1,1,231,0,0.421379," ","integrate((e*x+d)^3*(a+b*arcsin(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} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} e + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\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} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{3} + a d^{3} x + \frac{{\left(c x \arcsin\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*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*e + 1/3*(3*x^3*arcsin(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*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^3 + a*d^3*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^3/c","A",0
2,1,150,0,0.419547," ","integrate((e*x+d)^2*(a+b*arcsin(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} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d e + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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 \arcsin\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*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*e + 1/9*(3*x^3*arcsin(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*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2/c","A",0
3,1,81,0,0.414994," ","integrate((e*x+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b e + a d x + \frac{{\left(c x \arcsin\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*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*e + a*d*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d/c","A",0
4,1,29,0,0.415627," ","integrate(a+b*arcsin(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b}{c}"," ",0,"a*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b/c","A",0
5,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x+d),x, algorithm=""maxima"")","b \int \frac{\arctan\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(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
6,-2,0,0,0.000000," ","integrate((a+b*arcsin(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
7,-2,0,0,0.000000," ","integrate((a+b*arcsin(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
8,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","-\frac{{\left({\left(c e^{4} x^{3} + 3 \, c d e^{3} x^{2} + 3 \, c d^{2} e^{2} x + c d^{3} e\right)} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{4} x^{7} + 3 \, c^{4} d e^{3} x^{6} - 3 \, c^{2} d^{2} e^{2} x^{3} - c^{2} d^{3} e x^{2} + {\left(3 \, c^{4} d^{2} e^{2} - c^{2} e^{4}\right)} x^{5} + {\left(c^{4} d^{3} e - 3 \, c^{2} d e^{3}\right)} x^{4} - {\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)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}} - \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,"-1/3*(3*(c*e^4*x^3 + 3*c*d*e^3*x^2 + 3*c*d^2*e^2*x + c*d^3*e)*integrate(1/3*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^4*x^7 + 3*c^4*d*e^3*x^6 - 3*c^2*d^2*e^2*x^3 - c^2*d^3*e*x^2 + (3*c^4*d^2*e^2 - c^2*e^4)*x^5 + (c^4*d^3*e - 3*c^2*d*e^3)*x^4 + (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^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e) - 1/3*a/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","F",0
9,0,0,0,0.000000," ","integrate((e*x+d)^3*(a+b*arcsin(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 \arcsin\left(c x\right)^{2} + \frac{3}{2} \, a^{2} d^{2} e x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d^{2} e + \frac{2}{3} \, {\left(3 \, x^{3} \arcsin\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} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b e^{3} - 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \arcsin\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{{\left(b^{2} c e^{3} x^{4} + 4 \, b^{2} c d e^{2} x^{3} + 6 \, b^{2} c d^{2} e x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{2 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/4*a^2*e^3*x^4 + a^2*d*e^2*x^3 + b^2*d^3*x*arcsin(c*x)^2 + 3/2*a^2*d^2*e*x^2 + 3/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d^2*e + 2/3*(3*x^3*arcsin(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*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*e^3 - 2*b^2*d^3*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d^3*x + 2*(c*x*arcsin(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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(1/2*(b^2*c*e^3*x^4 + 4*b^2*c*d*e^2*x^3 + 6*b^2*c*d^2*e*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
