1,1,229,0,0.312077," ","integrate((e*x+d)^3*arccosh(c*x),x, algorithm=""maxima"")","-\frac{1}{96} \, {\left(\frac{6 \, \sqrt{c^{2} x^{2} - 1} e^{3} x^{3}}{c^{2}} + \frac{32 \, \sqrt{c^{2} x^{2} - 1} d e^{2} x^{2}}{c^{2}} + \frac{72 \, \sqrt{c^{2} x^{2} - 1} d^{2} e x}{c^{2}} + \frac{96 \, \sqrt{c^{2} x^{2} - 1} d^{3}}{c^{2}} + \frac{72 \, d^{2} e \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}} + \frac{9 \, \sqrt{c^{2} x^{2} - 1} e^{3} x}{c^{4}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} d e^{2}}{c^{4}} + \frac{9 \, e^{3} \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c + \frac{1}{4} \, {\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \operatorname{arcosh}\left(c x\right)"," ",0,"-1/96*(6*sqrt(c^2*x^2 - 1)*e^3*x^3/c^2 + 32*sqrt(c^2*x^2 - 1)*d*e^2*x^2/c^2 + 72*sqrt(c^2*x^2 - 1)*d^2*e*x/c^2 + 96*sqrt(c^2*x^2 - 1)*d^3/c^2 + 72*d^2*e*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3 + 9*sqrt(c^2*x^2 - 1)*e^3*x/c^4 + 64*sqrt(c^2*x^2 - 1)*d*e^2/c^4 + 9*e^3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c + 1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*arccosh(c*x)","A",0
2,1,140,0,0.487651," ","integrate((e*x+d)^2*arccosh(c*x),x, algorithm=""maxima"")","-\frac{1}{18} \, {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} e^{2} x^{2}}{c^{2}} + \frac{9 \, \sqrt{c^{2} x^{2} - 1} d e x}{c^{2}} + \frac{18 \, \sqrt{c^{2} x^{2} - 1} d^{2}}{c^{2}} + \frac{9 \, d e \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} e^{2}}{c^{4}}\right)} c + \frac{1}{3} \, {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)} \operatorname{arcosh}\left(c x\right)"," ",0,"-1/18*(2*sqrt(c^2*x^2 - 1)*e^2*x^2/c^2 + 9*sqrt(c^2*x^2 - 1)*d*e*x/c^2 + 18*sqrt(c^2*x^2 - 1)*d^2/c^2 + 9*d*e*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3 + 4*sqrt(c^2*x^2 - 1)*e^2/c^4)*c + 1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)*arccosh(c*x)","A",0
3,1,82,0,0.460315," ","integrate((e*x+d)*arccosh(c*x),x, algorithm=""maxima"")","-\frac{1}{4} \, c {\left(\frac{\sqrt{c^{2} x^{2} - 1} e x}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} d}{c^{2}} + \frac{e \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)} + \frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \operatorname{arcosh}\left(c x\right)"," ",0,"-1/4*c*(sqrt(c^2*x^2 - 1)*e*x/c^2 + 4*sqrt(c^2*x^2 - 1)*d/c^2 + e*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3) + 1/2*(e*x^2 + 2*d*x)*arccosh(c*x)","A",0
4,0,0,0,0.000000," ","integrate(arccosh(c*x)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(c x\right)}{e x + d}\,{d x}"," ",0,"integrate(arccosh(c*x)/(e*x + d), x)","F",0
5,-2,0,0,0.000000," ","integrate(arccosh(c*x)/(e*x+d)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
6,-2,0,0,0.000000," ","integrate(arccosh(c*x)/(e*x+d)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
7,-2,0,0,0.000000," ","integrate(arccosh(c*x)/(e*x+d)^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
8,0,0,0,0.000000," ","integrate((e*x+d)^3*arccosh(c*x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - \int \frac{{\left(c^{3} e^{3} x^{6} + 4 \, c^{3} d e^{2} x^{5} - 6 \, c d^{2} e x^{2} - 4 \, c d^{3} x + {\left(6 \, c^{3} d^{2} e - c e^{3}\right)} x^{4} + 4 \, {\left(c^{3} d^{3} - c d e^{2}\right)} x^{3} + {\left(c^{2} e^{3} x^{5} + 4 \, c^{2} d e^{2} x^{4} + 6 \, c^{2} d^{2} e x^{3} + 4 \, c^{2} d^{3} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{2 \, {\left(c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x\right)}}\,{d x}"," ",0,"1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - integrate(1/2*(c^3*e^3*x^6 + 4*c^3*d*e^2*x^5 - 6*c*d^2*e*x^2 - 4*c*d^3*x + (6*c^3*d^2*e - c*e^3)*x^4 + 4*(c^3*d^3 - c*d*e^2)*x^3 + (c^2*e^3*x^5 + 4*c^2*d*e^2*x^4 + 6*c^2*d^2*e*x^3 + 4*c^2*d^3*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x)","F",0
9,0,0,0,0.000000," ","integrate((e*x+d)^2*arccosh(c*x)^2,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - \int \frac{2 \, {\left(c^{3} e^{2} x^{5} + 3 \, c^{3} d e x^{4} - 3 \, c d e x^{2} - 3 \, c d^{2} x + {\left(3 \, c^{3} d^{2} - c e^{2}\right)} x^{3} + {\left(c^{2} e^{2} x^{4} + 3 \, c^{2} d e x^{3} + 3 \, c^{2} d^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x\right)}}\,{d x}"," ",0,"1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - integrate(2/3*(c^3*e^2*x^5 + 3*c^3*d*e*x^4 - 3*c*d*e*x^2 - 3*c*d^2*x + (3*c^3*d^2 - c*e^2)*x^3 + (c^2*e^2*x^4 + 3*c^2*d*e*x^3 + 3*c^2*d^2*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x)","F",0
10,0,0,0,0.000000," ","integrate((e*x+d)*arccosh(c*x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - \int \frac{{\left(c^{3} e x^{4} + 2 \, c^{3} d x^{3} - c e x^{2} - 2 \, c d x + {\left(c^{2} e x^{3} + 2 \, c^{2} d x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}\,{d x}"," ",0,"1/2*(e*x^2 + 2*d*x)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - integrate((c^3*e*x^4 + 2*c^3*d*x^3 - c*e*x^2 - 2*c*d*x + (c^2*e*x^3 + 2*c^2*d*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x)","F",0
11,0,0,0,0.000000," ","integrate(arccosh(c*x)^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(c x\right)^{2}}{e x + d}\,{d x}"," ",0,"integrate(arccosh(c*x)^2/(e*x + d), x)","F",0
12,-2,0,0,0.000000," ","integrate(arccosh(c*x)^2/(e*x+d)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
13,-2,0,0,0.000000," ","integrate(arccosh(c*x)^2/(e*x+d)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
14,1,265,0,0.389303," ","integrate((e*x+d)^3*(a+b*arccosh(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{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d^{2} e + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\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{arcosh}\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 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b e^{3} + a d^{3} x + \frac{{\left(c x \operatorname{arcosh}\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*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d^2*e + 1/3*(3*x^3*arccosh(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*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*e^3 + a*d^3*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^3/c","A",0
15,1,167,0,0.437526," ","integrate((e*x+d)^2*(a+b*arccosh(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{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d e + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\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{arcosh}\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*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d*e + 1/9*(3*x^3*arccosh(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*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^2/c","A",0
16,1,99,0,0.440292," ","integrate((e*x+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b e + a d x + \frac{{\left(c x \operatorname{arcosh}\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*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*e + a*d*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d/c","A",0
17,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x+d),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
18,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x+d)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
19,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x+d)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
20,0,0,0,0.000000," ","integrate((a+b*arccosh(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)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\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 - 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 x + 1} \sqrt{c x - 1}\right) + {\left(c^{6} d^{6} + 3 \, c^{5} d^{5} e + 3 \, c^{4} d^{4} e^{2} + c^{3} d^{3} e^{3} + {\left(c^{6} d^{3} e^{3} + 3 \, c^{5} d^{2} e^{4} + 3 \, c^{4} d e^{5} + c^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{6} d^{4} e^{2} + 3 \, c^{5} d^{3} e^{3} + 3 \, c^{4} d^{2} e^{4} + c^{3} d e^{5}\right)} x^{2} + 3 \, {\left(c^{6} d^{5} e + 3 \, c^{5} d^{4} e^{2} + 3 \, c^{4} d^{3} e^{3} + c^{3} d^{2} e^{4}\right)} x\right)} \log\left(c x + 1\right) + {\left(c^{6} d^{6} - 3 \, c^{5} d^{5} e + 3 \, c^{4} d^{4} e^{2} - c^{3} d^{3} e^{3} + {\left(c^{6} d^{3} e^{3} - 3 \, c^{5} d^{2} e^{4} + 3 \, c^{4} d e^{5} - c^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{6} d^{4} e^{2} - 3 \, c^{5} d^{3} e^{3} + 3 \, c^{4} d^{2} e^{4} - c^{3} d e^{5}\right)} x^{2} + 3 \, {\left(c^{6} d^{5} e - 3 \, c^{5} d^{4} e^{2} + 3 \, c^{4} d^{3} e^{3} - c^{3} d^{2} e^{4}\right)} x\right)} \log\left(c x - 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}\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)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 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 - 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*x + 1)*sqrt(c*x - 1)) + (c^6*d^6 + 3*c^5*d^5*e + 3*c^4*d^4*e^2 + c^3*d^3*e^3 + (c^6*d^3*e^3 + 3*c^5*d^2*e^4 + 3*c^4*d*e^5 + c^3*e^6)*x^3 + 3*(c^6*d^4*e^2 + 3*c^5*d^3*e^3 + 3*c^4*d^2*e^4 + c^3*d*e^5)*x^2 + 3*(c^6*d^5*e + 3*c^5*d^4*e^2 + 3*c^4*d^3*e^3 + c^3*d^2*e^4)*x)*log(c*x + 1) + (c^6*d^6 - 3*c^5*d^5*e + 3*c^4*d^4*e^2 - c^3*d^3*e^3 + (c^6*d^3*e^3 - 3*c^5*d^2*e^4 + 3*c^4*d*e^5 - c^3*e^6)*x^3 + 3*(c^6*d^4*e^2 - 3*c^5*d^3*e^3 + 3*c^4*d^2*e^4 - c^3*d*e^5)*x^2 + 3*(c^6*d^5*e - 3*c^5*d^4*e^2 + 3*c^4*d^3*e^3 - c^3*d^2*e^4)*x)*log(c*x - 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))*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
21,0,0,0,0.000000," ","integrate((e*x+d)^3*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} e^{3} x^{4} + a^{2} d e^{2} x^{3} + b^{2} d^{3} x \operatorname{arcosh}\left(c x\right)^{2} + \frac{3}{2} \, a^{2} d^{2} e x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} a b d^{2} e + \frac{2}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\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{1}{16} \, {\left(8 \, x^{4} \operatorname{arcosh}\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 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} a b e^{3} + 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b d^{3}}{c} + \frac{1}{4} \, {\left(b^{2} e^{3} x^{4} + 4 \, b^{2} d e^{2} x^{3} + 6 \, b^{2} d^{2} e x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - \int \frac{{\left(b^{2} c^{3} e^{3} x^{6} + 4 \, b^{2} c^{3} d e^{2} x^{5} - 4 \, b^{2} c d e^{2} x^{3} - 6 \, b^{2} c d^{2} e x^{2} + {\left(6 \, c^{3} d^{2} e - c e^{3}\right)} b^{2} x^{4} + {\left(b^{2} c^{2} e^{3} x^{5} + 4 \, b^{2} c^{2} d e^{2} x^{4} + 6 \, b^{2} c^{2} d^{2} e x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{2 \, {\left(c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x\right)}}\,{d x}"," ",0,"1/4*a^2*e^3*x^4 + a^2*d*e^2*x^3 + b^2*d^3*x*arccosh(c*x)^2 + 3/2*a^2*d^2*e*x^2 + 3/2*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*a*b*d^2*e + 2/3*(3*x^3*arccosh(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 + 1/16*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*a*b*e^3 + 2*b^2*d^3*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*d^3*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b*d^3/c + 1/4*(b^2*e^3*x^4 + 4*b^2*d*e^2*x^3 + 6*b^2*d^2*e*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - integrate(1/2*(b^2*c^3*e^3*x^6 + 4*b^2*c^3*d*e^2*x^5 - 4*b^2*c*d*e^2*x^3 - 6*b^2*c*d^2*e*x^2 + (6*c^3*d^2*e - c*e^3)*b^2*x^4 + (b^2*c^2*e^3*x^5 + 4*b^2*c^2*d*e^2*x^4 + 6*b^2*c^2*d^2*e*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x)","F",0
22,0,0,0,0.000000," ","integrate((e*x+d)^2*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} e^{2} x^{3} + b^{2} d^{2} x \operatorname{arcosh}\left(c x\right)^{2} + a^{2} d e x^{2} + {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} a b d e + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\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} + 2 \, b^{2} d^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b d^{2}}{c} + \frac{1}{3} \, {\left(b^{2} e^{2} x^{3} + 3 \, b^{2} d e x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - \int \frac{2 \, {\left(b^{2} c^{3} e^{2} x^{5} + 3 \, b^{2} c^{3} d e x^{4} - b^{2} c e^{2} x^{3} - 3 \, b^{2} c d e x^{2} + {\left(b^{2} c^{2} e^{2} x^{4} + 3 \, b^{2} c^{2} d e x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x\right)}}\,{d x}"," ",0,"1/3*a^2*e^2*x^3 + b^2*d^2*x*arccosh(c*x)^2 + a^2*d*e*x^2 + (2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*a*b*d*e + 2/9*(3*x^3*arccosh(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*b^2*d^2*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*d^2*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b*d^2/c + 1/3*(b^2*e^2*x^3 + 3*b^2*d*e*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - integrate(2/3*(b^2*c^3*e^2*x^5 + 3*b^2*c^3*d*e*x^4 - b^2*c*e^2*x^3 - 3*b^2*c*d*e*x^2 + (b^2*c^2*e^2*x^4 + 3*b^2*c^2*d*e*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x)","F",0
23,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","b^{2} d x \operatorname{arcosh}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} a b e + \frac{1}{2} \, {\left(x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - 2 \, \int \frac{{\left(c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} c^{2} x^{3} - c x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}\,{d x}\right)} b^{2} e + 2 \, b^{2} d {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b d}{c}"," ",0,"b^2*d*x*arccosh(c*x)^2 + 1/2*a^2*e*x^2 + 1/2*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*a*b*e + 1/2*(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - 2*integrate((c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*c^2*x^3 - c*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x), x))*b^2*e + 2*b^2*d*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*d*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b*d/c","F",0
24,0,0,0,0.000000," ","integrate((a+b*arccosh(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 x + 1} \sqrt{c x - 1}\right)^{2}}{e x + d} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x + d}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(e*x + d) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x + d), x)","F",0
25,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(e*x+d)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
26,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(e*x+d)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c*d>0)', see `assume?` for more details)Is e-c*d positive, negative or zero?","F(-2)",0
27,0,0,0,0.000000," ","integrate((e*x+d)^3/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{3}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^3/(b*arccosh(c*x) + a), x)","F",0
28,0,0,0,0.000000," ","integrate((e*x+d)^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{2}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^2/(b*arccosh(c*x) + a), x)","F",0
29,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{e x + d}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)/(b*arccosh(c*x) + a), x)","F",0
30,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)*(b*arccosh(c*x) + a)), x)","F",0
31,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)}^{2} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)^2*(b*arccosh(c*x) + a)), x)","F",0
32,0,0,0,0.000000," ","integrate((e*x+d)^2/(a+b*arccosh(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 x + 1} \sqrt{c x - 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 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 + {\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 x + 1\right)} {\left(c x - 1\right)} + c d^{2} - {\left(2 \, c^{3} d^{2} - 3 \, c e^{2}\right)} x^{2} + {\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 x + 1} \sqrt{c x - 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{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*x + 1)*sqrt(c*x - 1))/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 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 + (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*x + 1)*(c*x - 1) + c*d^2 - (2*c^3*d^2 - 3*c*e^2)*x^2 + (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*x + 1)*sqrt(c*x - 1))/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
33,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*arccosh(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 x + 1} \sqrt{c x - 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 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} + {\left(2 \, c^{3} e x^{3} + c^{3} d x^{2} + c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, c e x + {\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 x + 1} \sqrt{c x - 1} + c d}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{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*x + 1)*sqrt(c*x - 1))/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 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^3*e*x^3 + c^3*d*x^2 + c*d)*(c*x + 1)*(c*x - 1) + 2*c*e*x + (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*x + 1)*sqrt(c*x - 1) + c*d)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{a b c^{3} e x^{3} + a b c^{3} d x^{2} - a b c e x - a b c d + {\left(a b c^{2} e x^{2} + a b c^{2} d x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \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 x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{4} d x^{3} + 2 \, c^{2} e x^{2} - c^{2} d x - e\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c d}{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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1} + {\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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(a*b*c^3*e*x^3 + a*b*c^3*d*x^2 - a*b*c*e*x - a*b*c*d + (a*b*c^2*e*x^2 + a*b*c^2*d*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 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*x + 1)*(c*x - 1) + (2*c^4*d*x^3 + 2*c^2*e*x^2 - c^2*d*x - e)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*d)/(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*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 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*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{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(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 x + 1} \sqrt{c x - 1} + {\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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{c^{5} e x^{5} - c^{5} d x^{4} - 2 \, c^{3} e x^{3} + 2 \, c^{3} d x^{2} + {\left(c^{3} e x^{3} - c^{3} d x^{2} - 3 \, c e x - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + c e x + {\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 x + 1} \sqrt{c x - 1} - c d}{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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1} + {\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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(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 + (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*x + 1)*sqrt(c*x - 1) + (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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 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^3*e*x^3 - c^3*d*x^2 - 3*c*e*x - c*d)*(c*x + 1)*(c*x - 1) + c*e*x + (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*x + 1)*sqrt(c*x - 1) - c*d)/(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*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 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*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
36,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arccosh(c*x))^3,x, algorithm=""maxima"")","\frac{{\left(b^{3} e x + b^{3} d\right)} {\left(e x + d\right)}^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{3}}{e {\left(m + 1\right)}} + \frac{{\left(e x + d\right)}^{m + 1} a^{3}}{e {\left(m + 1\right)}} + \int -\frac{3 \, {\left({\left({\left(b^{3} c^{2} d x + a b^{2} e {\left(m + 1\right)} - {\left(a b^{2} c^{2} e {\left(m + 1\right)} - b^{3} c^{2} e\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} {\left(e x + d\right)}^{m} + {\left(b^{3} c^{3} d x^{2} - b^{3} c d - {\left(a b^{2} c^{3} e {\left(m + 1\right)} - b^{3} c^{3} e\right)} x^{3} + {\left(a b^{2} c e {\left(m + 1\right)} - b^{3} c e\right)} x\right)} {\left(e x + d\right)}^{m}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - {\left({\left(a^{2} b c^{2} e {\left(m + 1\right)} x^{2} - a^{2} b e {\left(m + 1\right)}\right)} \sqrt{c x + 1} \sqrt{c x - 1} {\left(e x + d\right)}^{m} + {\left(a^{2} b c^{3} e {\left(m + 1\right)} x^{3} - a^{2} b c e {\left(m + 1\right)} x\right)} {\left(e x + d\right)}^{m}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\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 x + 1} \sqrt{c x - 1}}\,{d x}"," ",0,"(b^3*e*x + b^3*d)*(e*x + d)^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^3/(e*(m + 1)) + (e*x + d)^(m + 1)*a^3/(e*(m + 1)) + integrate(-3*(((b^3*c^2*d*x + a*b^2*e*(m + 1) - (a*b^2*c^2*e*(m + 1) - b^3*c^2*e)*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1)*(e*x + d)^m + (b^3*c^3*d*x^2 - b^3*c*d - (a*b^2*c^3*e*(m + 1) - b^3*c^3*e)*x^3 + (a*b^2*c*e*(m + 1) - b^3*c*e)*x)*(e*x + d)^m)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 - ((a^2*b*c^2*e*(m + 1)*x^2 - a^2*b*e*(m + 1))*sqrt(c*x + 1)*sqrt(c*x - 1)*(e*x + d)^m + (a^2*b*c^3*e*(m + 1)*x^3 - a^2*b*c*e*(m + 1)*x)*(e*x + d)^m)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 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*x + 1)*sqrt(c*x - 1)), x)","F",0
