*c^4*d*e^4)*x + (d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + c^6*e^4 + c^4*e^4 + (15*c^2*d^4*e^4 + d^4*e^4)*x^4 + 4*(5*c^3*d^3*e^4 + c*d^3*e^4)*x^3 + 3*(5*c^4*d^2*e^4 + 2*c^2*d^2*e^4)*x^2 + 2*(3*c^5*d*e^4 + 2*c^3*d*e^4)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
260,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \operatorname{arsinh}\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*arcsinh(b*x + a)^3, x)","F",0
261,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \operatorname{arsinh}\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*arcsinh(b*x + a)^2, x)","F",0
262,1,238,0,0.709961," ","integrate(arcsinh(b*x+a)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(x^{2} + \frac{2 \, a x}{b} + \frac{2 \, \operatorname{arsinh}\left(b x + a\right) \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{2}} - \frac{\operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{2}}{b^{2}}\right)} b - \frac{1}{2} \, {\left(\frac{a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x - \frac{{\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{b}\right)} \operatorname{arsinh}\left(b x + a\right)"," ",0,"-1/4*(x^2 + 2*a*x/b + 2*arcsinh(b*x + a)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 - arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^2/b^2)*b - 1/2*(a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x - (a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b)*arcsinh(b*x + a)","B",0
263,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(1/2)/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{\operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/arcsinh(b*x + a), x)","F",0
264,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(1/2)/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} + \int \frac{{\left(2 \, b^{2} x^{2} + 4 \, a b x + 2 \, a^{2} - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 2 \, a^{3} + {\left(6 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(2 \, b^{4} x^{4} + 8 \, a b^{3} x^{3} + 2 \, a^{4} + 3 \, {\left(4 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 3 \, a^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} + 2 \, a^{2} + 4 \, {\left(a^{3} b + a b\right)} x + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-((b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) + integrate(((2*b^2*x^2 + 4*a*b*x + 2*a^2 - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 2*(2*b^3*x^3 + 6*a*b^2*x^2 + 2*a^3 + (6*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (2*b^4*x^4 + 8*a*b^3*x^3 + 2*a^4 + 3*(4*a^2*b^2 + b^2)*x^2 + 3*a^2 + 2*(4*a^3*b + 3*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^4*x^4 + 4*a*b^3*x^3 + a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + (b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + 2*a*b*x + a^2) + 2*a^2 + 4*(a^3*b + a*b)*x + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
265,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(1/2)/arcsinh(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + {\left(6 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(2 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + {\left(3 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 3 \, a^{5} + 5 \, {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 5 \, a^{3} + 15 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(15 \, a^{4} b + 15 \, a^{2} b + 2 \, b\right)} x + 2 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{6} x^{6} + 18 \, a b^{5} x^{5} + 3 \, a^{6} + {\left(45 \, a^{2} b^{4} + 7 \, b^{4}\right)} x^{4} + 7 \, a^{4} + 4 \, {\left(15 \, a^{3} b^{3} + 7 \, a b^{3}\right)} x^{3} + {\left(45 \, a^{4} b^{2} + 42 \, a^{2} b^{2} + 5 \, b^{2}\right)} x^{2} + 5 \, a^{2} + 2 \, {\left(9 \, a^{5} b + 14 \, a^{3} b + 5 \, a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left({\left(2 \, b^{4} x^{4} + 8 \, a b^{3} x^{3} + 2 \, a^{4} + {\left(12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(4 \, a^{3} b + a b\right)} x - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + {\left(6 \, b^{5} x^{5} + 30 \, a b^{4} x^{4} + 6 \, a^{5} + {\left(60 \, a^{2} b^{3} + 7 \, b^{3}\right)} x^{3} + 7 \, a^{3} + 3 \, {\left(20 \, a^{3} b^{2} + 7 \, a b^{2}\right)} x^{2} + {\left(30 \, a^{4} b + 21 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(6 \, b^{6} x^{6} + 36 \, a b^{5} x^{5} + 6 \, a^{6} + {\left(90 \, a^{2} b^{4} + 11 \, b^{4}\right)} x^{4} + 11 \, a^{4} + 4 \, {\left(30 \, a^{3} b^{3} + 11 \, a b^{3}\right)} x^{3} + 6 \, {\left(15 \, a^{4} b^{2} + 11 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 6 \, a^{2} + 4 \, {\left(9 \, a^{5} b + 11 \, a^{3} b + 3 \, a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(2 \, b^{7} x^{7} + 14 \, a b^{6} x^{6} + 2 \, a^{7} + {\left(42 \, a^{2} b^{5} + 5 \, b^{5}\right)} x^{5} + 5 \, a^{5} + 5 \, {\left(14 \, a^{3} b^{4} + 5 \, a b^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{4} b^{3} + 25 \, a^{2} b^{3} + 2 \, b^{3}\right)} x^{3} + 4 \, a^{3} + 2 \, {\left(21 \, a^{5} b^{2} + 25 \, a^{3} b^{2} + 6 \, a b^{2}\right)} x^{2} + {\left(14 \, a^{6} b + 25 \, a^{4} b + 12 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{7} x^{6} + 6 \, a b^{6} x^{5} + a^{6} b + 3 \, a^{4} b + 3 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{4} + 4 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{3} + 3 \, a^{2} b + 3 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + a^{4} b + a^{2} b + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{2} + a b^{2}\right)} x + 3 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + a^{5} b + 2 \, a^{3} b + 2 \, {\left(5 \, a^{2} b^{4} + b^{4}\right)} x^{3} + 2 \, {\left(5 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{2} + a b + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{2} + b^{2}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int \frac{{\left(4 \, b^{4} x^{4} + 16 \, a b^{3} x^{3} + 4 \, a^{4} + 2 \, {\left(12 \, a^{2} b^{2} - b^{2}\right)} x^{2} - 2 \, a^{2} + 4 \, {\left(4 \, a^{3} b - a b\right)} x + 3\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{5}{2}} + 2 \, {\left(8 \, b^{5} x^{5} + 40 \, a b^{4} x^{4} + 8 \, a^{5} + 4 \, {\left(20 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 4 \, a^{3} + 4 \, {\left(20 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(40 \, a^{4} b + 12 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 2 \, {\left(12 \, b^{6} x^{6} + 72 \, a b^{5} x^{5} + 12 \, a^{6} + 18 \, {\left(10 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 18 \, a^{4} + 24 \, {\left(10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + 6 \, {\left(30 \, a^{4} b^{2} + 18 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 6 \, a^{2} + 12 \, {\left(6 \, a^{5} b + 6 \, a^{3} b + a b\right)} x - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(8 \, b^{7} x^{7} + 56 \, a b^{6} x^{6} + 8 \, a^{7} + 4 \, {\left(42 \, a^{2} b^{5} + 5 \, b^{5}\right)} x^{5} + 20 \, a^{5} + 20 \, {\left(14 \, a^{3} b^{4} + 5 \, a b^{4}\right)} x^{4} + 5 \, {\left(56 \, a^{4} b^{3} + 40 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 15 \, a^{3} + {\left(168 \, a^{5} b^{2} + 200 \, a^{3} b^{2} + 45 \, a b^{2}\right)} x^{2} + {\left(56 \, a^{6} b + 100 \, a^{4} b + 45 \, a^{2} b + 3 \, b\right)} x + 3 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(4 \, b^{8} x^{8} + 32 \, a b^{7} x^{7} + 4 \, a^{8} + 14 \, {\left(8 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 14 \, a^{6} + 28 \, {\left(8 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + {\left(280 \, a^{4} b^{4} + 210 \, a^{2} b^{4} + 17 \, b^{4}\right)} x^{4} + 17 \, a^{4} + 4 \, {\left(56 \, a^{5} b^{3} + 70 \, a^{3} b^{3} + 17 \, a b^{3}\right)} x^{3} + 2 \, {\left(56 \, a^{6} b^{2} + 105 \, a^{4} b^{2} + 51 \, a^{2} b^{2} + 4 \, b^{2}\right)} x^{2} + 8 \, a^{2} + 4 \, {\left(8 \, a^{7} b + 21 \, a^{5} b + 17 \, a^{3} b + 4 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{8} x^{8} + 8 \, a b^{7} x^{7} + a^{8} + 4 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 4 \, a^{6} + 8 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 6 \, a^{4} + 8 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 4 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + {\left(10 \, a^{2} b^{3} + b^{3}\right)} x^{3} + a^{3} + {\left(10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 3 \, a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{6} x^{6} + 6 \, a b^{5} x^{5} + a^{6} + {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 2 \, a^{4} + 4 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(3 \, a^{5} b + 4 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, a^{2} + 8 \, {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + 4 \, {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*((b^4*x^4 + 4*a*b^3*x^3 + a^4 + (6*a^2*b^2 + b^2)*x^2 + a^2 + 2*(2*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + (3*b^5*x^5 + 15*a*b^4*x^4 + 3*a^5 + 5*(6*a^2*b^3 + b^3)*x^3 + 5*a^3 + 15*(2*a^3*b^2 + a*b^2)*x^2 + (15*a^4*b + 15*a^2*b + 2*b)*x + 2*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^6*x^6 + 18*a*b^5*x^5 + 3*a^6 + (45*a^2*b^4 + 7*b^4)*x^4 + 7*a^4 + 4*(15*a^3*b^3 + 7*a*b^3)*x^3 + (45*a^4*b^2 + 42*a^2*b^2 + 5*b^2)*x^2 + 5*a^2 + 2*(9*a^5*b + 14*a^3*b + 5*a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + ((2*b^4*x^4 + 8*a*b^3*x^3 + 2*a^4 + (12*a^2*b^2 + b^2)*x^2 + a^2 + 2*(4*a^3*b + a*b)*x - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + (6*b^5*x^5 + 30*a*b^4*x^4 + 6*a^5 + (60*a^2*b^3 + 7*b^3)*x^3 + 7*a^3 + 3*(20*a^3*b^2 + 7*a*b^2)*x^2 + (30*a^4*b + 21*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (6*b^6*x^6 + 36*a*b^5*x^5 + 6*a^6 + (90*a^2*b^4 + 11*b^4)*x^4 + 11*a^4 + 4*(30*a^3*b^3 + 11*a*b^3)*x^3 + 6*(15*a^4*b^2 + 11*a^2*b^2 + b^2)*x^2 + 6*a^2 + 4*(9*a^5*b + 11*a^3*b + 3*a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (2*b^7*x^7 + 14*a*b^6*x^6 + 2*a^7 + (42*a^2*b^5 + 5*b^5)*x^5 + 5*a^5 + 5*(14*a^3*b^4 + 5*a*b^4)*x^4 + 2*(35*a^4*b^3 + 25*a^2*b^3 + 2*b^3)*x^3 + 4*a^3 + 2*(21*a^5*b^2 + 25*a^3*b^2 + 6*a*b^2)*x^2 + (14*a^6*b + 25*a^4*b + 12*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^7*x^6 + 6*a*b^6*x^5 + a^6*b + 3*a^4*b + 3*(5*a^2*b^5 + b^5)*x^4 + 4*(5*a^3*b^4 + 3*a*b^4)*x^3 + 3*a^2*b + 3*(5*a^4*b^3 + 6*a^2*b^3 + b^3)*x^2 + (b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^5*x^4 + 4*a*b^4*x^3 + a^4*b + a^2*b + (6*a^2*b^3 + b^3)*x^2 + 2*(2*a^3*b^2 + a*b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 6*(a^5*b^2 + 2*a^3*b^2 + a*b^2)*x + 3*(b^6*x^5 + 5*a*b^5*x^4 + a^5*b + 2*a^3*b + 2*(5*a^2*b^4 + b^4)*x^3 + 2*(5*a^3*b^3 + 3*a*b^3)*x^2 + a*b + (5*a^4*b^2 + 6*a^2*b^2 + b^2)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(1/2*((4*b^4*x^4 + 16*a*b^3*x^3 + 4*a^4 + 2*(12*a^2*b^2 - b^2)*x^2 - 2*a^2 + 4*(4*a^3*b - a*b)*x + 3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(5/2) + 2*(8*b^5*x^5 + 40*a*b^4*x^4 + 8*a^5 + 4*(20*a^2*b^3 + b^3)*x^3 + 4*a^3 + 4*(20*a^3*b^2 + 3*a*b^2)*x^2 + (40*a^4*b + 12*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 2*(12*b^6*x^6 + 72*a*b^5*x^5 + 12*a^6 + 18*(10*a^2*b^4 + b^4)*x^4 + 18*a^4 + 24*(10*a^3*b^3 + 3*a*b^3)*x^3 + 6*(30*a^4*b^2 + 18*a^2*b^2 + b^2)*x^2 + 6*a^2 + 12*(6*a^5*b + 6*a^3*b + a*b)*x - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 2*(8*b^7*x^7 + 56*a*b^6*x^6 + 8*a^7 + 4*(42*a^2*b^5 + 5*b^5)*x^5 + 20*a^5 + 20*(14*a^3*b^4 + 5*a*b^4)*x^4 + 5*(56*a^4*b^3 + 40*a^2*b^3 + 3*b^3)*x^3 + 15*a^3 + (168*a^5*b^2 + 200*a^3*b^2 + 45*a*b^2)*x^2 + (56*a^6*b + 100*a^4*b + 45*a^2*b + 3*b)*x + 3*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (4*b^8*x^8 + 32*a*b^7*x^7 + 4*a^8 + 14*(8*a^2*b^6 + b^6)*x^6 + 14*a^6 + 28*(8*a^3*b^5 + 3*a*b^5)*x^5 + (280*a^4*b^4 + 210*a^2*b^4 + 17*b^4)*x^4 + 17*a^4 + 4*(56*a^5*b^3 + 70*a^3*b^3 + 17*a*b^3)*x^3 + 2*(56*a^6*b^2 + 105*a^4*b^2 + 51*a^2*b^2 + 4*b^2)*x^2 + 8*a^2 + 4*(8*a^7*b + 21*a^5*b + 17*a^3*b + 4*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^8*x^8 + 8*a*b^7*x^7 + a^8 + 4*(7*a^2*b^6 + b^6)*x^6 + 4*a^6 + 8*(7*a^3*b^5 + 3*a*b^5)*x^5 + 2*(35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 6*a^4 + 8*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + (b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*(7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + 4*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + (10*a^2*b^3 + b^3)*x^3 + a^3 + (10*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 3*a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 6*(b^6*x^6 + 6*a*b^5*x^5 + a^6 + (15*a^2*b^4 + 2*b^4)*x^4 + 2*a^4 + 4*(5*a^3*b^3 + 2*a*b^3)*x^3 + (15*a^4*b^2 + 12*a^2*b^2 + b^2)*x^2 + a^2 + 2*(3*a^5*b + 4*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*a^2 + 8*(a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x + 4*(b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
266,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(3/2)*arcsinh(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*arcsinh(b*x + a)^3, x)","F",0
267,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(3/2)*arcsinh(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*arcsinh(b*x + a)^2, x)","F",0
268,1,394,0,0.793451," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(3/2)*arcsinh(b*x+a),x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(b^{2} x^{4} + 4 \, a b x^{3} + 6 \, a^{2} x^{2} + \frac{4 \, a^{3} x}{b} + 5 \, x^{2} + \frac{10 \, a x}{b} + \frac{6 \, \operatorname{arsinh}\left(b x + a\right) \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{2}} - \frac{3 \, \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{2}}{b^{2}}\right)} b + \frac{1}{8} \, {\left(2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x + \frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{b} + \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} - \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{b^{2}} - \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} {\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} - \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{b^{3}}\right)} \operatorname{arsinh}\left(b x + a\right)"," ",0,"-1/16*(b^2*x^4 + 4*a*b*x^3 + 6*a^2*x^2 + 4*a^3*x/b + 5*x^2 + 10*a*x/b + 6*arcsinh(b*x + a)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 - 3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^2/b^2)*b + 1/8*(2*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x + 2*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/b + 3*(a^2*b^2 - (a^2 + 1)*b^2)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - 3*(a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^2 - 3*(a^2*b^2 - (a^2 + 1)*b^2)*(a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - 3*(a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^3)*arcsinh(b*x + a)","B",0
269,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{\operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/arcsinh(b*x + a), x)","F",0