10,0,0,0,0.000000," ","integrate((e*x+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} e^{2} x^{3} + b^{2} d^{2} x \arcsin\left(c x\right)^{2} + a^{2} d e x^{2} + {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d e + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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} \arcsin\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \arcsin\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{2 \, {\left(b^{2} c e^{2} x^{3} + 3 \, b^{2} c d e x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/3*a^2*e^2*x^3 + b^2*d^2*x*arcsin(c*x)^2 + a^2*d*e*x^2 + (2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d*e + 2/9*(3*x^3*arcsin(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)*arcsin(c*x)/c) + a^2*d^2*x + 2*(c*x*arcsin(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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(2/3*(b^2*c*e^2*x^3 + 3*b^2*c*d*e*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
11,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","b^{2} d x \arcsin\left(c x\right)^{2} + \frac{1}{2} \, a^{2} e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b e + \frac{1}{2} \, {\left(x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, c \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} x^{2} - 1}\,{d x}\right)} b^{2} e - 2 \, b^{2} d {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d}{c}"," ",0,"b^2*d*x*arcsin(c*x)^2 + 1/2*a^2*e*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*e + 1/2*(x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*c*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x))*b^2*e - 2*b^2*d*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d/c","F",0
12,1,72,0,0.426582," ","integrate((a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","b^{2} x \arcsin\left(c x\right)^{2} - 2 \, b^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b}{c}"," ",0,"b^2*x*arcsin(c*x)^2 - 2*b^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b/c","A",0
13,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\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*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(e*x + d), x)","F",0
14,-2,0,0,0.000000," ","integrate((a+b*arcsin(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
15,-2,0,0,0.000000," ","integrate((a+b*arcsin(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
16,0,0,0,0.000000," ","integrate((e*x+d)^3/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{3}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^3/(b*arcsin(c*x) + a), x)","F",0
17,0,0,0,0.000000," ","integrate((e*x+d)^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{2}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^2/(b*arcsin(c*x) + a), x)","F",0
18,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{e x + d}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)/(b*arcsin(c*x) + a), x)","F",0
19,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsin(c*x) + a), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)*(b*arcsin(c*x) + a)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)^2*(b*arcsin(c*x) + a)), x)","F",0
22,-1,0,0,0.000000," ","integrate((e*x+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,-1,0,0,0.000000," ","integrate((e*x+d)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{-\sqrt{c x + 1} \sqrt{-c x + 1} + \frac{{\left(b^{2} c^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c^{2}\right)} \int \frac{\sqrt{-c x + 1} x}{\sqrt{c x + 1} {\left(c x - 1\right)} {\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)}}\,{d x}}{b}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"((b^2*c^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c^2)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x/(a*b*c^2*x^2 - a*b + (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) - sqrt(c*x + 1)*sqrt(-c*x + 1))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