37,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arccosh(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 x + 1} \sqrt{c x - 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 x + 1} \sqrt{c x - 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 x + 1} \sqrt{c x - 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 x + 1} \sqrt{c x - 1}}\,{d x}"," ",0,"(b^2*e*x + b^2*d)*(e*x + d)^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 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*x + 1)*sqrt(c*x - 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*x + 1)*sqrt(c*x - 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*x + 1)*sqrt(c*x - 1)), x)","F",0
38,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arccosh(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 x + 1} \sqrt{c x - 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 x + 1} \sqrt{c x - 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*x + 1)*sqrt(c*x - 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*x + 1)*sqrt(c*x - 1)), x)) + (e*x + d)^(m + 1)*a/(e*(m + 1))","F",0
39,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{m}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^m/(b*arccosh(c*x) + a), x)","F",0
40,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} {\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 x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1} + {\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 x + 1\right)} {\left(c x - 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 x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1)*(e*x + d)^m + (c^3*x^3 - c*x)*(e*x + d)^m)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((c^3*e*(m + 1)*x^3 + c^3*d*x^2 - c*e*(m - 1)*x + c*d)*(c*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 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*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 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*x + 1)*(c*x - 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*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
41,1,385,0,0.324614," ","integrate((d*x^2+c)^4*arccosh(a*x),x, algorithm=""maxima"")","-\frac{1}{99225} \, {\left(\frac{1225 \, \sqrt{a^{2} x^{2} - 1} d^{4} x^{8}}{a^{2}} + \frac{8100 \, \sqrt{a^{2} x^{2} - 1} c d^{3} x^{6}}{a^{2}} + \frac{23814 \, \sqrt{a^{2} x^{2} - 1} c^{2} d^{2} x^{4}}{a^{2}} + \frac{1400 \, \sqrt{a^{2} x^{2} - 1} d^{4} x^{6}}{a^{4}} + \frac{44100 \, \sqrt{a^{2} x^{2} - 1} c^{3} d x^{2}}{a^{2}} + \frac{9720 \, \sqrt{a^{2} x^{2} - 1} c d^{3} x^{4}}{a^{4}} + \frac{99225 \, \sqrt{a^{2} x^{2} - 1} c^{4}}{a^{2}} + \frac{31752 \, \sqrt{a^{2} x^{2} - 1} c^{2} d^{2} x^{2}}{a^{4}} + \frac{1680 \, \sqrt{a^{2} x^{2} - 1} d^{4} x^{4}}{a^{6}} + \frac{88200 \, \sqrt{a^{2} x^{2} - 1} c^{3} d}{a^{4}} + \frac{12960 \, \sqrt{a^{2} x^{2} - 1} c d^{3} x^{2}}{a^{6}} + \frac{63504 \, \sqrt{a^{2} x^{2} - 1} c^{2} d^{2}}{a^{6}} + \frac{2240 \, \sqrt{a^{2} x^{2} - 1} d^{4} x^{2}}{a^{8}} + \frac{25920 \, \sqrt{a^{2} x^{2} - 1} c d^{3}}{a^{8}} + \frac{4480 \, \sqrt{a^{2} x^{2} - 1} d^{4}}{a^{10}}\right)} a + \frac{1}{315} \, {\left(35 \, d^{4} x^{9} + 180 \, c d^{3} x^{7} + 378 \, c^{2} d^{2} x^{5} + 420 \, c^{3} d x^{3} + 315 \, c^{4} x\right)} \operatorname{arcosh}\left(a x\right)"," ",0,"-1/99225*(1225*sqrt(a^2*x^2 - 1)*d^4*x^8/a^2 + 8100*sqrt(a^2*x^2 - 1)*c*d^3*x^6/a^2 + 23814*sqrt(a^2*x^2 - 1)*c^2*d^2*x^4/a^2 + 1400*sqrt(a^2*x^2 - 1)*d^4*x^6/a^4 + 44100*sqrt(a^2*x^2 - 1)*c^3*d*x^2/a^2 + 9720*sqrt(a^2*x^2 - 1)*c*d^3*x^4/a^4 + 99225*sqrt(a^2*x^2 - 1)*c^4/a^2 + 31752*sqrt(a^2*x^2 - 1)*c^2*d^2*x^2/a^4 + 1680*sqrt(a^2*x^2 - 1)*d^4*x^4/a^6 + 88200*sqrt(a^2*x^2 - 1)*c^3*d/a^4 + 12960*sqrt(a^2*x^2 - 1)*c*d^3*x^2/a^6 + 63504*sqrt(a^2*x^2 - 1)*c^2*d^2/a^6 + 2240*sqrt(a^2*x^2 - 1)*d^4*x^2/a^8 + 25920*sqrt(a^2*x^2 - 1)*c*d^3/a^8 + 4480*sqrt(a^2*x^2 - 1)*d^4/a^10)*a + 1/315*(35*d^4*x^9 + 180*c*d^3*x^7 + 378*c^2*d^2*x^5 + 420*c^3*d*x^3 + 315*c^4*x)*arccosh(a*x)","A",0
42,1,257,0,0.406895," ","integrate((d*x^2+c)^3*arccosh(a*x),x, algorithm=""maxima"")","-\frac{1}{3675} \, {\left(\frac{75 \, \sqrt{a^{2} x^{2} - 1} d^{3} x^{6}}{a^{2}} + \frac{441 \, \sqrt{a^{2} x^{2} - 1} c d^{2} x^{4}}{a^{2}} + \frac{1225 \, \sqrt{a^{2} x^{2} - 1} c^{2} d x^{2}}{a^{2}} + \frac{90 \, \sqrt{a^{2} x^{2} - 1} d^{3} x^{4}}{a^{4}} + \frac{3675 \, \sqrt{a^{2} x^{2} - 1} c^{3}}{a^{2}} + \frac{588 \, \sqrt{a^{2} x^{2} - 1} c d^{2} x^{2}}{a^{4}} + \frac{2450 \, \sqrt{a^{2} x^{2} - 1} c^{2} d}{a^{4}} + \frac{120 \, \sqrt{a^{2} x^{2} - 1} d^{3} x^{2}}{a^{6}} + \frac{1176 \, \sqrt{a^{2} x^{2} - 1} c d^{2}}{a^{6}} + \frac{240 \, \sqrt{a^{2} x^{2} - 1} d^{3}}{a^{8}}\right)} a + \frac{1}{35} \, {\left(5 \, d^{3} x^{7} + 21 \, c d^{2} x^{5} + 35 \, c^{2} d x^{3} + 35 \, c^{3} x\right)} \operatorname{arcosh}\left(a x\right)"," ",0,"-1/3675*(75*sqrt(a^2*x^2 - 1)*d^3*x^6/a^2 + 441*sqrt(a^2*x^2 - 1)*c*d^2*x^4/a^2 + 1225*sqrt(a^2*x^2 - 1)*c^2*d*x^2/a^2 + 90*sqrt(a^2*x^2 - 1)*d^3*x^4/a^4 + 3675*sqrt(a^2*x^2 - 1)*c^3/a^2 + 588*sqrt(a^2*x^2 - 1)*c*d^2*x^2/a^4 + 2450*sqrt(a^2*x^2 - 1)*c^2*d/a^4 + 120*sqrt(a^2*x^2 - 1)*d^3*x^2/a^6 + 1176*sqrt(a^2*x^2 - 1)*c*d^2/a^6 + 240*sqrt(a^2*x^2 - 1)*d^3/a^8)*a + 1/35*(5*d^3*x^7 + 21*c*d^2*x^5 + 35*c^2*d*x^3 + 35*c^3*x)*arccosh(a*x)","A",0
43,1,154,0,0.310471," ","integrate((d*x^2+c)^2*arccosh(a*x),x, algorithm=""maxima"")","-\frac{1}{225} \, {\left(\frac{9 \, \sqrt{a^{2} x^{2} - 1} d^{2} x^{4}}{a^{2}} + \frac{50 \, \sqrt{a^{2} x^{2} - 1} c d x^{2}}{a^{2}} + \frac{225 \, \sqrt{a^{2} x^{2} - 1} c^{2}}{a^{2}} + \frac{12 \, \sqrt{a^{2} x^{2} - 1} d^{2} x^{2}}{a^{4}} + \frac{100 \, \sqrt{a^{2} x^{2} - 1} c d}{a^{4}} + \frac{24 \, \sqrt{a^{2} x^{2} - 1} d^{2}}{a^{6}}\right)} a + \frac{1}{15} \, {\left(3 \, d^{2} x^{5} + 10 \, c d x^{3} + 15 \, c^{2} x\right)} \operatorname{arcosh}\left(a x\right)"," ",0,"-1/225*(9*sqrt(a^2*x^2 - 1)*d^2*x^4/a^2 + 50*sqrt(a^2*x^2 - 1)*c*d*x^2/a^2 + 225*sqrt(a^2*x^2 - 1)*c^2/a^2 + 12*sqrt(a^2*x^2 - 1)*d^2*x^2/a^4 + 100*sqrt(a^2*x^2 - 1)*c*d/a^4 + 24*sqrt(a^2*x^2 - 1)*d^2/a^6)*a + 1/15*(3*d^2*x^5 + 10*c*d*x^3 + 15*c^2*x)*arccosh(a*x)","A",0
44,1,74,0,0.312438," ","integrate((d*x^2+c)*arccosh(a*x),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(\frac{\sqrt{a^{2} x^{2} - 1} d x^{2}}{a^{2}} + \frac{9 \, \sqrt{a^{2} x^{2} - 1} c}{a^{2}} + \frac{2 \, \sqrt{a^{2} x^{2} - 1} d}{a^{4}}\right)} a + \frac{1}{3} \, {\left(d x^{3} + 3 \, c x\right)} \operatorname{arcosh}\left(a x\right)"," ",0,"-1/9*(sqrt(a^2*x^2 - 1)*d*x^2/a^2 + 9*sqrt(a^2*x^2 - 1)*c/a^2 + 2*sqrt(a^2*x^2 - 1)*d/a^4)*a + 1/3*(d*x^3 + 3*c*x)*arccosh(a*x)","A",0
45,0,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(arccosh(a*x)/(d*x^2 + c), x)","F",0
46,0,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(arccosh(a*x)/(d*x^2 + c)^2, x)","F",0
47,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arccosh(a*x),x, algorithm=""maxima"")","\int \sqrt{d x^{2} + c} \operatorname{arcosh}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*arccosh(a*x), x)","F",0
48,0,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(arccosh(a*x)/sqrt(d*x^2 + c), x)","F",0
49,-2,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
50,-2,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
51,-2,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
52,-2,0,0,0.000000," ","integrate(arccosh(a*x)/(d*x^2+c)^(9/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
53,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a f^{3} - \frac{1}{15} \, a g^{3} {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} + \frac{3}{8} \, a f g^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2} d} + \frac{\sqrt{d} \arcsin\left(c x\right)}{c^{3}}\right)} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a f^{2} g}{c^{2} d} + \int \sqrt{-c^{2} d x^{2} + d} b g^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, \sqrt{-c^{2} d x^{2} + d} b f g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, \sqrt{-c^{2} d x^{2} + d} b f^{2} g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \sqrt{-c^{2} d x^{2} + d} b f^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a*f^3 - 1/15*a*g^3*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d)) + 3/8*a*f*g^2*(sqrt(-c^2*d*x^2 + d)*x/c^2 - 2*(-c^2*d*x^2 + d)^(3/2)*x/(c^2*d) + sqrt(d)*arcsin(c*x)/c^3) - (-c^2*d*x^2 + d)^(3/2)*a*f^2*g/(c^2*d) + integrate(sqrt(-c^2*d*x^2 + d)*b*g^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*sqrt(-c^2*d*x^2 + d)*b*f*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*sqrt(-c^2*d*x^2 + d)*b*f^2*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + sqrt(-c^2*d*x^2 + d)*b*f^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
54,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a f^{2} + \frac{1}{8} \, a g^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2} d} + \frac{\sqrt{d} \arcsin\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a f g}{3 \, c^{2} d} + \int \sqrt{-c^{2} d x^{2} + d} b g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 2 \, \sqrt{-c^{2} d x^{2} + d} b f g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \sqrt{-c^{2} d x^{2} + d} b f^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a*f^2 + 1/8*a*g^2*(sqrt(-c^2*d*x^2 + d)*x/c^2 - 2*(-c^2*d*x^2 + d)^(3/2)*x/(c^2*d) + sqrt(d)*arcsin(c*x)/c^3) - 2/3*(-c^2*d*x^2 + d)^(3/2)*a*f*g/(c^2*d) + integrate(sqrt(-c^2*d*x^2 + d)*b*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2*sqrt(-c^2*d*x^2 + d)*b*f*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + sqrt(-c^2*d*x^2 + d)*b*f^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
55,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a f - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a g}{3 \, c^{2} d} + \int \sqrt{-c^{2} d x^{2} + d} b g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \sqrt{-c^{2} d x^{2} + d} b f \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a*f - 1/3*(-c^2*d*x^2 + d)^(3/2)*a*g/(c^2*d) + integrate(sqrt(-c^2*d*x^2 + d)*b*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + sqrt(-c^2*d*x^2 + d)*b*f*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
56,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/(g*x+f),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(g-c*f>0)', see `assume?` for more details)Is g-c*f zero or nonzero?","F(-2)",0
57,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/(g*x+f)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(g-c*f>0)', see `assume?` for more details)Is g-c*f zero or nonzero?","F(-2)",0
58,0,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a f^{3} - \frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a g^{3} + \frac{1}{16} \, a f g^{2} {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{2}} + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a f^{2} g}{5 \, c^{2} d} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b g^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b f g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b f^{2} g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b f^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a*f^3 - 1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a*g^3 + 1/16*a*f*g^2*(2*(-c^2*d*x^2 + d)^(3/2)*x/c^2 - 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*d*x/c^2 + 3*d^(3/2)*arcsin(c*x)/c^3) - 3/5*(-c^2*d*x^2 + d)^(5/2)*a*f^2*g/(c^2*d) + integrate((-c^2*d*x^2 + d)^(3/2)*b*g^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*(-c^2*d*x^2 + d)^(3/2)*b*f*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*(-c^2*d*x^2 + d)^(3/2)*b*f^2*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (-c^2*d*x^2 + d)^(3/2)*b*f^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
59,0,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a f^{2} + \frac{1}{48} \, a g^{2} {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{2}} + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a f g}{5 \, c^{2} d} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b f g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b f^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a*f^2 + 1/48*a*g^2*(2*(-c^2*d*x^2 + d)^(3/2)*x/c^2 - 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*d*x/c^2 + 3*d^(3/2)*arcsin(c*x)/c^3) - 2/5*(-c^2*d*x^2 + d)^(5/2)*a*f*g/(c^2*d) + integrate((-c^2*d*x^2 + d)^(3/2)*b*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2*(-c^2*d*x^2 + d)^(3/2)*b*f*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (-c^2*d*x^2 + d)^(3/2)*b*f^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
60,0,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a f - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a g}{5 \, c^{2} d} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b f \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a*f - 1/5*(-c^2*d*x^2 + d)^(5/2)*a*g/(c^2*d) + integrate((-c^2*d*x^2 + d)^(3/2)*b*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (-c^2*d*x^2 + d)^(3/2)*b*f*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
61,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/(g*x+f),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(g-c*f>0)', see `assume?` for more details)Is g-c*f zero or nonzero?","F(-2)",0
62,0,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a f^{3} + \frac{1}{128} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2}} - \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{2} d} + \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{2}} + \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{2}} + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} a f g^{2} - \frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a g^{3} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a f^{2} g}{7 \, c^{2} d} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b g^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b f g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b f^{2} g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b f^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a*f^3 + 1/128*(8*(-c^2*d*x^2 + d)^(5/2)*x/c^2 - 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^2*d) + 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^2 + 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^2 + 15*d^(5/2)*arcsin(c*x)/c^3)*a*f*g^2 - 1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a*g^3 - 3/7*(-c^2*d*x^2 + d)^(7/2)*a*f^2*g/(c^2*d) + integrate((-c^2*d*x^2 + d)^(5/2)*b*g^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*(-c^2*d*x^2 + d)^(5/2)*b*f*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*(-c^2*d*x^2 + d)^(5/2)*b*f^2*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (-c^2*d*x^2 + d)^(5/2)*b*f^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
63,0,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a f^{2} + \frac{1}{384} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2}} - \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{2} d} + \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{2}} + \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{2}} + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} a g^{2} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a f g}{7 \, c^{2} d} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b f g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b f^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a*f^2 + 1/384*(8*(-c^2*d*x^2 + d)^(5/2)*x/c^2 - 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^2*d) + 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^2 + 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^2 + 15*d^(5/2)*arcsin(c*x)/c^3)*a*g^2 - 2/7*(-c^2*d*x^2 + d)^(7/2)*a*f*g/(c^2*d) + integrate((-c^2*d*x^2 + d)^(5/2)*b*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2*(-c^2*d*x^2 + d)^(5/2)*b*f*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (-c^2*d*x^2 + d)^(5/2)*b*f^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
64,0,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a f - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a g}{7 \, c^{2} d} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b f \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a*f - 1/7*(-c^2*d*x^2 + d)^(7/2)*a*g/(c^2*d) + integrate((-c^2*d*x^2 + d)^(5/2)*b*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (-c^2*d*x^2 + d)^(5/2)*b*f*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
65,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/(g*x+f),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(g-c*f>0)', see `assume?` for more details)Is g-c*f zero or nonzero?","F(-2)",0
66,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a g^{3} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} - \frac{3}{2} \, a f g^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} + \frac{a f^{3} \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} a f^{2} g}{c^{2} d} + \int \frac{b g^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}} + \frac{3 \, b f g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}} + \frac{3 \, b f^{2} g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}} + \frac{b f^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"-1/3*a*g^3*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d)) - 3/2*a*f*g^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + a*f^3*arcsin(c*x)/(c*sqrt(d)) - 3*sqrt(-c^2*d*x^2 + d)*a*f^2*g/(c^2*d) + integrate(b*g^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d) + 3*b*f*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d) + 3*b*f^2*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d) + b*f^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
67,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a g^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} + \frac{a f^{2} \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a f g}{c^{2} d} + \int \frac{b g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}} + \frac{2 \, b f g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}} + \frac{b f^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"-1/2*a*g^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + a*f^2*arcsin(c*x)/(c*sqrt(d)) - 2*sqrt(-c^2*d*x^2 + d)*a*f*g/(c^2*d) + integrate(b*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d) + 2*b*f*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d) + b*f^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
68,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{a f \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{\sqrt{-c^{2} d x^{2} + d} a g}{c^{2} d} + \int \frac{b g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}} + \frac{b f \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"a*f*arcsin(c*x)/(c*sqrt(d)) - sqrt(-c^2*d*x^2 + d)*a*g/(c^2*d) + integrate(b*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d) + b*f*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
69,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{b \operatorname{arcosh}\left(c x\right) + a}{\sqrt{-c^{2} d x^{2} + d} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)/(sqrt(-c^2*d*x^2 + d)*(g*x + f)), x)","F",0
70,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{b \operatorname{arcosh}\left(c x\right) + a}{\sqrt{-c^{2} d x^{2} + d} {\left(g x + f\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)/(sqrt(-c^2*d*x^2 + d)*(g*x + f)^2), x)","F",0
71,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{b c f^{3} \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, d} - a g^{3} {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} + 3 \, a f g^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + \frac{b f^{3} x \operatorname{arcosh}\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a f^{3} x}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{3 \, a f^{2} g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \int \frac{b g^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{3 \, b f g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{3 \, b f^{2} g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*b*c*f^3*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2)/d - a*g^3*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d)) + 3*a*f*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + b*f^3*x*arccosh(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*f^3*x/(sqrt(-c^2*d*x^2 + d)*d) + 3*a*f^2*g/(sqrt(-c^2*d*x^2 + d)*c^2*d) + integrate(b*g^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2) + 3*b*f*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2) + 3*b*f^2*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{b c f^{2} \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, d} + a g^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + \frac{b f^{2} x \operatorname{arcosh}\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a f^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{2 \, a f g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \int \frac{b g^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, b f g x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*b*c*f^2*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2)/d + a*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + b*f^2*x*arccosh(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*f^2*x/(sqrt(-c^2*d*x^2 + d)*d) + 2*a*f*g/(sqrt(-c^2*d*x^2 + d)*c^2*d) + integrate(b*g^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2) + 2*b*f*g*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