270,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 2 \, a^{2} + 4 \, {\left(a^{3} b + a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + 2 \, {\left(5 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 2 \, {\left(5 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 6 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(b^{2} x + a b\right)} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} + \int \frac{{\left(4 \, b^{4} x^{4} + 16 \, a b^{3} x^{3} + 4 \, a^{4} + 3 \, {\left(8 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 3 \, a^{2} + 2 \, {\left(8 \, a^{3} b + 3 \, a b\right)} x - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 4 \, {\left(2 \, b^{5} x^{5} + 10 \, a b^{4} x^{4} + 2 \, a^{5} + {\left(20 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + {\left(20 \, a^{3} b^{2} + 9 \, a b^{2}\right)} x^{2} + {\left(10 \, a^{4} b + 9 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(4 \, b^{6} x^{6} + 24 \, a b^{5} x^{5} + 4 \, a^{6} + 3 \, {\left(20 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 9 \, a^{4} + 4 \, {\left(20 \, a^{3} b^{3} + 9 \, a b^{3}\right)} x^{3} + 6 \, {\left(10 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 6 \, a^{2} + 12 \, {\left(2 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} + 2 \, a^{2} + 4 \, {\left(a^{3} b + a b\right)} x + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-((b^4*x^4 + 4*a*b^3*x^3 + a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + 2*a^2 + 4*(a^3*b + a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (b^5*x^5 + 5*a*b^4*x^4 + a^5 + 2*(5*a^2*b^3 + b^3)*x^3 + 2*a^3 + 2*(5*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 6*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^3*x^2 + 2*a*b^2*x + a^2*b + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) + integrate(((4*b^4*x^4 + 16*a*b^3*x^3 + 4*a^4 + 3*(8*a^2*b^2 + b^2)*x^2 + 3*a^2 + 2*(8*a^3*b + 3*a*b)*x - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 4*(2*b^5*x^5 + 10*a*b^4*x^4 + 2*a^5 + (20*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + (20*a^3*b^2 + 9*a*b^2)*x^2 + (10*a^4*b + 9*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (4*b^6*x^6 + 24*a*b^5*x^5 + 4*a^6 + 3*(20*a^2*b^4 + 3*b^4)*x^4 + 9*a^4 + 4*(20*a^3*b^3 + 9*a*b^3)*x^3 + 6*(10*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + 6*a^2 + 12*(2*a^5*b + 3*a^3*b + a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^4*x^4 + 4*a*b^3*x^3 + a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + (b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x^2 + 2*a*b*x + a^2) + 2*a^2 + 4*(a^3*b + a*b)*x + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
271,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(b^{6} x^{6} + 6 \, a b^{5} x^{5} + a^{6} + {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 2 \, a^{4} + 4 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(3 \, a^{5} b + 4 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + {\left(3 \, b^{7} x^{7} + 21 \, a b^{6} x^{6} + 3 \, a^{7} + {\left(63 \, a^{2} b^{5} + 8 \, b^{5}\right)} x^{5} + 8 \, a^{5} + 5 \, {\left(21 \, a^{3} b^{4} + 8 \, a b^{4}\right)} x^{4} + {\left(105 \, a^{4} b^{3} + 80 \, a^{2} b^{3} + 7 \, b^{3}\right)} x^{3} + 7 \, a^{3} + {\left(63 \, a^{5} b^{2} + 80 \, a^{3} b^{2} + 21 \, a b^{2}\right)} x^{2} + {\left(21 \, a^{6} b + 40 \, a^{4} b + 21 \, a^{2} b + 2 \, b\right)} x + 2 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{8} x^{8} + 24 \, a b^{7} x^{7} + 3 \, a^{8} + 2 \, {\left(42 \, a^{2} b^{6} + 5 \, b^{6}\right)} x^{6} + 10 \, a^{6} + 12 \, {\left(14 \, a^{3} b^{5} + 5 \, a b^{5}\right)} x^{5} + 6 \, {\left(35 \, a^{4} b^{4} + 25 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 12 \, a^{4} + 8 \, {\left(21 \, a^{5} b^{3} + 25 \, a^{3} b^{3} + 6 \, a b^{3}\right)} x^{3} + 6 \, {\left(14 \, a^{6} b^{2} + 25 \, a^{4} b^{2} + 12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 6 \, a^{2} + 12 \, {\left(2 \, a^{7} b + 5 \, a^{5} b + 4 \, a^{3} b + a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left({\left(4 \, b^{6} x^{6} + 24 \, a b^{5} x^{5} + 4 \, a^{6} + {\left(60 \, a^{2} b^{4} + 7 \, b^{4}\right)} x^{4} + 7 \, a^{4} + 4 \, {\left(20 \, a^{3} b^{3} + 7 \, a b^{3}\right)} x^{3} + 2 \, {\left(30 \, a^{4} b^{2} + 21 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 2 \, a^{2} + 4 \, {\left(6 \, a^{5} b + 7 \, a^{3} b + a b\right)} x - 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 3 \, {\left(4 \, b^{7} x^{7} + 28 \, a b^{6} x^{6} + 4 \, a^{7} + 3 \, {\left(28 \, a^{2} b^{5} + 3 \, b^{5}\right)} x^{5} + 9 \, a^{5} + 5 \, {\left(28 \, a^{3} b^{4} + 9 \, a b^{4}\right)} x^{4} + 2 \, {\left(70 \, a^{4} b^{3} + 45 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 6 \, a^{3} + 6 \, {\left(14 \, a^{5} b^{2} + 15 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(28 \, a^{6} b + 45 \, a^{4} b + 18 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(12 \, b^{8} x^{8} + 96 \, a b^{7} x^{7} + 12 \, a^{8} + 3 \, {\left(112 \, a^{2} b^{6} + 11 \, b^{6}\right)} x^{6} + 33 \, a^{6} + 6 \, {\left(112 \, a^{3} b^{5} + 33 \, a b^{5}\right)} x^{5} + {\left(840 \, a^{4} b^{4} + 495 \, a^{2} b^{4} + 31 \, b^{4}\right)} x^{4} + 31 \, a^{4} + 4 \, {\left(168 \, a^{5} b^{3} + 165 \, a^{3} b^{3} + 31 \, a b^{3}\right)} x^{3} + {\left(336 \, a^{6} b^{2} + 495 \, a^{4} b^{2} + 186 \, a^{2} b^{2} + 11 \, b^{2}\right)} x^{2} + 11 \, a^{2} + 2 \, {\left(48 \, a^{7} b + 99 \, a^{5} b + 62 \, a^{3} b + 11 \, a b\right)} x + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(4 \, b^{9} x^{9} + 36 \, a b^{8} x^{8} + 4 \, a^{9} + {\left(144 \, a^{2} b^{7} + 13 \, b^{7}\right)} x^{7} + 13 \, a^{7} + 7 \, {\left(48 \, a^{3} b^{6} + 13 \, a b^{6}\right)} x^{6} + 3 \, {\left(168 \, a^{4} b^{5} + 91 \, a^{2} b^{5} + 5 \, b^{5}\right)} x^{5} + 15 \, a^{5} + {\left(504 \, a^{5} b^{4} + 455 \, a^{3} b^{4} + 75 \, a b^{4}\right)} x^{4} + {\left(336 \, a^{6} b^{3} + 455 \, a^{4} b^{3} + 150 \, a^{2} b^{3} + 7 \, b^{3}\right)} x^{3} + 7 \, a^{3} + 3 \, {\left(48 \, a^{7} b^{2} + 91 \, a^{5} b^{2} + 50 \, a^{3} b^{2} + 7 \, a b^{2}\right)} x^{2} + {\left(36 \, a^{8} b + 91 \, a^{6} b + 75 \, a^{4} b + 21 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(b^{9} x^{9} + 9 \, a b^{8} x^{8} + a^{9} + 4 \, {\left(9 \, a^{2} b^{7} + b^{7}\right)} x^{7} + 4 \, a^{7} + 28 \, {\left(3 \, a^{3} b^{6} + a b^{6}\right)} x^{6} + 6 \, {\left(21 \, a^{4} b^{5} + 14 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 6 \, a^{5} + 2 \, {\left(63 \, a^{5} b^{4} + 70 \, a^{3} b^{4} + 15 \, a b^{4}\right)} x^{4} + 4 \, {\left(21 \, a^{6} b^{3} + 35 \, a^{4} b^{3} + 15 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 4 \, a^{3} + 12 \, {\left(3 \, a^{7} b^{2} + 7 \, a^{5} b^{2} + 5 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(9 \, a^{8} b + 28 \, a^{6} b + 30 \, a^{4} b + 12 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{7} x^{6} + 6 \, a b^{6} x^{5} + a^{6} b + 3 \, a^{4} b + 3 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{4} + 4 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{3} + 3 \, a^{2} b + 3 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + a^{4} b + a^{2} b + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{2} + a b^{2}\right)} x + 3 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + a^{5} b + 2 \, a^{3} b + 2 \, {\left(5 \, a^{2} b^{4} + b^{4}\right)} x^{3} + 2 \, {\left(5 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{2} + a b + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{2} + b^{2}\right)} x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + b\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int \frac{{\left(16 \, b^{6} x^{6} + 96 \, a b^{5} x^{5} + 16 \, a^{6} + 10 \, {\left(24 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 10 \, a^{4} + 40 \, {\left(8 \, a^{3} b^{3} + a b^{3}\right)} x^{3} + 3 \, {\left(80 \, a^{4} b^{2} + 20 \, a^{2} b^{2} - b^{2}\right)} x^{2} - 3 \, a^{2} + 2 \, {\left(48 \, a^{5} b + 20 \, a^{3} b - 3 \, a b\right)} x + 3\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{5}{2}} + 4 \, {\left(16 \, b^{7} x^{7} + 112 \, a b^{6} x^{6} + 16 \, a^{7} + {\left(336 \, a^{2} b^{5} + 23 \, b^{5}\right)} x^{5} + 23 \, a^{5} + 5 \, {\left(112 \, a^{3} b^{4} + 23 \, a b^{4}\right)} x^{4} + {\left(560 \, a^{4} b^{3} + 230 \, a^{2} b^{3} + 7 \, b^{3}\right)} x^{3} + 7 \, a^{3} + {\left(336 \, a^{5} b^{2} + 230 \, a^{3} b^{2} + 21 \, a b^{2}\right)} x^{2} + {\left(112 \, a^{6} b + 115 \, a^{4} b + 21 \, a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 12 \, {\left(8 \, b^{8} x^{8} + 64 \, a b^{7} x^{7} + 8 \, a^{8} + 2 \, {\left(112 \, a^{2} b^{6} + 9 \, b^{6}\right)} x^{6} + 18 \, a^{6} + 4 \, {\left(112 \, a^{3} b^{5} + 27 \, a b^{5}\right)} x^{5} + {\left(560 \, a^{4} b^{4} + 270 \, a^{2} b^{4} + 13 \, b^{4}\right)} x^{4} + 13 \, a^{4} + 4 \, {\left(112 \, a^{5} b^{3} + 90 \, a^{3} b^{3} + 13 \, a b^{3}\right)} x^{3} + {\left(224 \, a^{6} b^{2} + 270 \, a^{4} b^{2} + 78 \, a^{2} b^{2} + 3 \, b^{2}\right)} x^{2} + 3 \, a^{2} + 2 \, {\left(32 \, a^{7} b + 54 \, a^{5} b + 26 \, a^{3} b + 3 \, a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 4 \, {\left(16 \, b^{9} x^{9} + 144 \, a b^{8} x^{8} + 16 \, a^{9} + {\left(576 \, a^{2} b^{7} + 49 \, b^{7}\right)} x^{7} + 49 \, a^{7} + 7 \, {\left(192 \, a^{3} b^{6} + 49 \, a b^{6}\right)} x^{6} + 3 \, {\left(672 \, a^{4} b^{5} + 343 \, a^{2} b^{5} + 18 \, b^{5}\right)} x^{5} + 54 \, a^{5} + {\left(2016 \, a^{5} b^{4} + 1715 \, a^{3} b^{4} + 270 \, a b^{4}\right)} x^{4} + {\left(1344 \, a^{6} b^{3} + 1715 \, a^{4} b^{3} + 540 \, a^{2} b^{3} + 25 \, b^{3}\right)} x^{3} + 25 \, a^{3} + 3 \, {\left(192 \, a^{7} b^{2} + 343 \, a^{5} b^{2} + 180 \, a^{3} b^{2} + 25 \, a b^{2}\right)} x^{2} + {\left(144 \, a^{8} b + 343 \, a^{6} b + 270 \, a^{4} b + 75 \, a^{2} b + 4 \, b\right)} x + 4 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(16 \, b^{10} x^{10} + 160 \, a b^{9} x^{9} + 16 \, a^{10} + 2 \, {\left(360 \, a^{2} b^{8} + 31 \, b^{8}\right)} x^{8} + 62 \, a^{8} + 16 \, {\left(120 \, a^{3} b^{7} + 31 \, a b^{7}\right)} x^{7} + 7 \, {\left(480 \, a^{4} b^{6} + 248 \, a^{2} b^{6} + 13 \, b^{6}\right)} x^{6} + 91 \, a^{6} + 14 \, {\left(288 \, a^{5} b^{5} + 248 \, a^{3} b^{5} + 39 \, a b^{5}\right)} x^{5} + {\left(3360 \, a^{6} b^{4} + 4340 \, a^{4} b^{4} + 1365 \, a^{2} b^{4} + 61 \, b^{4}\right)} x^{4} + 61 \, a^{4} + 4 \, {\left(480 \, a^{7} b^{3} + 868 \, a^{5} b^{3} + 455 \, a^{3} b^{3} + 61 \, a b^{3}\right)} x^{3} + {\left(720 \, a^{8} b^{2} + 1736 \, a^{6} b^{2} + 1365 \, a^{4} b^{2} + 366 \, a^{2} b^{2} + 17 \, b^{2}\right)} x^{2} + 17 \, a^{2} + 2 \, {\left(80 \, a^{9} b + 248 \, a^{7} b + 273 \, a^{5} b + 122 \, a^{3} b + 17 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, {\left(b^{8} x^{8} + 8 \, a b^{7} x^{7} + a^{8} + 4 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 4 \, a^{6} + 8 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 6 \, a^{4} + 8 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 4 \, {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 4 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + {\left(10 \, a^{2} b^{3} + b^{3}\right)} x^{3} + a^{3} + {\left(10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 3 \, a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 6 \, {\left(b^{6} x^{6} + 6 \, a b^{5} x^{5} + a^{6} + {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 2 \, a^{4} + 4 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(3 \, a^{5} b + 4 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + 4 \, a^{2} + 8 \, {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + 4 \, {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*((b^6*x^6 + 6*a*b^5*x^5 + a^6 + (15*a^2*b^4 + 2*b^4)*x^4 + 2*a^4 + 4*(5*a^3*b^3 + 2*a*b^3)*x^3 + (15*a^4*b^2 + 12*a^2*b^2 + b^2)*x^2 + a^2 + 2*(3*a^5*b + 4*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + (3*b^7*x^7 + 21*a*b^6*x^6 + 3*a^7 + (63*a^2*b^5 + 8*b^5)*x^5 + 8*a^5 + 5*(21*a^3*b^4 + 8*a*b^4)*x^4 + (105*a^4*b^3 + 80*a^2*b^3 + 7*b^3)*x^3 + 7*a^3 + (63*a^5*b^2 + 80*a^3*b^2 + 21*a*b^2)*x^2 + (21*a^6*b + 40*a^4*b + 21*a^2*b + 2*b)*x + 2*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^8*x^8 + 24*a*b^7*x^7 + 3*a^8 + 2*(42*a^2*b^6 + 5*b^6)*x^6 + 10*a^6 + 12*(14*a^3*b^5 + 5*a*b^5)*x^5 + 6*(35*a^4*b^4 + 25*a^2*b^4 + 2*b^4)*x^4 + 12*a^4 + 8*(21*a^5*b^3 + 25*a^3*b^3 + 6*a*b^3)*x^3 + 6*(14*a^6*b^2 + 25*a^4*b^2 + 12*a^2*b^2 + b^2)*x^2 + 6*a^2 + 12*(2*a^7*b + 5*a^5*b + 4*a^3*b + a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + ((4*b^6*x^6 + 24*a*b^5*x^5 + 4*a^6 + (60*a^2*b^4 + 7*b^4)*x^4 + 7*a^4 + 4*(20*a^3*b^3 + 7*a*b^3)*x^3 + 2*(30*a^4*b^2 + 21*a^2*b^2 + b^2)*x^2 + 2*a^2 + 4*(6*a^5*b + 7*a^3*b + a*b)*x - 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 3*(4*b^7*x^7 + 28*a*b^6*x^6 + 4*a^7 + 3*(28*a^2*b^5 + 3*b^5)*x^5 + 9*a^5 + 5*(28*a^3*b^4 + 9*a*b^4)*x^4 + 2*(70*a^4*b^3 + 45*a^2*b^3 + 3*b^3)*x^3 + 6*a^3 + 6*(14*a^5*b^2 + 15*a^3*b^2 + 3*a*b^2)*x^2 + (28*a^6*b + 45*a^4*b + 18*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (12*b^8*x^8 + 96*a*b^7*x^7 + 12*a^8 + 3*(112*a^2*b^6 + 11*b^6)*x^6 + 33*a^6 + 6*(112*a^3*b^5 + 33*a*b^5)*x^5 + (840*a^4*b^4 + 495*a^2*b^4 + 31*b^4)*x^4 + 31*a^4 + 4*(168*a^5*b^3 + 165*a^3*b^3 + 31*a*b^3)*x^3 + (336*a^6*b^2 + 495*a^4*b^2 + 186*a^2*b^2 + 11*b^2)*x^2 + 11*a^2 + 2*(48*a^7*b + 99*a^5*b + 62*a^3*b + 11*a*b)*x + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (4*b^9*x^9 + 36*a*b^8*x^8 + 4*a^9 + (144*a^2*b^7 + 13*b^7)*x^7 + 13*a^7 + 7*(48*a^3*b^6 + 13*a*b^6)*x^6 + 3*(168*a^4*b^5 + 91*a^2*b^5 + 5*b^5)*x^5 + 15*a^5 + (504*a^5*b^4 + 455*a^3*b^4 + 75*a*b^4)*x^4 + (336*a^6*b^3 + 455*a^4*b^3 + 150*a^2*b^3 + 7*b^3)*x^3 + 7*a^3 + 3*(48*a^7*b^2 + 91*a^5*b^2 + 50*a^3*b^2 + 7*a*b^2)*x^2 + (36*a^8*b + 91*a^6*b + 75*a^4*b + 21*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (b^9*x^9 + 9*a*b^8*x^8 + a^9 + 4*(9*a^2*b^7 + b^7)*x^7 + 4*a^7 + 28*(3*a^3*b^6 + a*b^6)*x^6 + 6*(21*a^4*b^5 + 14*a^2*b^5 + b^5)*x^5 + 6*a^5 + 2*(63*a^5*b^4 + 70*a^3*b^4 + 15*a*b^4)*x^4 + 4*(21*a^6*b^3 + 35*a^4*b^3 + 15*a^2*b^3 + b^3)*x^3 + 4*a^3 + 12*(3*a^7*b^2 + 7*a^5*b^2 + 5*a^3*b^2 + a*b^2)*x^2 + (9*a^8*b + 28*a^6*b + 30*a^4*b + 12*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^7*x^6 + 6*a*b^6*x^5 + a^6*b + 3*a^4*b + 3*(5*a^2*b^5 + b^5)*x^4 + 4*(5*a^3*b^4 + 3*a*b^4)*x^3 + 3*a^2*b + 3*(5*a^4*b^3 + 6*a^2*b^3 + b^3)*x^2 + (b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^5*x^4 + 4*a*b^4*x^3 + a^4*b + a^2*b + (6*a^2*b^3 + b^3)*x^2 + 2*(2*a^3*b^2 + a*b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 6*(a^5*b^2 + 2*a^3*b^2 + a*b^2)*x + 3*(b^6*x^5 + 5*a*b^5*x^4 + a^5*b + 2*a^3*b + 2*(5*a^2*b^4 + b^4)*x^3 + 2*(5*a^3*b^3 + 3*a*b^3)*x^2 + a*b + (5*a^4*b^2 + 6*a^2*b^2 + b^2)*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + b)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(1/2*((16*b^6*x^6 + 96*a*b^5*x^5 + 16*a^6 + 10*(24*a^2*b^4 + b^4)*x^4 + 10*a^4 + 40*(8*a^3*b^3 + a*b^3)*x^3 + 3*(80*a^4*b^2 + 20*a^2*b^2 - b^2)*x^2 - 3*a^2 + 2*(48*a^5*b + 20*a^3*b - 3*a*b)*x + 3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(5/2) + 4*(16*b^7*x^7 + 112*a*b^6*x^6 + 16*a^7 + (336*a^2*b^5 + 23*b^5)*x^5 + 23*a^5 + 5*(112*a^3*b^4 + 23*a*b^4)*x^4 + (560*a^4*b^3 + 230*a^2*b^3 + 7*b^3)*x^3 + 7*a^3 + (336*a^5*b^2 + 230*a^3*b^2 + 21*a*b^2)*x^2 + (112*a^6*b + 115*a^4*b + 21*a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 12*(8*b^8*x^8 + 64*a*b^7*x^7 + 8*a^8 + 2*(112*a^2*b^6 + 9*b^6)*x^6 + 18*a^6 + 4*(112*a^3*b^5 + 27*a*b^5)*x^5 + (560*a^4*b^4 + 270*a^2*b^4 + 13*b^4)*x^4 + 13*a^4 + 4*(112*a^5*b^3 + 90*a^3*b^3 + 13*a*b^3)*x^3 + (224*a^6*b^2 + 270*a^4*b^2 + 78*a^2*b^2 + 3*b^2)*x^2 + 3*a^2 + 2*(32*a^7*b + 54*a^5*b + 26*a^3*b + 3*a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 4*(16*b^9*x^9 + 144*a*b^8*x^8 + 16*a^9 + (576*a^2*b^7 + 49*b^7)*x^7 + 49*a^7 + 7*(192*a^3*b^6 + 49*a*b^6)*x^6 + 3*(672*a^4*b^5 + 343*a^2*b^5 + 18*b^5)*x^5 + 54*a^5 + (2016*a^5*b^4 + 1715*a^3*b^4 + 270*a*b^4)*x^4 + (1344*a^6*b^3 + 1715*a^4*b^3 + 540*a^2*b^3 + 25*b^3)*x^3 + 25*a^3 + 3*(192*a^7*b^2 + 343*a^5*b^2 + 180*a^3*b^2 + 25*a*b^2)*x^2 + (144*a^8*b + 343*a^6*b + 270*a^4*b + 75*a^2*b + 4*b)*x + 4*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (16*b^10*x^10 + 160*a*b^9*x^9 + 16*a^10 + 2*(360*a^2*b^8 + 31*b^8)*x^8 + 62*a^8 + 16*(120*a^3*b^7 + 31*a*b^7)*x^7 + 7*(480*a^4*b^6 + 248*a^2*b^6 + 13*b^6)*x^6 + 91*a^6 + 14*(288*a^5*b^5 + 248*a^3*b^5 + 39*a*b^5)*x^5 + (3360*a^6*b^4 + 4340*a^4*b^4 + 1365*a^2*b^4 + 61*b^4)*x^4 + 61*a^4 + 4*(480*a^7*b^3 + 868*a^5*b^3 + 455*a^3*b^3 + 61*a*b^3)*x^3 + (720*a^8*b^2 + 1736*a^6*b^2 + 1365*a^4*b^2 + 366*a^2*b^2 + 17*b^2)*x^2 + 17*a^2 + 2*(80*a^9*b + 248*a^7*b + 273*a^5*b + 122*a^3*b + 17*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((b^8*x^8 + 8*a*b^7*x^7 + a^8 + 4*(7*a^2*b^6 + b^6)*x^6 + 4*a^6 + 8*(7*a^3*b^5 + 3*a*b^5)*x^5 + 2*(35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 6*a^4 + 8*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + (b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 4*(7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + 4*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + (10*a^2*b^3 + b^3)*x^3 + a^3 + (10*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 3*a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 6*(b^6*x^6 + 6*a*b^5*x^5 + a^6 + (15*a^2*b^4 + 2*b^4)*x^4 + 2*a^4 + 4*(5*a^3*b^3 + 2*a*b^3)*x^3 + (15*a^4*b^2 + 12*a^2*b^2 + b^2)*x^2 + a^2 + 2*(3*a^5*b + 4*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + 4*a^2 + 8*(a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x + 4*(b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