25,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{{\left(e x + d\right)}^{m + 1} a^{2}}{e {\left(m + 1\right)}} + \frac{{\left(b^{2} e x + b^{2} d\right)} {\left(e x + d\right)}^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(e m + e\right)} \int \frac{{\left(b^{2} c e x + b^{2} c d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} {\left(e x + d\right)}^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(a b e m + a b e - {\left(a b c^{2} e m + a b c^{2} e\right)} x^{2}\right)} {\left(e x + d\right)}^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c^{2} e m + c^{2} e\right)} x^{2} - e m - e}\,{d x}}{e m + e}"," ",0,"(e*x + d)^(m + 1)*a^2/(e*(m + 1)) + ((b^2*e*x + b^2*d)*(e*x + d)^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + (e*m + e)*integrate(2*((b^2*c*e*x + b^2*c*d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*(e*x + d)^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (a*b*e*m + a*b*e - (a*b*c^2*e*m + a*b*c^2*e)*x^2)*(e*x + d)^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/((c^2*e*m + c^2*e)*x^2 - e*m - e), x))/(e*m + e)","F",0
28,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{{\left({\left(e x + d\right)} {\left(e x + d\right)}^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + \frac{{\left(e m + e\right)} {\left(e \int \frac{\sqrt{-c x + 1} {\left(e x + d\right)}^{m} x}{\sqrt{c x + 1} c x - \sqrt{c x + 1}}\,{d x} + d \int \frac{\sqrt{-c x + 1} {\left(e x + d\right)}^{m}}{\sqrt{c x + 1} c x - \sqrt{c x + 1}}\,{d x}\right)} c}{e {\left(m + 1\right)}}\right)} b}{e m + e} + \frac{{\left(e x + d\right)}^{m + 1} a}{e {\left(m + 1\right)}}"," ",0,"((e*x + d)*(e*x + d)^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (e*m + e)*integrate((c*e*x + c*d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*(e*x + d)^m/((c^2*e*m + c^2*e)*x^2 - e*m - e), x))*b/(e*m + e) + (e*x + d)^(m + 1)*a/(e*(m + 1))","F",0
29,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x + d\right)}^{m}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x + d)^m/(b*arcsin(c*x) + a), x)","F",0
30,-1,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(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} + \sqrt{d} \int {\left(b g^{3} x^{3} + 3 \, b f g^{2} x^{2} + 3 \, b f^{2} g x + b f^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate((b*g^3*x^3 + 3*b*f*g^2*x^2 + 3*b*f^2*g*x + b*f^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
32,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(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} + \sqrt{d} \int {\left(b g^{2} x^{2} + 2 \, b f g x + b f^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate((b*g^2*x^2 + 2*b*f*g*x + b*f^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
33,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(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 + \sqrt{d} \int {\left(b g x + b f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a g}{3 \, c^{2} d}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a*f + sqrt(d)*integrate((b*g*x + b*f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a*g/(c^2*d)","F",0
34,-2,0,0,0.000000," ","integrate((a+b*arcsin(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
35,-2,0,0,0.000000," ","integrate((a+b*arcsin(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
36,0,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(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} + \sqrt{d} \int -{\left(b c^{2} d g^{3} x^{5} + 3 \, b c^{2} d f g^{2} x^{4} - 3 \, b d f^{2} g x - b d f^{3} + {\left(3 \, b c^{2} d f^{2} g - b d g^{3}\right)} x^{3} + {\left(b c^{2} d f^{3} - 3 \, b d f g^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate(-(b*c^2*d*g^3*x^5 + 3*b*c^2*d*f*g^2*x^4 - 3*b*d*f^2*g*x - b*d*f^3 + (3*b*c^2*d*f^2*g - b*d*g^3)*x^3 + (b*c^2*d*f^3 - 3*b*d*f*g^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
37,0,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(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} + \sqrt{d} \int -{\left(b c^{2} d g^{2} x^{4} + 2 \, b c^{2} d f g x^{3} - 2 \, b d f g x - b d f^{2} + {\left(b c^{2} d f^{2} - b d g^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate(-(b*c^2*d*g^2*x^4 + 2*b*c^2*d*f*g*x^3 - 2*b*d*f*g*x - b*d*f^2 + (b*c^2*d*f^2 - b*d*g^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
38,0,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(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} + \sqrt{d} \int -{\left(b c^{2} d g x^{3} + b c^{2} d f x^{2} - b d g x - b d f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate(-(b*c^2*d*g*x^3 + b*c^2*d*f*x^2 - b*d*g*x - b*d*f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