73,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{b c f \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, d} + b g {\left(\frac{\frac{{\left(c \sqrt{d} x + \sqrt{c x + 1} \sqrt{c x - 1} \sqrt{d}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c x + 1}} + \frac{\sqrt{c x + 1} \sqrt{c x - 1} \sqrt{d}}{\sqrt{-c x + 1}}}{\sqrt{c x + 1} c^{3} d^{2} x + {\left(c x + 1\right)} \sqrt{c x - 1} c^{2} d^{2}} - \int \frac{c^{2} x^{3} + c x^{2} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)} - x}{\sqrt{-c x + 1} {\left({\left(c^{2} d^{\frac{3}{2}} x^{2} - d^{\frac{3}{2}}\right)} e^{\left(\frac{3}{2} \, \log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} + 2 \, {\left(c^{3} d^{\frac{3}{2}} x^{3} - c d^{\frac{3}{2}} x\right)} e^{\left(\log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)} + {\left(c^{4} d^{\frac{3}{2}} x^{4} - c^{2} d^{\frac{3}{2}} x^{2}\right)} \sqrt{c x + 1}\right)}}\,{d x}\right)} + \frac{b f x \operatorname{arcosh}\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a f x}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"-1/2*b*c*f*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2)/d + b*g*(((c*sqrt(d)*x + sqrt(c*x + 1)*sqrt(c*x - 1)*sqrt(d))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c*x + 1) + sqrt(c*x + 1)*sqrt(c*x - 1)*sqrt(d)/sqrt(-c*x + 1))/(sqrt(c*x + 1)*c^3*d^2*x + (c*x + 1)*sqrt(c*x - 1)*c^2*d^2) - integrate((c^2*x^3 + c*x^2*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1)) - x)/(sqrt(-c*x + 1)*((c^2*d^(3/2)*x^2 - d^(3/2))*e^(3/2*log(c*x + 1) + log(c*x - 1)) + 2*(c^3*d^(3/2)*x^3 - c*d^(3/2)*x)*e^(log(c*x + 1) + 1/2*log(c*x - 1)) + (c^4*d^(3/2)*x^4 - c^2*d^(3/2)*x^2)*sqrt(c*x + 1))), x)) + b*f*x*arccosh(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*f*x/(sqrt(-c^2*d*x^2 + d)*d) + a*g/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
74,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{b \operatorname{arcosh}\left(c x\right) + a}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)/((-c^2*d*x^2 + d)^(3/2)*(g*x + f)), x)","F",0
75,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(g x + f\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arccosh(c*x) + a)^n/sqrt(-c^2*x^2 + 1), x)","F",0
76,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arccosh(c*x))^n/(-c*x+1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(g x + f\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arccosh(c*x) + a)^n/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
77,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arccosh(c*x))^n/(c*d1*x+d1)^(1/2)/(-c*d2*x+d2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(g x + f\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{c d_{1} x + d_{1}} \sqrt{-c d_{2} x + d_{2}}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arccosh(c*x) + a)^n/(sqrt(c*d1*x + d1)*sqrt(-c*d2*x + d2)), x)","F",0
78,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\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*arccosh(c*x) + a)^n*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","F",0
79,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\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*arccosh(c*x) + a)^2*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","F",0
80,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\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*arccosh(c*x) + a)*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","F",0
81,0,0,0,0.000000," ","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
82,0,0,0,0.000000," ","integrate(log(h*(g*x+f)^m)/(a+b*arccosh(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{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(log((g*x + f)^m*h)/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)), x)","F",0
83,1,321,0,0.335425," ","integrate(x^3*arccosh(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcosh}\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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*arccosh(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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/b^5 + 55*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^2 - 1)*a/b^5)*b","B",0
84,1,212,0,0.497984," ","integrate(x^2*arccosh(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcosh}\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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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 \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*arccosh(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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/b^4 - 5*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*a*x/b^3 + 9*(a^2 - 1)*a*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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
85,1,151,0,0.335313," ","integrate(x*arccosh(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcosh}\left(b x + a\right) - \frac{1}{4} \, b {\left(\frac{3 \, a^{2} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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)} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*arccosh(b*x + a) - 1/4*b*(3*a^2*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/b^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*x/b^2 - (a^2 - 1)*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/b^3 - 3*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*a/b^3)","B",0
86,1,30,0,0.300501," ","integrate(arccosh(b*x+a),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \operatorname{arcosh}\left(b x + a\right) - \sqrt{{\left(b x + a\right)}^{2} - 1}}{b}"," ",0,"((b*x + a)*arccosh(b*x + a) - sqrt((b*x + a)^2 - 1))/b","A",0
87,0,0,0,0.000000," ","integrate(arccosh(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arccosh(b*x + a)/x, x)","F",0
88,-2,0,0,0.000000," ","integrate(arccosh(b*x+a)/x^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
89,-2,0,0,0.000000," ","integrate(arccosh(b*x+a)/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
90,-2,0,0,0.000000," ","integrate(arccosh(b*x+a)/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
91,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arccosh(d*x + c) + a), x)","F",0
92,0,0,0,0.000000," ","integrate(1/(a-b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(-b*arccosh(d*x + c) + a), x)","F",0
93,1,1241,0,0.388499," ","integrate((d*e*x+c*e)^4*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(d*x + c) - sqrt((d*x + c)^2 - 1))*b*c^4*e^4/d","B",0
94,1,797,0,0.439878," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(d*x + c) - sqrt((d*x + c)^2 - 1))*b*c^3*e^3/d","B",0
95,1,449,0,0.499835," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(d*x + c) - sqrt((d*x + c)^2 - 1))*b*c^2*e^2/d","B",0
96,1,203,0,0.307863," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a d e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(d*x + c) - sqrt((d*x + c)^2 - 1))*b*c*e/d","B",0
97,1,35,0,0.340645," ","integrate(a+b*arccosh(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left({\left(d x + c\right)} \operatorname{arcosh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} - 1}\right)} b}{d}"," ",0,"a*x + ((d*x + c)*arccosh(d*x + c) - sqrt((d*x + c)^2 - 1))*b/d","A",0
98,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e),x, algorithm=""maxima"")","b \int \frac{\log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d*e*x + c*e), x) + a*log(d*e*x + c*e)/(d*e)","F",0
99,1,80,0,0.545290," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-b {\left(\frac{\operatorname{arcosh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\arcsin\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*(arccosh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsin(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
100,1,118,0,0.618066," ","integrate((a+b*arccosh(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{arcosh}\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) - arccosh(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
101,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^4,x, algorithm=""maxima"")","\frac{1}{6} \, b {\left(\frac{2 \, d^{2} x^{2} + 4 \, c d x + 2 \, c^{2} - {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \log\left(d x + c + 1\right) + {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \log\left(d x + c - 1\right) - 2 \, \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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}} - 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)} e^{\left(\frac{1}{2} \, \log\left(d x + c + 1\right) + \frac{1}{2} \, \log\left(d x + c - 1\right)\right)}\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 + 4*c*d*x + 2*c^2 - (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*log(d*x + c + 1) + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*log(d*x + c - 1) - 2*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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) - 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)*e^(1/2*log(d*x + c + 1) + 1/2*log(d*x + c - 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
102,1,260,0,0.562373," ","integrate((a+b*arccosh(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 x + c + 1} \sqrt{d x + c - 1}} - \frac{3 \, \operatorname{arcosh}\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*x + c + 1)*sqrt(d*x + c - 1)) - 3*arccosh(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
103,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^6,x, algorithm=""maxima"")","\frac{1}{30} \, b {\left(\frac{6 \, d^{4} x^{4} + 24 \, c d^{3} x^{3} + 6 \, c^{4} + 2 \, {\left(18 \, c^{2} d^{2} + d^{2}\right)} x^{2} + 2 \, c^{2} + 4 \, {\left(6 \, c^{3} d + c d\right)} x - 3 \, {\left(d^{5} x^{5} + 5 \, c d^{4} x^{4} + 10 \, c^{2} d^{3} x^{3} + 10 \, c^{3} d^{2} x^{2} + 5 \, c^{4} d x + c^{5}\right)} \log\left(d x + c + 1\right) + 3 \, {\left(d^{5} x^{5} + 5 \, c d^{4} x^{4} + 10 \, c^{2} d^{3} x^{3} + 10 \, c^{3} d^{2} x^{2} + 5 \, c^{4} d x + c^{5}\right)} \log\left(d x + c - 1\right) - 6 \, \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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}} - 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)} e^{\left(\frac{1}{2} \, \log\left(d x + c + 1\right) + \frac{1}{2} \, \log\left(d x + c - 1\right)\right)}\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*((6*d^4*x^4 + 24*c*d^3*x^3 + 6*c^4 + 2*(18*c^2*d^2 + d^2)*x^2 + 2*c^2 + 4*(6*c^3*d + c*d)*x - 3*(d^5*x^5 + 5*c*d^4*x^4 + 10*c^2*d^3*x^3 + 10*c^3*d^2*x^2 + 5*c^4*d*x + c^5)*log(d*x + c + 1) + 3*(d^5*x^5 + 5*c*d^4*x^4 + 10*c^2*d^3*x^3 + 10*c^3*d^2*x^2 + 5*c^4*d*x + c^5)*log(d*x + c - 1) - 6*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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) - 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)*e^(1/2*log(d*x + c + 1) + 1/2*log(d*x + c - 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
104,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
105,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{2 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
106,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
107,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} d e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}\,{d x}"," ",0,"1/2*a^2*d*e*x^2 + 1/2*(2*x^2*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
108,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^2,x, algorithm=""maxima"")","{\left(x \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2} - \int \frac{2 \, {\left(d^{3} x^{3} + 2 \, c d^{2} x^{2} + {\left(d^{2} x^{2} + c d x\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(c^{2} d - d\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}\,{d x}\right)} b^{2} + a^{2} x + \frac{2 \, {\left({\left(d x + c\right)} \operatorname{arcosh}\left(d x + c\right) - \sqrt{{\left(d x + c\right)}^{2} - 1}\right)} a b}{d}"," ",0,"(x*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 - integrate(2*(d^3*x^3 + 2*c*d^2*x^2 + (d^2*x^2 + c*d*x)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (c^2*d - d)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x))*b^2 + a^2*x + 2*((d*x + c)*arccosh(d*x + c) - sqrt((d*x + c)^2 - 1))*a*b/d","F",0
109,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d e x + c e} + \frac{2 \, a b \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d*e*x + c*e) + 2*a*b*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d*e*x + c*e), x)","F",0
110,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-b^{2} {\left(\frac{\log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d^{2} e^{2} x + c d e^{2}} - \int \frac{2 \, {\left(d^{2} x^{2} + 2 \, c d x + \sqrt{d x + c + 1} {\left(d x + c\right)} \sqrt{d x + c - 1} + c^{2} - 1\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 2 \, {\left(2 \, c^{3} d e^{2} - c d e^{2}\right)} x}\,{d x}\right)} - 2 \, a b {\left(\frac{\operatorname{arcosh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\arcsin\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d^2*e^2*x + c*d*e^2) - integrate(2*(d^2*x^2 + 2*c*d*x + sqrt(d*x + c + 1)*(d*x + c)*sqrt(d*x + c - 1) + c^2 - 1)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + 2*(2*c^3*d*e^2 - c*d*e^2)*x), x)) - 2*a*b*(arccosh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsin(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
111,1,229,0,0.693973," ","integrate((a+b*arccosh(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{arcosh}\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{arcosh}\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{arcosh}\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*arccosh(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) - arccosh(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*arccosh(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
112,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, {\left(3 \, c^{2} d - d\right)} a b + {\left(3 \, c^{2} d - d\right)} b^{2}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 + 1} \sqrt{d x + c - 1} + {\left(7 \, c^{6} d e^{4} - 5 \, c^{4} d e^{4}\right)} x\right)}}\,{d x}"," ",0,"-1/3*b^2*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (3*(3*c^2*d - d)*a*b + (3*c^2*d - d)*b^2)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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 + (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 + 1)*sqrt(d*x + c - 1) + (7*c^6*d*e^4 - 5*c^4*d*e^4)*x), x)","F",0
113,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*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*x + c + 1)*sqrt(d*x + c - 1) + 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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
114,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{4 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*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*x + c + 1)*sqrt(d*x + c - 1) + 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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
115,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*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*x + c + 1)*sqrt(d*x + c - 1) + 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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
116,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} d e x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{2 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c\right)}}\,{d x}"," ",0,"1/2*a^3*d*e*x^2 + 3/4*(2*x^2*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*(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*x + c + 1)*sqrt(d*x + c - 1) + 2*(2*(2*c^3*d*e - c*d*e)*a*b^2 - (c^3*d*e - c*d*e)*b^3)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","b^{3} x \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{3} + a^{3} x + \frac{3 \, {\left({\left(d x + c\right)} \operatorname{arcosh}\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left({\left(3 \, c^{2} d - d\right)} a b^{2} - {\left(c^{2} d - d\right)} b^{3}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}\,{d x}"," ",0,"b^3*x*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^3 + a^3*x + 3*((d*x + c)*arccosh(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 + ((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*x + c + 1)*sqrt(d*x + c - 1) + ((3*c^2*d - d)*a*b^2 - (c^2*d - d)*b^3)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{3}}{d e x + c e} + \frac{3 \, a b^{2} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d e x + c e} + \frac{3 \, a^{2} b \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^3/(d*e*x + c*e) + 3*a*b^2*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d*e*x + c*e) + 3*a^2*b*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d*e*x + c*e), x)","F",0
119,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{b^{3} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{3}}{d^{2} e^{2} x + c d e^{2}} - 3 \, a^{2} b {\left(\frac{\operatorname{arcosh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\arcsin\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left({\left(3 \, c^{2} d - d\right)} a b^{2} + {\left(3 \, c^{2} d - d\right)} b^{3}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{2} - 3 \, c^{2} d e^{2}\right)} x}\,{d x}"," ",0,"-b^3*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^3/(d^2*e^2*x + c*d*e^2) - 3*a^2*b*(arccosh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsin(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + ((3*c^2*d - d)*a*b^2 + (3*c^2*d - d)*b^3)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^2 - 3*c^2*d*e^2)*x), x)","F",0
120,0,0,0,0.000000," ","integrate((a+b*arccosh(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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 + \sqrt{d x + c + 1} {\left(d x + c\right)} \sqrt{d x + c - 1} + c^{2} - 1\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{3} - 3 \, c^{2} d e^{3}\right)} x\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{arcosh}\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{arcosh}\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*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + sqrt(d*x + c + 1)*(d*x + c)*sqrt(d*x + c - 1) + c^2 - 1)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^3 - 3*c^2*d*e^3)*x), 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) - arccosh(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*arccosh(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
121,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{b^{3} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, {\left(3 \, c^{2} d - d\right)} a b^{2} + {\left(3 \, c^{2} d - d\right)} b^{3}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 + 1} \sqrt{d x + c - 1} + {\left(7 \, c^{6} d e^{4} - 5 \, c^{4} d e^{4}\right)} x}\,{d x}"," ",0,"-1/3*b^3*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (3*(3*c^2*d - d)*a*b^2 + (3*c^2*d - d)*b^3)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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 + (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 + 1)*sqrt(d*x + c - 1) + (7*c^6*d*e^4 - 5*c^4*d*e^4)*x), x)","F",0
122,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*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*x + c + 1)*sqrt(d*x + c - 1) + 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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
123,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(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{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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 \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}\right)}}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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*arccosh(d*x + c) - d*(2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x^2/d^2 - 15*c^3*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^4 - 5*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*c*x/d^3 + 9*(c^2 - 1)*c*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*(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*x + c + 1)*sqrt(d*x + c - 1) + 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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
124,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\frac{1}{2} \, a^{4} d e x^{2} + {\left(2 \, x^{2} \operatorname{arcosh}\left(d x + c\right) - d {\left(\frac{3 \, c^{2} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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)} \log\left(2 \, d^{2} x + 2 \, c d + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} - 1} d\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{arcosh}\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 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\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}\right)}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}\,{d x}"," ",0,"1/2*a^4*d*e*x^2 + (2*x^2*arccosh(d*x + c) - d*(3*c^2*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/d^3 + sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*x/d^2 - (c^2 - 1)*log(2*d^2*x + 2*c*d + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 - 1)*d)/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)*arccosh(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*(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*x + c + 1)*sqrt(d*x + c - 1) + 2*(2*(2*c^3*d*e - c*d*e)*a*b^3 - (c^3*d*e - c*d*e)*b^4)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","b^{4} x \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{4} + a^{4} x + \frac{4 \, {\left({\left(d x + c\right)} \operatorname{arcosh}\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left({\left(3 \, c^{2} d - d\right)} a b^{3} - {\left(c^{2} d - d\right)} b^{4}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}\right)}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}\,{d x}"," ",0,"b^4*x*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^4 + a^4*x + 4*((d*x + c)*arccosh(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 + ((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*x + c + 1)*sqrt(d*x + c - 1) + ((3*c^2*d - d)*a*b^3 - (c^2*d - d)*b^4)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
126,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{4}}{d e x + c e} + \frac{4 \, a b^{3} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{3}}{d e x + c e} + \frac{6 \, a^{2} b^{2} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2}}{d e x + c e} + \frac{4 \, a^{3} b \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^4/(d*e*x + c*e) + 4*a*b^3*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^3/(d*e*x + c*e) + 6*a^2*b^2*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2/(d*e*x + c*e) + 4*a^3*b*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d*e*x + c*e), x)","F",0