272,1,179,0,0.768916," ","integrate(arcsinh(b*x+a)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(b x + a\right)^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} - \frac{3 \, \operatorname{arsinh}\left(b x + a\right)^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{2}}{2 \, b} + \frac{\operatorname{arsinh}\left(b x + a\right) \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{3}}{b} - \frac{\operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{4}}{4 \, b}"," ",0,"arcsinh(b*x + a)^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b - 3/2*arcsinh(b*x + a)^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^2/b + arcsinh(b*x + a)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^3/b - 1/4*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^4/b","B",0
273,1,132,0,0.779195," ","integrate(arcsinh(b*x+a)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(b x + a\right)^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} - \frac{\operatorname{arsinh}\left(b x + a\right) \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{2}}{b} + \frac{\operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{3}}{3 \, b}"," ",0,"arcsinh(b*x + a)^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b - arcsinh(b*x + a)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^2/b + 1/3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^3/b","B",0
274,1,84,0,0.520695," ","integrate(arcsinh(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(b x + a\right) \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} - \frac{\operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)^{2}}{2 \, b}"," ",0,"arcsinh(b*x + a)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b - 1/2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))^2/b","B",0
275,0,0,0,0.000000," ","integrate(1/arcsinh(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*arcsinh(b*x + a)), x)","F",0
276,1,150,0,0.770592," ","integrate(1/arcsinh(b*x+a)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + a}{{\left({\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} {\left(b^{2} x + a b\right)} + {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + b\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}"," ",0,"-(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + a)/(((b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + (b^3*x^2 + 2*a*b^2*x + a^2*b + b)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)))","B",0
277,0,0,0,0.000000," ","integrate(1/arcsinh(b*x+a)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + {\left(6 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(2 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + {\left(3 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 3 \, a^{5} + 5 \, {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 5 \, a^{3} + 15 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(15 \, a^{4} b + 15 \, a^{2} b + 2 \, b\right)} x + 2 \, a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + 2 \, {\left(5 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 2 \, {\left(5 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} - {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{5}{2}} - {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(5 \, a^{4} b + 6 \, a^{2} b + b\right)} x + {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 2 \, a^{2} + 4 \, {\left(a^{3} b + a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(3 \, b^{6} x^{6} + 18 \, a b^{5} x^{5} + 3 \, a^{6} + {\left(45 \, a^{2} b^{4} + 7 \, b^{4}\right)} x^{4} + 7 \, a^{4} + 4 \, {\left(15 \, a^{3} b^{3} + 7 \, a b^{3}\right)} x^{3} + {\left(45 \, a^{4} b^{2} + 42 \, a^{2} b^{2} + 5 \, b^{2}\right)} x^{2} + 5 \, a^{2} + 2 \, {\left(9 \, a^{5} b + 14 \, a^{3} b + 5 \, a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a}{2 \, {\left({\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 3 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + a^{4} b + a^{2} b + {\left(6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 3 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + a^{5} b + 2 \, a^{3} b + 2 \, {\left(5 \, a^{2} b^{4} + b^{4}\right)} x^{3} + 2 \, {\left(5 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{2} + a b + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{2} + b^{2}\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(b^{7} x^{6} + 6 \, a b^{6} x^{5} + a^{6} b + 3 \, a^{4} b + 3 \, {\left(5 \, a^{2} b^{5} + b^{5}\right)} x^{4} + 4 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{3} + 3 \, a^{2} b + 3 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{3} + b^{3}\right)} x^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{2} + a b^{2}\right)} x + b\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)^{2}} + \int -\frac{2 \, b^{6} x^{6} + 12 \, a b^{5} x^{5} + 2 \, a^{6} + 3 \, {\left(10 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 3 \, a^{4} + 4 \, {\left(10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} - {\left(2 \, b^{2} x^{2} + 4 \, a b x + 2 \, a^{2} + 3\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 6 \, {\left(5 \, a^{4} b^{2} + 3 \, a^{2} b^{2}\right)} x^{2} - 4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 12 \, {\left(a^{5} b + a^{3} b\right)} x + 4 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + 2 \, {\left(5 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 2 \, {\left(5 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 6 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 1}{2 \, {\left({\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{5}{2}} + 4 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + {\left(10 \, a^{2} b^{3} + b^{3}\right)} x^{3} + a^{3} + {\left(10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 3 \, a^{2} b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{2} + 6 \, {\left(b^{6} x^{6} + 6 \, a b^{5} x^{5} + a^{6} + {\left(15 \, a^{2} b^{4} + 2 \, b^{4}\right)} x^{4} + 2 \, a^{4} + 4 \, {\left(5 \, a^{3} b^{3} + 2 \, a b^{3}\right)} x^{3} + {\left(15 \, a^{4} b^{2} + 12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(3 \, a^{5} b + 4 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 4 \, {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + a^{7} + 3 \, {\left(7 \, a^{2} b^{5} + b^{5}\right)} x^{5} + 3 \, a^{5} + 5 \, {\left(7 \, a^{3} b^{4} + 3 \, a b^{4}\right)} x^{4} + {\left(35 \, a^{4} b^{3} + 30 \, a^{2} b^{3} + 3 \, b^{3}\right)} x^{3} + 3 \, a^{3} + 3 \, {\left(7 \, a^{5} b^{2} + 10 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(7 \, a^{6} b + 15 \, a^{4} b + 9 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(b^{8} x^{8} + 8 \, a b^{7} x^{7} + a^{8} + 4 \, {\left(7 \, a^{2} b^{6} + b^{6}\right)} x^{6} + 4 \, a^{6} + 8 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{4} b^{4} + 30 \, a^{2} b^{4} + 3 \, b^{4}\right)} x^{4} + 6 \, a^{4} + 8 \, {\left(7 \, a^{5} b^{3} + 10 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + 4 \, {\left(7 \, a^{6} b^{2} + 15 \, a^{4} b^{2} + 9 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 4 \, a^{2} + 8 \, {\left(a^{7} b + 3 \, a^{5} b + 3 \, a^{3} b + a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-1/2*(b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (b^4*x^4 + 4*a*b^3*x^3 + a^4 + (6*a^2*b^2 + b^2)*x^2 + a^2 + 2*(2*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + (3*b^5*x^5 + 15*a*b^4*x^4 + 3*a^5 + 5*(6*a^2*b^3 + b^3)*x^3 + 5*a^3 + 15*(2*a^3*b^2 + a*b^2)*x^2 + (15*a^4*b + 15*a^2*b + 2*b)*x + 2*a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + (b^5*x^5 + 5*a*b^4*x^4 + a^5 + 2*(5*a^2*b^3 + b^3)*x^3 + 2*a^3 + 2*(5*a^3*b^2 + 3*a*b^2)*x^2 - (b^2*x^2 + 2*a*b*x + a^2 + 1)^(5/2) - (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (5*a^4*b + 6*a^2*b + b)*x + (b^4*x^4 + 4*a*b^3*x^3 + a^4 + 2*(3*a^2*b^2 + b^2)*x^2 + 2*a^2 + 4*(a^3*b + a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + a)*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (3*b^6*x^6 + 18*a*b^5*x^5 + 3*a^6 + (45*a^2*b^4 + 7*b^4)*x^4 + 7*a^4 + 4*(15*a^3*b^3 + 7*a*b^3)*x^3 + (45*a^4*b^2 + 42*a^2*b^2 + 5*b^2)*x^2 + 5*a^2 + 2*(9*a^5*b + 14*a^3*b + 5*a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + a)/(((b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 3*(b^5*x^4 + 4*a*b^4*x^3 + a^4*b + a^2*b + (6*a^2*b^3 + b^3)*x^2 + 2*(2*a^3*b^2 + a*b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 3*(b^6*x^5 + 5*a*b^5*x^4 + a^5*b + 2*a^3*b + 2*(5*a^2*b^4 + b^4)*x^3 + 2*(5*a^3*b^3 + 3*a*b^3)*x^2 + a*b + (5*a^4*b^2 + 6*a^2*b^2 + b^2)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (b^7*x^6 + 6*a*b^6*x^5 + a^6*b + 3*a^4*b + 3*(5*a^2*b^5 + b^5)*x^4 + 4*(5*a^3*b^4 + 3*a*b^4)*x^3 + 3*a^2*b + 3*(5*a^4*b^3 + 6*a^2*b^3 + b^3)*x^2 + 6*(a^5*b^2 + 2*a^3*b^2 + a*b^2)*x + b)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))^2) + integrate(-1/2*(2*b^6*x^6 + 12*a*b^5*x^5 + 2*a^6 + 3*(10*a^2*b^4 + b^4)*x^4 + 3*a^4 + 4*(10*a^3*b^3 + 3*a*b^3)*x^3 - (2*b^2*x^2 + 4*a*b*x + 2*a^2 + 3)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 6*(5*a^4*b^2 + 3*a^2*b^2)*x^2 - 4*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 12*(a^5*b + a^3*b)*x + 4*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + 2*(5*a^2*b^3 + b^3)*x^3 + 2*a^3 + 2*(5*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 6*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 1)/(((b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(5/2) + 4*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + (10*a^2*b^3 + b^3)*x^3 + a^3 + (10*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 3*a^2*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^2 + 6*(b^6*x^6 + 6*a*b^5*x^5 + a^6 + (15*a^2*b^4 + 2*b^4)*x^4 + 2*a^4 + 4*(5*a^3*b^3 + 2*a*b^3)*x^3 + (15*a^4*b^2 + 12*a^2*b^2 + b^2)*x^2 + a^2 + 2*(3*a^5*b + 4*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 4*(b^7*x^7 + 7*a*b^6*x^6 + a^7 + 3*(7*a^2*b^5 + b^5)*x^5 + 3*a^5 + 5*(7*a^3*b^4 + 3*a*b^4)*x^4 + (35*a^4*b^3 + 30*a^2*b^3 + 3*b^3)*x^3 + 3*a^3 + 3*(7*a^5*b^2 + 10*a^3*b^2 + 3*a*b^2)*x^2 + (7*a^6*b + 15*a^4*b + 9*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (b^8*x^8 + 8*a*b^7*x^7 + a^8 + 4*(7*a^2*b^6 + b^6)*x^6 + 4*a^6 + 8*(7*a^3*b^5 + 3*a*b^5)*x^5 + 2*(35*a^4*b^4 + 30*a^2*b^4 + 3*b^4)*x^4 + 6*a^4 + 8*(7*a^5*b^3 + 10*a^3*b^3 + 3*a*b^3)*x^3 + 4*(7*a^6*b^2 + 15*a^4*b^2 + 9*a^2*b^2 + b^2)*x^2 + 4*a^2 + 8*(a^7*b + 3*a^5*b + 3*a^3*b + a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
278,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^3/(b^2*x^2+2*a*b*x+a^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(b x + a\right)^{3}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsinh(b*x + a)^3/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2), x)","F",0
279,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)^2/(b^2*x^2+2*a*b*x+a^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(b x + a\right)^{2}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsinh(b*x + a)^2/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2), x)","F",0
280,1,119,0,0.600444," ","integrate(arcsinh(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(3/2),x, algorithm=""maxima"")","-{\left(\frac{b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{a b}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\right)} \operatorname{arsinh}\left(b x + a\right) - \frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b}"," ",0,"-(b^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + a*b/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)))*arcsinh(b*x + a) - 1/2*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b","B",0
281,0,0,0,0.000000," ","integrate(1/(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a),x, algorithm=""maxima"")","\int \frac{1}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/((b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*arcsinh(b*x + a)), x)","F",0
282,0,0,0,0.000000," ","integrate(1/(b^2*x^2+2*a*b*x+a^2+1)^(3/2)/arcsinh(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left({\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} {\left(b^{2} x + a b\right)} + {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + b\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} - \int \frac{2 \, b^{4} x^{4} + 8 \, a b^{3} x^{3} + 2 \, a^{4} + {\left(12 \, a^{2} b^{2} + b^{2}\right)} x^{2} + {\left(2 \, b^{2} x^{2} + 4 \, a b x + 2 \, a^{2} + 1\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + a^{2} + 2 \, {\left(4 \, a^{3} b + a b\right)} x + 2 \, {\left(2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 2 \, a^{3} + {\left(6 \, a^{2} b + b\right)} x + a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 1}{{\left({\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + a^{4} + {\left(6 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2} + 2 \, {\left(2 \, a^{3} b + a b\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} + 2 \, {\left(b^{5} x^{5} + 5 \, a b^{4} x^{4} + a^{5} + 2 \, {\left(5 \, a^{2} b^{3} + b^{3}\right)} x^{3} + 2 \, a^{3} + 2 \, {\left(5 \, a^{3} b^{2} + 3 \, a b^{2}\right)} x^{2} + {\left(5 \, a^{4} b + 6 \, a^{2} b + b\right)} x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} + {\left(b^{6} x^{6} + 6 \, a b^{5} x^{5} + a^{6} + 3 \, {\left(5 \, a^{2} b^{4} + b^{4}\right)} x^{4} + 3 \, a^{4} + 4 \, {\left(5 \, a^{3} b^{3} + 3 \, a b^{3}\right)} x^{3} + 3 \, {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{2} + b^{2}\right)} x^{2} + 3 \, a^{2} + 6 \, {\left(a^{5} b + 2 \, a^{3} b + a b\right)} x + 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} \log\left(b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}\,{d x}"," ",0,"-(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/(((b^2*x^2 + 2*a*b*x + a^2 + 1)*(b^2*x + a*b) + (b^3*x^2 + 2*a*b^2*x + a^2*b + b)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))) - integrate((2*b^4*x^4 + 8*a*b^3*x^3 + 2*a^4 + (12*a^2*b^2 + b^2)*x^2 + (2*b^2*x^2 + 4*a*b*x + 2*a^2 + 1)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + a^2 + 2*(4*a^3*b + a*b)*x + 2*(2*b^3*x^3 + 6*a*b^2*x^2 + 2*a^3 + (6*a^2*b + b)*x + a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 1)/(((b^4*x^4 + 4*a*b^3*x^3 + a^4 + (6*a^2*b^2 + b^2)*x^2 + a^2 + 2*(2*a^3*b + a*b)*x)*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2) + 2*(b^5*x^5 + 5*a*b^4*x^4 + a^5 + 2*(5*a^2*b^3 + b^3)*x^3 + 2*a^3 + 2*(5*a^3*b^2 + 3*a*b^2)*x^2 + (5*a^4*b + 6*a^2*b + b)*x + a)*(b^2*x^2 + 2*a*b*x + a^2 + 1) + (b^6*x^6 + 6*a*b^5*x^5 + a^6 + 3*(5*a^2*b^4 + b^4)*x^4 + 3*a^4 + 4*(5*a^3*b^3 + 3*a*b^3)*x^3 + 3*(5*a^4*b^2 + 6*a^2*b^2 + b^2)*x^2 + 3*a^2 + 6*(a^5*b + 2*a^3*b + a*b)*x + 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*log(b*x + a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))), x)","F",0