39,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(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
40,0,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(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} + \sqrt{d} \int {\left(b c^{4} d^{2} g^{3} x^{7} + 3 \, b c^{4} d^{2} f g^{2} x^{6} + 3 \, b d^{2} f^{2} g x + b d^{2} f^{3} + {\left(3 \, b c^{4} d^{2} f^{2} g - 2 \, b c^{2} d^{2} g^{3}\right)} x^{5} + {\left(b c^{4} d^{2} f^{3} - 6 \, b c^{2} d^{2} f g^{2}\right)} x^{4} - {\left(6 \, b c^{2} d^{2} f^{2} g - b d^{2} g^{3}\right)} x^{3} - {\left(2 \, b c^{2} d^{2} f^{3} - 3 \, b d^{2} f g^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate((b*c^4*d^2*g^3*x^7 + 3*b*c^4*d^2*f*g^2*x^6 + 3*b*d^2*f^2*g*x + b*d^2*f^3 + (3*b*c^4*d^2*f^2*g - 2*b*c^2*d^2*g^3)*x^5 + (b*c^4*d^2*f^3 - 6*b*c^2*d^2*f*g^2)*x^4 - (6*b*c^2*d^2*f^2*g - b*d^2*g^3)*x^3 - (2*b*c^2*d^2*f^3 - 3*b*d^2*f*g^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
41,0,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(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} + \sqrt{d} \int {\left(b c^{4} d^{2} g^{2} x^{6} + 2 \, b c^{4} d^{2} f g x^{5} - 4 \, b c^{2} d^{2} f g x^{3} + 2 \, b d^{2} f g x + b d^{2} f^{2} + {\left(b c^{4} d^{2} f^{2} - 2 \, b c^{2} d^{2} g^{2}\right)} x^{4} - {\left(2 \, b c^{2} d^{2} f^{2} - b d^{2} g^{2}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate((b*c^4*d^2*g^2*x^6 + 2*b*c^4*d^2*f*g*x^5 - 4*b*c^2*d^2*f*g*x^3 + 2*b*d^2*f*g*x + b*d^2*f^2 + (b*c^4*d^2*f^2 - 2*b*c^2*d^2*g^2)*x^4 - (2*b*c^2*d^2*f^2 - b*d^2*g^2)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
42,0,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(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} + \sqrt{d} \int {\left(b c^{4} d^{2} g x^{5} + b c^{4} d^{2} f x^{4} - 2 \, b c^{2} d^{2} g x^{3} - 2 \, b c^{2} d^{2} f x^{2} + b d^{2} g x + b d^{2} f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\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) + sqrt(d)*integrate((b*c^4*d^2*g*x^5 + b*c^4*d^2*f*x^4 - 2*b*c^2*d^2*g*x^3 - 2*b*c^2*d^2*f*x^2 + b*d^2*g*x + b*d^2*f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
43,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(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
44,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(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{b f^{3} \arcsin\left(c x\right)^{2}}{2 \, c \sqrt{d}} + \frac{3 \, b f^{2} g x}{c \sqrt{d}} + \frac{a f^{3} \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} b f^{2} g \arcsin\left(c x\right)}{c^{2} d} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} a f^{2} g}{c^{2} d} - \sqrt{d} \int \frac{{\left(b g^{3} x^{3} + 3 \, b f g^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{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))) + 1/2*b*f^3*arcsin(c*x)^2/(c*sqrt(d)) + 3*b*f^2*g*x/(c*sqrt(d)) + a*f^3*arcsin(c*x)/(c*sqrt(d)) - 3*sqrt(-c^2*d*x^2 + d)*b*f^2*g*arcsin(c*x)/(c^2*d) - 3*sqrt(-c^2*d*x^2 + d)*a*f^2*g/(c^2*d) - sqrt(d)*integrate((b*g^3*x^3 + 3*b*f*g^2*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d*x^2 - d), x)","F",0
45,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(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{b f^{2} \arcsin\left(c x\right)^{2}}{2 \, c \sqrt{d}} + \frac{b g^{2} \int \frac{x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x}}{\sqrt{d}} + \frac{2 \, b f g x}{c \sqrt{d}} + \frac{a f^{2} \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} b f g \arcsin\left(c x\right)}{c^{2} d} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a f g}{c^{2} d}"," ",0,"-1/2*a*g^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + 1/2*b*f^2*arcsin(c*x)^2/(c*sqrt(d)) + b*g^2*integrate(x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d) + 2*b*f*g*x/(c*sqrt(d)) + a*f^2*arcsin(c*x)/(c*sqrt(d)) - 2*sqrt(-c^2*d*x^2 + d)*b*f*g*arcsin(c*x)/(c^2*d) - 2*sqrt(-c^2*d*x^2 + d)*a*f*g/(c^2*d)","F",0