127,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{b^{4} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{4}}{d^{2} e^{2} x + c d e^{2}} - 4 \, a^{3} b {\left(\frac{\operatorname{arcosh}\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\arcsin\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left({\left(3 \, c^{2} d - d\right)} a b^{3} + {\left(3 \, c^{2} d - d\right)} b^{4}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{2} - 3 \, c^{2} d e^{2}\right)} x}\,{d x}"," ",0,"-b^4*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^4/(d^2*e^2*x + c*d*e^2) - 4*a^3*b*(arccosh(d*x + c)/(d^2*e^2*x + c*d*e^2) + arcsin(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + ((3*c^2*d - d)*a*b^3 + (3*c^2*d - d)*b^4)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^2 - 3*c^2*d*e^2)*x), x)","F",0
128,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{b^{4} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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{arcosh}\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{arcosh}\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{arcosh}\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(2 \, {\left(3 \, c^{2} d - d\right)} a b^{3} + {\left(3 \, c^{2} d - d\right)} b^{4}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 + 1} \sqrt{d x + c - 1} + 2 \, {\left(3 \, c^{5} d e^{3} - 2 \, c^{3} d e^{3}\right)} x}\,{d x}"," ",0,"-1/2*b^4*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*arccosh(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) - arccosh(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*arccosh(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (2*(3*c^2*d - d)*a*b^3 + (3*c^2*d - d)*b^4)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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 + 1)*sqrt(d*x + c - 1) + 2*(3*c^5*d*e^3 - 2*c^3*d*e^3)*x), x)","F",0
129,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^4/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{b^{4} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, {\left(3 \, c^{2} d - d\right)} a b^{3} + {\left(3 \, c^{2} d - d\right)} b^{4}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 + 1} \sqrt{d x + c - 1} + {\left(7 \, c^{6} d e^{4} - 5 \, c^{4} d e^{4}\right)} x\right)}}\,{d x}"," ",0,"-1/3*b^4*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (3*(3*c^2*d - d)*a*b^3 + (3*c^2*d - d)*b^4)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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 + (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 + 1)*sqrt(d*x + c - 1) + (7*c^6*d*e^4 - 5*c^4*d*e^4)*x), x)","F",0
130,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arccosh(d*x + c) + a), x)","F",0
131,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arccosh(d*x + c) + a), x)","F",0
132,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arccosh(d*x + c) + a), x)","F",0
133,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{d e x + c e}{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arccosh(d*x + c) + a), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(1/(b*arccosh(d*x + c) + a), x)","F",0
135,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arccosh(d*x + c) + a)), x)","F",0
136,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(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(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 + 1} \sqrt{d x + c - 1} + {\left(7 \, c^{6} d e^{4} - 5 \, c^{4} d e^{4}\right)} x}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d - d\right)} a b + {\left(a b d^{2} x + a b c d\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)} + \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} + {\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 x + c + 1\right)} {\left(d x + c - 1\right)} + 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(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 x + c + 1} \sqrt{d x + c - 1} + 20 \, {\left(2 \, c^{7} d e^{4} - 3 \, c^{5} d e^{4} + c^{3} d e^{4}\right)} x}{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(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} a b + 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 x + c + 1} \sqrt{d x + c - 1} + {\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(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} b^{2} + 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}\,{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 + (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 + 1)*sqrt(d*x + c - 1) + (7*c^6*d*e^4 - 5*c^4*d*e^4)*x)/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d - d)*a*b + (a*b*d^2*x + a*b*c*d)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + 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 + (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*x + c + 1)*(d*x + c - 1) + 10*(14*c^6*d^2*e^4 - 15*c^4*d^2*e^4 + 3*c^2*d^2*e^4)*x^2 + (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*x + c + 1)*sqrt(d*x + c - 1) + 20*(2*c^7*d*e^4 - 3*c^5*d*e^4 + c^3*d*e^4)*x)/(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 + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*a*b + 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*x + c + 1)*sqrt(d*x + c - 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 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*b^2 + 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
137,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(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} + {\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 + 1} \sqrt{d x + c - 1} + 2 \, {\left(3 \, c^{5} d e^{3} - 2 \, c^{3} d e^{3}\right)} x}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d - d\right)} a b + {\left(a b d^{2} x + a b c d\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)} + \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} + 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 x + c + 1\right)} {\left(d x + c - 1\right)} + 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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 4 \, {\left(7 \, c^{6} d e^{3} - 10 \, c^{4} d e^{3} + 3 \, c^{2} d e^{3}\right)} x}{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(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} a b + 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 x + c + 1} \sqrt{d x + c - 1} + {\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(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} b^{2} + 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}\,{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 + (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 + 1)*sqrt(d*x + c - 1) + 2*(3*c^5*d*e^3 - 2*c^3*d*e^3)*x)/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d - d)*a*b + (a*b*d^2*x + a*b*c*d)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + 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 + 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*x + c + 1)*(d*x + c - 1) + 4*(21*c^5*d^2*e^3 - 20*c^3*d^2*e^3 + 3*c*d^2*e^3)*x^2 + (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*x + c + 1)*sqrt(d*x + c - 1) + 4*(7*c^6*d*e^3 - 10*c^4*d*e^3 + 3*c^2*d*e^3)*x)/(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 + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*a*b + 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*x + c + 1)*sqrt(d*x + c - 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 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*b^2 + 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
138,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{2} - 3 \, c^{2} d e^{2}\right)} x}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d - d\right)} a b + {\left(a b d^{2} x + a b c d\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)} + \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} + {\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 x + c + 1\right)} {\left(d x + c - 1\right)} + 3 \, {\left(15 \, c^{4} d^{2} e^{2} - 12 \, c^{2} d^{2} e^{2} + d^{2} e^{2}\right)} x^{2} + {\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 x + c + 1} \sqrt{d x + c - 1} + 6 \, {\left(3 \, c^{5} d e^{2} - 4 \, c^{3} d e^{2} + c d e^{2}\right)} x}{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(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} a b + 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 x + c + 1} \sqrt{d x + c - 1} + {\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(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} b^{2} + 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}\,{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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^2 - 3*c^2*d*e^2)*x)/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d - d)*a*b + (a*b*d^2*x + a*b*c*d)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + 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*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*x + c + 1)*(d*x + c - 1) + 3*(15*c^4*d^2*e^2 - 12*c^2*d^2*e^2 + d^2*e^2)*x^2 + (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*x + c + 1)*sqrt(d*x + c - 1) + 6*(3*c^5*d*e^2 - 4*c^3*d*e^2 + c*d*e^2)*x)/(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 + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*a*b + 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*x + c + 1)*sqrt(d*x + c - 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 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*b^2 + 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
139,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(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} + {\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 + 1} \sqrt{d x + c - 1} + 2 \, {\left(2 \, c^{3} d e - c d e\right)} x}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d - d\right)} a b + {\left(a b d^{2} x + a b c d\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)} + \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} + 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 x + c + 1\right)} {\left(d x + c - 1\right)} + 4 \, {\left(5 \, c^{3} d^{2} e - 3 \, c d^{2} e\right)} x^{2} + {\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 x + c + 1} \sqrt{d x + c - 1} + 2 \, c e + 2 \, {\left(5 \, c^{4} d e - 6 \, c^{2} d e + d e\right)} x}{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(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} a b + 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 x + c + 1} \sqrt{d x + c - 1} + {\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(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} b^{2} + 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}\,{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 + (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 + 1)*sqrt(d*x + c - 1) + 2*(2*c^3*d*e - c*d*e)*x)/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d - d)*a*b + (a*b*d^2*x + a*b*c*d)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + 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 + 2*(d^3*e*x^3 + 3*c*d^2*e*x^2 + 3*c^2*d*e*x + c^3*e)*(d*x + c + 1)*(d*x + c - 1) + 4*(5*c^3*d^2*e - 3*c*d^2*e)*x^2 + (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*x + c + 1)*sqrt(d*x + c - 1) + 2*c*e + 2*(5*c^4*d*e - 6*c^2*d*e + d*e)*x)/(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 + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*a*b + 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*x + c + 1)*sqrt(d*x + c - 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 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*b^2 + 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
140,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}{a b d^{3} x^{2} + 2 \, a b c d^{2} x + {\left(c^{2} d - d\right)} a b + {\left(a b d^{2} x + a b c d\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)} + \int \frac{d^{4} x^{4} + 4 \, c d^{3} x^{3} + c^{4} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + 2 \, {\left(3 \, c^{2} d^{2} - d^{2}\right)} x^{2} + {\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 x + c + 1} \sqrt{d x + c - 1} - 2 \, c^{2} + 4 \, {\left(c^{3} d - c d\right)} x + 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(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} a b + 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 x + c + 1} \sqrt{d x + c - 1} + {\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(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{4} - 2 \, c^{2} + 1\right)} b^{2} + 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}\,{d x}"," ",0,"-(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c)/(a*b*d^3*x^2 + 2*a*b*c*d^2*x + (c^2*d - d)*a*b + (a*b*d^2*x + a*b*c*d)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + integrate((d^4*x^4 + 4*c*d^3*x^3 + c^4 + (d^2*x^2 + 2*c*d*x + c^2 + 1)*(d*x + c + 1)*(d*x + c - 1) + 2*(3*c^2*d^2 - d^2)*x^2 + (2*d^3*x^3 + 6*c*d^2*x^2 + 2*c^3 + (6*c^2*d - d)*x - c)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) - 2*c^2 + 4*(c^3*d - c*d)*x + 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 + (a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*a*b + 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*x + c + 1)*sqrt(d*x + c - 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 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(d*x + c + 1)*(d*x + c - 1) + (c^4 - 2*c^2 + 1)*b^2 + 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
141,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^2,x, algorithm=""maxima"")","-\frac{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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(a b d^{3} e x^{2} + 2 \, a b c d^{2} e x + a b c^{2} d e\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)} + \int \frac{2 \, {\left(d x + c + 1\right)} {\left(d x + c\right)} {\left(d x + c - 1\right)} + {\left(2 \, d^{2} x^{2} + 4 \, c d x + 2 \, c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 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(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 x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{6} e - 2 \, c^{4} e + c^{2} e\right)} a b + 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 x + c + 1} \sqrt{d x + c - 1} + {\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(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 x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(c^{6} e - 2 \, c^{4} e + c^{2} e\right)} b^{2} + 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}\,{d x}"," ",0,"-(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - 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 + (a*b*d^3*e*x^2 + 2*a*b*c*d^2*e*x + a*b*c^2*d*e)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + integrate((2*(d*x + c + 1)*(d*x + c)*(d*x + c - 1) + (2*d^2*x^2 + 4*c*d*x + 2*c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 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 + (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*x + c + 1)*(d*x + c - 1) + (c^6*e - 2*c^4*e + c^2*e)*a*b + 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*x + c + 1)*sqrt(d*x + c - 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 + (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*x + c + 1)*(d*x + c - 1) + (c^6*e - 2*c^4*e + c^2*e)*b^2 + 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
142,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(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(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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 1\right)}^{\frac{3}{2}} + {\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} + {\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 x + c + 1\right)} {\left(d x + c - 1\right)} + 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(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 x + c + 1} \sqrt{d x + c - 1} + {\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} + {\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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 1\right)}^{\frac{3}{2}} + 3 \, {\left(7 \, c^{5} d^{2} - 10 \, c^{3} d^{2} + 3 \, c d^{2}\right)} b x^{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 x + c + 1\right)} {\left(d x + c - 1\right)} + {\left(7 \, c^{6} d - 15 \, c^{4} d + 9 \, c^{2} d - d\right)} b x + {\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 x + c + 1} \sqrt{d x + c - 1} + {\left(c^{7} - 3 \, c^{5} + 3 \, c^{3} - c\right)} b\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{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(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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 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 x + c + 1\right)} {\left(d x + c - 1\right)} + {\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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 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 x + c + 1\right)} {\left(d x + c - 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2} + 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 x + c + 1} \sqrt{d x + c - 1} + 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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 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 x + c + 1\right)} {\left(d x + c - 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)\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} + {\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 x + c + 1\right)}^{2} {\left(d x + c - 1\right)}^{2} + 2 \, {\left(35 \, c^{4} d^{4} - 30 \, c^{2} d^{4} + 3 \, d^{4}\right)} x^{4} + {\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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 1\right)}^{\frac{3}{2}} + 6 \, c^{4} + 8 \, {\left(7 \, c^{5} d^{3} - 10 \, c^{3} d^{3} + 3 \, c d^{3}\right)} x^{3} + 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 x + c + 1\right)} {\left(d x + c - 1\right)} + 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^{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 x + c + 1} \sqrt{d x + c - 1} - 4 \, c^{2} + 8 \, {\left(c^{7} d - 3 \, c^{5} d + 3 \, c^{3} d - c d\right)} x + 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} + {\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 x + c + 1\right)}^{2} {\left(d x + c - 1\right)}^{2} + 8 \, {\left(c^{7} d - 3 \, c^{5} d + 3 \, c^{3} d - c d\right)} a b^{2} x + 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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 1\right)}^{\frac{3}{2}} + {\left(c^{8} - 4 \, c^{6} + 6 \, c^{4} - 4 \, c^{2} + 1\right)} a b^{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 x + c + 1\right)} {\left(d x + c - 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 x + c + 1} \sqrt{d x + c - 1} + {\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} + {\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 x + c + 1\right)}^{2} {\left(d x + c - 1\right)}^{2} + 8 \, {\left(c^{7} d - 3 \, c^{5} d + 3 \, c^{3} d - c d\right)} b^{3} x + 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 x + c + 1\right)}^{\frac{3}{2}} {\left(d x + c - 1\right)}^{\frac{3}{2}} + {\left(c^{8} - 4 \, c^{6} + 6 \, c^{4} - 4 \, c^{2} + 1\right)} b^{3} + 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 x + c + 1\right)} {\left(d x + c - 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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)\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 + ((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*x + c + 1)^(3/2)*(d*x + c - 1)^(3/2) + ((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*(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*x + c + 1)*(d*x + c - 1) + 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 + (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*x + c + 1)*sqrt(d*x + c - 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 + (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*x + c + 1)^(3/2)*(d*x + c - 1)^(3/2) + 3*(7*c^5*d^2 - 10*c^3*d^2 + 3*c*d^2)*b*x^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*x + c + 1)*(d*x + c - 1) + (7*c^6*d - 15*c^4*d + 9*c^2*d - d)*b*x + (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*x + c + 1)*sqrt(d*x + c - 1) + (c^7 - 3*c^5 + 3*c^3 - c)*b)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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 + (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*x + c + 1)^(3/2)*(d*x + c - 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*x + c + 1)*(d*x + c - 1) + (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*x + c + 1)^(3/2)*(d*x + c - 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*x + c + 1)*(d*x + c - 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 + 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*x + c + 1)*sqrt(d*x + c - 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*x + c + 1)^(3/2)*(d*x + c - 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*x + c + 1)*(d*x + c - 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)) + 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 + (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*x + c + 1)^2*(d*x + c - 1)^2 + 2*(35*c^4*d^4 - 30*c^2*d^4 + 3*d^4)*x^4 + (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*x + c + 1)^(3/2)*(d*x + c - 1)^(3/2) + 6*c^4 + 8*(7*c^5*d^3 - 10*c^3*d^3 + 3*c*d^3)*x^3 + 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*x + c + 1)*(d*x + c - 1) + 4*(7*c^6*d^2 - 15*c^4*d^2 + 9*c^2*d^2 - d^2)*x^2 + (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*x + c + 1)*sqrt(d*x + c - 1) - 4*c^2 + 8*(c^7*d - 3*c^5*d + 3*c^3*d - c*d)*x + 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 + (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*x + c + 1)^2*(d*x + c - 1)^2 + 8*(c^7*d - 3*c^5*d + 3*c^3*d - c*d)*a*b^2*x + 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*x + c + 1)^(3/2)*(d*x + c - 1)^(3/2) + (c^8 - 4*c^6 + 6*c^4 - 4*c^2 + 1)*a*b^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*x + c + 1)*(d*x + c - 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*x + c + 1)*sqrt(d*x + c - 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 + (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*x + c + 1)^2*(d*x + c - 1)^2 + 8*(c^7*d - 3*c^5*d + 3*c^3*d - c*d)*b^3*x + 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*x + c + 1)^(3/2)*(d*x + c - 1)^(3/2) + (c^8 - 4*c^6 + 6*c^4 - 4*c^2 + 1)*b^3 + 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*x + c + 1)*(d*x + c - 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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)), x)","F",0