283,1,102,0,0.652663," ","integrate(x^3*arcsinh(a*x^2),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arsinh}\left(a x^{2}\right) + \frac{1}{16} \, a {\left(\frac{\log\left(a + \frac{\sqrt{a^{2} x^{4} + 1}}{x^{2}}\right)}{a^{3}} - \frac{\log\left(-a + \frac{\sqrt{a^{2} x^{4} + 1}}{x^{2}}\right)}{a^{3}} + \frac{2 \, \sqrt{a^{2} x^{4} + 1}}{{\left(a^{4} - \frac{{\left(a^{2} x^{4} + 1\right)} a^{2}}{x^{4}}\right)} x^{2}}\right)}"," ",0,"1/4*x^4*arcsinh(a*x^2) + 1/16*a*(log(a + sqrt(a^2*x^4 + 1)/x^2)/a^3 - log(-a + sqrt(a^2*x^4 + 1)/x^2)/a^3 + 2*sqrt(a^2*x^4 + 1)/((a^4 - (a^2*x^4 + 1)*a^2/x^4)*x^2))","B",0
284,0,0,0,0.000000," ","integrate(x^2*arcsinh(a*x^2),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left(a x^{2} + \sqrt{a^{2} x^{4} + 1}\right) - \frac{2}{9} \, x^{3} - 2 \, a \int \frac{x^{4}}{3 \, {\left(a^{3} x^{6} + a x^{2} + {\left(a^{2} x^{4} + 1\right)}^{\frac{3}{2}}\right)}}\,{d x} - \frac{i \, \sqrt{2} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)}}{12 \, a^{\frac{3}{2}}} - \frac{i \, \sqrt{2} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)}}{12 \, a^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{12 \, a^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{12 \, a^{\frac{3}{2}}}"," ",0,"1/3*x^3*log(a*x^2 + sqrt(a^2*x^4 + 1)) - 2/9*x^3 - 2*a*integrate(1/3*x^4/(a^3*x^6 + a*x^2 + (a^2*x^4 + 1)^(3/2)), x) - 1/12*I*sqrt(2)*(log(1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1))/a^(3/2) - 1/12*I*sqrt(2)*(log(1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1))/a^(3/2) - 1/12*sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/a^(3/2) + 1/12*sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/a^(3/2)","F",0
285,1,30,0,0.310011," ","integrate(x*arcsinh(a*x^2),x, algorithm=""maxima"")","\frac{a x^{2} \operatorname{arsinh}\left(a x^{2}\right) - \sqrt{a^{2} x^{4} + 1}}{2 \, a}"," ",0,"1/2*(a*x^2*arcsinh(a*x^2) - sqrt(a^2*x^4 + 1))/a","A",0
286,0,0,0,0.000000," ","integrate(arcsinh(a*x^2),x, algorithm=""maxima"")","-2 \, a \int \frac{x^{2}}{a^{3} x^{6} + a x^{2} + {\left(a^{2} x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x} + x \log\left(a x^{2} + \sqrt{a^{2} x^{4} + 1}\right) - 2 \, x - \frac{i \, \sqrt{2} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)}}{4 \, \sqrt{a}} - \frac{i \, \sqrt{2} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)}}{4 \, \sqrt{a}} + \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{4 \, \sqrt{a}} - \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{4 \, \sqrt{a}}"," ",0,"-2*a*integrate(x^2/(a^3*x^6 + a*x^2 + (a^2*x^4 + 1)^(3/2)), x) + x*log(a*x^2 + sqrt(a^2*x^4 + 1)) - 2*x - 1/4*I*sqrt(2)*(log(1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1))/sqrt(a) - 1/4*I*sqrt(2)*(log(1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1))/sqrt(a) + 1/4*sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/sqrt(a) - 1/4*sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/sqrt(a)","F",0
287,0,0,0,0.000000," ","integrate(arcsinh(a*x^2)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x^{2}\right)}{x}\,{d x}"," ",0,"integrate(arcsinh(a*x^2)/x, x)","F",0
288,0,0,0,0.000000," ","integrate(arcsinh(a*x^2)/x^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{i \, \sqrt{2} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)}}{a^{\frac{3}{2}}} + \frac{i \, \sqrt{2} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)}}{a^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}}\right)} + 2 \, a \int \frac{1}{a^{3} x^{6} + a x^{2} + {\left(a^{2} x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x} - \frac{\log\left(a x^{2} + \sqrt{a^{2} x^{4} + 1}\right)}{x}"," ",0,"-1/4*a^2*(I*sqrt(2)*(log(1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1))/a^(3/2) + I*sqrt(2)*(log(1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1))/a^(3/2) + sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/a^(3/2) - sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/a^(3/2)) + 2*a*integrate(1/(a^3*x^6 + a*x^2 + (a^2*x^4 + 1)^(3/2)), x) - log(a*x^2 + sqrt(a^2*x^4 + 1))/x","F",0
289,1,46,0,0.365798," ","integrate(arcsinh(a*x^2)/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\log\left(\sqrt{a^{2} x^{4} + 1} + 1\right) - \log\left(\sqrt{a^{2} x^{4} + 1} - 1\right)\right)} - \frac{\operatorname{arsinh}\left(a x^{2}\right)}{2 \, x^{2}}"," ",0,"-1/4*a*(log(sqrt(a^2*x^4 + 1) + 1) - log(sqrt(a^2*x^4 + 1) - 1)) - 1/2*arcsinh(a*x^2)/x^2","A",0
290,0,0,0,0.000000," ","integrate(arcsinh(a*x^2)/x^4,x, algorithm=""maxima"")","-\frac{1}{12} i \, \sqrt{2} a^{\frac{3}{2}} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)} - \frac{1}{12} i \, \sqrt{2} a^{\frac{3}{2}} {\left(\log\left(\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right) - \log\left(-\frac{i \, \sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}} + 1\right)\right)} + \frac{1}{12} \, \sqrt{2} a^{\frac{3}{2}} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right) - \frac{1}{12} \, \sqrt{2} a^{\frac{3}{2}} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right) + 2 \, a \int \frac{1}{3 \, {\left(a^{3} x^{8} + a x^{4} + {\left(a^{2} x^{6} + x^{2}\right)} \sqrt{a^{2} x^{4} + 1}\right)}}\,{d x} - \frac{\log\left(a x^{2} + \sqrt{a^{2} x^{4} + 1}\right)}{3 \, x^{3}}"," ",0,"-1/12*I*sqrt(2)*a^(3/2)*(log(1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a) + 1)) - 1/12*I*sqrt(2)*a^(3/2)*(log(1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1) - log(-1/2*I*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a) + 1)) + 1/12*sqrt(2)*a^(3/2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1) - 1/12*sqrt(2)*a^(3/2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1) + 2*a*integrate(1/3/(a^3*x^8 + a*x^4 + (a^2*x^6 + x^2)*sqrt(a^2*x^4 + 1)), x) - 1/3*log(a*x^2 + sqrt(a^2*x^4 + 1))/x^3","F",0
291,0,0,0,0.000000," ","integrate(arcsinh(a*x^5)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arcsinh(a*x^5)/x, x)","F",0
292,1,46,0,0.863960," ","integrate(x^2*arcsinh(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arsinh}\left(\sqrt{x}\right) - \frac{1}{18} \, \sqrt{x + 1} x^{\frac{5}{2}} + \frac{5}{72} \, \sqrt{x + 1} x^{\frac{3}{2}} - \frac{5}{48} \, \sqrt{x + 1} \sqrt{x} + \frac{5}{48} \, \operatorname{arsinh}\left(\sqrt{x}\right)"," ",0,"1/3*x^3*arcsinh(sqrt(x)) - 1/18*sqrt(x + 1)*x^(5/2) + 5/72*sqrt(x + 1)*x^(3/2) - 5/48*sqrt(x + 1)*sqrt(x) + 5/48*arcsinh(sqrt(x))","A",0
293,1,36,0,0.785595," ","integrate(x*arcsinh(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arsinh}\left(\sqrt{x}\right) - \frac{1}{8} \, \sqrt{x + 1} x^{\frac{3}{2}} + \frac{3}{16} \, \sqrt{x + 1} \sqrt{x} - \frac{3}{16} \, \operatorname{arsinh}\left(\sqrt{x}\right)"," ",0,"1/2*x^2*arcsinh(sqrt(x)) - 1/8*sqrt(x + 1)*x^(3/2) + 3/16*sqrt(x + 1)*sqrt(x) - 3/16*arcsinh(sqrt(x))","A",0
294,1,23,0,0.849964," ","integrate(arcsinh(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arsinh}\left(\sqrt{x}\right) - \frac{1}{2} \, \sqrt{x + 1} \sqrt{x} + \frac{1}{2} \, \operatorname{arsinh}\left(\sqrt{x}\right)"," ",0,"x*arcsinh(sqrt(x)) - 1/2*sqrt(x + 1)*sqrt(x) + 1/2*arcsinh(sqrt(x))","A",0
295,0,0,0,0.000000," ","integrate(arcsinh(x^(1/2))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arcsinh(sqrt(x))/x, x)","F",0
296,1,20,0,0.860497," ","integrate(arcsinh(x^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\sqrt{x + 1}}{\sqrt{x}} - \frac{\operatorname{arsinh}\left(\sqrt{x}\right)}{x}"," ",0,"-sqrt(x + 1)/sqrt(x) - arcsinh(sqrt(x))/x","A",0
297,1,30,0,0.840580," ","integrate(arcsinh(x^(1/2))/x^3,x, algorithm=""maxima"")","\frac{\sqrt{x + 1}}{3 \, \sqrt{x}} - \frac{\sqrt{x + 1}}{6 \, x^{\frac{3}{2}}} - \frac{\operatorname{arsinh}\left(\sqrt{x}\right)}{2 \, x^{2}}"," ",0,"1/3*sqrt(x + 1)/sqrt(x) - 1/6*sqrt(x + 1)/x^(3/2) - 1/2*arcsinh(sqrt(x))/x^2","A",0
298,1,40,0,0.888800," ","integrate(arcsinh(x^(1/2))/x^4,x, algorithm=""maxima"")","-\frac{8 \, \sqrt{x + 1}}{45 \, \sqrt{x}} + \frac{4 \, \sqrt{x + 1}}{45 \, x^{\frac{3}{2}}} - \frac{\sqrt{x + 1}}{15 \, x^{\frac{5}{2}}} - \frac{\operatorname{arsinh}\left(\sqrt{x}\right)}{3 \, x^{3}}"," ",0,"-8/45*sqrt(x + 1)/sqrt(x) + 4/45*sqrt(x + 1)/x^(3/2) - 1/15*sqrt(x + 1)/x^(5/2) - 1/3*arcsinh(sqrt(x))/x^3","A",0
299,1,50,0,0.858287," ","integrate(arcsinh(x^(1/2))/x^5,x, algorithm=""maxima"")","\frac{4 \, \sqrt{x + 1}}{35 \, \sqrt{x}} - \frac{2 \, \sqrt{x + 1}}{35 \, x^{\frac{3}{2}}} + \frac{3 \, \sqrt{x + 1}}{70 \, x^{\frac{5}{2}}} - \frac{\sqrt{x + 1}}{28 \, x^{\frac{7}{2}}} - \frac{\operatorname{arsinh}\left(\sqrt{x}\right)}{4 \, x^{4}}"," ",0,"4/35*sqrt(x + 1)/sqrt(x) - 2/35*sqrt(x + 1)/x^(3/2) + 3/70*sqrt(x + 1)/x^(5/2) - 1/28*sqrt(x + 1)/x^(7/2) - 1/4*arcsinh(sqrt(x))/x^4","A",0
300,1,69,0,0.459642," ","integrate(x^2*arcsinh(a/x),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arsinh}\left(\frac{a}{x}\right) - \frac{1}{12} \, {\left(a^{2} \log\left(\sqrt{\frac{a^{2}}{x^{2}} + 1} + 1\right) - a^{2} \log\left(\sqrt{\frac{a^{2}}{x^{2}} + 1} - 1\right) - 2 \, x^{2} \sqrt{\frac{a^{2}}{x^{2}} + 1}\right)} a"," ",0,"1/3*x^3*arcsinh(a/x) - 1/12*(a^2*log(sqrt(a^2/x^2 + 1) + 1) - a^2*log(sqrt(a^2/x^2 + 1) - 1) - 2*x^2*sqrt(a^2/x^2 + 1))*a","A",0
301,1,27,0,0.317689," ","integrate(x*arcsinh(a/x),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arsinh}\left(\frac{a}{x}\right) + \frac{1}{2} \, a x \sqrt{\frac{a^{2}}{x^{2}} + 1}"," ",0,"1/2*x^2*arcsinh(a/x) + 1/2*a*x*sqrt(a^2/x^2 + 1)","A",0
302,1,43,0,0.630659," ","integrate(arcsinh(a/x),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\log\left(\sqrt{\frac{a^{2}}{x^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{a^{2}}{x^{2}} + 1} - 1\right)\right)} + x \operatorname{arsinh}\left(\frac{a}{x}\right)"," ",0,"1/2*a*(log(sqrt(a^2/x^2 + 1) + 1) - log(sqrt(a^2/x^2 + 1) - 1)) + x*arcsinh(a/x)","A",0
303,0,0,0,0.000000," ","integrate(arcsinh(a/x)/x,x, algorithm=""maxima"")","a \int \frac{x \log\left(x\right)}{a^{3} + a x^{2} + {\left(a^{2} + x^{2}\right)}^{\frac{3}{2}}}\,{d x} + \log\left(a + \sqrt{a^{2} + x^{2}}\right) \log\left(x\right) - \frac{1}{2} \, \log\left(x\right)^{2} - \frac{1}{2} \, \log\left(x\right) \log\left(\frac{x^{2}}{a^{2}} + 1\right) - \frac{1}{4} \, {\rm Li}_2\left(-\frac{x^{2}}{a^{2}}\right)"," ",0,"a*integrate(x*log(x)/(a^3 + a*x^2 + (a^2 + x^2)^(3/2)), x) + log(a + sqrt(a^2 + x^2))*log(x) - 1/2*log(x)^2 - 1/2*log(x)*log(x^2/a^2 + 1) - 1/4*dilog(-x^2/a^2)","F",0
304,1,30,0,0.667029," ","integrate(arcsinh(a/x)/x^2,x, algorithm=""maxima"")","-\frac{\frac{a \operatorname{arsinh}\left(\frac{a}{x}\right)}{x} - \sqrt{\frac{a^{2}}{x^{2}} + 1}}{a}"," ",0,"-(a*arcsinh(a/x)/x - sqrt(a^2/x^2 + 1))/a","A",0
305,1,97,0,0.633178," ","integrate(arcsinh(a/x)/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{2 \, x \sqrt{\frac{a^{2}}{x^{2}} + 1}}{a^{2} x^{2} {\left(\frac{a^{2}}{x^{2}} + 1\right)} - a^{4}} - \frac{\log\left(x \sqrt{\frac{a^{2}}{x^{2}} + 1} + a\right)}{a^{3}} + \frac{\log\left(x \sqrt{\frac{a^{2}}{x^{2}} + 1} - a\right)}{a^{3}}\right)} - \frac{\operatorname{arsinh}\left(\frac{a}{x}\right)}{2 \, x^{2}}"," ",0,"1/8*a*(2*x*sqrt(a^2/x^2 + 1)/(a^2*x^2*(a^2/x^2 + 1) - a^4) - log(x*sqrt(a^2/x^2 + 1) + a)/a^3 + log(x*sqrt(a^2/x^2 + 1) - a)/a^3) - 1/2*arcsinh(a/x)/x^2","B",0
306,1,47,0,0.462051," ","integrate(arcsinh(a/x)/x^4,x, algorithm=""maxima"")","\frac{1}{9} \, a {\left(\frac{{\left(\frac{a^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}}}{a^{4}} - \frac{3 \, \sqrt{\frac{a^{2}}{x^{2}} + 1}}{a^{4}}\right)} - \frac{\operatorname{arsinh}\left(\frac{a}{x}\right)}{3 \, x^{3}}"," ",0,"1/9*a*((a^2/x^2 + 1)^(3/2)/a^4 - 3*sqrt(a^2/x^2 + 1)/a^4) - 1/3*arcsinh(a/x)/x^3","A",0
307,0,0,0,0.000000," ","integrate(x^m*arcsinh(a*x^n),x, algorithm=""maxima"")","-a n \int \frac{e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)}}{a^{3} {\left(m + 1\right)} x^{3 \, n} + a {\left(m + 1\right)} x^{n} + {\left(a^{2} {\left(m + 1\right)} x^{2 \, n} + m + 1\right)} \sqrt{a^{2} x^{2 \, n} + 1}}\,{d x} + n \int \frac{x^{m}}{a^{2} {\left(m + 1\right)} x^{2 \, n} + m + 1}\,{d x} + \frac{{\left(m + 1\right)} x x^{m} \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right) - n x x^{m}}{m^{2} + 2 \, m + 1}"," ",0,"-a*n*integrate(e^(m*log(x) + n*log(x))/(a^3*(m + 1)*x^(3*n) + a*(m + 1)*x^n + (a^2*(m + 1)*x^(2*n) + m + 1)*sqrt(a^2*x^(2*n) + 1)), x) + n*integrate(x^m/(a^2*(m + 1)*x^(2*n) + m + 1), x) + ((m + 1)*x*x^m*log(a*x^n + sqrt(a^2*x^(2*n) + 1)) - n*x*x^m)/(m^2 + 2*m + 1)","F",0
308,0,0,0,0.000000," ","integrate(x^2*arcsinh(a*x^n),x, algorithm=""maxima"")","-\frac{1}{9} \, n x^{3} + \frac{1}{3} \, x^{3} \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right) - a n \int \frac{x^{2} x^{n}}{3 \, {\left(a^{3} x^{3 \, n} + a x^{n} + {\left(a^{2} x^{2 \, n} + 1\right)}^{\frac{3}{2}}\right)}}\,{d x} + n \int \frac{x^{2}}{3 \, {\left(a^{2} x^{2 \, n} + 1\right)}}\,{d x}"," ",0,"-1/9*n*x^3 + 1/3*x^3*log(a*x^n + sqrt(a^2*x^(2*n) + 1)) - a*n*integrate(1/3*x^2*x^n/(a^3*x^(3*n) + a*x^n + (a^2*x^(2*n) + 1)^(3/2)), x) + n*integrate(1/3*x^2/(a^2*x^(2*n) + 1), x)","F",0
309,0,0,0,0.000000," ","integrate(x*arcsinh(a*x^n),x, algorithm=""maxima"")","-\frac{1}{4} \, n x^{2} - a n \int \frac{x x^{n}}{2 \, {\left(a^{3} x^{3 \, n} + a x^{n} + {\left(a^{2} x^{2 \, n} + 1\right)}^{\frac{3}{2}}\right)}}\,{d x} + \frac{1}{2} \, x^{2} \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right) + n \int \frac{x}{2 \, {\left(a^{2} x^{2 \, n} + 1\right)}}\,{d x}"," ",0,"-1/4*n*x^2 - a*n*integrate(1/2*x*x^n/(a^3*x^(3*n) + a*x^n + (a^2*x^(2*n) + 1)^(3/2)), x) + 1/2*x^2*log(a*x^n + sqrt(a^2*x^(2*n) + 1)) + n*integrate(1/2*x/(a^2*x^(2*n) + 1), x)","F",0
310,0,0,0,0.000000," ","integrate(arcsinh(a*x^n),x, algorithm=""maxima"")","-a n \int \frac{x^{n}}{a^{3} x^{3 \, n} + a x^{n} + {\left(a^{2} x^{2 \, n} + 1\right)}^{\frac{3}{2}}}\,{d x} - n x + n \int \frac{1}{a^{2} x^{2 \, n} + 1}\,{d x} + x \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right)"," ",0,"-a*n*integrate(x^n/(a^3*x^(3*n) + a*x^n + (a^2*x^(2*n) + 1)^(3/2)), x) - n*x + n*integrate(1/(a^2*x^(2*n) + 1), x) + x*log(a*x^n + sqrt(a^2*x^(2*n) + 1))","F",0