46,1,90,0,0.454833," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b f \arcsin\left(c x\right)^{2}}{2 \, c \sqrt{d}} + \frac{b g x}{c \sqrt{d}} + \frac{a f \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{\sqrt{-c^{2} d x^{2} + d} b g \arcsin\left(c x\right)}{c^{2} d} - \frac{\sqrt{-c^{2} d x^{2} + d} a g}{c^{2} d}"," ",0,"1/2*b*f*arcsin(c*x)^2/(c*sqrt(d)) + b*g*x/(c*sqrt(d)) + a*f*arcsin(c*x)/(c*sqrt(d)) - sqrt(-c^2*d*x^2 + d)*b*g*arcsin(c*x)/(c^2*d) - sqrt(-c^2*d*x^2 + d)*a*g/(c^2*d)","A",0
47,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{b \arcsin\left(c x\right) + a}{\sqrt{-c^{2} d x^{2} + d} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)/(sqrt(-c^2*d*x^2 + d)*(g*x + f)), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{b \arcsin\left(c x\right) + a}{\sqrt{-c^{2} d x^{2} + d} {\left(g x + f\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)/(sqrt(-c^2*d*x^2 + d)*(g*x + f)^2), x)","F",0
49,-1,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","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 \arcsin\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} + \sqrt{d} \int \frac{{\left(b g^{2} x^{2} + 2 \, b f g x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x} - \frac{b f^{2} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, c d^{\frac{3}{2}}} + \frac{2 \, a f g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"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*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*f^2*x/(sqrt(-c^2*d*x^2 + d)*d) + sqrt(d)*integrate((b*g^2*x^2 + 2*b*f*g*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) - 1/2*b*f^2*log(x^2 - 1/c^2)/(c*d^(3/2)) + 2*a*f*g/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
51,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{b f x \arcsin\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{b f \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, c d^{\frac{3}{2}}} + \frac{\frac{1}{2} \, {\left(\sqrt{c x + 1} \sqrt{-c x + 1} c^{3} d^{2} {\left(\frac{2 \, x}{c^{2} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} + 2 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b g}{\sqrt{c x + 1} \sqrt{-c x + 1} c^{2} d^{\frac{3}{2}}} + \frac{a g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"b*f*x*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*f*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/2*b*f*log(x^2 - 1/c^2)/(c*d^(3/2)) + (sqrt(c*x + 1)*sqrt(-c*x + 1)*c^3*d^2*integrate(x^2/(c^4*d^2*x^4 - c^2*d^2*x^2 + (c^2*d^2*x^2 - d^2)*e^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b*g/(sqrt(c*x + 1)*sqrt(-c*x + 1)*c^2*d^(3/2)) + a*g/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
52,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{b \arcsin\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*arcsin(c*x) + a)/((-c^2*d*x^2 + d)^(3/2)*(g*x + f)), x)","F",0
53,0,0,0,0.000000," ","integrate((g*x+f)^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c f^{4} {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b f^{4} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} - \frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d^{2}} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} a g^{4} + \frac{1}{3} \, a f^{4} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \frac{4}{3} \, a f g^{3} {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} - 2 \, a f^{2} g^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} - \sqrt{d} \int \frac{{\left(b g^{4} x^{4} + 4 \, b f g^{3} x^{3} + 6 \, b f^{2} g^{2} x^{2} + 4 \, b f^{3} g x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}\,{d x} + \frac{4 \, a f^{3} g}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"1/6*b*c*f^4*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 1/3*b*f^4*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*(x*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) - x/(sqrt(-c^2*d*x^2 + d)*c^4*d^2) + 3*arcsin(c*x)/(c^5*d^(5/2)))*a*g^4 + 1/3*a*f^4*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) + 4/3*a*f*g^3*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) - 2*a*f^2*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d)) - sqrt(d)*integrate((b*g^4*x^4 + 4*b*f*g^3*x^3 + 6*b*f^2*g^2*x^2 + 4*b*f^3*g*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 4/3*a*f^3*g/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