147,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{4} \sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4*sqrt(b*arccosh(d*x + c) + a), x)","F",0
155,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} \sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*sqrt(b*arccosh(d*x + c) + a), x)","F",0
156,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} \sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*sqrt(b*arccosh(d*x + c) + a), x)","F",0
157,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} \sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)*sqrt(b*arccosh(d*x + c) + a), x)","F",0
158,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(d*x + c) + a), x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(1/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}{d e x + c e}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(d*x + c) + a)/(d*e*x + c*e), x)","F",0
160,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
161,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
162,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
163,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(3/2), x)","F",0
164,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(3/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(3/2)/(d*e*x + c*e), x)","F",0
165,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
168,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(5/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(5/2)/(d*e*x + c*e), x)","F",0
170,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arccosh(d*x + c) + a)^(7/2), x)","F",0
171,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arccosh(d*x + c) + a)^(7/2), x)","F",0
172,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(7/2), x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^(7/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(7/2)/(d*e*x + c*e), x)","F",0
174,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/sqrt(b*arccosh(d*x + c) + a), x)","F",0
175,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/sqrt(b*arccosh(d*x + c) + a), x)","F",0
176,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/sqrt(b*arccosh(d*x + c) + a), x)","F",0
177,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/sqrt(b*arccosh(d*x + c) + a), x)","F",0
178,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arccosh(d*x + c) + a), x)","F",0
179,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} \sqrt{b \operatorname{arcosh}\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*sqrt(b*arccosh(d*x + c) + a)), x)","F",0
180,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
182,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arccosh(d*x + c) + a)^(3/2), x)","F",0
184,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(-3/2), x)","F",0
185,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arccosh(d*x + c) + a)^(3/2)), x)","F",0
186,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
187,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
188,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
189,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arccosh(d*x + c) + a)^(5/2), x)","F",0
190,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(-5/2), x)","F",0
191,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arccosh(d*x + c) + a)^(5/2)), x)","F",0
192,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arccosh(d*x + c) + a)^(7/2), x)","F",0
193,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arccosh(d*x + c) + a)^(7/2), x)","F",0
194,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arccosh(d*x + c) + a)^(7/2), x)","F",0
195,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arccosh(d*x + c) + a)^(7/2), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x + c) + a)^(-7/2), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arccosh(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \operatorname{arcosh}\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arccosh(d*x + c) + a)^(7/2)), x)","F",0
198,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{9}{2}} a}{9 \, d e} + \frac{1}{405} \, {\left(\frac{90 \, {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d} - \frac{20 \, {\left(d x + c\right)}^{\frac{9}{2}} e^{\frac{7}{2}} + 36 \, {\left(d x + c\right)}^{\frac{5}{2}} e^{\frac{7}{2}} + 45 i \, e^{\frac{7}{2}} {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)} - 45 \, e^{\frac{7}{2}} \log\left(\sqrt{d x + c} + 1\right) + 45 \, e^{\frac{7}{2}} \log\left(\sqrt{d x + c} - 1\right) + 180 \, \sqrt{d x + c} e^{\frac{7}{2}}}{d} + 405 \, \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(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c\right)}}\,{d x}\right)} b"," ",0,"2/9*(d*e*x + c*e)^(9/2)*a/(d*e) + 1/405*(90*(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/d - (20*(d*x + c)^(9/2)*e^(7/2) + 36*(d*x + c)^(5/2)*e^(7/2) + 45*I*e^(7/2)*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1)) - 45*e^(7/2)*log(sqrt(d*x + c) + 1) + 45*e^(7/2)*log(sqrt(d*x + c) - 1) + 180*sqrt(d*x + c)*e^(7/2))/d + 405*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 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x))*b","F",0
199,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d e x + c e\right)}^{\frac{7}{2}} a}{7 \, d e} + \frac{1}{147} \, {\left(\frac{42 \, {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d} - \frac{12 \, {\left(d x + c\right)}^{\frac{7}{2}} e^{\frac{5}{2}} + 28 \, {\left(d x + c\right)}^{\frac{3}{2}} e^{\frac{5}{2}} - 21 i \, e^{\frac{5}{2}} {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)} - 21 \, e^{\frac{5}{2}} \log\left(\sqrt{d x + c} + 1\right) + 21 \, e^{\frac{5}{2}} \log\left(\sqrt{d x + c} - 1\right)}{d} + 147 \, \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(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c\right)}}\,{d x}\right)} b"," ",0,"2/7*(d*e*x + c*e)^(7/2)*a/(d*e) + 1/147*(42*(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/d - (12*(d*x + c)^(7/2)*e^(5/2) + 28*(d*x + c)^(3/2)*e^(5/2) - 21*I*e^(5/2)*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1)) - 21*e^(5/2)*log(sqrt(d*x + c) + 1) + 21*e^(5/2)*log(sqrt(d*x + c) - 1))/d + 147*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 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x))*b","F",0
200,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\frac{1}{25} \, {\left(\frac{10 \, {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d} - \frac{4 \, {\left(d x + c\right)}^{\frac{5}{2}} e^{\frac{3}{2}} + 5 i \, e^{\frac{3}{2}} {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)} - 5 \, e^{\frac{3}{2}} \log\left(\sqrt{d x + c} + 1\right) + 5 \, e^{\frac{3}{2}} \log\left(\sqrt{d x + c} - 1\right) + 20 \, \sqrt{d x + c} e^{\frac{3}{2}}}{d} + 25 \, \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(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c\right)}}\,{d x}\right)} b + \frac{2 \, {\left(d e x + c e\right)}^{\frac{5}{2}} a}{5 \, d e}"," ",0,"1/25*(10*(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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/d - (4*(d*x + c)^(5/2)*e^(3/2) + 5*I*e^(3/2)*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1)) - 5*e^(3/2)*log(sqrt(d*x + c) + 1) + 5*e^(3/2)*log(sqrt(d*x + c) - 1) + 20*sqrt(d*x + c)*e^(3/2))/d + 25*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 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x))*b + 2/5*(d*e*x + c*e)^(5/2)*a/(d*e)","F",0
201,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))*(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{1}{9} \, {\left(\frac{6 \, {\left(d \sqrt{e} x + c \sqrt{e}\right)} \sqrt{d x + c} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d} - \frac{4 \, {\left(d x + c\right)}^{\frac{3}{2}} \sqrt{e} - 3 i \, \sqrt{e} {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)} - 3 \, \sqrt{e} \log\left(\sqrt{d x + c} + 1\right) + 3 \, \sqrt{e} \log\left(\sqrt{d x + c} - 1\right)}{d} + 9 \, \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(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c\right)}}\,{d x}\right)} b + \frac{2 \, {\left(d e x + c e\right)}^{\frac{3}{2}} a}{3 \, d e}"," ",0,"1/9*(6*(d*sqrt(e)*x + c*sqrt(e))*sqrt(d*x + c)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/d - (4*(d*x + c)^(3/2)*sqrt(e) - 3*I*sqrt(e)*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1)) - 3*sqrt(e)*log(sqrt(d*x + c) + 1) + 3*sqrt(e)*log(sqrt(d*x + c) - 1))/d + 9*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 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x))*b + 2/3*(d*e*x + c*e)^(3/2)*a/(d*e)","F",0
202,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","-b {\left(\frac{\frac{i \, {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)}}{\sqrt{e}} - \frac{\log\left(\sqrt{d x + c} + 1\right)}{\sqrt{e}} + \frac{\log\left(\sqrt{d x + c} - 1\right)}{\sqrt{e}} + \frac{4 \, \sqrt{d x + c}}{\sqrt{e}}}{d} - \frac{2 \, {\left(d \sqrt{e} x + c \sqrt{e}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{\sqrt{d x + c} d e} - \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 + {\left(d^{2} e x^{2} + 2 \, c d e x + c^{2} e - e\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} - c e + {\left(3 \, c^{2} d e - d e\right)} x\right)} \sqrt{d x + c}}\,{d x}\right)} + \frac{2 \, \sqrt{d e x + c e} a}{d e}"," ",0,"-b*((I*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1))/sqrt(e) - log(sqrt(d*x + c) + 1)/sqrt(e) + log(sqrt(d*x + c) - 1)/sqrt(e) + 4*sqrt(d*x + c)/sqrt(e))/d - 2*(d*sqrt(e)*x + c*sqrt(e))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(sqrt(d*x + c)*d*e) - integrate(2*(d*sqrt(e)*x + c*sqrt(e))/((d^3*e*x^3 + 3*c*d^2*e*x^2 + c^3*e + (d^2*e*x^2 + 2*c*d*e*x + c^2*e - e)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) - c*e + (3*c^2*d*e - d*e)*x)*sqrt(d*x + c)), x)) + 2*sqrt(d*e*x + c*e)*a/(d*e)","F",0
203,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","b {\left(\frac{-\frac{i \, {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)}}{e^{\frac{3}{2}}} - \frac{\log\left(\sqrt{d x + c} + 1\right)}{e^{\frac{3}{2}}} + \frac{\log\left(\sqrt{d x + c} - 1\right)}{e^{\frac{3}{2}}}}{d} - \frac{2 \, \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{\sqrt{d x + c} d e^{\frac{3}{2}}} - 2 \, \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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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,"b*((-I*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1))/e^(3/2) - log(sqrt(d*x + c) + 1)/e^(3/2) + log(sqrt(d*x + c) - 1)/e^(3/2))/d - 2*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(sqrt(d*x + c)*d*e^(3/2)) - 2*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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 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*x + c)), x)) - 2*a/(sqrt(d*e*x + c*e)*d*e)","F",0
204,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(6 \, \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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 2 \, {\left(2 \, c^{3} d e^{3} - c d e^{3}\right)} x\right)} \sqrt{d x + c}}\,{d x} + \frac{\sqrt{e} {\left(-\frac{i \, {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)}}{e^{3}} + \frac{\log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{\log\left(\sqrt{d x + c} - 1\right)}{e^{3}}\right)}}{d} + \frac{2 \, \sqrt{e} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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,"-1/3*(6*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 + (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*x + c + 1)*sqrt(d*x + c - 1) + 2*(2*c^3*d*e^3 - c*d*e^3)*x)*sqrt(d*x + c)), x) + sqrt(e)*(-I*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1))/e^3 + log(sqrt(d*x + c) + 1)/e^3 - log(sqrt(d*x + c) - 1)/e^3)/d + 2*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/((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
205,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{1}{5} \, {\left(10 \, \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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{4} - 3 \, c^{2} d e^{4}\right)} x\right)} \sqrt{d x + c}}\,{d x} + \frac{\sqrt{e} {\left(\frac{i \, {\left(\log\left(i \, \sqrt{d x + c} + 1\right) - \log\left(-i \, \sqrt{d x + c} + 1\right)\right)}}{e^{4}} + \frac{\log\left(\sqrt{d x + c} + 1\right)}{e^{4}} - \frac{\log\left(\sqrt{d x + c} - 1\right)}{e^{4}} - \frac{4}{\sqrt{d x + c} e^{4}}\right)}}{d} + \frac{2 \, \sqrt{e} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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,"-1/5*(10*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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^4 - 3*c^2*d*e^4)*x)*sqrt(d*x + c)), x) + sqrt(e)*(I*(log(I*sqrt(d*x + c) + 1) - log(-I*sqrt(d*x + c) + 1))/e^4 + log(sqrt(d*x + c) + 1)/e^4 - log(sqrt(d*x + c) - 1)/e^4 - 4/(sqrt(d*x + c)*e^4))/d + 2*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/((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
206,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{9 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
207,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{7 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
208,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
209,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
210,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 + 1} \sqrt{d x + c - 1} + 2 \, {\left(2 \, c^{3} d e - c d e\right)} x}\,{d x}"," ",0,"2*sqrt(d*x + c)*b^2*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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 + (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 + 1)*sqrt(d*x + c - 1) + 2*(2*c^3*d*e - c*d*e)*x), x)","F",0
211,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{\frac{3}{2}} - 3 \, c^{2} d e^{\frac{3}{2}}\right)} x}\,{d x}"," ",0,"-2*sqrt(d*x + c)*b^2*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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 + (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 + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^(3/2) - 3*c^2*d*e^(3/2))*x), x)","F",0
212,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 2 \, {\left(3 \, c^{5} d e^{\frac{5}{2}} - 2 \, c^{3} d e^{\frac{5}{2}}\right)} x\right)}}\,{d x}"," ",0,"-2/3*sqrt(d*x + c)*b^2*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + 2*(3*c^5*d*e^(5/2) - 2*c^3*d*e^(5/2))*x), x)","F",0
213,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(7 \, c^{6} d e^{\frac{7}{2}} - 5 \, c^{4} d e^{\frac{7}{2}}\right)} x\right)}}\,{d x}"," ",0,"-2/5*sqrt(d*x + c)*b^2*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (7*c^6*d*e^(7/2) - 5*c^4*d*e^(7/2))*x), x)","F",0
214,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)\right)}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
215,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - c}\,{d x}"," ",0,"2/3*(b^3*d*sqrt(e)*x + b^3*c*sqrt(e))*sqrt(d*x + c)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
216,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{3}}{\sqrt{d x + c} d e} + \int \frac{3 \, {\left({\left({\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(a b^{2} d^{3} \sqrt{e} - 2 \, b^{3} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(a b^{2} c d^{2} \sqrt{e} - 2 \, b^{3} c d^{2} \sqrt{e}\right)} x^{2} - {\left(2 \, b^{3} c^{2} \sqrt{e} - {\left(c^{2} \sqrt{e} - \sqrt{e}\right)} a 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 x + c + 1} \sqrt{d x + c - 1} + {\left({\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)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 \, 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 + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)\right)}}{{\left(d^{2} e x^{2} + 2 \, c d e x + c^{2} e - e\right)} \sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^3/(sqrt(d*x + c)*d*e) + integrate(3*(((c^3*sqrt(e) - c*sqrt(e))*a*b^2 - 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 + 3*(a*b^2*c*d^2*sqrt(e) - 2*b^3*c*d^2*sqrt(e))*x^2 - (2*b^3*c^2*sqrt(e) - (c^2*sqrt(e) - sqrt(e))*a*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*x + c + 1)*sqrt(d*x + c - 1) + ((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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 + (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 + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/((d^2*e*x^2 + 2*c*d*e*x + c^2*e - e)*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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
217,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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({\left(c^{3} - c\right)} a b^{2} + 2 \, {\left(c^{3} - c\right)} b^{3} + {\left(a b^{2} d^{3} + 2 \, b^{3} d^{3}\right)} x^{3} + 3 \, {\left(a b^{2} c d^{2} + 2 \, b^{3} c d^{2}\right)} x^{2} + {\left(2 \, b^{3} c^{2} + {\left(c^{2} - 1\right)} a 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 x + c + 1} \sqrt{d x + c - 1} + {\left({\left(3 \, c^{2} d - d\right)} a b^{2} + 2 \, {\left(3 \, c^{2} d - d\right)} b^{3}\right)} x\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)^{2} + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^3/(sqrt(d*x + c)*d*e^(3/2)) - 2*a^3/(sqrt(d*e*x + c*e)*d*e) + integrate(3*(((c^3 - c)*a*b^2 + 2*(c^3 - c)*b^3 + (a*b^2*d^3 + 2*b^3*d^3)*x^3 + 3*(a*b^2*c*d^2 + 2*b^3*c*d^2)*x^2 + (2*b^3*c^2 + (c^2 - 1)*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*x + c + 1)*sqrt(d*x + c - 1) + ((3*c^2*d - d)*a*b^2 + 2*(3*c^2*d - d)*b^3)*x)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + 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 + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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
218,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \sqrt{e} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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(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 x + c + 1} \sqrt{d x + c - 1} + {\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)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 \, 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 + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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(((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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 + 3*(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 + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/((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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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
219,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x+c))^3/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, b^{3} \sqrt{e} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(5 \, {\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(5 \, a b^{2} d^{3} \sqrt{e} + 2 \, b^{3} d^{3} \sqrt{e}\right)} x^{3} + 3 \, {\left(5 \, a b^{2} c d^{2} \sqrt{e} + 2 \, b^{3} c d^{2} \sqrt{e}\right)} x^{2} + {\left(2 \, b^{3} c^{2} \sqrt{e} + 5 \, {\left(c^{2} \sqrt{e} - \sqrt{e}\right)} a 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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, {\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)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 \, 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 + {\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 x + c + 1} \sqrt{d x + c - 1}\right)} \log\left(d x + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*((5*(c^3*sqrt(e) - c*sqrt(e))*a*b^2 + 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 + 3*(5*a*b^2*c*d^2*sqrt(e) + 2*b^3*c*d^2*sqrt(e))*x^2 + (2*b^3*c^2*sqrt(e) + 5*(c^2*sqrt(e) - sqrt(e))*a*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*x + c + 1)*sqrt(d*x + c - 1) + (5*(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)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 + 5*(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 + (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*x + c + 1)*sqrt(d*x + c - 1))*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/((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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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
220,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)\right)}}{5 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