311,0,0,0,0.000000," ","integrate(arcsinh(a*x^n)/x,x, algorithm=""maxima"")","-a n \int \frac{x^{n} \log\left(x\right)}{a^{3} x x^{3 \, n} + a x x^{n} + {\left(a^{2} x x^{2 \, n} + x\right)} \sqrt{a^{2} x^{2 \, n} + 1}}\,{d x} - \frac{1}{2} \, n \log\left(x\right)^{2} + n \int \frac{\log\left(x\right)}{a^{2} x x^{2 \, n} + x}\,{d x} + \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right) \log\left(x\right)"," ",0,"-a*n*integrate(x^n*log(x)/(a^3*x*x^(3*n) + a*x*x^n + (a^2*x*x^(2*n) + x)*sqrt(a^2*x^(2*n) + 1)), x) - 1/2*n*log(x)^2 + n*integrate(log(x)/(a^2*x*x^(2*n) + x), x) + log(a*x^n + sqrt(a^2*x^(2*n) + 1))*log(x)","F",0
312,0,0,0,0.000000," ","integrate(arcsinh(a*x^n)/x^2,x, algorithm=""maxima"")","a n \int \frac{x^{n}}{a^{3} x^{2} x^{3 \, n} + a x^{2} x^{n} + {\left(a^{2} x^{2} x^{2 \, n} + x^{2}\right)} \sqrt{a^{2} x^{2 \, n} + 1}}\,{d x} - n \int \frac{1}{a^{2} x^{2} x^{2 \, n} + x^{2}}\,{d x} - \frac{n + \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right)}{x}"," ",0,"a*n*integrate(x^n/(a^3*x^2*x^(3*n) + a*x^2*x^n + (a^2*x^2*x^(2*n) + x^2)*sqrt(a^2*x^(2*n) + 1)), x) - n*integrate(1/(a^2*x^2*x^(2*n) + x^2), x) - (n + log(a*x^n + sqrt(a^2*x^(2*n) + 1)))/x","F",0
313,0,0,0,0.000000," ","integrate(arcsinh(a*x^n)/x^3,x, algorithm=""maxima"")","a n \int \frac{x^{n}}{2 \, {\left(a^{3} x^{3} x^{3 \, n} + a x^{3} x^{n} + {\left(a^{2} x^{3} x^{2 \, n} + x^{3}\right)} \sqrt{a^{2} x^{2 \, n} + 1}\right)}}\,{d x} - n \int \frac{1}{2 \, {\left(a^{2} x^{3} x^{2 \, n} + x^{3}\right)}}\,{d x} - \frac{n + 2 \, \log\left(a x^{n} + \sqrt{a^{2} x^{2 \, n} + 1}\right)}{4 \, x^{2}}"," ",0,"a*n*integrate(1/2*x^n/(a^3*x^3*x^(3*n) + a*x^3*x^n + (a^2*x^3*x^(2*n) + x^3)*sqrt(a^2*x^(2*n) + 1)), x) - n*integrate(1/2/(a^2*x^3*x^(2*n) + x^3), x) - 1/4*(n + 2*log(a*x^n + sqrt(a^2*x^(2*n) + 1)))/x^2","F",0
314,0,0,0,0.000000," ","integrate((a+b*arcsinh(I+d*x^2))^4,x, algorithm=""maxima"")","b^{4} x \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{4} + 4 \, {\left(x \operatorname{arsinh}\left(d x^{2} + i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2 i} d}\right)} a^{3} b + a^{4} x + \int \frac{{\left(4 \, {\left(a b^{3} d^{2} - 2 \, b^{4} d^{2}\right)} x^{4} - 8 \, a b^{3} + {\left(12 i \, a b^{3} d - 16 i \, b^{4} d\right)} x^{2} + {\left(4 \, {\left(a b^{3} d^{\frac{3}{2}} - 2 \, b^{4} d^{\frac{3}{2}}\right)} x^{3} + {\left(8 i \, a b^{3} \sqrt{d} - 8 i \, b^{4} \sqrt{d}\right)} x\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{3} + {\left(6 \, a^{2} b^{2} d^{2} x^{4} + 18 i \, a^{2} b^{2} d x^{2} - 12 \, a^{2} b^{2} + {\left(6 \, a^{2} b^{2} d^{\frac{3}{2}} x^{3} + 12 i \, a^{2} b^{2} \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{2}}{d^{2} x^{4} + 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i} - 2}\,{d x}"," ",0,"b^4*x*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^4 + 4*(x*arcsinh(d*x^2 + I) - 2*(d^(3/2)*x^2 + 2*I*sqrt(d))/(sqrt(d*x^2 + 2*I)*d))*a^3*b + a^4*x + integrate(((4*(a*b^3*d^2 - 2*b^4*d^2)*x^4 - 8*a*b^3 + (12*I*a*b^3*d - 16*I*b^4*d)*x^2 + (4*(a*b^3*d^(3/2) - 2*b^4*d^(3/2))*x^3 + (8*I*a*b^3*sqrt(d) - 8*I*b^4*sqrt(d))*x)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^3 + (6*a^2*b^2*d^2*x^4 + 18*I*a^2*b^2*d*x^2 - 12*a^2*b^2 + (6*a^2*b^2*d^(3/2)*x^3 + 12*I*a^2*b^2*sqrt(d)*x)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^2)/(d^2*x^4 + 3*I*d*x^2 + (d^(3/2)*x^3 + 2*I*sqrt(d)*x)*sqrt(d*x^2 + 2*I) - 2), x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*arcsinh(I+d*x^2))^3,x, algorithm=""maxima"")","b^{3} x \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{3} + 3 \, {\left(x \operatorname{arsinh}\left(d x^{2} + i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2 i} d}\right)} a^{2} b + a^{3} x + \int \frac{{\left(3 \, {\left(a b^{2} d^{2} - 2 \, b^{3} d^{2}\right)} x^{4} - 6 \, a b^{2} + {\left(9 i \, a b^{2} d - 12 i \, b^{3} d\right)} x^{2} + {\left(3 \, {\left(a b^{2} d^{\frac{3}{2}} - 2 \, b^{3} d^{\frac{3}{2}}\right)} x^{3} + {\left(6 i \, a b^{2} \sqrt{d} - 6 i \, b^{3} \sqrt{d}\right)} x\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{2}}{d^{2} x^{4} + 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i} - 2}\,{d x}"," ",0,"b^3*x*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^3 + 3*(x*arcsinh(d*x^2 + I) - 2*(d^(3/2)*x^2 + 2*I*sqrt(d))/(sqrt(d*x^2 + 2*I)*d))*a^2*b + a^3*x + integrate((3*(a*b^2*d^2 - 2*b^3*d^2)*x^4 - 6*a*b^2 + (9*I*a*b^2*d - 12*I*b^3*d)*x^2 + (3*(a*b^2*d^(3/2) - 2*b^3*d^(3/2))*x^3 + (6*I*a*b^2*sqrt(d) - 6*I*b^3*sqrt(d))*x)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^2/(d^2*x^4 + 3*I*d*x^2 + (d^(3/2)*x^3 + 2*I*sqrt(d)*x)*sqrt(d*x^2 + 2*I) - 2), x)","F",0
316,0,0,0,0.000000," ","integrate((a+b*arcsinh(I+d*x^2))^2,x, algorithm=""maxima"")","2 \, {\left(x \operatorname{arsinh}\left(d x^{2} + i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2 i} d}\right)} a b + {\left(x \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{2} - \int \frac{{\left(4 \, d^{2} x^{4} + 8 i \, d x^{2} + {\left(4 \, d^{\frac{3}{2}} x^{3} + 4 i \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)}{d^{2} x^{4} + 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i} - 2}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"2*(x*arcsinh(d*x^2 + I) - 2*(d^(3/2)*x^2 + 2*I*sqrt(d))/(sqrt(d*x^2 + 2*I)*d))*a*b + (x*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^2 - integrate((4*d^2*x^4 + 8*I*d*x^2 + (4*d^(3/2)*x^3 + 4*I*sqrt(d)*x)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)/(d^2*x^4 + 3*I*d*x^2 + (d^(3/2)*x^3 + 2*I*sqrt(d)*x)*sqrt(d*x^2 + 2*I) - 2), x))*b^2 + a^2*x","F",0
317,1,44,0,0.729052," ","integrate(a+b*arcsinh(I+d*x^2),x, algorithm=""maxima"")","{\left(x \operatorname{arsinh}\left(d x^{2} + i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2 i} d}\right)} b + a x"," ",0,"(x*arcsinh(d*x^2 + I) - 2*(d^(3/2)*x^2 + 2*I*sqrt(d))/(sqrt(d*x^2 + 2*I)*d))*b + a*x","A",0
318,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arsinh}\left(d x^{2} + i\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsinh(d*x^2 + I) + a), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2))^2,x, algorithm=""maxima"")","-\frac{d^{2} x^{4} + 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i} - 2}{2 \, a b d^{2} x^{3} + 4 i \, a b d x + {\left(2 \, b^{2} d^{2} x^{3} + 4 i \, b^{2} d x + {\left(2 \, b^{2} d^{\frac{3}{2}} x^{2} + 2 i \, b^{2} \sqrt{d}\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right) + 2 \, {\left(a b d^{\frac{3}{2}} x^{2} + i \, a b \sqrt{d}\right)} \sqrt{d x^{2} + 2 i}} + \int \frac{2 \, d^{3} x^{6} + 6 i \, d^{2} x^{4} + {\left(2 \, d^{2} x^{4} + 2 i \, d x^{2} - 4\right)} {\left(d x^{2} + 2 i\right)} + 2 \, {\left(2 \, d^{\frac{5}{2}} x^{5} + 4 i \, d^{\frac{3}{2}} x^{3} - \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i} + 8 i}{4 \, a b d^{3} x^{6} + 16 i \, a b d^{2} x^{4} - 16 \, a b d x^{2} + {\left(4 \, a b d^{2} x^{4} + 8 i \, a b d x^{2} - 4 \, a b\right)} {\left(d x^{2} + 2 i\right)} + {\left(4 \, b^{2} d^{3} x^{6} + 16 i \, b^{2} d^{2} x^{4} - 16 \, b^{2} d x^{2} + 4 \, {\left(b^{2} d^{2} x^{4} + 2 i \, b^{2} d x^{2} - b^{2}\right)} {\left(d x^{2} + 2 i\right)} + 8 \, {\left(b^{2} d^{\frac{5}{2}} x^{5} + 3 i \, b^{2} d^{\frac{3}{2}} x^{3} - 2 \, b^{2} \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right) + {\left(8 \, a b d^{\frac{5}{2}} x^{5} + 24 i \, a b d^{\frac{3}{2}} x^{3} - 16 \, a b \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i}}\,{d x}"," ",0,"-(d^2*x^4 + 3*I*d*x^2 + (d^(3/2)*x^3 + 2*I*sqrt(d)*x)*sqrt(d*x^2 + 2*I) - 2)/(2*a*b*d^2*x^3 + 4*I*a*b*d*x + (2*b^2*d^2*x^3 + 4*I*b^2*d*x + (2*b^2*d^(3/2)*x^2 + 2*I*b^2*sqrt(d))*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I) + 2*(a*b*d^(3/2)*x^2 + I*a*b*sqrt(d))*sqrt(d*x^2 + 2*I)) + integrate((2*d^3*x^6 + 6*I*d^2*x^4 + (2*d^2*x^4 + 2*I*d*x^2 - 4)*(d*x^2 + 2*I) + 2*(2*d^(5/2)*x^5 + 4*I*d^(3/2)*x^3 - sqrt(d)*x)*sqrt(d*x^2 + 2*I) + 8*I)/(4*a*b*d^3*x^6 + 16*I*a*b*d^2*x^4 - 16*a*b*d*x^2 + (4*a*b*d^2*x^4 + 8*I*a*b*d*x^2 - 4*a*b)*(d*x^2 + 2*I) + (4*b^2*d^3*x^6 + 16*I*b^2*d^2*x^4 - 16*b^2*d*x^2 + 4*(b^2*d^2*x^4 + 2*I*b^2*d*x^2 - b^2)*(d*x^2 + 2*I) + 8*(b^2*d^(5/2)*x^5 + 3*I*b^2*d^(3/2)*x^3 - 2*b^2*sqrt(d)*x)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I) + (8*a*b*d^(5/2)*x^5 + 24*I*a*b*d^(3/2)*x^3 - 16*a*b*sqrt(d)*x)*sqrt(d*x^2 + 2*I)), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(a d^{\frac{11}{2}} + 2 \, b d^{\frac{11}{2}}\right)} x^{10} + {\left(24 i \, a d^{\frac{9}{2}} + 56 i \, b d^{\frac{9}{2}}\right)} x^{8} - 4 \, {\left(11 \, a d^{\frac{7}{2}} + 36 \, b d^{\frac{7}{2}}\right)} x^{6} + {\left(-8 i \, a d^{\frac{5}{2}} - 160 i \, b d^{\frac{5}{2}}\right)} x^{4} - 16 \, {\left(3 \, a d^{\frac{3}{2}} - 4 \, b d^{\frac{3}{2}}\right)} x^{2} + {\left(4 \, {\left(a d^{4} + 2 \, b d^{4}\right)} x^{7} + {\left(12 i \, a d^{3} + 32 i \, b d^{3}\right)} x^{5} - 8 \, {\left(2 \, a d^{2} + 5 \, b d^{2}\right)} x^{3} + {\left(-16 i \, a d - 16 i \, b d\right)} x\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(12 \, {\left(a d^{\frac{9}{2}} + 2 \, b d^{\frac{9}{2}}\right)} x^{8} + {\left(48 i \, a d^{\frac{7}{2}} + 120 i \, b d^{\frac{7}{2}}\right)} x^{6} - 8 \, {\left(8 \, a d^{\frac{5}{2}} + 25 \, b d^{\frac{5}{2}}\right)} x^{4} + {\left(-40 i \, a d^{\frac{3}{2}} - 120 i \, b d^{\frac{3}{2}}\right)} x^{2} + 16 \, a \sqrt{d} + 16 \, b \sqrt{d}\right)} {\left(d x^{2} + 2 i\right)} + {\left(4 \, b d^{\frac{11}{2}} x^{10} + 24 i \, b d^{\frac{9}{2}} x^{8} - 44 \, b d^{\frac{7}{2}} x^{6} - 8 i \, b d^{\frac{5}{2}} x^{4} - 48 \, b d^{\frac{3}{2}} x^{2} + {\left(4 \, b d^{4} x^{7} + 12 i \, b d^{3} x^{5} - 16 \, b d^{2} x^{3} - 16 i \, b d x\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(12 \, b d^{\frac{9}{2}} x^{8} + 48 i \, b d^{\frac{7}{2}} x^{6} - 64 \, b d^{\frac{5}{2}} x^{4} - 40 i \, b d^{\frac{3}{2}} x^{2} + 16 \, b \sqrt{d}\right)} {\left(d x^{2} + 2 i\right)} + {\left(12 \, b d^{5} x^{9} + 60 i \, b d^{4} x^{7} - 92 \, b d^{3} x^{5} - 28 i \, b d^{2} x^{3} - 24 \, b d x\right)} \sqrt{d x^{2} + 2 i} - 32 i \, b \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right) + {\left(12 \, {\left(a d^{5} + 2 \, b d^{5}\right)} x^{9} + {\left(60 i \, a d^{4} + 144 i \, b d^{4}\right)} x^{7} - 4 \, {\left(23 \, a d^{3} + 76 \, b d^{3}\right)} x^{5} + {\left(-28 i \, a d^{2} - 256 i \, b d^{2}\right)} x^{3} - 8 \, {\left(3 \, a d - 8 \, b d\right)} x\right)} \sqrt{d x^{2} + 2 i} - 32 i \, a \sqrt{d}}{32 \, a^{2} b^{2} d^{\frac{11}{2}} x^{9} + 192 i \, a^{2} b^{2} d^{\frac{9}{2}} x^{7} - 384 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} - 256 i \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} + {\left(32 \, b^{4} d^{\frac{11}{2}} x^{9} + 192 i \, b^{4} d^{\frac{9}{2}} x^{7} - 384 \, b^{4} d^{\frac{7}{2}} x^{5} - 256 i \, b^{4} d^{\frac{5}{2}} x^{3} + {\left(32 \, b^{4} d^{4} x^{6} + 96 i \, b^{4} d^{3} x^{4} - 96 \, b^{4} d^{2} x^{2} - 32 i \, b^{4} d\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(96 \, b^{4} d^{\frac{9}{2}} x^{7} + 384 i \, b^{4} d^{\frac{7}{2}} x^{5} - 480 \, b^{4} d^{\frac{5}{2}} x^{3} - 192 i \, b^{4} d^{\frac{3}{2}} x\right)} {\left(d x^{2} + 2 i\right)} + {\left(96 \, b^{4} d^{5} x^{8} + 480 i \, b^{4} d^{4} x^{6} - 768 \, b^{4} d^{3} x^{4} - 384 i \, b^{4} d^{2} x^{2}\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right)^{2} + {\left(32 \, a^{2} b^{2} d^{4} x^{6} + 96 i \, a^{2} b^{2} d^{3} x^{4} - 96 \, a^{2} b^{2} d^{2} x^{2} - 32 i \, a^{2} b^{2} d\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(96 \, a^{2} b^{2} d^{\frac{9}{2}} x^{7} + 384 i \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} - 480 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} - 192 i \, a^{2} b^{2} d^{\frac{3}{2}} x\right)} {\left(d x^{2} + 2 i\right)} + {\left(64 \, a b^{3} d^{\frac{11}{2}} x^{9} + 384 i \, a b^{3} d^{\frac{9}{2}} x^{7} - 768 \, a b^{3} d^{\frac{7}{2}} x^{5} - 512 i \, a b^{3} d^{\frac{5}{2}} x^{3} + {\left(64 \, a b^{3} d^{4} x^{6} + 192 i \, a b^{3} d^{3} x^{4} - 192 \, a b^{3} d^{2} x^{2} - 64 i \, a b^{3} d\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(192 \, a b^{3} d^{\frac{9}{2}} x^{7} + 768 i \, a b^{3} d^{\frac{7}{2}} x^{5} - 960 \, a b^{3} d^{\frac{5}{2}} x^{3} - 384 i \, a b^{3} d^{\frac{3}{2}} x\right)} {\left(d x^{2} + 2 i\right)} + {\left(192 \, a b^{3} d^{5} x^{8} + 960 i \, a b^{3} d^{4} x^{6} - 1536 \, a b^{3} d^{3} x^{4} - 768 i \, a b^{3} d^{2} x^{2}\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right) + {\left(96 \, a^{2} b^{2} d^{5} x^{8} + 480 i \, a^{2} b^{2} d^{4} x^{6} - 768 \, a^{2} b^{2} d^{3} x^{4} - 384 i \, a^{2} b^{2} d^{2} x^{2}\right)} \sqrt{d x^{2} + 2 i}} + \int \frac{d^{6} x^{12} + 8 i \, d^{5} x^{10} - 27 \, d^{4} x^{8} - 56 i \, d^{3} x^{6} + 88 \, d^{2} x^{4} + {\left(d^{4} x^{8} + 4 i \, d^{3} x^{6} - 3 \, d^{2} x^{4} + 8 i \, d x^{2} + 4\right)} {\left(d x^{2} + 2 i\right)}^{2} + 96 i \, d x^{2} + {\left(4 \, d^{\frac{9}{2}} x^{9} + 20 i \, d^{\frac{7}{2}} x^{7} - 30 \, d^{\frac{5}{2}} x^{5} + 2 i \, d^{\frac{3}{2}} x^{3} - 22 \, \sqrt{d} x\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(6 \, d^{5} x^{10} + 36 i \, d^{4} x^{8} - 78 \, d^{3} x^{6} - 72 i \, d^{2} x^{4} + 9 \, d x^{2} - 30 i\right)} {\left(d x^{2} + 2 i\right)} + {\left(4 \, d^{\frac{11}{2}} x^{11} + 28 i \, d^{\frac{9}{2}} x^{9} - 78 \, d^{\frac{7}{2}} x^{7} - 122 i \, d^{\frac{5}{2}} x^{5} + 122 \, d^{\frac{3}{2}} x^{3} + 60 i \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2 i} - 48}{8 \, a b^{2} d^{6} x^{12} + 64 i \, a b^{2} d^{5} x^{10} - 192 \, a b^{2} d^{4} x^{8} - 256 i \, a b^{2} d^{3} x^{6} + 128 \, a b^{2} d^{2} x^{4} + {\left(8 \, a b^{2} d^{4} x^{8} + 32 i \, a b^{2} d^{3} x^{6} - 48 \, a b^{2} d^{2} x^{4} - 32 i \, a b^{2} d x^{2} + 8 \, a b^{2}\right)} {\left(d x^{2} + 2 i\right)}^{2} + {\left(32 \, a b^{2} d^{\frac{9}{2}} x^{9} + 160 i \, a b^{2} d^{\frac{7}{2}} x^{7} - 288 \, a b^{2} d^{\frac{5}{2}} x^{5} - 224 i \, a b^{2} d^{\frac{3}{2}} x^{3} + 64 \, a b^{2} \sqrt{d} x\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(48 \, a b^{2} d^{5} x^{10} + 288 i \, a b^{2} d^{4} x^{8} - 624 \, a b^{2} d^{3} x^{6} - 576 i \, a b^{2} d^{2} x^{4} + 192 \, a b^{2} d x^{2}\right)} {\left(d x^{2} + 2 i\right)} + {\left(8 \, b^{3} d^{6} x^{12} + 64 i \, b^{3} d^{5} x^{10} - 192 \, b^{3} d^{4} x^{8} - 256 i \, b^{3} d^{3} x^{6} + 128 \, b^{3} d^{2} x^{4} + {\left(8 \, b^{3} d^{4} x^{8} + 32 i \, b^{3} d^{3} x^{6} - 48 \, b^{3} d^{2} x^{4} - 32 i \, b^{3} d x^{2} + 8 \, b^{3}\right)} {\left(d x^{2} + 2 i\right)}^{2} + {\left(32 \, b^{3} d^{\frac{9}{2}} x^{9} + 160 i \, b^{3} d^{\frac{7}{2}} x^{7} - 288 \, b^{3} d^{\frac{5}{2}} x^{5} - 224 i \, b^{3} d^{\frac{3}{2}} x^{3} + 64 \, b^{3} \sqrt{d} x\right)} {\left(d x^{2} + 2 i\right)}^{\frac{3}{2}} + {\left(48 \, b^{3} d^{5} x^{10} + 288 i \, b^{3} d^{4} x^{8} - 624 \, b^{3} d^{3} x^{6} - 576 i \, b^{3} d^{2} x^{4} + 192 \, b^{3} d x^{2}\right)} {\left(d x^{2} + 2 i\right)} + {\left(32 \, b^{3} d^{\frac{11}{2}} x^{11} + 224 i \, b^{3} d^{\frac{9}{2}} x^{9} - 576 \, b^{3} d^{\frac{7}{2}} x^{7} - 640 i \, b^{3} d^{\frac{5}{2}} x^{5} + 256 \, b^{3} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} + 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2 i} \sqrt{d} x + i\right) + {\left(32 \, a b^{2} d^{\frac{11}{2}} x^{11} + 224 i \, a b^{2} d^{\frac{9}{2}} x^{9} - 576 \, a b^{2} d^{\frac{7}{2}} x^{7} - 640 i \, a b^{2} d^{\frac{5}{2}} x^{5} + 256 \, a b^{2} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} + 2 i}}\,{d x}"," ",0,"-(4*(a*d^(11/2) + 