54,-1,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c f^{2} {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b f^{2} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a f^{2} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} - \frac{1}{3} \, a g^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} - \sqrt{d} \int \frac{{\left(b g^{2} x^{2} + 2 \, b f g x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}\,{d x} + \frac{2 \, a f g}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"1/6*b*c*f^2*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 1/3*b*f^2*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a*f^2*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) - 1/3*a*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d)) - sqrt(d)*integrate((b*g^2*x^2 + 2*b*f*g*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 2/3*a*f*g/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
56,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c f {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b f {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a f {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \frac{\frac{b g \int \frac{x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x + 1\right)}^{\frac{5}{2}} {\left(c x - 1\right)}^{2} \sqrt{-c x + 1}}\,{d x}}{d^{2}}}{\sqrt{d}} + \frac{a g}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"1/6*b*c*f*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 1/3*b*f*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a*f*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) + b*g*integrate(x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d) + 1/3*a*g/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
57,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{b \arcsin\left(c x\right) + a}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)/((-c^2*d*x^2 + d)^(5/2)*(g*x + f)), x)","F",0
58,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))^2*(-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^{2} f^{3} - \frac{1}{15} \, a^{2} 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^{2} 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^{2} f^{2} g}{c^{2} d} + \sqrt{d} \int {\left({\left(b^{2} g^{3} x^{3} + 3 \, b^{2} f g^{2} x^{2} + 3 \, b^{2} f^{2} g x + b^{2} f^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{3} x^{3} + 3 \, a b f g^{2} x^{2} + 3 \, a b f^{2} g x + a b f^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a^2*f^3 - 1/15*a^2*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^2*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^2*f^2*g/(c^2*d) + sqrt(d)*integrate(((b^2*g^3*x^3 + 3*b^2*f*g^2*x^2 + 3*b^2*f^2*g*x + b^2*f^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^3*x^3 + 3*a*b*f*g^2*x^2 + 3*a*b*f^2*g*x + a*b*f^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
59,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2*(-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^{2} f^{2} + \frac{1}{8} \, a^{2} 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^{2} f g}{3 \, c^{2} d} + \sqrt{d} \int {\left({\left(b^{2} g^{2} x^{2} + 2 \, b^{2} f g x + b^{2} f^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{2} x^{2} + 2 \, a b f g x + a b f^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a^2*f^2 + 1/8*a^2*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^2*f*g/(c^2*d) + sqrt(d)*integrate(((b^2*g^2*x^2 + 2*b^2*f*g*x + b^2*f^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^2*x^2 + 2*a*b*f*g*x + a*b*f^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
60,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2*(-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^{2} f - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2} g}{3 \, c^{2} d} + \sqrt{d} \int {\left({\left(b^{2} g x + b^{2} f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g x + a b f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a^2*f - 1/3*(-c^2*d*x^2 + d)^(3/2)*a^2*g/(c^2*d) + sqrt(d)*integrate(((b^2*g*x + b^2*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g*x + a*b*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
61,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2*(-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