221,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\right)\right)}}{3 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)} \sqrt{d x + c + 1} \sqrt{d x + c - 1} + {\left(3 \, c^{2} d - d\right)} x - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (d^2*x^2 + 2*c*d*x + c^2 - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + (3*c^2*d - d)*x - c), x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} - {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 x + c + 1} \sqrt{d x + c - 1} + 2 \, {\left(2 \, c^{3} d \sqrt{e} - c d \sqrt{e}\right)} x}\,{d x}"," ",0,"2*sqrt(d*x + c)*b^4*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) - ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^2 - 2*((a^3*b*d^2*x^2 + 2*a^3*b*c*d*x + (c^2 - 1)*a^3*b)*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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) + (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*x + c + 1)*sqrt(d*x + c - 1) + 2*(2*c^3*d*sqrt(e) - c*d*sqrt(e))*x), x)","F",0
223,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 x + c + 1} \sqrt{d x + c - 1} + {\left(5 \, c^{4} d e^{2} - 3 \, c^{2} d e^{2}\right)} x}\,{d x}"," ",0,"-2*sqrt(d*x + c)*b^4*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + ((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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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 + (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*x + c + 1)*sqrt(d*x + c - 1) + (5*c^4*d*e^2 - 3*c^2*d*e^2)*x), x)","F",0
224,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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} + {\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 + 1} \sqrt{d x + c - 1} + 2 \, {\left(3 \, c^{5} d e^{3} - 2 \, c^{3} d e^{3}\right)} x\right)}}\,{d x}"," ",0,"-2/3*sqrt(d*x + c)*b^4*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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 + (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 + 1)*sqrt(d*x + c - 1) + 2*(3*c^5*d*e^3 - 2*c^3*d*e^3)*x), x)","F",0
225,0,0,0,0.000000," ","integrate((a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c} \sqrt{d x + c - 1} + {\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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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(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 + 1} \sqrt{d x + c - 1} + {\left(7 \, c^{6} d e^{4} - 5 \, c^{4} d e^{4}\right)} x\right)}}\,{d x}"," ",0,"-2/5*sqrt(d*x + c)*b^4*sqrt(e)*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c)*sqrt(d*x + c - 1) + (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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(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 + (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 + 1)*sqrt(d*x + c - 1) + (7*c^6*d*e^4 - 5*c^4*d*e^4)*x), x)","F",0
226,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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)} + {\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 x + c + 1} \sqrt{d x + c - 1} - c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} - d {\left(m + 1\right)}\right)} x}\,{d x}"," ",0,"(b^4*d*e^m*x + b^4*c*e^m)*(d*x + c)^m*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) - m - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) - c*(m + 1) + (3*c^2*d*(m + 1) - d*(m + 1))*x), x)","F",0
227,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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)} + {\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 x + c + 1} \sqrt{d x + c - 1} - c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} - d {\left(m + 1\right)}\right)} x}\,{d x}"," ",0,"(b^3*d*e^m*x + b^3*c*e^m)*(d*x + c)^m*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c))/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) - m - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) - c*(m + 1) + (3*c^2*d*(m + 1) - d*(m + 1))*x), x)","F",0
228,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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 x + c + 1} \sqrt{d x + c - 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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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)} + {\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 x + c + 1} \sqrt{d x + c - 1} - c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} - d {\left(m + 1\right)}\right)} x}\,{d x}"," ",0,"(b^2*d*e^m*x + b^2*c*e^m)*(d*x + c)^m*log(d*x + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)^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*x + c + 1)*sqrt(d*x + c - 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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(d^3*(m + 1)*x^3 + 3*c*d^2*(m + 1)*x^2 + c^3*(m + 1) + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) - m - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) - c*(m + 1) + (3*c^2*d*(m + 1) - d*(m + 1))*x), x)","F",0
229,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arccosh(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 + \sqrt{d x + c + 1} \sqrt{d x + c - 1} + c\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)} + {\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 x + c + 1} \sqrt{d x + c - 1} - c {\left(m + 1\right)} + {\left(3 \, c^{2} d {\left(m + 1\right)} - d {\left(m + 1\right)}\right)} x}\,{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 + sqrt(d*x + c + 1)*sqrt(d*x + c - 1) + c)/(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) + (d^2*(m + 1)*x^2 + 2*c*d*(m + 1)*x + c^2*(m + 1) - m - 1)*sqrt(d*x + c + 1)*sqrt(d*x + c - 1) - c*(m + 1) + (3*c^2*d*(m + 1) - d*(m + 1))*x), x)) + (d*e*x + c*e)^(m + 1)*a/(d*e*(m + 1))","F",0
230,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m/(a+b*arccosh(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{m}}{b \operatorname{arcosh}\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^m/(b*arccosh(d*x + c) + a), x)","F",0
231,0,0,0,0.000000," ","integrate(arccosh(a*x^5)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arccosh(a*x^5)/x, x)","F",0
232,1,56,0,0.504503," ","integrate(x^2*arccosh(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcosh}\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} \, \log\left(2 \, \sqrt{x - 1} + 2 \, \sqrt{x}\right)"," ",0,"1/3*x^3*arccosh(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*log(2*sqrt(x - 1) + 2*sqrt(x))","A",0
233,1,46,0,0.376953," ","integrate(x*arccosh(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcosh}\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} \, \log\left(2 \, \sqrt{x - 1} + 2 \, \sqrt{x}\right)"," ",0,"1/2*x^2*arccosh(sqrt(x)) - 1/8*sqrt(x - 1)*x^(3/2) - 3/16*sqrt(x - 1)*sqrt(x) - 3/16*log(2*sqrt(x - 1) + 2*sqrt(x))","A",0
234,1,33,0,0.619807," ","integrate(arccosh(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arcosh}\left(\sqrt{x}\right) - \frac{1}{2} \, \sqrt{x - 1} \sqrt{x} - \frac{1}{2} \, \log\left(2 \, \sqrt{x - 1} + 2 \, \sqrt{x}\right)"," ",0,"x*arccosh(sqrt(x)) - 1/2*sqrt(x - 1)*sqrt(x) - 1/2*log(2*sqrt(x - 1) + 2*sqrt(x))","A",0
235,0,0,0,0.000000," ","integrate(arccosh(x^(1/2))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arccosh(sqrt(x))/x, x)","F",0
236,1,19,0,1.300447," ","integrate(arccosh(x^(1/2))/x^2,x, algorithm=""maxima"")","\frac{\sqrt{x - 1}}{\sqrt{x}} - \frac{\operatorname{arcosh}\left(\sqrt{x}\right)}{x}"," ",0,"sqrt(x - 1)/sqrt(x) - arccosh(sqrt(x))/x","A",0
237,1,30,0,0.805443," ","integrate(arccosh(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{arcosh}\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*arccosh(sqrt(x))/x^2","A",0
238,1,17,0,0.799081," ","integrate(arccosh(1/x),x, algorithm=""maxima"")","x \operatorname{arcosh}\left(\frac{1}{x}\right) - \arctan\left(\sqrt{\frac{1}{x^{2}} - 1}\right)"," ",0,"x*arccosh(1/x) - arctan(sqrt(1/x^2 - 1))","B",0
239,0,0,0,0.000000," ","integrate(arccosh(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 x^{n} + 1} \sqrt{a x^{n} - 1}}\,{d x} - \frac{1}{2} \, n \log\left(x\right)^{2} + n \int \frac{\log\left(x\right)}{2 \, {\left(a x x^{n} + x\right)}}\,{d x} - n \int \frac{\log\left(x\right)}{2 \, {\left(a x x^{n} - x\right)}}\,{d x} + \log\left(a x^{n} + \sqrt{a x^{n} + 1} \sqrt{a x^{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*x^n + 1)*sqrt(a*x^n - 1)), x) - 1/2*n*log(x)^2 + n*integrate(1/2*log(x)/(a*x*x^n + x), x) - n*integrate(1/2*log(x)/(a*x*x^n - x), x) + log(a*x^n + sqrt(a*x^n + 1)*sqrt(a*x^n - 1))*log(x)","F",0
240,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2+1))^4,x, algorithm=""maxima"")","b^{4} x \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right)^{4} + 6 \, a^{2} b^{2} x \operatorname{arcosh}\left(d x^{2} + 1\right)^{2} + 24 \, a^{2} b^{2} d {\left(\frac{2 \, x}{d} - \frac{{\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d x^{2}} + 1\right)}{\sqrt{d x^{2} + 2} d^{2}}\right)} + 4 \, {\left(x \operatorname{arcosh}\left(d x^{2} + 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2} d}\right)} a^{3} b + a^{4} x + \int \frac{4 \, {\left({\left(a b^{3} d^{2} - 2 \, b^{4} d^{2}\right)} x^{4} + 2 \, a b^{3} + {\left(3 \, a b^{3} d - 4 \, b^{4} d\right)} x^{2} + {\left({\left(a b^{3} d - 2 \, b^{4} d\right)} \sqrt{d} x^{3} + 2 \, {\left(a b^{3} - b^{4}\right)} \sqrt{d} x\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right)^{3}}{d^{2} x^{4} + 3 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2} + 2}\,{d x}"," ",0,"b^4*x*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1)^4 + 6*a^2*b^2*x*arccosh(d*x^2 + 1)^2 + 24*a^2*b^2*d*(2*x/d - (d^(3/2)*x^2 + 2*sqrt(d))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d*x^2) + 1)/(sqrt(d*x^2 + 2)*d^2)) + 4*(x*arccosh(d*x^2 + 1) - 2*(d^(3/2)*x^2 + 2*sqrt(d))/(sqrt(d*x^2 + 2)*d))*a^3*b + a^4*x + integrate(4*((a*b^3*d^2 - 2*b^4*d^2)*x^4 + 2*a*b^3 + (3*a*b^3*d - 4*b^4*d)*x^2 + ((a*b^3*d - 2*b^4*d)*sqrt(d)*x^3 + 2*(a*b^3 - b^4)*sqrt(d)*x)*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1)^3/(d^2*x^4 + 3*d*x^2 + (d^(3/2)*x^3 + 2*sqrt(d)*x)*sqrt(d*x^2 + 2) + 2), x)","F",0
241,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2+1))^3,x, algorithm=""maxima"")","3 \, a b^{2} x \operatorname{arcosh}\left(d x^{2} + 1\right)^{2} + 12 \, a b^{2} d {\left(\frac{2 \, x}{d} - \frac{{\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d x^{2}} + 1\right)}{\sqrt{d x^{2} + 2} d^{2}}\right)} + 3 \, {\left(x \operatorname{arcosh}\left(d x^{2} + 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2} d}\right)} a^{2} b + {\left(x \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right)^{3} - \int \frac{6 \, {\left(d^{2} x^{4} + 2 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + \sqrt{d} x\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right)^{2}}{d^{2} x^{4} + 3 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2} + 2}\,{d x}\right)} b^{3} + a^{3} x"," ",0,"3*a*b^2*x*arccosh(d*x^2 + 1)^2 + 12*a*b^2*d*(2*x/d - (d^(3/2)*x^2 + 2*sqrt(d))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d*x^2) + 1)/(sqrt(d*x^2 + 2)*d^2)) + 3*(x*arccosh(d*x^2 + 1) - 2*(d^(3/2)*x^2 + 2*sqrt(d))/(sqrt(d*x^2 + 2)*d))*a^2*b + (x*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1)^3 - integrate(6*(d^2*x^4 + 2*d*x^2 + (d^(3/2)*x^3 + sqrt(d)*x)*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1)^2/(d^2*x^4 + 3*d*x^2 + (d^(3/2)*x^3 + 2*sqrt(d)*x)*sqrt(d*x^2 + 2) + 2), x))*b^3 + a^3*x","F",0
242,1,128,0,0.744115," ","integrate((a+b*arccosh(d*x^2+1))^2,x, algorithm=""maxima"")","b^{2} x \operatorname{arcosh}\left(d x^{2} + 1\right)^{2} + 4 \, b^{2} d {\left(\frac{2 \, x}{d} - \frac{{\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d x^{2}} + 1\right)}{\sqrt{d x^{2} + 2} d^{2}}\right)} + 2 \, {\left(x \operatorname{arcosh}\left(d x^{2} + 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2} d}\right)} a b + a^{2} x"," ",0,"b^2*x*arccosh(d*x^2 + 1)^2 + 4*b^2*d*(2*x/d - (d^(3/2)*x^2 + 2*sqrt(d))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d*x^2) + 1)/(sqrt(d*x^2 + 2)*d^2)) + 2*(x*arccosh(d*x^2 + 1) - 2*(d^(3/2)*x^2 + 2*sqrt(d))/(sqrt(d*x^2 + 2)*d))*a*b + a^2*x","A",0
243,1,44,0,0.948777," ","integrate(a+b*arccosh(d*x^2+1),x, algorithm=""maxima"")","{\left(x \operatorname{arcosh}\left(d x^{2} + 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} + 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} + 2} d}\right)} b + a x"," ",0,"(x*arccosh(d*x^2 + 1) - 2*(d^(3/2)*x^2 + 2*sqrt(d))/(sqrt(d*x^2 + 2)*d))*b + a*x","A",0
244,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arcosh}\left(d x^{2} + 1\right) + a}\,{d x}"," ",0,"integrate(1/(b*arccosh(d*x^2 + 1) + a), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1))^2,x, algorithm=""maxima"")","-\frac{d^{2} x^{4} + 3 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} + 2 \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2} + 2}{2 \, {\left(a b d^{2} x^{3} + 2 \, a b d x + {\left(b^{2} d^{2} x^{3} + 2 \, b^{2} d x + {\left(b^{2} d^{\frac{3}{2}} x^{2} + b^{2} \sqrt{d}\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right) + {\left(a b d^{\frac{3}{2}} x^{2} + a b \sqrt{d}\right)} \sqrt{d x^{2} + 2}\right)}} + \int \frac{d^{3} x^{6} + 3 \, d^{2} x^{4} + {\left(d^{2} x^{4} + d x^{2} + 2\right)} {\left(d x^{2} + 2\right)} + {\left(2 \, d^{\frac{5}{2}} x^{5} + 4 \, d^{\frac{3}{2}} x^{3} + \sqrt{d} x\right)} \sqrt{d x^{2} + 2} - 4}{2 \, {\left(a b d^{3} x^{6} + 4 \, a b d^{2} x^{4} + 4 \, a b d x^{2} + {\left(a b d^{2} x^{4} + 2 \, a b d x^{2} + a b\right)} {\left(d x^{2} + 2\right)} + {\left(b^{2} d^{3} x^{6} + 4 \, b^{2} d^{2} x^{4} + 4 \, b^{2} d x^{2} + {\left(b^{2} d^{2} x^{4} + 2 \, b^{2} d x^{2} + b^{2}\right)} {\left(d x^{2} + 2\right)} + 2 \, {\left(b^{2} d^{\frac{5}{2}} x^{5} + 3 \, b^{2} d^{\frac{3}{2}} x^{3} + 2 \, b^{2} \sqrt{d} x\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right) + 2 \, {\left(a b d^{\frac{5}{2}} x^{5} + 3 \, a b d^{\frac{3}{2}} x^{3} + 2 \, a b \sqrt{d} x\right)} \sqrt{d x^{2} + 2}\right)}}\,{d x}"," ",0,"-1/2*(d^2*x^4 + 3*d*x^2 + (d^(3/2)*x^3 + 2*sqrt(d)*x)*sqrt(d*x^2 + 2) + 2)/(a*b*d^2*x^3 + 2*a*b*d*x + (b^2*d^2*x^3 + 2*b^2*d*x + (b^2*d^(3/2)*x^2 + b^2*sqrt(d))*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1) + (a*b*d^(3/2)*x^2 + a*b*sqrt(d))*sqrt(d*x^2 + 2)) + integrate(1/2*(d^3*x^6 + 3*d^2*x^4 + (d^2*x^4 + d*x^2 + 2)*(d*x^2 + 2) + (2*d^(5/2)*x^5 + 4*d^(3/2)*x^3 + sqrt(d)*x)*sqrt(d*x^2 + 2) - 4)/(a*b*d^3*x^6 + 4*a*b*d^2*x^4 + 4*a*b*d*x^2 + (a*b*d^2*x^4 + 2*a*b*d*x^2 + a*b)*(d*x^2 + 2) + (b^2*d^3*x^6 + 4*b^2*d^2*x^4 + 4*b^2*d*x^2 + (b^2*d^2*x^4 + 2*b^2*d*x^2 + b^2)*(d*x^2 + 2) + 2*(b^2*d^(5/2)*x^5 + 3*b^2*d^(3/2)*x^3 + 2*b^2*sqrt(d)*x)*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1) + 2*(a*b*d^(5/2)*x^5 + 3*a*b*d^(3/2)*x^3 + 2*a*b*sqrt(d)*x)*sqrt(d*x^2 + 2)), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1))^3,x, algorithm=""maxima"")","-\frac{{\left(a d^{5} + 2 \, b d^{5}\right)} \sqrt{d} x^{10} + 2 \, {\left(3 \, a d^{4} + 7 \, b d^{4}\right)} \sqrt{d} x^{8} + {\left(11 \, a d^{3} + 36 \, b d^{3}\right)} \sqrt{d} x^{6} + 2 \, {\left(a d^{2} + 20 \, b d^{2}\right)} \sqrt{d} x^{4} - 4 \, {\left(3 \, a d - 4 \, b d\right)} \sqrt{d} x^{2} + {\left({\left(a d^{4} + 2 \, b d^{4}\right)} x^{7} + {\left(3 \, a d^{3} + 8 \, b d^{3}\right)} x^{5} + 2 \, {\left(2 \, a d^{2} + 5 \, b d^{2}\right)} x^{3} + 4 \, {\left(a d + b d\right)} x\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + {\left(3 \, {\left(a d^{4} + 2 \, b d^{4}\right)} \sqrt{d} x^{8} + 6 \, {\left(2 \, a d^{3} + 5 \, b d^{3}\right)} \sqrt{d} x^{6} + 2 \, {\left(8 \, a d^{2} + 25 \, b d^{2}\right)} \sqrt{d} x^{4} + 10 \, {\left(a d + 3 \, b d\right)} \sqrt{d} x^{2} + 4 \, {\left(a + b\right)} \sqrt{d}\right)} {\left(d x^{2} + 2\right)} + {\left(b d^{\frac{11}{2}} x^{10} + 6 \, b d^{\frac{9}{2}} x^{8} + 11 \, b d^{\frac{7}{2}} x^{6} + 2 \, b d^{\frac{5}{2}} x^{4} - 12 \, b d^{\frac{3}{2}} x^{2} + {\left(b d^{4} x^{7} + 3 \, b d^{3} x^{5} + 4 \, b d^{2} x^{3} + 4 \, b d x\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + {\left(3 \, b d^{\frac{9}{2}} x^{8} + 12 \, b d^{\frac{7}{2}} x^{6} + 16 \, b d^{\frac{5}{2}} x^{4} + 10 \, b d^{\frac{3}{2}} x^{2} + 4 \, b \sqrt{d}\right)} {\left(d x^{2} + 2\right)} + {\left(3 \, b d^{5} x^{9} + 15 \, b d^{4} x^{7} + 23 \, b d^{3} x^{5} + 7 \, b d^{2} x^{3} - 6 \, b d x\right)} \sqrt{d x^{2} + 2} - 8 \, b \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right) + {\left(3 \, {\left(a d^{5} + 2 \, b d^{5}\right)} x^{9} + 3 \, {\left(5 \, a d^{4} + 12 \, b d^{4}\right)} x^{7} + {\left(23 \, a d^{3} + 76 \, b d^{3}\right)} x^{5} + {\left(7 \, a d^{2} + 64 \, b d^{2}\right)} x^{3} - 2 \, {\left(3 \, a d - 8 \, b d\right)} x\right)} \sqrt{d x^{2} + 2} - 8 \, a \sqrt{d}}{8 \, {\left(a^{2} b^{2} d^{\frac{11}{2}} x^{9} + 6 \, a^{2} b^{2} d^{\frac{9}{2}} x^{7} + 12 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} + 8 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} + {\left(b^{4} d^{\frac{11}{2}} x^{9} + 6 \, b^{4} d^{\frac{9}{2}} x^{7} + 12 \, b^{4} d^{\frac{7}{2}} x^{5} + 8 \, b^{4} d^{\frac{5}{2}} x^{3} + {\left(b^{4} d^{4} x^{6} + 3 \, b^{4} d^{3} x^{4} + 3 \, b^{4} d^{2} x^{2} + b^{4} d\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{\frac{9}{2}} x^{7} + 4 \, b^{4} d^{\frac{7}{2}} x^{5} + 5 \, b^{4} d^{\frac{5}{2}} x^{3} + 2 \, b^{4} d^{\frac{3}{2}} x\right)} {\left(d x^{2} + 2\right)} + 3 \, {\left(b^{4} d^{5} x^{8} + 5 \, b^{4} d^{4} x^{6} + 8 \, b^{4} d^{3} x^{4} + 4 \, b^{4} d^{2} x^{2}\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{6} + 3 \, a^{2} b^{2} d^{3} x^{4} + 3 \, a^{2} b^{2} d^{2} x^{2} + a^{2} b^{2} d\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{\frac{9}{2}} x^{7} + 4 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} + 5 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} + 2 \, a^{2} b^{2} d^{\frac{3}{2}} x\right)} {\left(d x^{2} + 2\right)} + 2 \, {\left(a b^{3} d^{\frac{11}{2}} x^{9} + 6 \, a b^{3} d^{\frac{9}{2}} x^{7} + 12 \, a b^{3} d^{\frac{7}{2}} x^{5} + 8 \, a b^{3} d^{\frac{5}{2}} x^{3} + {\left(a b^{3} d^{4} x^{6} + 3 \, a b^{3} d^{3} x^{4} + 3 \, a b^{3} d^{2} x^{2} + a b^{3} d\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{\frac{9}{2}} x^{7} + 4 \, a b^{3} d^{\frac{7}{2}} x^{5} + 5 \, a b^{3} d^{\frac{5}{2}} x^{3} + 2 \, a b^{3} d^{\frac{3}{2}} x\right)} {\left(d x^{2} + 2\right)} + 3 \, {\left(a b^{3} d^{5} x^{8} + 5 \, a b^{3} d^{4} x^{6} + 8 \, a b^{3} d^{3} x^{4} + 4 \, a b^{3} d^{2} x^{2}\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right) + 3 \, {\left(a^{2} b^{2} d^{5} x^{8} + 5 \, a^{2} b^{2} d^{4} x^{6} + 8 \, a^{2} b^{2} d^{3} x^{4} + 4 \, a^{2} b^{2} d^{2} x^{2}\right)} \sqrt{d x^{2} + 2}\right)}} + \int \frac{d^{6} x^{12} + 8 \, d^{5} x^{10} + 27 \, d^{4} x^{8} + 56 \, d^{3} x^{6} + 88 \, d^{2} x^{4} + {\left(d^{4} x^{8} + 4 \, d^{3} x^{6} + 3 \, d^{2} x^{4} - 8 \, d x^{2} + 4\right)} {\left(d x^{2} + 2\right)}^{2} + 96 \, d x^{2} + 2 \, {\left(2 \, d^{\frac{9}{2}} x^{9} + 10 \, d^{\frac{7}{2}} x^{7} + 15 \, d^{\frac{5}{2}} x^{5} - d^{\frac{3}{2}} x^{3} - 11 \, \sqrt{d} x\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + 3 \, {\left(2 \, d^{5} x^{10} + 12 \, d^{4} x^{8} + 26 \, d^{3} x^{6} + 24 \, d^{2} x^{4} + 3 \, d x^{2} - 10\right)} {\left(d x^{2} + 2\right)} + 2 \, {\left(2 \, d^{\frac{11}{2}} x^{11} + 14 \, d^{\frac{9}{2}} x^{9} + 39 \, d^{\frac{7}{2}} x^{7} + 61 \, d^{\frac{5}{2}} x^{5} + 61 \, d^{\frac{3}{2}} x^{3} + 30 \, \sqrt{d} x\right)} \sqrt{d x^{2} + 2} + 48}{8 \, {\left(a b^{2} d^{6} x^{12} + 8 \, a b^{2} d^{5} x^{10} + 24 \, a b^{2} d^{4} x^{8} + 32 \, a b^{2} d^{3} x^{6} + 16 \, a b^{2} d^{2} x^{4} + {\left(a b^{2} d^{4} x^{8} + 4 \, a b^{2} d^{3} x^{6} + 6 \, a b^{2} d^{2} x^{4} + 4 \, a b^{2} d x^{2} + a b^{2}\right)} {\left(d x^{2} + 2\right)}^{2} + 4 \, {\left(a b^{2} d^{\frac{9}{2}} x^{9} + 5 \, a b^{2} d^{\frac{7}{2}} x^{7} + 9 \, a b^{2} d^{\frac{5}{2}} x^{5} + 7 \, a b^{2} d^{\frac{3}{2}} x^{3} + 2 \, a b^{2} \sqrt{d} x\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{5} x^{10} + 6 \, a b^{2} d^{4} x^{8} + 13 \, a b^{2} d^{3} x^{6} + 12 \, a b^{2} d^{2} x^{4} + 4 \, a b^{2} d x^{2}\right)} {\left(d x^{2} + 2\right)} + {\left(b^{3} d^{6} x^{12} + 8 \, b^{3} d^{5} x^{10} + 24 \, b^{3} d^{4} x^{8} + 32 \, b^{3} d^{3} x^{6} + 16 \, b^{3} d^{2} x^{4} + {\left(b^{3} d^{4} x^{8} + 4 \, b^{3} d^{3} x^{6} + 6 \, b^{3} d^{2} x^{4} + 4 \, b^{3} d x^{2} + b^{3}\right)} {\left(d x^{2} + 2\right)}^{2} + 4 \, {\left(b^{3} d^{\frac{9}{2}} x^{9} + 5 \, b^{3} d^{\frac{7}{2}} x^{7} + 9 \, b^{3} d^{\frac{5}{2}} x^{5} + 7 \, b^{3} d^{\frac{3}{2}} x^{3} + 2 \, b^{3} \sqrt{d} x\right)} {\left(d x^{2} + 2\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{5} x^{10} + 6 \, b^{3} d^{4} x^{8} + 13 \, b^{3} d^{3} x^{6} + 12 \, b^{3} d^{2} x^{4} + 4 \, b^{3} d x^{2}\right)} {\left(d x^{2} + 2\right)} + 4 \, {\left(b^{3} d^{\frac{11}{2}} x^{11} + 7 \, b^{3} d^{\frac{9}{2}} x^{9} + 18 \, b^{3} d^{\frac{7}{2}} x^{7} + 20 \, b^{3} d^{\frac{5}{2}} x^{5} + 8 \, b^{3} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} + 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} + 2} \sqrt{d} x + 1\right) + 4 \, {\left(a b^{2} d^{\frac{11}{2}} x^{11} + 7 \, a b^{2} d^{\frac{9}{2}} x^{9} + 18 \, a b^{2} d^{\frac{7}{2}} x^{7} + 20 \, a b^{2} d^{\frac{5}{2}} x^{5} + 8 \, a b^{2} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} + 2}\right)}}\,{d x}"," ",0,"-1/8*((a*d^5 + 2*b*d^5)*sqrt(d)*x^10 + 2*(3*a*d^4 + 7*b*d^4)*sqrt(d)*x^8 + (11*a*d^3 + 36*b*d^3)*sqrt(d)*x^6 + 2*(a*d^2 + 20*b*d^2)*sqrt(d)*x^4 - 4*(3*a*d - 4*b*d)*sqrt(d)*x^2 + ((a*d^4 + 2*b*d^4)*x^7 + (3*a*d^3 + 8*b*d^3)*x^5 + 2*(2*a*d^2 + 5*b*d^2)*x^3 + 4*(a*d + b*d)*x)*(d*x^2 + 2)^(3/2) + (3*(a*d^4 + 2*b*d^4)*sqrt(d)*x^8 + 6*(2*a*d^3 + 5*b*d^3)*sqrt(d)*x^6 + 2*(8*a*d^2 + 25*b*d^2)*sqrt(d)*x^4 + 10*(a*d + 3*b*d)*sqrt(d)*x^2 + 4*(a + b)*sqrt(d))*(d*x^2 + 2) + (b*d^(11/2)*x^10 + 6*b*d^(9/2)*x^8 + 11*b*d^(7/2)*x^6 + 2*b*d^(5/2)*x^4 - 12*b*d^(3/2)*x^2 + (b*d^4*x^7 + 3*b*d^3*x^5 + 4*b*d^2*x^3 + 4*b*d*x)*(d*x^2 + 2)^(3/2) + (3*b*d^(9/2)*x^8 + 12*b*d^(7/2)*x^6 + 16*b*d^(5/2)*x^4 + 10*b*d^(3/2)*x^2 + 4*b*sqrt(d))*(d*x^2 + 2) + (3*b*d^5*x^9 + 15*b*d^4*x^7 + 23*b*d^3*x^5 + 7*b*d^2*x^3 - 6*b*d*x)*sqrt(d*x^2 + 2) - 8*b*sqrt(d))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1) + (3*(a*d^5 + 2*b*d^5)*x^9 + 3*(5*a*d^4 + 12*b*d^4)*x^7 + (23*a*d^3 + 76*b*d^3)*x^5 + (7*a*d^2 + 64*b*d^2)*x^3 - 2*(3*a*d - 8*b*d)*x)*sqrt(d*x^2 + 2) - 8*a*sqrt(d))/(a^2*b^2*d^(11/2)*x^9 + 6*a^2*b^2*d^(9/2)*x^7 + 12*a^2*b^2*d^(7/2)*x^5 + 8*a^2*b^2*d^(5/2)*x^3 + (b^4*d^(11/2)*x^9 + 6*b^4*d^(9/2)*x^7 + 12*b^4*d^(7/2)*x^5 + 8*b^4*d^(5/2)*x^3 + (b^4*d^4*x^6 + 3*b^4*d^3*x^4 + 3*b^4*d^2*x^2 + b^4*d)*(d*x^2 + 2)^(3/2) + 3*(b^4*d^(9/2)*x^7 + 4*b^4*d^(7/2)*x^5 + 5*b^4*d^(5/2)*x^3 + 2*b^4*d^(3/2)*x)*(d*x^2 + 2) + 3*(b^4*d^5*x^8 + 5*b^4*d^4*x^6 + 8*b^4*d^3*x^4 + 4*b^4*d^2*x^2)*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1)^2 + (a^2*b^2*d^4*x^6 + 3*a^2*b^2*d^3*x^4 + 3*a^2*b^2*d^2*x^2 + a^2*b^2*d)*(d*x^2 + 2)^(3/2) + 3*(a^2*b^2*d^(9/2)*x^7 + 4*a^2*b^2*d^(7/2)*x^5 + 5*a^2*b^2*d^(5/2)*x^3 + 2*a^2*b^2*d^(3/2)*x)*(d*x^2 + 2) + 2*(a*b^3*d^(11/2)*x^9 + 6*a*b^3*d^(9/2)*x^7 + 12*a*b^3*d^(7/2)*x^5 + 8*a*b^3*d^(5/2)*x^3 + (a*b^3*d^4*x^6 + 3*a*b^3*d^3*x^4 + 3*a*b^3*d^2*x^2 + a*b^3*d)*(d*x^2 + 2)^(3/2) + 3*(a*b^3*d^(9/2)*x^7 + 4*a*b^3*d^(7/2)*x^5 + 5*a*b^3*d^(5/2)*x^3 + 2*a*b^3*d^(3/2)*x)*(d*x^2 + 2) + 3*(a*b^3*d^5*x^8 + 5*a*b^3*d^4*x^6 + 8*a*b^3*d^3*x^4 + 4*a*b^3*d^2*x^2)*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1) + 3*(a^2*b^2*d^5*x^8 + 5*a^2*b^2*d^4*x^6 + 8*a^2*b^2*d^3*x^4 + 4*a^2*b^2*d^2*x^2)*sqrt(d*x^2 + 2)) + integrate(1/8*(d^6*x^12 + 8*d^5*x^10 + 27*d^4*x^8 + 56*d^3*x^6 + 88*d^2*x^4 + (d^4*x^8 + 4*d^3*x^6 + 3*d^2*x^4 - 8*d*x^2 + 4)*(d*x^2 + 2)^2 + 96*d*x^2 + 2*(2*d^(9/2)*x^9 + 10*d^(7/2)*x^7 + 15*d^(5/2)*x^5 - d^(3/2)*x^3 - 11*sqrt(d)*x)*(d*x^2 + 2)^(3/2) + 3*(2*d^5*x^10 + 12*d^4*x^8 + 26*d^3*x^6 + 24*d^2*x^4 + 3*d*x^2 - 10)*(d*x^2 + 2) + 2*(2*d^(11/2)*x^11 + 14*d^(9/2)*x^9 + 39*d^(7/2)*x^7 + 61*d^(5/2)*x^5 + 61*d^(3/2)*x^3 + 30*sqrt(d)*x)*sqrt(d*x^2 + 2) + 48)/(a*b^2*d^6*x^12 + 8*a*b^2*d^5*x^10 + 24*a*b^2*d^4*x^8 + 32*a*b^2*d^3*x^6 + 16*a*b^2*d^2*x^4 + (a*b^2*d^4*x^8 + 4*a*b^2*d^3*x^6 + 6*a*b^2*d^2*x^4 + 4*a*b^2*d*x^2 + a*b^2)*(d*x^2 + 2)^2 + 4*(a*b^2*d^(9/2)*x^9 + 5*a*b^2*d^(7/2)*x^7 + 9*a*b^2*d^(5/2)*x^5 + 7*a*b^2*d^(3/2)*x^3 + 2*a*b^2*sqrt(d)*x)*(d*x^2 + 2)^(3/2) + 6*(a*b^2*d^5*x^10 + 6*a*b^2*d^4*x^8 + 13*a*b^2*d^3*x^6 + 12*a*b^2*d^2*x^4 + 4*a*b^2*d*x^2)*(d*x^2 + 2) + (b^3*d^6*x^12 + 8*b^3*d^5*x^10 + 24*b^3*d^4*x^8 + 32*b^3*d^3*x^6 + 16*b^3*d^2*x^4 + (b^3*d^4*x^8 + 4*b^3*d^3*x^6 + 6*b^3*d^2*x^4 + 4*b^3*d*x^2 + b^3)*(d*x^2 + 2)^2 + 4*(b^3*d^(9/2)*x^9 + 5*b^3*d^(7/2)*x^7 + 9*b^3*d^(5/2)*x^5 + 7*b^3*d^(3/2)*x^3 + 2*b^3*sqrt(d)*x)*(d*x^2 + 2)^(3/2) + 6*(b^3*d^5*x^10 + 6*b^3*d^4*x^8 + 13*b^3*d^3*x^6 + 12*b^3*d^2*x^4 + 4*b^3*d*x^2)*(d*x^2 + 2) + 4*(b^3*d^(11/2)*x^11 + 7*b^3*d^(9/2)*x^9 + 18*b^3*d^(7/2)*x^7 + 20*b^3*d^(5/2)*x^5 + 8*b^3*d^(3/2)*x^3)*sqrt(d*x^2 + 2))*log(d*x^2 + sqrt(d*x^2 + 2)*sqrt(d)*x + 1) + 4*(a*b^2*d^(11/2)*x^11 + 7*a*b^2*d^(9/2)*x^9 + 18*a*b^2*d^(7/2)*x^7 + 20*a*b^2*d^(5/2)*x^5 + 8*a*b^2*d^(3/2)*x^3)*sqrt(d*x^2 + 2)), x)","F",0