2*b*d^(11/2))*x^10 + (24*I*a*d^(9/2) + 56*I*b*d^(9/2))*x^8 - 4*(11*a*d^(7/2) + 36*b*d^(7/2))*x^6 + (-8*I*a*d^(5/2) - 160*I*b*d^(5/2))*x^4 - 16*(3*a*d^(3/2) - 4*b*d^(3/2))*x^2 + (4*(a*d^4 + 2*b*d^4)*x^7 + (12*I*a*d^3 + 32*I*b*d^3)*x^5 - 8*(2*a*d^2 + 5*b*d^2)*x^3 + (-16*I*a*d - 16*I*b*d)*x)*(d*x^2 + 2*I)^(3/2) + (12*(a*d^(9/2) + 2*b*d^(9/2))*x^8 + (48*I*a*d^(7/2) + 120*I*b*d^(7/2))*x^6 - 8*(8*a*d^(5/2) + 25*b*d^(5/2))*x^4 + (-40*I*a*d^(3/2) - 120*I*b*d^(3/2))*x^2 + 16*a*sqrt(d) + 16*b*sqrt(d))*(d*x^2 + 2*I) + (4*b*d^(11/2)*x^10 + 24*I*b*d^(9/2)*x^8 - 44*b*d^(7/2)*x^6 - 8*I*b*d^(5/2)*x^4 - 48*b*d^(3/2)*x^2 + (4*b*d^4*x^7 + 12*I*b*d^3*x^5 - 16*b*d^2*x^3 - 16*I*b*d*x)*(d*x^2 + 2*I)^(3/2) + (12*b*d^(9/2)*x^8 + 48*I*b*d^(7/2)*x^6 - 64*b*d^(5/2)*x^4 - 40*I*b*d^(3/2)*x^2 + 16*b*sqrt(d))*(d*x^2 + 2*I) + (12*b*d^5*x^9 + 60*I*b*d^4*x^7 - 92*b*d^3*x^5 - 28*I*b*d^2*x^3 - 24*b*d*x)*sqrt(d*x^2 + 2*I) - 32*I*b*sqrt(d))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I) + (12*(a*d^5 + 2*b*d^5)*x^9 + (60*I*a*d^4 + 144*I*b*d^4)*x^7 - 4*(23*a*d^3 + 76*b*d^3)*x^5 + (-28*I*a*d^2 - 256*I*b*d^2)*x^3 - 8*(3*a*d - 8*b*d)*x)*sqrt(d*x^2 + 2*I) - 32*I*a*sqrt(d))/(32*a^2*b^2*d^(11/2)*x^9 + 192*I*a^2*b^2*d^(9/2)*x^7 - 384*a^2*b^2*d^(7/2)*x^5 - 256*I*a^2*b^2*d^(5/2)*x^3 + (32*b^4*d^(11/2)*x^9 + 192*I*b^4*d^(9/2)*x^7 - 384*b^4*d^(7/2)*x^5 - 256*I*b^4*d^(5/2)*x^3 + (32*b^4*d^4*x^6 + 96*I*b^4*d^3*x^4 - 96*b^4*d^2*x^2 - 32*I*b^4*d)*(d*x^2 + 2*I)^(3/2) + (96*b^4*d^(9/2)*x^7 + 384*I*b^4*d^(7/2)*x^5 - 480*b^4*d^(5/2)*x^3 - 192*I*b^4*d^(3/2)*x)*(d*x^2 + 2*I) + (96*b^4*d^5*x^8 + 480*I*b^4*d^4*x^6 - 768*b^4*d^3*x^4 - 384*I*b^4*d^2*x^2)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I)^2 + (32*a^2*b^2*d^4*x^6 + 96*I*a^2*b^2*d^3*x^4 - 96*a^2*b^2*d^2*x^2 - 32*I*a^2*b^2*d)*(d*x^2 + 2*I)^(3/2) + (96*a^2*b^2*d^(9/2)*x^7 + 384*I*a^2*b^2*d^(7/2)*x^5 - 480*a^2*b^2*d^(5/2)*x^3 - 192*I*a^2*b^2*d^(3/2)*x)*(d*x^2 + 2*I) + (64*a*b^3*d^(11/2)*x^9 + 384*I*a*b^3*d^(9/2)*x^7 - 768*a*b^3*d^(7/2)*x^5 - 512*I*a*b^3*d^(5/2)*x^3 + (64*a*b^3*d^4*x^6 + 192*I*a*b^3*d^3*x^4 - 192*a*b^3*d^2*x^2 - 64*I*a*b^3*d)*(d*x^2 + 2*I)^(3/2) + (192*a*b^3*d^(9/2)*x^7 + 768*I*a*b^3*d^(7/2)*x^5 - 960*a*b^3*d^(5/2)*x^3 - 384*I*a*b^3*d^(3/2)*x)*(d*x^2 + 2*I) + (192*a*b^3*d^5*x^8 + 960*I*a*b^3*d^4*x^6 - 1536*a*b^3*d^3*x^4 - 768*I*a*b^3*d^2*x^2)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I) + (96*a^2*b^2*d^5*x^8 + 480*I*a^2*b^2*d^4*x^6 - 768*a^2*b^2*d^3*x^4 - 384*I*a^2*b^2*d^2*x^2)*sqrt(d*x^2 + 2*I)) + integrate((d^6*x^12 + 8*I*d^5*x^10 - 27*d^4*x^8 - 56*I*d^3*x^6 + 88*d^2*x^4 + (d^4*x^8 + 4*I*d^3*x^6 - 3*d^2*x^4 + 8*I*d*x^2 + 4)*(d*x^2 + 2*I)^2 + 96*I*d*x^2 + (4*d^(9/2)*x^9 + 20*I*d^(7/2)*x^7 - 30*d^(5/2)*x^5 + 2*I*d^(3/2)*x^3 - 22*sqrt(d)*x)*(d*x^2 + 2*I)^(3/2) + (6*d^5*x^10 + 36*I*d^4*x^8 - 78*d^3*x^6 - 72*I*d^2*x^4 + 9*d*x^2 - 30*I)*(d*x^2 + 2*I) + (4*d^(11/2)*x^11 + 28*I*d^(9/2)*x^9 - 78*d^(7/2)*x^7 - 122*I*d^(5/2)*x^5 + 122*d^(3/2)*x^3 + 60*I*sqrt(d)*x)*sqrt(d*x^2 + 2*I) - 48)/(8*a*b^2*d^6*x^12 + 64*I*a*b^2*d^5*x^10 - 192*a*b^2*d^4*x^8 - 256*I*a*b^2*d^3*x^6 + 128*a*b^2*d^2*x^4 + (8*a*b^2*d^4*x^8 + 32*I*a*b^2*d^3*x^6 - 48*a*b^2*d^2*x^4 - 32*I*a*b^2*d*x^2 + 8*a*b^2)*(d*x^2 + 2*I)^2 + (32*a*b^2*d^(9/2)*x^9 + 160*I*a*b^2*d^(7/2)*x^7 - 288*a*b^2*d^(5/2)*x^5 - 224*I*a*b^2*d^(3/2)*x^3 + 64*a*b^2*sqrt(d)*x)*(d*x^2 + 2*I)^(3/2) + (48*a*b^2*d^5*x^10 + 288*I*a*b^2*d^4*x^8 - 624*a*b^2*d^3*x^6 - 576*I*a*b^2*d^2*x^4 + 192*a*b^2*d*x^2)*(d*x^2 + 2*I) + (8*b^3*d^6*x^12 + 64*I*b^3*d^5*x^10 - 192*b^3*d^4*x^8 - 256*I*b^3*d^3*x^6 + 128*b^3*d^2*x^4 + (8*b^3*d^4*x^8 + 32*I*b^3*d^3*x^6 - 48*b^3*d^2*x^4 - 32*I*b^3*d*x^2 + 8*b^3)*(d*x^2 + 2*I)^2 + (32*b^3*d^(9/2)*x^9 + 160*I*b^3*d^(7/2)*x^7 - 288*b^3*d^(5/2)*x^5 - 224*I*b^3*d^(3/2)*x^3 + 64*b^3*sqrt(d)*x)*(d*x^2 + 2*I)^(3/2) + (48*b^3*d^5*x^10 + 288*I*b^3*d^4*x^8 - 624*b^3*d^3*x^6 - 576*I*b^3*d^2*x^4 + 192*b^3*d*x^2)*(d*x^2 + 2*I) + (32*b^3*d^(11/2)*x^11 + 224*I*b^3*d^(9/2)*x^9 - 576*b^3*d^(7/2)*x^7 - 640*I*b^3*d^(5/2)*x^5 + 256*b^3*d^(3/2)*x^3)*sqrt(d*x^2 + 2*I))*log(d*x^2 + sqrt(d*x^2 + 2*I)*sqrt(d)*x + I) + (32*a*b^2*d^(11/2)*x^11 + 224*I*a*b^2*d^(9/2)*x^9 - 576*a*b^2*d^(7/2)*x^7 - 640*I*a*b^2*d^(5/2)*x^5 + 256*a*b^2*d^(3/2)*x^3)*sqrt(d*x^2 + 2*I)), x)","F",0
321,0,0,0,0.000000," ","integrate((a+b*arcsinh(-I+d*x^2))^4,x, algorithm=""maxima"")","b^{4} x \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{4} + 4 \, {\left(x \operatorname{arsinh}\left(d x^{2} - i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2 i} d}\right)} a^{3} b + a^{4} x + \int \frac{{\left(4 \, {\left(a b^{3} d^{2} - 2 \, b^{4} d^{2}\right)} x^{4} - 8 \, a b^{3} + {\left(-12 i \, a b^{3} d + 16 i \, b^{4} d\right)} x^{2} + {\left(4 \, {\left(a b^{3} d^{\frac{3}{2}} - 2 \, b^{4} d^{\frac{3}{2}}\right)} x^{3} + {\left(-8 i \, a b^{3} \sqrt{d} + 8 i \, b^{4} \sqrt{d}\right)} x\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{3} + {\left(6 \, a^{2} b^{2} d^{2} x^{4} - 18 i \, a^{2} b^{2} d x^{2} - 12 \, a^{2} b^{2} + {\left(6 \, a^{2} b^{2} d^{\frac{3}{2}} x^{3} - 12 i \, a^{2} b^{2} \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{2}}{d^{2} x^{4} - 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i} - 2}\,{d x}"," ",0,"b^4*x*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^4 + 4*(x*arcsinh(d*x^2 - I) - 2*(d^(3/2)*x^2 - 2*I*sqrt(d))/(sqrt(d*x^2 - 2*I)*d))*a^3*b + a^4*x + integrate(((4*(a*b^3*d^2 - 2*b^4*d^2)*x^4 - 8*a*b^3 + (-12*I*a*b^3*d + 16*I*b^4*d)*x^2 + (4*(a*b^3*d^(3/2) - 2*b^4*d^(3/2))*x^3 + (-8*I*a*b^3*sqrt(d) + 8*I*b^4*sqrt(d))*x)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^3 + (6*a^2*b^2*d^2*x^4 - 18*I*a^2*b^2*d*x^2 - 12*a^2*b^2 + (6*a^2*b^2*d^(3/2)*x^3 - 12*I*a^2*b^2*sqrt(d)*x)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^2)/(d^2*x^4 - 3*I*d*x^2 + (d^(3/2)*x^3 - 2*I*sqrt(d)*x)*sqrt(d*x^2 - 2*I) - 2), x)","F",0
322,0,0,0,0.000000," ","integrate((a+b*arcsinh(-I+d*x^2))^3,x, algorithm=""maxima"")","b^{3} x \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{3} + 3 \, {\left(x \operatorname{arsinh}\left(d x^{2} - i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2 i} d}\right)} a^{2} b + a^{3} x + \int \frac{{\left(3 \, {\left(a b^{2} d^{2} - 2 \, b^{3} d^{2}\right)} x^{4} - 6 \, a b^{2} + {\left(-9 i \, a b^{2} d + 12 i \, b^{3} d\right)} x^{2} + {\left(3 \, {\left(a b^{2} d^{\frac{3}{2}} - 2 \, b^{3} d^{\frac{3}{2}}\right)} x^{3} + {\left(-6 i \, a b^{2} \sqrt{d} + 6 i \, b^{3} \sqrt{d}\right)} x\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{2}}{d^{2} x^{4} - 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i} - 2}\,{d x}"," ",0,"b^3*x*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^3 + 3*(x*arcsinh(d*x^2 - I) - 2*(d^(3/2)*x^2 - 2*I*sqrt(d))/(sqrt(d*x^2 - 2*I)*d))*a^2*b + a^3*x + integrate((3*(a*b^2*d^2 - 2*b^3*d^2)*x^4 - 6*a*b^2 + (-9*I*a*b^2*d + 12*I*b^3*d)*x^2 + (3*(a*b^2*d^(3/2) - 2*b^3*d^(3/2))*x^3 + (-6*I*a*b^2*sqrt(d) + 6*I*b^3*sqrt(d))*x)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^2/(d^2*x^4 - 3*I*d*x^2 + (d^(3/2)*x^3 - 2*I*sqrt(d)*x)*sqrt(d*x^2 - 2*I) - 2), x)","F",0
323,0,0,0,0.000000," ","integrate((a+b*arcsinh(-I+d*x^2))^2,x, algorithm=""maxima"")","2 \, {\left(x \operatorname{arsinh}\left(d x^{2} - i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2 i} d}\right)} a b + {\left(x \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{2} - \int \frac{{\left(4 \, d^{2} x^{4} - 8 i \, d x^{2} + {\left(4 \, d^{\frac{3}{2}} x^{3} - 4 i \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)}{d^{2} x^{4} - 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i} - 2}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"2*(x*arcsinh(d*x^2 - I) - 2*(d^(3/2)*x^2 - 2*I*sqrt(d))/(sqrt(d*x^2 - 2*I)*d))*a*b + (x*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^2 - integrate((4*d^2*x^4 - 8*I*d*x^2 + (4*d^(3/2)*x^3 - 4*I*sqrt(d)*x)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)/(d^2*x^4 - 3*I*d*x^2 + (d^(3/2)*x^3 - 2*I*sqrt(d)*x)*sqrt(d*x^2 - 2*I) - 2), x))*b^2 + a^2*x","F",0
324,1,44,0,0.703771," ","integrate(a+b*arcsinh(-I+d*x^2),x, algorithm=""maxima"")","{\left(x \operatorname{arsinh}\left(d x^{2} - i\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 i \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2 i} d}\right)} b + a x"," ",0,"(x*arcsinh(d*x^2 - I) - 2*(d^(3/2)*x^2 - 2*I*sqrt(d))/(sqrt(d*x^2 - 2*I)*d))*b + a*x","A",0
325,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arsinh}\left(d x^{2} - i\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsinh(d*x^2 - I) + a), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2))^2,x, algorithm=""maxima"")","-\frac{d^{2} x^{4} - 3 i \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 i \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i} - 2}{2 \, a b d^{2} x^{3} - 4 i \, a b d x + {\left(2 \, b^{2} d^{2} x^{3} - 4 i \, b^{2} d x + {\left(2 \, b^{2} d^{\frac{3}{2}} x^{2} - 2 i \, b^{2} \sqrt{d}\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right) + 2 \, {\left(a b d^{\frac{3}{2}} x^{2} - i \, a b \sqrt{d}\right)} \sqrt{d x^{2} - 2 i}} + \int \frac{2 \, d^{3} x^{6} - 6 i \, d^{2} x^{4} + {\left(2 \, d^{2} x^{4} - 2 i \, d x^{2} - 4\right)} {\left(d x^{2} - 2 i\right)} + 2 \, {\left(2 \, d^{\frac{5}{2}} x^{5} - 4 i \, d^{\frac{3}{2}} x^{3} - \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i} - 8 i}{4 \, a b d^{3} x^{6} - 16 i \, a b d^{2} x^{4} - 16 \, a b d x^{2} + {\left(4 \, a b d^{2} x^{4} - 8 i \, a b d x^{2} - 4 \, a b\right)} {\left(d x^{2} - 2 i\right)} + {\left(4 \, b^{2} d^{3} x^{6} - 16 i \, b^{2} d^{2} x^{4} - 16 \, b^{2} d x^{2} + 4 \, {\left(b^{2} d^{2} x^{4} - 2 i \, b^{2} d x^{2} - b^{2}\right)} {\left(d x^{2} - 2 i\right)} + 8 \, {\left(b^{2} d^{\frac{5}{2}} x^{5} - 3 i \, b^{2} d^{\frac{3}{2}} x^{3} - 2 \, b^{2} \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right) + {\left(8 \, a b d^{\frac{5}{2}} x^{5} - 24 i \, a b d^{\frac{3}{2}} x^{3} - 16 \, a b \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i}}\,{d x}"," ",0,"-(d^2*x^4 - 3*I*d*x^2 + (d^(3/2)*x^3 - 2*I*sqrt(d)*x)*sqrt(d*x^2 - 2*I) - 2)/(2*a*b*d^2*x^3 - 4*I*a*b*d*x + (2*b^2*d^2*x^3 - 4*I*b^2*d*x + (2*b^2*d^(3/2)*x^2 - 2*I*b^2*sqrt(d))*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I) + 2*(a*b*d^(3/2)*x^2 - I*a*b*sqrt(d))*sqrt(d*x^2 - 2*I)) + integrate((2*d^3*x^6 - 6*I*d^2*x^4 + (2*d^2*x^4 - 2*I*d*x^2 - 4)*(d*x^2 - 2*I) + 2*(2*d^(5/2)*x^5 - 4*I*d^(3/2)*x^3 - sqrt(d)*x)*sqrt(d*x^2 - 2*I) - 8*I)/(4*a*b*d^3*x^6 - 16*I*a*b*d^2*x^4 - 16*a*b*d*x^2 + (4*a*b*d^2*x^4 - 8*I*a*b*d*x^2 - 4*a*b)*(d*x^2 - 2*I) + (4*b^2*d^3*x^6 - 16*I*b^2*d^2*x^4 - 16*b^2*d*x^2 + 4*(b^2*d^2*x^4 - 2*I*b^2*d*x^2 - b^2)*(d*x^2 - 2*I) + 8*(b^2*d^(5/2)*x^5 - 3*I*b^2*d^(3/2)*x^3 - 2*b^2*sqrt(d)*x)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I) + (8*a*b*d^(5/2)*x^5 - 24*I*a*b*d^(3/2)*x^3 - 16*a*b*sqrt(d)*x)*sqrt(d*x^2 - 2*I)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(a d^{\frac{11}{2}} + 2 \, b d^{\frac{11}{2}}\right)} x^{10} + {\left(-24 i \, a d^{\frac{9}{2}} - 56 i \, b d^{\frac{9}{2}}\right)} x^{8} - 4 \, {\left(11 \, a d^{\frac{7}{2}} + 36 \, b d^{\frac{7}{2}}\right)} x^{6} + {\left(8 i \, a d^{\frac{5}{2}} + 160 i \, b d^{\frac{5}{2}}\right)} x^{4} - 16 \, {\left(3 \, a d^{\frac{3}{2}} - 4 \, b d^{\frac{3}{2}}\right)} x^{2} + {\left(4 \, {\left(a d^{4} + 2 \, b d^{4}\right)} x^{7} + {\left(-12 i \, a d^{3} - 32 i \, b d^{3}\right)} x^{5} - 8 \, {\left(2 \, a d^{2} + 5 \, b d^{2}\right)} x^{3} + {\left(16 i \, a d + 16 i \, b d\right)} x\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(12 \, {\left(a d^{\frac{9}{2}} + 2 \, b d^{\frac{9}{2}}\right)} x^{8} + {\left(-48 i \, a d^{\frac{7}{2}} - 120 i \, b d^{\frac{7}{2}}\right)} x^{6} - 8 \, {\left(8 \, a d^{\frac{5}{2}} + 25 \, b d^{\frac{5}{2}}\right)} x^{4} + {\left(40 i \, a d^{\frac{3}{2}} + 120 i \, b d^{\frac{3}{2}}\right)} x^{2} + 16 \, a \sqrt{d} + 16 \, b \sqrt{d}\right)} {\left(d x^{2} - 2 i\right)} + {\left(4 \, b d^{\frac{11}{2}} x^{10} - 24 i \, b d^{\frac{9}{2}} x^{8} - 44 \, b d^{\frac{7}{2}} x^{6} + 8 i \, b d^{\frac{5}{2}} x^{4} - 48 \, b d^{\frac{3}{2}} x^{2} + {\left(4 \, b d^{4} x^{7} - 12 i \, b d^{3} x^{5} - 16 \, b d^{2} x^{3} + 16 i \, b d x\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(12 \, b d^{\frac{9}{2}} x^{8} - 48 i \, b d^{\frac{7}{2}} x^{6} - 64 \, b d^{\frac{5}{2}} x^{4} + 40 i \, b d^{\frac{3}{2}} x^{2} + 16 \, b \sqrt{d}\right)} {\left(d x^{2} - 2 i\right)} + {\left(12 \, b d^{5} x^{9} - 60 i \, b d^{4} x^{7} - 92 \, b d^{3} x^{5} + 28 i \, b d^{2} x^{3} - 24 \, b d x\right)} \sqrt{d x^{2} - 2 i} + 32 i \, b \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right) + {\left(12 \, {\left(a d^{5} + 2 \, b d^{5}\right)} x^{9} + {\left(-60 i \, a d^{4} - 144 i \, b d^{4}\right)} x^{7} - 4 \, {\left(23 \, a d^{3} + 76 \, b d^{3}\right)} x^{5} + {\left(28 i \, a d^{2} + 256 i \, b d^{2}\right)} x^{3} - 8 \, {\left(3 \, a d - 8 \, b d\right)} x\right)} \sqrt{d x^{2} - 2 i} + 32 i \, a \sqrt{d}}{32 \, a^{2} b^{2} d^{\frac{11}{2}} x^{9} - 192 i \, a^{2} b^{2} d^{\frac{9}{2}} x^{7} - 384 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} + 256 i \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} + {\left(32 \, b^{4} d^{\frac{11}{2}} x^{9} - 192 i \, b^{4} d^{\frac{9}{2}} x^{7} - 384 \, b^{4} d^{\frac{7}{2}} x^{5} + 256 i \, b^{4} d^{\frac{5}{2}} x^{3} + {\left(32 \, b^{4} d^{4} x^{6} - 96 i \, b^{4} d^{3} x^{4} - 96 \, b^{4} d^{2} x^{2} + 32 i \, b^{4} d\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(96 \, b^{4} d^{\frac{9}{2}} x^{7} - 384 i \, b^{4} d^{\frac{7}{2}} x^{5} - 480 \, b^{4} d^{\frac{5}{2}} x^{3} + 192 i \, b^{4} d^{\frac{3}{2}} x\right)} {\left(d x^{2} - 2 i\right)} + {\left(96 \, b^{4} d^{5} x^{8} - 480 i \, b^{4} d^{4} x^{6} - 768 \, b^{4} d^{3} x^{4} + 384 i \, b^{4} d^{2} x^{2}\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right)^{2} + {\left(32 \, a^{2} b^{2} d^{4} x^{6} - 96 i \, a^{2} b^{2} d^{3} x^{4} - 96 \, a^{2} b^{2} d^{2} x^{2} + 32 i \, a^{2} b^{2} d\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(96 \, a^{2} b^{2} d^{\frac{9}{2}} x^{7} - 384 i \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} - 480 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} + 192 i \, a^{2} b^{2} d^{\frac{3}{2}} x\right)} {\left(d x^{2} - 2 i\right)} + {\left(64 \, a b^{3} d^{\frac{11}{2}} x^{9} - 384 i \, a b^{3} d^{\frac{9}{2}} x^{7} - 768 \, a b^{3} d^{\frac{7}{2}} x^{5} + 512 i \, a b^{3} d^{\frac{5}{2}} x^{3} + {\left(64 \, a b^{3} d^{4} x^{6} - 192 i \, a b^{3} d^{3} x^{4} - 192 \, a b^{3} d^{2} x^{2} + 64 i \, a b^{3} d\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(192 \, a b^{3} d^{\frac{9}{2}} x^{7} - 768 i \, a b^{3} d^{\frac{7}{2}} x^{5} - 960 \, a b^{3} d^{\frac{5}{2}} x^{3} + 384 i \, a b^{3} d^{\frac{3}{2}} x\right)} {\left(d x^{2} - 2 i\right)} + {\left(192 \, a b^{3} d^{5} x^{8} - 960 i \, a b^{3} d^{4} x^{6} - 1536 \, a b^{3} d^{3} x^{4} + 768 i \, a b^{3} d^{2} x^{2}\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right) + {\left(96 \, a^{2} b^{2} d^{5} x^{8} - 480 i \, a^{2} b^{2} d^{4} x^{6} - 768 \, a^{2} b^{2} d^{3} x^{4} + 384 i \, a^{2} b^{2} d^{2} x^{2}\right)} \sqrt{d x^{2} - 2 i}} + \int \frac{d^{6} x^{12} - 8 i \, d^{5} x^{10} - 27 \, d^{4} x^{8} + 56 i \, d^{3} x^{6} + 88 \, d^{2} x^{4} + {\left(d^{4} x^{8} - 4 i \, d^{3} x^{6} - 3 \, d^{2} x^{4} - 8 i \, d x^{2} + 4\right)} {\left(d x^{2} - 2 i\right)}^{2} - 96 i \, d x^{2} + {\left(4 \, d^{\frac{9}{2}} x^{9} - 20 i \, d^{\frac{7}{2}} x^{7} - 30 \, d^{\frac{5}{2}} x^{5} - 2 i \, d^{\frac{3}{2}} x^{3} - 22 \, \sqrt{d} x\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(6 \, d^{5} x^{10} - 36 i \, d^{4} x^{8} - 78 \, d^{3} x^{6} + 72 i \, d^{2} x^{4} + 9 \, d x^{2} + 30 i\right)} {\left(d x^{2} - 2 i\right)} + {\left(4 \, d^{\frac{11}{2}} x^{11} - 28 i \, d^{\frac{9}{2}} x^{9} - 78 \, d^{\frac{7}{2}} x^{7} + 122 i \, d^{\frac{5}{2}} x^{5} + 122 \, d^{\frac{3}{2}} x^{3} - 60 i \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2 i} - 48}{8 \, a b^{2} d^{6} x^{12} - 64 i \, a b^{2} d^{5} x^{10} - 192 \, a b^{2} d^{4} x^{8} + 256 i \, a b^{2} d^{3} x^{6} + 128 \, a b^{2} d^{2} x^{4} + {\left(8 \, a b^{2} d^{4} x^{8} - 32 i \, a b^{2} d^{3} x^{6} - 48 \, a b^{2} d^{2} x^{4} + 32 i \, a b^{2} d x^{2} + 8 \, a b^{2}\right)} {\left(d x^{2} - 2 i\right)}^{2} + {\left(32 \, a b^{2} d^{\frac{9}{2}} x^{9} - 160 i \, a b^{2} d^{\frac{7}{2}} x^{7} - 288 \, a b^{2} d^{\frac{5}{2}} x^{5} + 224 i \, a b^{2} d^{\frac{3}{2}} x^{3} + 64 \, a b^{2} \sqrt{d} x\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(48 \, a b^{2} d^{5} x^{10} - 288 i \, a b^{2} d^{4} x^{8} - 624 \, a b^{2} d^{3} x^{6} + 576 i \, a b^{2} d^{2} x^{4} + 192 \, a b^{2} d x^{2}\right)} {\left(d x^{2} - 2 i\right)} + {\left(8 \, b^{3} d^{6} x^{12} - 64 i \, b^{3} d^{5} x^{10} - 192 \, b^{3} d^{4} x^{8} + 256 i \, b^{3} d^{3} x^{6} + 128 \, b^{3} d^{2} x^{4} + {\left(8 \, b^{3} d^{4} x^{8} - 32 i \, b^{3} d^{3} x^{6} - 48 \, b^{3} d^{2} x^{4} + 32 i \, b^{3} d x^{2} + 8 \, b^{3}\right)} {\left(d x^{2} - 2 i\right)}^{2} + {\left(32 \, b^{3} d^{\frac{9}{2}} x^{9} - 160 i \, b^{3} d^{\frac{7}{2}} x^{7} - 288 \, b^{3} d^{\frac{5}{2}} x^{5} + 224 i \, b^{3} d^{\frac{3}{2}} x^{3} + 64 \, b^{3} \sqrt{d} x\right)} {\left(d x^{2} - 2 i\right)}^{\frac{3}{2}} + {\left(48 \, b^{3} d^{5} x^{10} - 288 i \, b^{3} d^{4} x^{8} - 624 \, b^{3} d^{3} x^{6} + 576 i \, b^{3} d^{2} x^{4} + 192 \, b^{3} d x^{2}\right)} {\left(d x^{2} - 2 i\right)} + {\left(32 \, b^{3} d^{\frac{11}{2}} x^{11} - 224 i \, b^{3} d^{\frac{9}{2}} x^{9} - 576 \, b^{3} d^{\frac{7}{2}} x^{7} + 640 i \, b^{3} d^{\frac{5}{2}} x^{5} + 256 \, b^{3} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} - 2 i}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2 i} \sqrt{d} x - i\right) + {\left(32 \, a b^{2} d^{\frac{11}{2}} x^{11} - 224 i \, a b^{2} d^{\frac{9}{2}} x^{9} - 576 \, a b^{2} d^{\frac{7}{2}} x^{7} + 640 i \, a b^{2} d^{\frac{5}{2}} x^{5} + 256 \, a b^{2} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} - 2 i}}\,{d x}"," ",0,"-(4*(a*d^(11/2) + 2*b*d^(11/2))*x^10 + (-24*I*a*d^(9/2) - 56*I*b*d^(9/2))*x^8 - 4*(11*a*d^(7/2) + 36*b*d^(7/2))*x^6 + (8*I*a*d^(5/2) + 160*I*b*d^(5/2))*x^4 - 16*(3*a*d^(3/2) - 4*b*d^(3/2))*x^2 + (4*(a*d^4 + 2*b*d^4)*x^7 + (-12*I*a*d^3 - 32*I*b*d^3)*x^5 - 8*(2*a*d^2 + 5*b*d^2)*x^3 + (16*I*a*d + 16*I*b*d)*x)*(d*x^2 - 2*I)^(3/2) + (12*(a*d^(9/2) + 2*b*d^(9/2))*x^8 + (-48*I*a*d^(7/2) - 120*I*b*d^(7/2))*x^6 - 8*(8*a*d^(5/2) + 25*b*d^(5/2))*x^4 + (40*I*a*d^(3/2) + 120*I*b*d^(3/2))*x^2 + 16*a*sqrt(d) + 16*b*sqrt(d))*(d*x^2 - 2*I) + (4*b*d^(11/2)*x^10 - 24*I*b*d^(9/2)*x^8 - 44*b*d^(7/2)*x^6 + 8*I*b*d^(5/2)*x^4 - 48*b*d^(3/2)*x^2 + (4*b*d^4*x^7 - 12*I*b*d^3*x^5 - 16*b*d^2*x^3 + 16*I*b*d*x)*(d*x^2 - 2*I)^(3/2) + (12*b*d^(9/2)*x^8 - 48*I*b*d^(7/2)*x^6 - 64*b*d^(5/2)*x^4 + 40*I*b*d^(3/2)*x^2 + 16*b*sqrt(d))*(d*x^2 - 2*I) + (12*b*d^5*x^9 - 60*I*b*d^4*x^7 - 92*b*d^3*x^5 + 28*I*b*d^2*x^3 - 24*b*d*x)*sqrt(d*x^2 - 2*I) + 32*I*b*sqrt(d))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I) + (12*(a*d^5 + 2*b*d^5)*x^9 + (-60*I*a*d^4 - 144*I*b*d^4)*x^7 - 4*(23*a*d^3 + 76*b*d^3)*x^5 + (28*I*a*d^2 + 256*I*b*d^2)*x^3 - 8*(3*a*d - 8*b*d)*x)*sqrt(d*x^2 - 2*I) + 32*I*a*sqrt(d))/(32*a^2*b^2*d^(11/2)*x^9 - 192*I*a^2*b^2*d^(9/2)*x^7 - 384*a^2*b^2*d^(7/2)*x^5 + 256*I*a^2*b^2*d^(5/2)*x^3 + (32*b^4*d^(11/2)*x^9 - 192*I*b^4*d^(9/2)*x^7 - 384*b^4*d^(7/2)*x^5 + 256*I*b^4*d^(5/2)*x^3 + (32*b^4*d^4*x^6 - 96*I*b^4*d^3*x^4 - 96*b^4*d^2*x^2 + 32*I*b^4*d)*(d*x^2 - 2*I)^(3/2) + (96*b^4*d^(9/2)*x^7 - 384*I*b^4*d^(7/2)*x^5 - 480*b^4*d^(5/2)*x^3 + 192*I*b^4*d^(3/2)*x)*(d*x^2 - 2*I) + (96*b^4*d^5*x^8 - 480*I*b^4*d^4*x^6 - 768*b^4*d^3*x^4 + 384*I*b^4*d^2*x^2)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I)^2 + (32*a^2*b^2*d^4*x^6 - 96*I*a^2*b^2*d^3*x^4 - 96*a^2*b^2*d^2*x^2 + 32*I*a^2*b^2*d)*(d*x^2 - 2*I)^(3/2) + (96*a^2*b^2*d^(9/2)*x^7 - 384*I*a^2*b^2*d^(7/2)*x^5 - 480*a^2*b^2*d^(5/2)*x^3 + 192*I*a^2*b^2*d^(3/2)*x)*(d*x^2 - 2*I) + (64*a*b^3*d^(11/2)*x^9 - 384*I*a*b^3*d^(9/2)*x^7 - 768*a*b^3*d^(7/2)*x^5 + 512*I*a*b^3*d^(5/2)*x^3 + (64*a*b^3*d^4*x^6 - 192*I*a*b^3*d^3*x^4 - 192*a*b^3*d^2*x^2 + 64*I*a*b^3*d)*(d*x^2 - 2*I)^(3/2) + (192*a*b^3*d^(9/2)*x^7 - 768*I*a*b^3*d^(7/2)*x^5 - 960*a*b^3*d^(5/2)*x^3 + 384*I*a*b^3*d^(3/2)*x)*(d*x^2 - 2*I) + (192*a*b^3*d^5*x^8 - 960*I*a*b^3*d^4*x^6 - 1536*a*b^3*d^3*x^4 + 768*I*a*b^3*d^2*x^2)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I) + (96*a^2*b^2*d^5*x^8 - 480*I*a^2*b^2*d^4*x^6 - 768*a^2*b^2*d^3*x^4 + 384*I*a^2*b^2*d^2*x^2)*sqrt(d*x^2 - 2*I)) + integrate((d^6*x^12 - 8*I*d^5*x^10 - 27*d^4*x^8 + 56*I*d^3*x^6 + 88*d^2*x^4 + (d^4*x^8 - 4*I*d^3*x^6 - 3*d^2*x^4 - 8*I*d*x^2 + 4)*(d*x^2 - 2*I)^2 - 96*I*d*x^2 + (4*d^(9/2)*x^9 - 20*I*d^(7/2)*x^7 - 30*d^(5/2)*x^5 - 2*I*d^(3/2)*x^3 - 22*sqrt(d)*x)*(d*x^2 - 2*I)^(3/2) + (6*d^5*x^10 - 36*I*d^4*x^8 - 78*d^3*x^6 + 72*I*d^2*x^4 + 9*d*x^2 + 30*I)*(d*x^2 - 2*I) + (4*d^(11/2)*x^11 - 28*I*d^(9/2)*x^9 - 78*d^(7/2)*x^7 + 122*I*d^(5/2)*x^5 + 122*d^(3/2)*x^3 - 60*I*sqrt(d)*x)*sqrt(d*x^2 - 2*I) - 48)/(8*a*b^2*d^6*x^12 - 64*I*a*b^2*d^5*x^10 - 192*a*b^2*d^4*x^8 + 256*I*a*b^2*d^3*x^6 + 128*a*b^2*d^2*x^4 + (8*a*b^2*d^4*x^8 - 32*I*a*b^2*d^3*x^6 - 48*a*b^2*d^2*x^4 + 32*I*a*b^2*d*x^2 + 8*a*b^2)*(d*x^2 - 2*I)^2 + (32*a*b^2*d^(9/2)*x^9 - 160*I*a*b^2*d^(7/2)*x^7 - 288*a*b^2*d^(5/2)*x^5 + 224*I*a*b^2*d^(3/2)*x^3 + 64*a*b^2*sqrt(d)*x)*(d*x^2 - 2*I)^(3/2) + (48*a*b^2*d^5*x^10 - 288*I*a*b^2*d^4*x^8 - 624*a*b^2*d^3*x^6 + 576*I*a*b^2*d^2*x^4 + 192*a*b^2*d*x^2)*(d*x^2 - 2*I) + (8*b^3*d^6*x^12 - 64*I*b^3*d^5*x^10 - 192*b^3*d^4*x^8 + 256*I*b^3*d^3*x^6 + 128*b^3*d^2*x^4 + (8*b^3*d^4*x^8 - 32*I*b^3*d^3*x^6 - 48*b^3*d^2*x^4 + 32*I*b^3*d*x^2 + 8*b^3)*(d*x^2 - 2*I)^2 + (32*b^3*d^(9/2)*x^9 - 160*I*b^3*d^(7/2)*x^7 - 288*b^3*d^(5/2)*x^5 + 224*I*b^3*d^(3/2)*x^3 + 64*b^3*sqrt(d)*x)*(d*x^2 - 2*I)^(3/2) + (48*b^3*d^5*x^10 - 288*I*b^3*d^4*x^8 - 624*b^3*d^3*x^6 + 576*I*b^3*d^2*x^4 + 192*b^3*d*x^2)*(d*x^2 - 2*I) + (32*b^3*d^(11/2)*x^11 - 224*I*b^3*d^(9/2)*x^9 - 576*b^3*d^(7/2)*x^7 + 640*I*b^3*d^(5/2)*x^5 + 256*b^3*d^(3/2)*x^3)*sqrt(d*x^2 - 2*I))*log(d*x^2 + sqrt(d*x^2 - 2*I)*sqrt(d)*x - I) + (32*a*b^2*d^(11/2)*x^11 - 224*I*a*b^2*d^(9/2)*x^9 - 576*a*b^2*d^(7/2)*x^7 + 640*I*a*b^2*d^(5/2)*x^5 + 256*a*b^2*d^(3/2)*x^3)*sqrt(d*x^2 - 2*I)), x)","F",0
328,0,0,0,0.000000," ","integrate((a+b*arcsinh(I+d*x^2))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x^{2} + i\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 + I) + a)^(5/2), x)","F",0
329,0,0,0,0.000000," ","integrate((a+b*arcsinh(I+d*x^2))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x^{2} + i\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 + I) + a)^(3/2), x)","F",0
330,0,0,0,0.000000," ","integrate((a+b*arcsinh(I+d*x^2))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(d x^{2} + i\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x^2 + I) + a), x)","F",0
331,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arsinh}\left(d x^{2} + i\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsinh(d*x^2 + I) + a), x)","F",0
332,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x^{2} + i\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 + I) + a)^(-3/2), x)","F",0
333,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x^{2} + i\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 + I) + a)^(-5/2), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(I+d*x^2))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x^{2} + i\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 + I) + a)^(-7/2), x)","F",0
335,0,0,0,0.000000," ","integrate((a+b*arcsinh(-I+d*x^2))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x^{2} - i\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 - I) + a)^(5/2), x)","F",0
336,0,0,0,0.000000," ","integrate((a+b*arcsinh(-I+d*x^2))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arsinh}\left(d x^{2} - i\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 - I) + a)^(3/2), x)","F",0
337,0,0,0,0.000000," ","integrate((a+b*arcsinh(-I+d*x^2))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arsinh}\left(d x^{2} - i\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsinh(d*x^2 - I) + a), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arsinh}\left(d x^{2} - i\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsinh(d*x^2 - I) + a), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x^{2} - i\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 - I) + a)^(-3/2), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x^{2} - i\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 - I) + a)^(-5/2), x)","F",0
341,0,0,0,0.000000," ","integrate(1/(a+b*arcsinh(-I+d*x^2))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arsinh}\left(d x^{2} - i\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsinh(d*x^2 - I) + a)^(-7/2), x)","F",0
342,0,0,0,0.000000," ","integrate((a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(b \operatorname{arsinh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((b*arcsinh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
343,0,0,0,0.000000," ","integrate((a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{{\left(b^{3} \log\left(c x + 1\right) - b^{3} \log\left(-c x + 1\right)\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)^{3}}{2 \, c} + \int \frac{{\left(\sqrt{2} b^{3} + \sqrt{-c x + 1} b^{3}\right)} \log\left(c x + 1\right)^{3} - 6 \, {\left(\sqrt{2} a b^{2} + \sqrt{-c x + 1} a b^{2}\right)} \log\left(c x + 1\right)^{2} - 6 \, {\left(4 \, \sqrt{2} a b^{2} - 2 \, {\left(\sqrt{2} b^{3} + \sqrt{-c x + 1} b^{3}\right)} \log\left(c x + 1\right) + {\left(4 \, a b^{2} + {\left(b^{3} c x + b^{3}\right)} \log\left(c x + 1\right) - {\left(b^{3} c x + b^{3}\right)} \log\left(-c x + 1\right)\right)} \sqrt{-c x + 1}\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)^{2} + 12 \, {\left(\sqrt{2} a^{2} b + \sqrt{-c x + 1} a^{2} b\right)} \log\left(c x + 1\right) - 6 \, {\left(4 \, \sqrt{2} a^{2} b + 4 \, \sqrt{-c x + 1} a^{2} b + {\left(\sqrt{2} b^{3} + \sqrt{-c x + 1} b^{3}\right)} \log\left(c x + 1\right)^{2} - 4 \, {\left(\sqrt{2} a b^{2} + \sqrt{-c x + 1} a b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)}{8 \, {\left(\sqrt{2} c^{2} x^{2} + {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1} - \sqrt{2}\right)}}\,{d x}"," ",0,"1/2*a^3*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/2*(b^3*log(c*x + 1) - b^3*log(-c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1))^3/c + integrate(1/8*((sqrt(2)*b^3 + sqrt(-c*x + 1)*b^3)*log(c*x + 1)^3 - 6*(sqrt(2)*a*b^2 + sqrt(-c*x + 1)*a*b^2)*log(c*x + 1)^2 - 6*(4*sqrt(2)*a*b^2 - 2*(sqrt(2)*b^3 + sqrt(-c*x + 1)*b^3)*log(c*x + 1) + (4*a*b^2 + (b^3*c*x + b^3)*log(c*x + 1) - (b^3*c*x + b^3)*log(-c*x + 1))*sqrt(-c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1))^2 + 12*(sqrt(2)*a^2*b + sqrt(-c*x + 1)*a^2*b)*log(c*x + 1) - 6*(4*sqrt(2)*a^2*b + 4*sqrt(-c*x + 1)*a^2*b + (sqrt(2)*b^3 + sqrt(-c*x + 1)*b^3)*log(c*x + 1)^2 - 4*(sqrt(2)*a*b^2 + sqrt(-c*x + 1)*a*b^2)*log(c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1)))/(sqrt(2)*c^2*x^2 + (c^2*x^2 - 1)*sqrt(-c*x + 1) - sqrt(2)), x)","F",0
344,0,0,0,0.000000," ","integrate((a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{{\left(b^{2} \log\left(c x + 1\right) - b^{2} \log\left(-c x + 1\right)\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)^{2}}{2 \, c} + \int -\frac{{\left(\sqrt{2} b^{2} + \sqrt{-c x + 1} b^{2}\right)} \log\left(c x + 1\right)^{2} - 4 \, {\left(\sqrt{2} a b + \sqrt{-c x + 1} a b\right)} \log\left(c x + 1\right) + 2 \, {\left(4 \, \sqrt{2} a b - 2 \, {\left(\sqrt{2} b^{2} + \sqrt{-c x + 1} b^{2}\right)} \log\left(c x + 1\right) + {\left(4 \, a b + {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right) - {\left(b^{2} c x + b^{2}\right)} \log\left(-c x + 1\right)\right)} \sqrt{-c x + 1}\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)}{4 \, {\left(\sqrt{2} c^{2} x^{2} + {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1} - \sqrt{2}\right)}}\,{d x}"," ",0,"1/2*a^2*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/2*(b^2*log(c*x + 1) - b^2*log(-c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1))^2/c + integrate(-1/4*((sqrt(2)*b^2 + sqrt(-c*x + 1)*b^2)*log(c*x + 1)^2 - 4*(sqrt(2)*a*b + sqrt(-c*x + 1)*a*b)*log(c*x + 1) + 2*(4*sqrt(2)*a*b - 2*(sqrt(2)*b^2 + sqrt(-c*x + 1)*b^2)*log(c*x + 1) + (4*a*b + (b^2*c*x + b^2)*log(c*x + 1) - (b^2*c*x + b^2)*log(-c*x + 1))*sqrt(-c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1)))/(sqrt(2)*c^2*x^2 + (c^2*x^2 - 1)*sqrt(-c*x + 1) - sqrt(2)), x)","F",0
345,0,0,0,0.000000," ","integrate((a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{2 \, {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} + 2 \, \log\left(c x + 1\right) \log\left(-c x + 1\right) - \log\left(-c x + 1\right)^{2} - 4 \, {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)}{c} + 8 \, \int -\frac{\sqrt{2} \log\left(c x + 1\right) - \sqrt{2} \log\left(-c x + 1\right)}{4 \, {\left(\sqrt{2} c x + {\left(c x - 1\right)} \sqrt{-c x + 1} - \sqrt{2}\right)}}\,{d x}\right)} + \frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)}"," ",0,"-1/8*b*((2*(log(c*x + 1) - log(-c*x + 1))*log(c*x + 1) - log(c*x + 1)^2 + 2*log(c*x + 1)*log(-c*x + 1) - log(-c*x + 1)^2 - 4*(log(c*x + 1) - log(-c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1)))/c + 8*integrate(-1/4*(sqrt(2)*log(c*x + 1) - sqrt(2)*log(-c*x + 1))/(sqrt(2)*c*x + (c*x - 1)*sqrt(-c*x + 1) - sqrt(2)), x)) + 1/2*a*(log(c*x + 1)/c - log(c*x - 1)/c)","F",0
346,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x, algorithm=""maxima"")","-\int \frac{1}{{\left(c^{2} x^{2} - 1\right)} {\left(b \operatorname{arsinh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}}\,{d x}"," ",0,"-integrate(1/((c^2*x^2 - 1)*(b*arcsinh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)), x)","F",0