247,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2-1))^4,x, algorithm=""maxima"")","b^{4} x \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right)^{4} + 6 \, a^{2} b^{2} x \operatorname{arcosh}\left(d x^{2} - 1\right)^{2} + 24 \, a^{2} b^{2} d {\left(\frac{2 \, x}{d} - \frac{{\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d x^{2}} - 1\right)}{\sqrt{d x^{2} - 2} d^{2}}\right)} + 4 \, {\left(x \operatorname{arcosh}\left(d x^{2} - 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2} d}\right)} a^{3} b + a^{4} x + \int \frac{4 \, {\left({\left(a b^{3} d^{2} - 2 \, b^{4} d^{2}\right)} x^{4} + 2 \, a b^{3} - {\left(3 \, a b^{3} d - 4 \, b^{4} d\right)} x^{2} + {\left({\left(a b^{3} d - 2 \, b^{4} d\right)} \sqrt{d} x^{3} - 2 \, {\left(a b^{3} - b^{4}\right)} \sqrt{d} x\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right)^{3}}{d^{2} x^{4} - 3 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2} + 2}\,{d x}"," ",0,"b^4*x*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1)^4 + 6*a^2*b^2*x*arccosh(d*x^2 - 1)^2 + 24*a^2*b^2*d*(2*x/d - (d^(3/2)*x^2 - 2*sqrt(d))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d*x^2) - 1)/(sqrt(d*x^2 - 2)*d^2)) + 4*(x*arccosh(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(d*x^2 - 2)*d))*a^3*b + a^4*x + integrate(4*((a*b^3*d^2 - 2*b^4*d^2)*x^4 + 2*a*b^3 - (3*a*b^3*d - 4*b^4*d)*x^2 + ((a*b^3*d - 2*b^4*d)*sqrt(d)*x^3 - 2*(a*b^3 - b^4)*sqrt(d)*x)*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1)^3/(d^2*x^4 - 3*d*x^2 + (d^(3/2)*x^3 - 2*sqrt(d)*x)*sqrt(d*x^2 - 2) + 2), x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2-1))^3,x, algorithm=""maxima"")","3 \, a b^{2} x \operatorname{arcosh}\left(d x^{2} - 1\right)^{2} + 12 \, a b^{2} d {\left(\frac{2 \, x}{d} - \frac{{\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d x^{2}} - 1\right)}{\sqrt{d x^{2} - 2} d^{2}}\right)} + 3 \, {\left(x \operatorname{arcosh}\left(d x^{2} - 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2} d}\right)} a^{2} b + {\left(x \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right)^{3} - \int \frac{6 \, {\left(d^{2} x^{4} - 2 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - \sqrt{d} x\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right)^{2}}{d^{2} x^{4} - 3 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2} + 2}\,{d x}\right)} b^{3} + a^{3} x"," ",0,"3*a*b^2*x*arccosh(d*x^2 - 1)^2 + 12*a*b^2*d*(2*x/d - (d^(3/2)*x^2 - 2*sqrt(d))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d*x^2) - 1)/(sqrt(d*x^2 - 2)*d^2)) + 3*(x*arccosh(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(d*x^2 - 2)*d))*a^2*b + (x*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1)^3 - integrate(6*(d^2*x^4 - 2*d*x^2 + (d^(3/2)*x^3 - sqrt(d)*x)*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1)^2/(d^2*x^4 - 3*d*x^2 + (d^(3/2)*x^3 - 2*sqrt(d)*x)*sqrt(d*x^2 - 2) + 2), x))*b^3 + a^3*x","F",0
249,1,128,0,0.587588," ","integrate((a+b*arccosh(d*x^2-1))^2,x, algorithm=""maxima"")","b^{2} x \operatorname{arcosh}\left(d x^{2} - 1\right)^{2} + 4 \, b^{2} d {\left(\frac{2 \, x}{d} - \frac{{\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d x^{2}} - 1\right)}{\sqrt{d x^{2} - 2} d^{2}}\right)} + 2 \, {\left(x \operatorname{arcosh}\left(d x^{2} - 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2} d}\right)} a b + a^{2} x"," ",0,"b^2*x*arccosh(d*x^2 - 1)^2 + 4*b^2*d*(2*x/d - (d^(3/2)*x^2 - 2*sqrt(d))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d*x^2) - 1)/(sqrt(d*x^2 - 2)*d^2)) + 2*(x*arccosh(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(d*x^2 - 2)*d))*a*b + a^2*x","A",0
250,1,44,0,0.648923," ","integrate(a+b*arccosh(d*x^2-1),x, algorithm=""maxima"")","{\left(x \operatorname{arcosh}\left(d x^{2} - 1\right) - \frac{2 \, {\left(d^{\frac{3}{2}} x^{2} - 2 \, \sqrt{d}\right)}}{\sqrt{d x^{2} - 2} d}\right)} b + a x"," ",0,"(x*arccosh(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(d*x^2 - 2)*d))*b + a*x","A",0
251,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arcosh}\left(d x^{2} - 1\right) + a}\,{d x}"," ",0,"integrate(1/(b*arccosh(d*x^2 - 1) + a), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1))^2,x, algorithm=""maxima"")","-\frac{d^{2} x^{4} - 3 \, d x^{2} + {\left(d^{\frac{3}{2}} x^{3} - 2 \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2} + 2}{2 \, {\left(a b d^{2} x^{3} - 2 \, a b d x + {\left(b^{2} d^{2} x^{3} - 2 \, b^{2} d x + {\left(b^{2} d^{\frac{3}{2}} x^{2} - b^{2} \sqrt{d}\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right) + {\left(a b d^{\frac{3}{2}} x^{2} - a b \sqrt{d}\right)} \sqrt{d x^{2} - 2}\right)}} + \int \frac{d^{3} x^{6} - 3 \, d^{2} x^{4} + {\left(d^{2} x^{4} - d x^{2} + 2\right)} {\left(d x^{2} - 2\right)} + {\left(2 \, d^{\frac{5}{2}} x^{5} - 4 \, d^{\frac{3}{2}} x^{3} + \sqrt{d} x\right)} \sqrt{d x^{2} - 2} + 4}{2 \, {\left(a b d^{3} x^{6} - 4 \, a b d^{2} x^{4} + 4 \, a b d x^{2} + {\left(a b d^{2} x^{4} - 2 \, a b d x^{2} + a b\right)} {\left(d x^{2} - 2\right)} + {\left(b^{2} d^{3} x^{6} - 4 \, b^{2} d^{2} x^{4} + 4 \, b^{2} d x^{2} + {\left(b^{2} d^{2} x^{4} - 2 \, b^{2} d x^{2} + b^{2}\right)} {\left(d x^{2} - 2\right)} + 2 \, {\left(b^{2} d^{\frac{5}{2}} x^{5} - 3 \, b^{2} d^{\frac{3}{2}} x^{3} + 2 \, b^{2} \sqrt{d} x\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right) + 2 \, {\left(a b d^{\frac{5}{2}} x^{5} - 3 \, a b d^{\frac{3}{2}} x^{3} + 2 \, a b \sqrt{d} x\right)} \sqrt{d x^{2} - 2}\right)}}\,{d x}"," ",0,"-1/2*(d^2*x^4 - 3*d*x^2 + (d^(3/2)*x^3 - 2*sqrt(d)*x)*sqrt(d*x^2 - 2) + 2)/(a*b*d^2*x^3 - 2*a*b*d*x + (b^2*d^2*x^3 - 2*b^2*d*x + (b^2*d^(3/2)*x^2 - b^2*sqrt(d))*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1) + (a*b*d^(3/2)*x^2 - a*b*sqrt(d))*sqrt(d*x^2 - 2)) + integrate(1/2*(d^3*x^6 - 3*d^2*x^4 + (d^2*x^4 - d*x^2 + 2)*(d*x^2 - 2) + (2*d^(5/2)*x^5 - 4*d^(3/2)*x^3 + sqrt(d)*x)*sqrt(d*x^2 - 2) + 4)/(a*b*d^3*x^6 - 4*a*b*d^2*x^4 + 4*a*b*d*x^2 + (a*b*d^2*x^4 - 2*a*b*d*x^2 + a*b)*(d*x^2 - 2) + (b^2*d^3*x^6 - 4*b^2*d^2*x^4 + 4*b^2*d*x^2 + (b^2*d^2*x^4 - 2*b^2*d*x^2 + b^2)*(d*x^2 - 2) + 2*(b^2*d^(5/2)*x^5 - 3*b^2*d^(3/2)*x^3 + 2*b^2*sqrt(d)*x)*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1) + 2*(a*b*d^(5/2)*x^5 - 3*a*b*d^(3/2)*x^3 + 2*a*b*sqrt(d)*x)*sqrt(d*x^2 - 2)), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1))^3,x, algorithm=""maxima"")","-\frac{{\left(a d^{5} + 2 \, b d^{5}\right)} \sqrt{d} x^{10} - 2 \, {\left(3 \, a d^{4} + 7 \, b d^{4}\right)} \sqrt{d} x^{8} + {\left(11 \, a d^{3} + 36 \, b d^{3}\right)} \sqrt{d} x^{6} - 2 \, {\left(a d^{2} + 20 \, b d^{2}\right)} \sqrt{d} x^{4} - 4 \, {\left(3 \, a d - 4 \, b d\right)} \sqrt{d} x^{2} + {\left({\left(a d^{4} + 2 \, b d^{4}\right)} x^{7} - {\left(3 \, a d^{3} + 8 \, b d^{3}\right)} x^{5} + 2 \, {\left(2 \, a d^{2} + 5 \, b d^{2}\right)} x^{3} - 4 \, {\left(a d + b d\right)} x\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + {\left(3 \, {\left(a d^{4} + 2 \, b d^{4}\right)} \sqrt{d} x^{8} - 6 \, {\left(2 \, a d^{3} + 5 \, b d^{3}\right)} \sqrt{d} x^{6} + 2 \, {\left(8 \, a d^{2} + 25 \, b d^{2}\right)} \sqrt{d} x^{4} - 10 \, {\left(a d + 3 \, b d\right)} \sqrt{d} x^{2} + 4 \, {\left(a + b\right)} \sqrt{d}\right)} {\left(d x^{2} - 2\right)} + {\left(b d^{\frac{11}{2}} x^{10} - 6 \, b d^{\frac{9}{2}} x^{8} + 11 \, b d^{\frac{7}{2}} x^{6} - 2 \, b d^{\frac{5}{2}} x^{4} - 12 \, b d^{\frac{3}{2}} x^{2} + {\left(b d^{4} x^{7} - 3 \, b d^{3} x^{5} + 4 \, b d^{2} x^{3} - 4 \, b d x\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + {\left(3 \, b d^{\frac{9}{2}} x^{8} - 12 \, b d^{\frac{7}{2}} x^{6} + 16 \, b d^{\frac{5}{2}} x^{4} - 10 \, b d^{\frac{3}{2}} x^{2} + 4 \, b \sqrt{d}\right)} {\left(d x^{2} - 2\right)} + {\left(3 \, b d^{5} x^{9} - 15 \, b d^{4} x^{7} + 23 \, b d^{3} x^{5} - 7 \, b d^{2} x^{3} - 6 \, b d x\right)} \sqrt{d x^{2} - 2} + 8 \, b \sqrt{d}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right) + {\left(3 \, {\left(a d^{5} + 2 \, b d^{5}\right)} x^{9} - 3 \, {\left(5 \, a d^{4} + 12 \, b d^{4}\right)} x^{7} + {\left(23 \, a d^{3} + 76 \, b d^{3}\right)} x^{5} - {\left(7 \, a d^{2} + 64 \, b d^{2}\right)} x^{3} - 2 \, {\left(3 \, a d - 8 \, b d\right)} x\right)} \sqrt{d x^{2} - 2} + 8 \, a \sqrt{d}}{8 \, {\left(a^{2} b^{2} d^{\frac{11}{2}} x^{9} - 6 \, a^{2} b^{2} d^{\frac{9}{2}} x^{7} + 12 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} - 8 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} + {\left(b^{4} d^{\frac{11}{2}} x^{9} - 6 \, b^{4} d^{\frac{9}{2}} x^{7} + 12 \, b^{4} d^{\frac{7}{2}} x^{5} - 8 \, b^{4} d^{\frac{5}{2}} x^{3} + {\left(b^{4} d^{4} x^{6} - 3 \, b^{4} d^{3} x^{4} + 3 \, b^{4} d^{2} x^{2} - b^{4} d\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + 3 \, {\left(b^{4} d^{\frac{9}{2}} x^{7} - 4 \, b^{4} d^{\frac{7}{2}} x^{5} + 5 \, b^{4} d^{\frac{5}{2}} x^{3} - 2 \, b^{4} d^{\frac{3}{2}} x\right)} {\left(d x^{2} - 2\right)} + 3 \, {\left(b^{4} d^{5} x^{8} - 5 \, b^{4} d^{4} x^{6} + 8 \, b^{4} d^{3} x^{4} - 4 \, b^{4} d^{2} x^{2}\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right)^{2} + {\left(a^{2} b^{2} d^{4} x^{6} - 3 \, a^{2} b^{2} d^{3} x^{4} + 3 \, a^{2} b^{2} d^{2} x^{2} - a^{2} b^{2} d\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + 3 \, {\left(a^{2} b^{2} d^{\frac{9}{2}} x^{7} - 4 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} + 5 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} - 2 \, a^{2} b^{2} d^{\frac{3}{2}} x\right)} {\left(d x^{2} - 2\right)} + 2 \, {\left(a b^{3} d^{\frac{11}{2}} x^{9} - 6 \, a b^{3} d^{\frac{9}{2}} x^{7} + 12 \, a b^{3} d^{\frac{7}{2}} x^{5} - 8 \, a b^{3} d^{\frac{5}{2}} x^{3} + {\left(a b^{3} d^{4} x^{6} - 3 \, a b^{3} d^{3} x^{4} + 3 \, a b^{3} d^{2} x^{2} - a b^{3} d\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + 3 \, {\left(a b^{3} d^{\frac{9}{2}} x^{7} - 4 \, a b^{3} d^{\frac{7}{2}} x^{5} + 5 \, a b^{3} d^{\frac{5}{2}} x^{3} - 2 \, a b^{3} d^{\frac{3}{2}} x\right)} {\left(d x^{2} - 2\right)} + 3 \, {\left(a b^{3} d^{5} x^{8} - 5 \, a b^{3} d^{4} x^{6} + 8 \, a b^{3} d^{3} x^{4} - 4 \, a b^{3} d^{2} x^{2}\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right) + 3 \, {\left(a^{2} b^{2} d^{5} x^{8} - 5 \, a^{2} b^{2} d^{4} x^{6} + 8 \, a^{2} b^{2} d^{3} x^{4} - 4 \, a^{2} b^{2} d^{2} x^{2}\right)} \sqrt{d x^{2} - 2}\right)}} + \int \frac{d^{6} x^{12} - 8 \, d^{5} x^{10} + 27 \, d^{4} x^{8} - 56 \, d^{3} x^{6} + 88 \, d^{2} x^{4} + {\left(d^{4} x^{8} - 4 \, d^{3} x^{6} + 3 \, d^{2} x^{4} + 8 \, d x^{2} + 4\right)} {\left(d x^{2} - 2\right)}^{2} - 96 \, d x^{2} + 2 \, {\left(2 \, d^{\frac{9}{2}} x^{9} - 10 \, d^{\frac{7}{2}} x^{7} + 15 \, d^{\frac{5}{2}} x^{5} + d^{\frac{3}{2}} x^{3} - 11 \, \sqrt{d} x\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + 3 \, {\left(2 \, d^{5} x^{10} - 12 \, d^{4} x^{8} + 26 \, d^{3} x^{6} - 24 \, d^{2} x^{4} + 3 \, d x^{2} + 10\right)} {\left(d x^{2} - 2\right)} + 2 \, {\left(2 \, d^{\frac{11}{2}} x^{11} - 14 \, d^{\frac{9}{2}} x^{9} + 39 \, d^{\frac{7}{2}} x^{7} - 61 \, d^{\frac{5}{2}} x^{5} + 61 \, d^{\frac{3}{2}} x^{3} - 30 \, \sqrt{d} x\right)} \sqrt{d x^{2} - 2} + 48}{8 \, {\left(a b^{2} d^{6} x^{12} - 8 \, a b^{2} d^{5} x^{10} + 24 \, a b^{2} d^{4} x^{8} - 32 \, a b^{2} d^{3} x^{6} + 16 \, a b^{2} d^{2} x^{4} + {\left(a b^{2} d^{4} x^{8} - 4 \, a b^{2} d^{3} x^{6} + 6 \, a b^{2} d^{2} x^{4} - 4 \, a b^{2} d x^{2} + a b^{2}\right)} {\left(d x^{2} - 2\right)}^{2} + 4 \, {\left(a b^{2} d^{\frac{9}{2}} x^{9} - 5 \, a b^{2} d^{\frac{7}{2}} x^{7} + 9 \, a b^{2} d^{\frac{5}{2}} x^{5} - 7 \, a b^{2} d^{\frac{3}{2}} x^{3} + 2 \, a b^{2} \sqrt{d} x\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + 6 \, {\left(a b^{2} d^{5} x^{10} - 6 \, a b^{2} d^{4} x^{8} + 13 \, a b^{2} d^{3} x^{6} - 12 \, a b^{2} d^{2} x^{4} + 4 \, a b^{2} d x^{2}\right)} {\left(d x^{2} - 2\right)} + {\left(b^{3} d^{6} x^{12} - 8 \, b^{3} d^{5} x^{10} + 24 \, b^{3} d^{4} x^{8} - 32 \, b^{3} d^{3} x^{6} + 16 \, b^{3} d^{2} x^{4} + {\left(b^{3} d^{4} x^{8} - 4 \, b^{3} d^{3} x^{6} + 6 \, b^{3} d^{2} x^{4} - 4 \, b^{3} d x^{2} + b^{3}\right)} {\left(d x^{2} - 2\right)}^{2} + 4 \, {\left(b^{3} d^{\frac{9}{2}} x^{9} - 5 \, b^{3} d^{\frac{7}{2}} x^{7} + 9 \, b^{3} d^{\frac{5}{2}} x^{5} - 7 \, b^{3} d^{\frac{3}{2}} x^{3} + 2 \, b^{3} \sqrt{d} x\right)} {\left(d x^{2} - 2\right)}^{\frac{3}{2}} + 6 \, {\left(b^{3} d^{5} x^{10} - 6 \, b^{3} d^{4} x^{8} + 13 \, b^{3} d^{3} x^{6} - 12 \, b^{3} d^{2} x^{4} + 4 \, b^{3} d x^{2}\right)} {\left(d x^{2} - 2\right)} + 4 \, {\left(b^{3} d^{\frac{11}{2}} x^{11} - 7 \, b^{3} d^{\frac{9}{2}} x^{9} + 18 \, b^{3} d^{\frac{7}{2}} x^{7} - 20 \, b^{3} d^{\frac{5}{2}} x^{5} + 8 \, b^{3} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} - 2}\right)} \log\left(d x^{2} + \sqrt{d x^{2} - 2} \sqrt{d} x - 1\right) + 4 \, {\left(a b^{2} d^{\frac{11}{2}} x^{11} - 7 \, a b^{2} d^{\frac{9}{2}} x^{9} + 18 \, a b^{2} d^{\frac{7}{2}} x^{7} - 20 \, a b^{2} d^{\frac{5}{2}} x^{5} + 8 \, a b^{2} d^{\frac{3}{2}} x^{3}\right)} \sqrt{d x^{2} - 2}\right)}}\,{d x}"," ",0,"-1/8*((a*d^5 + 2*b*d^5)*sqrt(d)*x^10 - 2*(3*a*d^4 + 7*b*d^4)*sqrt(d)*x^8 + (11*a*d^3 + 36*b*d^3)*sqrt(d)*x^6 - 2*(a*d^2 + 20*b*d^2)*sqrt(d)*x^4 - 4*(3*a*d - 4*b*d)*sqrt(d)*x^2 + ((a*d^4 + 2*b*d^4)*x^7 - (3*a*d^3 + 8*b*d^3)*x^5 + 2*(2*a*d^2 + 5*b*d^2)*x^3 - 4*(a*d + b*d)*x)*(d*x^2 - 2)^(3/2) + (3*(a*d^4 + 2*b*d^4)*sqrt(d)*x^8 - 6*(2*a*d^3 + 5*b*d^3)*sqrt(d)*x^6 + 2*(8*a*d^2 + 25*b*d^2)*sqrt(d)*x^4 - 10*(a*d + 3*b*d)*sqrt(d)*x^2 + 4*(a + b)*sqrt(d))*(d*x^2 - 2) + (b*d^(11/2)*x^10 - 6*b*d^(9/2)*x^8 + 11*b*d^(7/2)*x^6 - 2*b*d^(5/2)*x^4 - 12*b*d^(3/2)*x^2 + (b*d^4*x^7 - 3*b*d^3*x^5 + 4*b*d^2*x^3 - 4*b*d*x)*(d*x^2 - 2)^(3/2) + (3*b*d^(9/2)*x^8 - 12*b*d^(7/2)*x^6 + 16*b*d^(5/2)*x^4 - 10*b*d^(3/2)*x^2 + 4*b*sqrt(d))*(d*x^2 - 2) + (3*b*d^5*x^9 - 15*b*d^4*x^7 + 23*b*d^3*x^5 - 7*b*d^2*x^3 - 6*b*d*x)*sqrt(d*x^2 - 2) + 8*b*sqrt(d))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1) + (3*(a*d^5 + 2*b*d^5)*x^9 - 3*(5*a*d^4 + 12*b*d^4)*x^7 + (23*a*d^3 + 76*b*d^3)*x^5 - (7*a*d^2 + 64*b*d^2)*x^3 - 2*(3*a*d - 8*b*d)*x)*sqrt(d*x^2 - 2) + 8*a*sqrt(d))/(a^2*b^2*d^(11/2)*x^9 - 6*a^2*b^2*d^(9/2)*x^7 + 12*a^2*b^2*d^(7/2)*x^5 - 8*a^2*b^2*d^(5/2)*x^3 + (b^4*d^(11/2)*x^9 - 6*b^4*d^(9/2)*x^7 + 12*b^4*d^(7/2)*x^5 - 8*b^4*d^(5/2)*x^3 + (b^4*d^4*x^6 - 3*b^4*d^3*x^4 + 3*b^4*d^2*x^2 - b^4*d)*(d*x^2 - 2)^(3/2) + 3*(b^4*d^(9/2)*x^7 - 4*b^4*d^(7/2)*x^5 + 5*b^4*d^(5/2)*x^3 - 2*b^4*d^(3/2)*x)*(d*x^2 - 2) + 3*(b^4*d^5*x^8 - 5*b^4*d^4*x^6 + 8*b^4*d^3*x^4 - 4*b^4*d^2*x^2)*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1)^2 + (a^2*b^2*d^4*x^6 - 3*a^2*b^2*d^3*x^4 + 3*a^2*b^2*d^2*x^2 - a^2*b^2*d)*(d*x^2 - 2)^(3/2) + 3*(a^2*b^2*d^(9/2)*x^7 - 4*a^2*b^2*d^(7/2)*x^5 + 5*a^2*b^2*d^(5/2)*x^3 - 2*a^2*b^2*d^(3/2)*x)*(d*x^2 - 2) + 2*(a*b^3*d^(11/2)*x^9 - 6*a*b^3*d^(9/2)*x^7 + 12*a*b^3*d^(7/2)*x^5 - 8*a*b^3*d^(5/2)*x^3 + (a*b^3*d^4*x^6 - 3*a*b^3*d^3*x^4 + 3*a*b^3*d^2*x^2 - a*b^3*d)*(d*x^2 - 2)^(3/2) + 3*(a*b^3*d^(9/2)*x^7 - 4*a*b^3*d^(7/2)*x^5 + 5*a*b^3*d^(5/2)*x^3 - 2*a*b^3*d^(3/2)*x)*(d*x^2 - 2) + 3*(a*b^3*d^5*x^8 - 5*a*b^3*d^4*x^6 + 8*a*b^3*d^3*x^4 - 4*a*b^3*d^2*x^2)*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1) + 3*(a^2*b^2*d^5*x^8 - 5*a^2*b^2*d^4*x^6 + 8*a^2*b^2*d^3*x^4 - 4*a^2*b^2*d^2*x^2)*sqrt(d*x^2 - 2)) + integrate(1/8*(d^6*x^12 - 8*d^5*x^10 + 27*d^4*x^8 - 56*d^3*x^6 + 88*d^2*x^4 + (d^4*x^8 - 4*d^3*x^6 + 3*d^2*x^4 + 8*d*x^2 + 4)*(d*x^2 - 2)^2 - 96*d*x^2 + 2*(2*d^(9/2)*x^9 - 10*d^(7/2)*x^7 + 15*d^(5/2)*x^5 + d^(3/2)*x^3 - 11*sqrt(d)*x)*(d*x^2 - 2)^(3/2) + 3*(2*d^5*x^10 - 12*d^4*x^8 + 26*d^3*x^6 - 24*d^2*x^4 + 3*d*x^2 + 10)*(d*x^2 - 2) + 2*(2*d^(11/2)*x^11 - 14*d^(9/2)*x^9 + 39*d^(7/2)*x^7 - 61*d^(5/2)*x^5 + 61*d^(3/2)*x^3 - 30*sqrt(d)*x)*sqrt(d*x^2 - 2) + 48)/(a*b^2*d^6*x^12 - 8*a*b^2*d^5*x^10 + 24*a*b^2*d^4*x^8 - 32*a*b^2*d^3*x^6 + 16*a*b^2*d^2*x^4 + (a*b^2*d^4*x^8 - 4*a*b^2*d^3*x^6 + 6*a*b^2*d^2*x^4 - 4*a*b^2*d*x^2 + a*b^2)*(d*x^2 - 2)^2 + 4*(a*b^2*d^(9/2)*x^9 - 5*a*b^2*d^(7/2)*x^7 + 9*a*b^2*d^(5/2)*x^5 - 7*a*b^2*d^(3/2)*x^3 + 2*a*b^2*sqrt(d)*x)*(d*x^2 - 2)^(3/2) + 6*(a*b^2*d^5*x^10 - 6*a*b^2*d^4*x^8 + 13*a*b^2*d^3*x^6 - 12*a*b^2*d^2*x^4 + 4*a*b^2*d*x^2)*(d*x^2 - 2) + (b^3*d^6*x^12 - 8*b^3*d^5*x^10 + 24*b^3*d^4*x^8 - 32*b^3*d^3*x^6 + 16*b^3*d^2*x^4 + (b^3*d^4*x^8 - 4*b^3*d^3*x^6 + 6*b^3*d^2*x^4 - 4*b^3*d*x^2 + b^3)*(d*x^2 - 2)^2 + 4*(b^3*d^(9/2)*x^9 - 5*b^3*d^(7/2)*x^7 + 9*b^3*d^(5/2)*x^5 - 7*b^3*d^(3/2)*x^3 + 2*b^3*sqrt(d)*x)*(d*x^2 - 2)^(3/2) + 6*(b^3*d^5*x^10 - 6*b^3*d^4*x^8 + 13*b^3*d^3*x^6 - 12*b^3*d^2*x^4 + 4*b^3*d*x^2)*(d*x^2 - 2) + 4*(b^3*d^(11/2)*x^11 - 7*b^3*d^(9/2)*x^9 + 18*b^3*d^(7/2)*x^7 - 20*b^3*d^(5/2)*x^5 + 8*b^3*d^(3/2)*x^3)*sqrt(d*x^2 - 2))*log(d*x^2 + sqrt(d*x^2 - 2)*sqrt(d)*x - 1) + 4*(a*b^2*d^(11/2)*x^11 - 7*a*b^2*d^(9/2)*x^9 + 18*a*b^2*d^(7/2)*x^7 - 20*a*b^2*d^(5/2)*x^5 + 8*a*b^2*d^(3/2)*x^3)*sqrt(d*x^2 - 2)), x)","F",0
254,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2+1))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x^{2} + 1\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 + 1) + a)^(5/2), x)","F",0
255,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2+1))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x^{2} + 1\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 + 1) + a)^(3/2), x)","F",0
256,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(d x^{2} + 1\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(d*x^2 + 1) + a), x)","F",0
257,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arcosh}\left(d x^{2} + 1\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arccosh(d*x^2 + 1) + a), x)","F",0
258,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x^{2} + 1\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 + 1) + a)^(-3/2), x)","F",0
259,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x^{2} + 1\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 + 1) + a)^(-5/2), x)","F",0
260,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2+1))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x^{2} + 1\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 + 1) + a)^(-7/2), x)","F",0
261,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2-1))^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x^{2} - 1\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 - 1) + a)^(5/2), x)","F",0
262,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2-1))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(d x^{2} - 1\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 - 1) + a)^(3/2), x)","F",0
263,0,0,0,0.000000," ","integrate((a+b*arccosh(d*x^2-1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(d x^{2} - 1\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(d*x^2 - 1) + a), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arcosh}\left(d x^{2} - 1\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arccosh(d*x^2 - 1) + a), x)","F",0
265,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x^{2} - 1\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 - 1) + a)^(-3/2), x)","F",0
266,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x^{2} - 1\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 - 1) + a)^(-5/2), x)","F",0
267,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(d*x^2-1))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(d x^{2} - 1\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(d*x^2 - 1) + a)^(-7/2), x)","F",0
268,0,0,0,0.000000," ","integrate((a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(b \operatorname{arcosh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((b*arccosh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
269,0,0,0,0.000000," ","integrate((a+b*arccosh((-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{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)^{3}}{2 \, c} + \int \frac{{\left({\left(c x + 1\right)} \sqrt{-c x + 1} b^{3} - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{3}\right)} \log\left(c x + 1\right)^{3} - 6 \, {\left({\left(c x + 1\right)} \sqrt{-c x + 1} a b^{2} - {\left(-c x + 1\right)}^{\frac{3}{2}} a b^{2}\right)} \log\left(c x + 1\right)^{2} - 6 \, {\left({\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)} {\left(c x + 1\right)} \sqrt{-c x + 1} - {\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)} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\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)} {\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)} {\left(c x - 1\right)} - 2 \, {\left({\left(c x + 1\right)} b^{3} + {\left(c x - 1\right)} b^{3}\right)} \log\left(c x + 1\right)\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} - 2 \, {\left({\left(c x + 1\right)} \sqrt{-c x + 1} b^{3} - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(\sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)^{2} + {\left({\left({\left(c x + 1\right)} b^{3} + {\left(c x - 1\right)} b^{3}\right)} \log\left(c x + 1\right)^{3} - 6 \, {\left({\left(c x + 1\right)} a b^{2} + {\left(c x - 1\right)} a b^{2}\right)} \log\left(c x + 1\right)^{2} + 12 \, {\left({\left(c x + 1\right)} a^{2} b + {\left(c x - 1\right)} a^{2} b\right)} \log\left(c x + 1\right)\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + 12 \, {\left({\left(c x + 1\right)} \sqrt{-c x + 1} a^{2} b - {\left(-c x + 1\right)}^{\frac{3}{2}} a^{2} b\right)} \log\left(c x + 1\right) - 6 \, {\left(4 \, {\left(c x + 1\right)} \sqrt{-c x + 1} a^{2} b - 4 \, {\left(-c x + 1\right)}^{\frac{3}{2}} a^{2} b + {\left({\left(c x + 1\right)} \sqrt{-c x + 1} b^{3} - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{3}\right)} \log\left(c x + 1\right)^{2} + {\left(4 \, {\left(c x + 1\right)} a^{2} b + 4 \, {\left(c x - 1\right)} a^{2} b + {\left({\left(c x + 1\right)} b^{3} + {\left(c x - 1\right)} b^{3}\right)} \log\left(c x + 1\right)^{2} - 4 \, {\left({\left(c x + 1\right)} a b^{2} + {\left(c x - 1\right)} a b^{2}\right)} \log\left(c x + 1\right)\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} - 4 \, {\left({\left(c x + 1\right)} \sqrt{-c x + 1} a b^{2} - {\left(-c x + 1\right)}^{\frac{3}{2}} a b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(\sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)}{8 \, {\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{-c x + 1} - {\left(c^{2} x^{2} - 1\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} + {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}}\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(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1))^3/c + integrate(1/8*(((c*x + 1)*sqrt(-c*x + 1)*b^3 - (-c*x + 1)^(3/2)*b^3)*log(c*x + 1)^3 - 6*((c*x + 1)*sqrt(-c*x + 1)*a*b^2 - (-c*x + 1)^(3/2)*a*b^2)*log(c*x + 1)^2 - 6*((4*a*b^2 + (b^3*c*x + b^3)*log(c*x + 1) - (b^3*c*x + b^3)*log(-c*x + 1))*(c*x + 1)*sqrt(-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))*(-c*x + 1)^(3/2) + ((4*a*b^2 + (b^3*c*x - b^3)*log(c*x + 1) - (b^3*c*x - b^3)*log(-c*x + 1))*(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))*(c*x - 1) - 2*((c*x + 1)*b^3 + (c*x - 1)*b^3)*log(c*x + 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) - 2*((c*x + 1)*sqrt(-c*x + 1)*b^3 - (-c*x + 1)^(3/2)*b^3)*log(c*x + 1))*log(sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1))^2 + (((c*x + 1)*b^3 + (c*x - 1)*b^3)*log(c*x + 1)^3 - 6*((c*x + 1)*a*b^2 + (c*x - 1)*a*b^2)*log(c*x + 1)^2 + 12*((c*x + 1)*a^2*b + (c*x - 1)*a^2*b)*log(c*x + 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + 12*((c*x + 1)*sqrt(-c*x + 1)*a^2*b - (-c*x + 1)^(3/2)*a^2*b)*log(c*x + 1) - 6*(4*(c*x + 1)*sqrt(-c*x + 1)*a^2*b - 4*(-c*x + 1)^(3/2)*a^2*b + ((c*x + 1)*sqrt(-c*x + 1)*b^3 - (-c*x + 1)^(3/2)*b^3)*log(c*x + 1)^2 + (4*(c*x + 1)*a^2*b + 4*(c*x - 1)*a^2*b + ((c*x + 1)*b^3 + (c*x - 1)*b^3)*log(c*x + 1)^2 - 4*((c*x + 1)*a*b^2 + (c*x - 1)*a*b^2)*log(c*x + 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) - 4*((c*x + 1)*sqrt(-c*x + 1)*a*b^2 - (-c*x + 1)^(3/2)*a*b^2)*log(c*x + 1))*log(sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1)))/((c^2*x^2 - 1)*(c*x + 1)*sqrt(-c*x + 1) - (c^2*x^2 - 1)*(-c*x + 1)^(3/2) + ((c^2*x^2 - 1)*(c*x + 1) + (c^2*x^2 - 1)*(c*x - 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1))), x)","F",0
270,0,0,0,0.000000," ","integrate((a+b*arccosh((-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{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)^{2}}{2 \, c} + \int -\frac{{\left({\left(c x + 1\right)} \sqrt{-c x + 1} b^{2} - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{2}\right)} \log\left(c x + 1\right)^{2} + {\left({\left({\left(c x + 1\right)} b^{2} + {\left(c x - 1\right)} b^{2}\right)} \log\left(c x + 1\right)^{2} - 4 \, {\left({\left(c x + 1\right)} a b + {\left(c x - 1\right)} a b\right)} \log\left(c x + 1\right)\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} - 4 \, {\left({\left(c x + 1\right)} \sqrt{-c x + 1} a b - {\left(-c x + 1\right)}^{\frac{3}{2}} a b\right)} \log\left(c x + 1\right) + 2 \, {\left({\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)} {\left(c x + 1\right)} \sqrt{-c x + 1} - {\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)} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\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)} {\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)} {\left(c x - 1\right)} - 2 \, {\left({\left(c x + 1\right)} b^{2} + {\left(c x - 1\right)} b^{2}\right)} \log\left(c x + 1\right)\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} - 2 \, {\left({\left(c x + 1\right)} \sqrt{-c x + 1} b^{2} - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{2}\right)} \log\left(c x + 1\right)\right)} \log\left(\sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)}{4 \, {\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{-c x + 1} - {\left(c^{2} x^{2} - 1\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} + {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}}\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(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1))^2/c + integrate(-1/4*(((c*x + 1)*sqrt(-c*x + 1)*b^2 - (-c*x + 1)^(3/2)*b^2)*log(c*x + 1)^2 + (((c*x + 1)*b^2 + (c*x - 1)*b^2)*log(c*x + 1)^2 - 4*((c*x + 1)*a*b + (c*x - 1)*a*b)*log(c*x + 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) - 4*((c*x + 1)*sqrt(-c*x + 1)*a*b - (-c*x + 1)^(3/2)*a*b)*log(c*x + 1) + 2*((4*a*b + (b^2*c*x + b^2)*log(c*x + 1) - (b^2*c*x + b^2)*log(-c*x + 1))*(c*x + 1)*sqrt(-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))*(-c*x + 1)^(3/2) + ((4*a*b + (b^2*c*x - b^2)*log(c*x + 1) - (b^2*c*x - b^2)*log(-c*x + 1))*(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))*(c*x - 1) - 2*((c*x + 1)*b^2 + (c*x - 1)*b^2)*log(c*x + 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) - 2*((c*x + 1)*sqrt(-c*x + 1)*b^2 - (-c*x + 1)^(3/2)*b^2)*log(c*x + 1))*log(sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1)))/((c^2*x^2 - 1)*(c*x + 1)*sqrt(-c*x + 1) - (c^2*x^2 - 1)*(-c*x + 1)^(3/2) + ((c^2*x^2 - 1)*(c*x + 1) + (c^2*x^2 - 1)*(c*x - 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1))), x)","F",0
271,0,0,0,0.000000," ","integrate((a+b*arccosh((-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{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)}{c} + 8 \, \int \frac{{\left(c x + 1\right)} \sqrt{-c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{2 \, {\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{-c x + 1} - {\left(c^{2} x^{2} - 1\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} + {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}}\right)}}\,{d x} + 8 \, \int -\frac{\sqrt{c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{4 \, {\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} + {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1}\right)}}\,{d x} - 8 \, \int \frac{\sqrt{c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{4 \, {\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} - {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1}\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(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1)))/c + 8*integrate(1/2*(c*x + 1)*sqrt(-c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/((c^2*x^2 - 1)*(c*x + 1)*sqrt(-c*x + 1) - (c^2*x^2 - 1)*(-c*x + 1)^(3/2) + ((c^2*x^2 - 1)*(c*x + 1) + (c^2*x^2 - 1)*(c*x - 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1))), x) + 8*integrate(-1/4*sqrt(c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/((c^2*x^2 - 1)*sqrt(c*x + 1) + (c^2*x^2 - 1)*sqrt(-c*x + 1)), x) - 8*integrate(1/4*sqrt(c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/((c^2*x^2 - 1)*sqrt(c*x + 1) - (c^2*x^2 - 1)*sqrt(-c*x + 1)), x)) + 1/2*a*(log(c*x + 1)/c - log(c*x - 1)/c)","F",0
272,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arccosh((-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{arcosh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}}\,{d x}"," ",0,"-integrate(1/((c^2*x^2 - 1)*(b*arccosh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)), x)","F",0
273,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arccosh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, c x \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + {\left(c x + 1\right)} \sqrt{-c x + 1} - {\left(-c x + 1\right)}^{\frac{3}{2}}\right)}}{2 \, {\left(c x + 1\right)} \sqrt{-c x + 1} a b c - 2 \, {\left(-c x + 1\right)}^{\frac{3}{2}} a b c - {\left({\left(c x - 1\right)} b^{2} c \log\left(c x + 1\right) - 2 \, {\left(c x - 1\right)} a b c\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} - {\left({\left(c x + 1\right)} \sqrt{-c x + 1} b^{2} c - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{2} c\right)} \log\left(c x + 1\right) + 2 \, {\left({\left(c x - 1\right)} b^{2} c \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + {\left(c x + 1\right)} \sqrt{-c x + 1} b^{2} c - {\left(-c x + 1\right)}^{\frac{3}{2}} b^{2} c\right)} \log\left(\sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)} - \int -\frac{2 \, {\left(2 \, {\left(c x + 1\right)} \sqrt{-c x + 1} {\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)} {\left(\sqrt{c x + 1} - \sqrt{-c x + 1}\right)} + {\left({\left(c x + 1\right)}^{2} + 2 \, {\left(c x + 1\right)} {\left(c x - 1\right)}\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}}\right)}}{2 \, {\left(a b c^{2} x^{2} - a b\right)} {\left(c x + 1\right)}^{2} \sqrt{-c x + 1} - 4 \, {\left(a b c^{2} x^{2} - a b\right)} {\left(c x + 1\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} {\left(-c x + 1\right)}^{\frac{5}{2}} + {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} \log\left(c x + 1\right) - 2 \, {\left(a b c^{2} x^{2} - a b\right)} {\left(-c x + 1\right)}^{\frac{3}{2}}\right)} {\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)} {\left(\sqrt{c x + 1} - \sqrt{-c x + 1}\right)} + 2 \, {\left(2 \, {\left(a b c^{2} x^{2} - a b\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} {\left(c x - 1\right)}^{2} - {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x - 1\right)}^{2}\right)} \log\left(c x + 1\right)\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} - {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x + 1\right)}^{2} \sqrt{-c x + 1} - 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x + 1\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(-c x + 1\right)}^{\frac{5}{2}}\right)} \log\left(c x + 1\right) - 2 \, {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} {\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)} {\left(\sqrt{c x + 1} - \sqrt{-c x + 1}\right)} - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x + 1\right)}^{2} \sqrt{-c x + 1} + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x + 1\right)} {\left(-c x + 1\right)}^{\frac{3}{2}} - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(-c x + 1\right)}^{\frac{5}{2}} - 2 \, {\left({\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} {\left(c x - 1\right)}^{2}\right)} \sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}}\right)} \log\left(\sqrt{\sqrt{c x + 1} + \sqrt{-c x + 1}} \sqrt{-\sqrt{c x + 1} + \sqrt{-c x + 1}} + \sqrt{-c x + 1}\right)}\,{d x}"," ",0,"2*(2*c*x*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + (c*x + 1)*sqrt(-c*x + 1) - (-c*x + 1)^(3/2))/(2*(c*x + 1)*sqrt(-c*x + 1)*a*b*c - 2*(-c*x + 1)^(3/2)*a*b*c - ((c*x - 1)*b^2*c*log(c*x + 1) - 2*(c*x - 1)*a*b*c)*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) - ((c*x + 1)*sqrt(-c*x + 1)*b^2*c - (-c*x + 1)^(3/2)*b^2*c)*log(c*x + 1) + 2*((c*x - 1)*b^2*c*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + (c*x + 1)*sqrt(-c*x + 1)*b^2*c - (-c*x + 1)^(3/2)*b^2*c)*log(sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1))) - integrate(-2*(2*(c*x + 1)*sqrt(-c*x + 1)*(sqrt(c*x + 1) + sqrt(-c*x + 1))*(sqrt(c*x + 1) - sqrt(-c*x + 1)) + ((c*x + 1)^2 + 2*(c*x + 1)*(c*x - 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)))/(2*(a*b*c^2*x^2 - a*b)*(c*x + 1)^2*sqrt(-c*x + 1) - 4*(a*b*c^2*x^2 - a*b)*(c*x + 1)*(-c*x + 1)^(3/2) + 2*(a*b*c^2*x^2 - a*b)*(-c*x + 1)^(5/2) + ((b^2*c^2*x^2 - b^2)*(-c*x + 1)^(3/2)*log(c*x + 1) - 2*(a*b*c^2*x^2 - a*b)*(-c*x + 1)^(3/2))*(sqrt(c*x + 1) + sqrt(-c*x + 1))*(sqrt(c*x + 1) - sqrt(-c*x + 1)) + 2*(2*(a*b*c^2*x^2 - a*b)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^2*x^2 - a*b)*(c*x - 1)^2 - ((b^2*c^2*x^2 - b^2)*(c*x + 1)*(c*x - 1) + (b^2*c^2*x^2 - b^2)*(c*x - 1)^2)*log(c*x + 1))*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) - ((b^2*c^2*x^2 - b^2)*(c*x + 1)^2*sqrt(-c*x + 1) - 2*(b^2*c^2*x^2 - b^2)*(c*x + 1)*(-c*x + 1)^(3/2) + (b^2*c^2*x^2 - b^2)*(-c*x + 1)^(5/2))*log(c*x + 1) - 2*((b^2*c^2*x^2 - b^2)*(-c*x + 1)^(3/2)*(sqrt(c*x + 1) + sqrt(-c*x + 1))*(sqrt(c*x + 1) - sqrt(-c*x + 1)) - (b^2*c^2*x^2 - b^2)*(c*x + 1)^2*sqrt(-c*x + 1) + 2*(b^2*c^2*x^2 - b^2)*(c*x + 1)*(-c*x + 1)^(3/2) - (b^2*c^2*x^2 - b^2)*(-c*x + 1)^(5/2) - 2*((b^2*c^2*x^2 - b^2)*(c*x + 1)*(c*x - 1) + (b^2*c^2*x^2 - b^2)*(c*x - 1)^2)*sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)))*log(sqrt(sqrt(c*x + 1) + sqrt(-c*x + 1))*sqrt(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + sqrt(-c*x + 1))), x)","F",0
274,0,0,0,0.000000," ","integrate(arccosh(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)} e^{\left(\frac{1}{2} \, \log\left(c e^{\left(b x + a\right)} + 1\right) + \frac{1}{2} \, \log\left(c e^{\left(b x + a\right)} - 1\right)\right)}}\,{d x} + x \log\left(c e^{\left(b x + a\right)} + \sqrt{c e^{\left(b x + a\right)} + 1} \sqrt{c e^{\left(b x + a\right)} - 1}\right) - \frac{b x \log\left(c e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-c e^{\left(b x + a\right)}\right)}{2 \, b} - \frac{b x \log\left(-c e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(c e^{\left(b x + a\right)}\right)}{2 \, 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)*e^(1/2*log(c*e^(b*x + a) + 1) + 1/2*log(c*e^(b*x + a) - 1))), x) + x*log(c*e^(b*x + a) + sqrt(c*e^(b*x + a) + 1)*sqrt(c*e^(b*x + a) - 1)) - 1/2*(b*x*log(c*e^(b*x + a) + 1) + dilog(-c*e^(b*x + a)))/b - 1/2*(b*x*log(-c*e^(b*x + a) + 1) + dilog(c*e^(b*x + a)))/b","F",0
275,1,495,0,0.325728," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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 \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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 \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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
276,1,275,0,0.318824," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(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} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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)} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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)*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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
277,1,177,0,0.309598," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))*x,x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2} + \frac{a^{3} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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 \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/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","A",0
278,1,143,0,0.308903," ","integrate(b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, b x^{2} + a x - \frac{a^{2} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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)} \log\left(2 \, b^{2} x + 2 \, a b + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} b\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*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/b + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*x + 1/2*(a^2 - 1)*log(2*b^2*x + 2*a*b + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*b)/b + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*a/b","B",0
279,-2,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
280,-2,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
281,-2,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
282,-2,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
283,-2,0,0,0.000000," ","integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
284,0,0,0,0.000000," ","integrate(exp(arccosh(b*x+a)^2)*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(\operatorname{arcosh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^3*e^(arccosh(b*x + a)^2), x)","F",0
285,0,0,0,0.000000," ","integrate(exp(arccosh(b*x+a)^2)*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\operatorname{arcosh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^2*e^(arccosh(b*x + a)^2), x)","F",0
286,0,0,0,0.000000," ","integrate(exp(arccosh(b*x+a)^2)*x,x, algorithm=""maxima"")","\int x e^{\left(\operatorname{arcosh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x*e^(arccosh(b*x + a)^2), x)","F",0
287,0,0,0,0.000000," ","integrate(exp(arccosh(b*x+a)^2),x, algorithm=""maxima"")","\int e^{\left(\operatorname{arcosh}\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(e^(arccosh(b*x + a)^2), x)","F",0
288,0,0,0,0.000000," ","integrate(exp(arccosh(b*x+a)^2)/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arcosh}\left(b x + a\right)^{2}\right)}}{x}\,{d x}"," ",0,"integrate(e^(arccosh(b*x + a)^2)/x, x)","F",0
289,0,0,0,0.000000," ","integrate(exp(arccosh(b*x+a)^2)/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arcosh}\left(b x + a\right)^{2}\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arccosh(b*x + a)^2)/x^2, x)","F",0
290,0,0,0,0.000000," ","integrate(arccosh(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(b x + a\right)}{d x + \frac{a d}{b}}\,{d x}"," ",0,"integrate(arccosh(b*x + a)/(d*x + a*d/b), x)","F",0
291,0,0,0,0.000000," ","integrate(x/arccosh(x)/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{x + 1} \sqrt{x - 1} \operatorname{arcosh}\left(x\right)}\,{d x}"," ",0,"integrate(x/(sqrt(x + 1)*sqrt(x - 1)*arccosh(x)), x)","F",0
292,1,37,0,0.303738," ","integrate(x^3*arccosh(b*x^4+a),x, algorithm=""maxima"")","\frac{{\left(b x^{4} + a\right)} \operatorname{arcosh}\left(b x^{4} + a\right) - \sqrt{{\left(b x^{4} + a\right)}^{2} - 1}}{4 \, b}"," ",0,"1/4*((b*x^4 + a)*arccosh(b*x^4 + a) - sqrt((b*x^4 + a)^2 - 1))/b","A",0
293,1,39,0,0.303165," ","integrate(x^(-1+n)*arccosh(a+b*x^n),x, algorithm=""maxima"")","\frac{{\left(b x^{n} + a\right)} \operatorname{arcosh}\left(b x^{n} + a\right) - \sqrt{{\left(b x^{n} + a\right)}^{2} - 1}}{b n}"," ",0,"((b*x^n + a)*arccosh(b*x^n + a) - sqrt((b*x^n + a)^2 - 1))/(b*n)","A",0
294,0,0,0,0.000000," ","integrate(arccosh(c/(b*x+a)),x, algorithm=""maxima"")","\frac{2 \, b x \log\left(\sqrt{b x + a + c} \sqrt{-b x - a + c} b x + \sqrt{b x + a + c} \sqrt{-b x - a + c} a + {\left(b x + a\right)} c\right) - 2 \, b x \log\left(b x + a\right) + {\left(a + c\right)} \log\left(b x + a + c\right) - 2 \, {\left(b x + a\right)} \log\left(b x + a\right) + {\left(a - c\right)} \log\left(-b x - a + c\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)} e^{\left(\frac{1}{2} \, \log\left(b x + a + c\right) + \frac{1}{2} \, \log\left(-b x - a + c\right)\right)}}\,{d x}"," ",0,"1/2*(2*b*x*log(sqrt(b*x + a + c)*sqrt(-b*x - a + c)*b*x + sqrt(b*x + a + c)*sqrt(-b*x - a + c)*a + (b*x + a)*c) - 2*b*x*log(b*x + a) + (a + c)*log(b*x + a + c) - 2*(b*x + a)*log(b*x + a) + (a - c)*log(-b*x - a + c))/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)*e^(1/2*log(b*x + a + c) + 1/2*log(-b*x - a + c))), x)","F",0
295,0,0,0,0.000000," ","integrate(arccosh((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(\sqrt{b x^{2} + 1}\right)^{n}}{\sqrt{b x^{2} + 1}}\,{d x}"," ",0,"integrate(arccosh(sqrt(b*x^2 + 1))^n/sqrt(b*x^2 + 1), x)","F",0
296,0,0,0,0.000000," ","integrate(1/arccosh((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{2} + 1} \operatorname{arcosh}\left(\sqrt{b x^{2} + 1}\right)}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + 1)*arccosh(sqrt(b*x^2 + 1))), x)","F",0