347,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arcsinh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(\sqrt{2} + \sqrt{-c x + 1}\right)}}{2 \, \sqrt{2} a b c^{2} x - 2 \, \sqrt{2} a b c - 4 \, \sqrt{-c x + 1} a b c - {\left(\sqrt{2} b^{2} c^{2} x - \sqrt{2} b^{2} c - 2 \, \sqrt{-c x + 1} b^{2} c\right)} \log\left(c x + 1\right) + 2 \, {\left(\sqrt{2} b^{2} c^{2} x - \sqrt{2} b^{2} c - 2 \, \sqrt{-c x + 1} b^{2} c\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right)} - \int \frac{4 \, c x + {\left(\sqrt{2} c x - 3 \, \sqrt{2}\right)} \sqrt{-c x + 1} - 4}{2 \, a b c^{3} x^{3} - 6 \, a b c^{2} x^{2} + 6 \, a b c x - 4 \, {\left(a b c x - a b\right)} {\left(c x - 1\right)} - 2 \, a b - {\left(b^{2} c^{3} x^{3} - 3 \, b^{2} c^{2} x^{2} + 3 \, b^{2} c x - 2 \, {\left(b^{2} c x - b^{2}\right)} {\left(c x - 1\right)} - b^{2} - 2 \, {\left(\sqrt{2} b^{2} c^{2} x^{2} - 2 \, \sqrt{2} b^{2} c x + \sqrt{2} b^{2}\right)} \sqrt{-c x + 1}\right)} \log\left(c x + 1\right) + 2 \, {\left(b^{2} c^{3} x^{3} - 3 \, b^{2} c^{2} x^{2} + 3 \, b^{2} c x - 2 \, {\left(b^{2} c x - b^{2}\right)} {\left(c x - 1\right)} - b^{2} - 2 \, {\left(\sqrt{2} b^{2} c^{2} x^{2} - 2 \, \sqrt{2} b^{2} c x + \sqrt{2} b^{2}\right)} \sqrt{-c x + 1}\right)} \log\left(\sqrt{2} + \sqrt{-c x + 1}\right) - 4 \, {\left(\sqrt{2} a b c^{2} x^{2} - 2 \, \sqrt{2} a b c x + \sqrt{2} a b\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-4*(sqrt(2) + sqrt(-c*x + 1))/(2*sqrt(2)*a*b*c^2*x - 2*sqrt(2)*a*b*c - 4*sqrt(-c*x + 1)*a*b*c - (sqrt(2)*b^2*c^2*x - sqrt(2)*b^2*c - 2*sqrt(-c*x + 1)*b^2*c)*log(c*x + 1) + 2*(sqrt(2)*b^2*c^2*x - sqrt(2)*b^2*c - 2*sqrt(-c*x + 1)*b^2*c)*log(sqrt(2) + sqrt(-c*x + 1))) - integrate((4*c*x + (sqrt(2)*c*x - 3*sqrt(2))*sqrt(-c*x + 1) - 4)/(2*a*b*c^3*x^3 - 6*a*b*c^2*x^2 + 6*a*b*c*x - 4*(a*b*c*x - a*b)*(c*x - 1) - 2*a*b - (b^2*c^3*x^3 - 3*b^2*c^2*x^2 + 3*b^2*c*x - 2*(b^2*c*x - b^2)*(c*x - 1) - b^2 - 2*(sqrt(2)*b^2*c^2*x^2 - 2*sqrt(2)*b^2*c*x + sqrt(2)*b^2)*sqrt(-c*x + 1))*log(c*x + 1) + 2*(b^2*c^3*x^3 - 3*b^2*c^2*x^2 + 3*b^2*c*x - 2*(b^2*c*x - b^2)*(c*x - 1) - b^2 - 2*(sqrt(2)*b^2*c^2*x^2 - 2*sqrt(2)*b^2*c*x + sqrt(2)*b^2)*sqrt(-c*x + 1))*log(sqrt(2) + sqrt(-c*x + 1)) - 4*(sqrt(2)*a*b*c^2*x^2 - 2*sqrt(2)*a*b*c*x + sqrt(2)*a*b)*sqrt(-c*x + 1)), x)","F",0
348,0,0,0,0.000000," ","integrate(arcsinh(c*exp(b*x+a)),x, algorithm=""maxima"")","-b c \int \frac{x e^{\left(b x + a\right)}}{c^{3} e^{\left(3 \, b x + 3 \, a\right)} + c e^{\left(b x + a\right)} + {\left(c^{2} e^{\left(2 \, b x + 2 \, a\right)} + 1\right)}^{\frac{3}{2}}}\,{d x} + x \log\left(c e^{\left(b x + a\right)} + \sqrt{c^{2} e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \frac{2 \, b x \log\left(c^{2} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-c^{2} e^{\left(2 \, b x + 2 \, a\right)}\right)}{4 \, b}"," ",0,"-b*c*integrate(x*e^(b*x + a)/(c^3*e^(3*b*x + 3*a) + c*e^(b*x + a) + (c^2*e^(2*b*x + 2*a) + 1)^(3/2)), x) + x*log(c*e^(b*x + a) + sqrt(c^2*e^(2*b*x + 2*a) + 1)) - 1/4*(2*b*x*log(c^2*e^(2*b*x + 2*a) + 1) + dilog(-c^2*e^(2*b*x + 2*a)))/b","F",0
349,1,491,0,0.698338," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))*x^3,x, algorithm=""maxima"")","\frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{5 \, b^{2}} - \frac{{\left(a^{2} + 1\right)} a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{5 \, b^{4}} - \frac{7 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a x}{20 \, b^{3}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a x}{5 \, b^{3}} + \frac{{\left(a^{2} + 1\right)}^{2} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{5 \, b^{4}} + \frac{7 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{12 \, b^{4}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a^{2}}{5 \, b^{4}} + \frac{7 \, {\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{40 \, b^{6}} - \frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} {\left(a^{2} + 1\right)}}{15 \, b^{4}} - \frac{7 \, {\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{40 \, b^{5}} - \frac{7 \, {\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} {\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{40 \, b^{6}} - \frac{7 \, {\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{40 \, b^{6}}"," ",0,"1/5*b*x^5 + 1/4*a*x^4 + 1/5*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x^2/b^2 - 1/5*(a^2 + 1)*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 7/20*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a*x/b^3 + 1/5*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a*x/b^3 + 1/5*(a^2 + 1)^2*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + 7/12*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/b^4 + 1/5*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a^2/b^4 + 7/40*(5*a^2*b^2 - (a^2 + 1)*b^2)*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^6 - 2/15*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*(a^2 + 1)/b^4 - 7/40*(5*a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^5 - 7/40*(5*a^2*b^2 - (a^2 + 1)*b^2)*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^6 - 7/40*(5*a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^6","B",0
350,1,273,0,0.691889," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))*x^2,x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{2}} - \frac{5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{12 \, b^{3}} - \frac{{\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} + \frac{{\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{8 \, b^{4}} + \frac{{\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} {\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} + \frac{{\left(5 \, a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{8 \, b^{5}}"," ",0,"1/4*b*x^4 + 1/3*a*x^3 + 1/4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x/b^2 - 5/12*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/b^3 - 1/8*(5*a^2*b^2 - (a^2 + 1)*b^2)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 1/8*(5*a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^4 + 1/8*(5*a^2*b^2 - (a^2 + 1)*b^2)*(a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 1/8*(5*a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^5","A",0
351,1,175,0,0.682305," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))*x,x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2} + \frac{a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{2 \, b} - \frac{{\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{2 \, b^{2}} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{2}}"," ",0,"1/3*b*x^3 + 1/2*a*x^2 + 1/2*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 - 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b - 1/2*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 - 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^2 + 1/3*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^2","B",0
352,1,141,0,0.463461," ","integrate(b*x+a+(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, b x^{2} + a x - \frac{a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b} + \frac{1}{2} \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x + \frac{{\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{2 \, b}"," ",0,"1/2*b*x^2 + a*x - 1/2*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x + 1/2*(a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b","B",0
353,1,160,0,0.344401," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))/x,x, algorithm=""maxima"")","b x + a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right) + a \log\left(x\right) - \sqrt{a^{2} + 1} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}"," ",0,"b*x + a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)) + a*log(x) - sqrt(a^2 + 1)*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x))) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)","A",0
354,1,170,0,0.356864," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{a b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{\sqrt{a^{2} + 1}} + b \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right) + b \log\left(x\right) - \frac{a}{x} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{x}"," ",0,"-a*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/sqrt(a^2 + 1) + b*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)) + b*log(x) - a/x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/x","A",0
355,1,313,0,0.963428," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))/x^3,x, algorithm=""maxima"")","\frac{a^{2} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, \sqrt{a^{2} + 1}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}}{2 \, {\left(a^{2} + 1\right)}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a b}{2 \, {\left(a^{2} + 1\right)} x} - \frac{b}{x} - \frac{a}{2 \, x^{2}} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{2 \, {\left(a^{2} + 1\right)} x^{2}}"," ",0,"1/2*a^2*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 1/2*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/sqrt(a^2 + 1) + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2/(a^2 + 1) + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*b/((a^2 + 1)*x) - b/x - 1/2*a/x^2 - 1/2*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/((a^2 + 1)*x^2)","B",0
356,1,352,0,0.562526," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))/x^4,x, algorithm=""maxima"")","-\frac{a^{3} b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{a b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a b^{3}}{2 \, {\left(a^{2} + 1\right)}^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} b^{2}}{2 \, {\left(a^{2} + 1\right)}^{2} x} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a b}{2 \, {\left(a^{2} + 1\right)}^{2} x^{2}} - \frac{b}{2 \, x^{2}} - \frac{a}{3 \, x^{3}} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, {\left(a^{2} + 1\right)} x^{3}}"," ",0,"-1/2*a^3*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + 1/2*a*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*b^3/(a^2 + 1)^2 - 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*b^2/((a^2 + 1)^2*x) + 1/2*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a*b/((a^2 + 1)^2*x^2) - 1/2*b/x^2 - 1/3*a/x^3 - 1/3*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/((a^2 + 1)*x^3)","B",0
357,1,594,0,0.452800," ","integrate((b*x+a+(1+(b*x+a)^2)^(1/2))/x^5,x, algorithm=""maxima"")","\frac{5 \, a^{4} b^{4} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{8 \, {\left(a^{2} + 1\right)}^{\frac{7}{2}}} - \frac{3 \, a^{2} b^{4} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{4 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} b^{4}}{8 \, {\left(a^{2} + 1\right)}^{3}} + \frac{b^{4} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{8 \, {\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}}{8 \, {\left(a^{2} + 1\right)}^{2}} + \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3} b^{3}}{8 \, {\left(a^{2} + 1\right)}^{3} x} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a b^{3}}{8 \, {\left(a^{2} + 1\right)}^{2} x} - \frac{5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2} b^{2}}{8 \, {\left(a^{2} + 1\right)}^{3} x^{2}} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} b^{2}}{8 \, {\left(a^{2} + 1\right)}^{2} x^{2}} + \frac{5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a b}{12 \, {\left(a^{2} + 1\right)}^{2} x^{3}} - \frac{b}{3 \, x^{3}} - \frac{a}{4 \, x^{4}} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{4 \, {\left(a^{2} + 1\right)} x^{4}}"," ",0,"5/8*a^4*b^4*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(7/2) - 3/4*a^2*b^4*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + 5/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*b^4/(a^2 + 1)^3 + 1/8*b^4*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 1/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4/(a^2 + 1)^2 + 5/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3*b^3/((a^2 + 1)^3*x) - 1/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*b^3/((a^2 + 1)^2*x) - 5/8*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2*b^2/((a^2 + 1)^3*x^2) + 1/8*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*b^2/((a^2 + 1)^2*x^2) + 5/12*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a*b/((a^2 + 1)^2*x^3) - 1/3*b/x^3 - 1/4*a/x^4 - 1/4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/((a^2 + 1)*x^4)","B",0
358,0,0,0,0.000000," ","integrate(exp(arcsinh(b*x+a)^2)*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(\operatorname{arsinh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^3*e^(arcsinh(b*x + a)^2), x)","F",0
359,0,0,0,0.000000," ","integrate(exp(arcsinh(b*x+a)^2)*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\operatorname{arsinh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^2*e^(arcsinh(b*x + a)^2), x)","F",0
360,0,0,0,0.000000," ","integrate(exp(arcsinh(b*x+a)^2)*x,x, algorithm=""maxima"")","\int x e^{\left(\operatorname{arsinh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x*e^(arcsinh(b*x + a)^2), x)","F",0
361,0,0,0,0.000000," ","integrate(exp(arcsinh(b*x+a)^2),x, algorithm=""maxima"")","\int e^{\left(\operatorname{arsinh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(e^(arcsinh(b*x + a)^2), x)","F",0
362,0,0,0,0.000000," ","integrate(exp(arcsinh(b*x+a)^2)/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arsinh}\left(b x + a\right)^{2}\right)}}{x}\,{d x}"," ",0,"integrate(e^(arcsinh(b*x + a)^2)/x, x)","F",0
363,0,0,0,0.000000," ","integrate(exp(arcsinh(b*x+a)^2)/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arsinh}\left(b x + a\right)^{2}\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arcsinh(b*x + a)^2)/x^2, x)","F",0
364,0,0,0,0.000000," ","integrate(arcsinh(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(b x + a\right)}{d x + \frac{a d}{b}}\,{d x}"," ",0,"integrate(arcsinh(b*x + a)/(d*x + a*d/b), x)","F",0
365,0,0,0,0.000000," ","integrate(x/arcsinh(x)/(x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{x^{2} + 1} \operatorname{arsinh}\left(x\right)}\,{d x}"," ",0,"integrate(x/(sqrt(x^2 + 1)*arcsinh(x)), x)","F",0
366,1,37,0,0.313987," ","integrate(x^3*arcsinh(b*x^4+a),x, algorithm=""maxima"")","\frac{{\left(b x^{4} + a\right)} \operatorname{arsinh}\left(b x^{4} + a\right) - \sqrt{{\left(b x^{4} + a\right)}^{2} + 1}}{4 \, b}"," ",0,"1/4*((b*x^4 + a)*arcsinh(b*x^4 + a) - sqrt((b*x^4 + a)^2 + 1))/b","A",0
367,1,39,0,0.345433," ","integrate(x^(-1+n)*arcsinh(a+b*x^n),x, algorithm=""maxima"")","\frac{{\left(b x^{n} + a\right)} \operatorname{arsinh}\left(b x^{n} + a\right) - \sqrt{{\left(b x^{n} + a\right)}^{2} + 1}}{b n}"," ",0,"((b*x^n + a)*arcsinh(b*x^n + a) - sqrt((b*x^n + a)^2 + 1))/(b*n)","A",0
368,0,0,0,0.000000," ","integrate(arcsinh(c/(b*x+a)),x, algorithm=""maxima"")","-\frac{i \, c {\left(\log\left(\frac{i \, {\left(b^{2} x + a b\right)}}{b c} + 1\right) - \log\left(-\frac{i \, {\left(b^{2} x + a b\right)}}{b c} + 1\right)\right)}}{2 \, b} + \frac{2 \, b x \log\left(c + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + c^{2}}\right) + a \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c^{2}\right) - 2 \, {\left(b x + a\right)} \log\left(b x + a\right)}{2 \, b} + \int \frac{b^{2} c x^{2} + a b c x}{b^{2} c x^{2} + 2 \, a b c x + a^{2} c + c^{3} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + c^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*I*c*(log(I*(b^2*x + a*b)/(b*c) + 1) - log(-I*(b^2*x + a*b)/(b*c) + 1))/b + 1/2*(2*b*x*log(c + sqrt(b^2*x^2 + 2*a*b*x + a^2 + c^2)) + a*log(b^2*x^2 + 2*a*b*x + a^2 + c^2) - 2*(b*x + a)*log(b*x + a))/b + integrate((b^2*c*x^2 + a*b*c*x)/(b^2*c*x^2 + 2*a*b*c*x + a^2*c + c^3 + (b^2*x^2 + 2*a*b*x + a^2 + c^2)^(3/2)), x)","F",0
369,1,1,0,0.779567," ","integrate(x/arcsinh(sinh(x)),x, algorithm=""maxima"")","x"," ",0,"x","A",0
370,0,0,0,0.000000," ","integrate(arcsinh((b*x^2-1)^(1/2))^n/(b*x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arsinh}\left(\sqrt{b x^{2} - 1}\right)^{n}}{\sqrt{b x^{2} - 1}}\,{d x}"," ",0,"integrate(arcsinh(sqrt(b*x^2 - 1))^n/sqrt(b*x^2 - 1), x)","F",0
371,0,0,0,0.000000," ","integrate(1/arcsinh((b*x^2-1)^(1/2))/(b*x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{2} - 1} \operatorname{arsinh}\left(\sqrt{b x^{2} - 1}\right)}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 - 1)*arcsinh(sqrt(b*x^2 - 1))), x)","F",0