62,0,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,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^{2} 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^{2} g^{3} + \frac{1}{16} \, a^{2} 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^{2} f^{2} g}{5 \, c^{2} d} + \sqrt{d} \int -{\left({\left(b^{2} c^{2} d g^{3} x^{5} + 3 \, b^{2} c^{2} d f g^{2} x^{4} - 3 \, b^{2} d f^{2} g x - b^{2} d f^{3} + {\left(3 \, b^{2} c^{2} d f^{2} g - b^{2} d g^{3}\right)} x^{3} + {\left(b^{2} c^{2} d f^{3} - 3 \, b^{2} d f g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d g^{3} x^{5} + 3 \, a b c^{2} d f g^{2} x^{4} - 3 \, a b d f^{2} g x - a b d f^{3} + {\left(3 \, a b c^{2} d f^{2} g - a b d g^{3}\right)} x^{3} + {\left(a b c^{2} d f^{3} - 3 \, a b d f g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{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^2*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^2*g^3 + 1/16*a^2*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^2*f^2*g/(c^2*d) + sqrt(d)*integrate(-((b^2*c^2*d*g^3*x^5 + 3*b^2*c^2*d*f*g^2*x^4 - 3*b^2*d*f^2*g*x - b^2*d*f^3 + (3*b^2*c^2*d*f^2*g - b^2*d*g^3)*x^3 + (b^2*c^2*d*f^3 - 3*b^2*d*f*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*g^3*x^5 + 3*a*b*c^2*d*f*g^2*x^4 - 3*a*b*d*f^2*g*x - a*b*d*f^3 + (3*a*b*c^2*d*f^2*g - a*b*d*g^3)*x^3 + (a*b*c^2*d*f^3 - 3*a*b*d*f*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*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)^(3/2)*(a+b*arcsin(c*x))^2,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^{2} f^{2} + \frac{1}{48} \, a^{2} 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^{2} f g}{5 \, c^{2} d} + \sqrt{d} \int -{\left({\left(b^{2} c^{2} d g^{2} x^{4} + 2 \, b^{2} c^{2} d f g x^{3} - 2 \, b^{2} d f g x - b^{2} d f^{2} + {\left(b^{2} c^{2} d f^{2} - b^{2} d g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d g^{2} x^{4} + 2 \, a b c^{2} d f g x^{3} - 2 \, a b d f g x - a b d f^{2} + {\left(a b c^{2} d f^{2} - a b d g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{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^2*f^2 + 1/48*a^2*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^2*f*g/(c^2*d) + sqrt(d)*integrate(-((b^2*c^2*d*g^2*x^4 + 2*b^2*c^2*d*f*g*x^3 - 2*b^2*d*f*g*x - b^2*d*f^2 + (b^2*c^2*d*f^2 - b^2*d*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*g^2*x^4 + 2*a*b*c^2*d*f*g*x^3 - 2*a*b*d*f*g*x - a*b*d*f^2 + (a*b*c^2*d*f^2 - a*b*d*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*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)^(3/2)*(a+b*arcsin(c*x))^2,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^{2} f - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a^{2} g}{5 \, c^{2} d} + \sqrt{d} \int -{\left({\left(b^{2} c^{2} d g x^{3} + b^{2} c^{2} d f x^{2} - b^{2} d g x - b^{2} d f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d g x^{3} + a b c^{2} d f x^{2} - a b d g x - a b d f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{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^2*f - 1/5*(-c^2*d*x^2 + d)^(5/2)*a^2*g/(c^2*d) + sqrt(d)*integrate(-((b^2*c^2*d*g*x^3 + b^2*c^2*d*f*x^2 - b^2*d*g*x - b^2*d*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*g*x^3 + a*b*c^2*d*f*x^2 - a*b*d*g*x - a*b*d*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
65,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^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
66,0,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,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^{2} 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^{2} 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^{2} g^{3} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a^{2} f^{2} g}{7 \, c^{2} d} + \sqrt{d} \int {\left({\left(b^{2} c^{4} d^{2} g^{3} x^{7} + 3 \, b^{2} c^{4} d^{2} f g^{2} x^{6} + 3 \, b^{2} d^{2} f^{2} g x + b^{2} d^{2} f^{3} + {\left(3 \, b^{2} c^{4} d^{2} f^{2} g - 2 \, b^{2} c^{2} d^{2} g^{3}\right)} x^{5} + {\left(b^{2} c^{4} d^{2} f^{3} - 6 \, b^{2} c^{2} d^{2} f g^{2}\right)} x^{4} - {\left(6 \, b^{2} c^{2} d^{2} f^{2} g - b^{2} d^{2} g^{3}\right)} x^{3} - {\left(2 \, b^{2} c^{2} d^{2} f^{3} - 3 \, b^{2} d^{2} f g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{4} d^{2} g^{3} x^{7} + 3 \, a b c^{4} d^{2} f g^{2} x^{6} + 3 \, a b d^{2} f^{2} g x + a b d^{2} f^{3} + {\left(3 \, a b c^{4} d^{2} f^{2} g - 2 \, a b c^{2} d^{2} g^{3}\right)} x^{5} + {\left(a b c^{4} d^{2} f^{3} - 6 \, a b c^{2} d^{2} f g^{2}\right)} x^{4} - {\left(6 \, a b c^{2} d^{2} f^{2} g - a b d^{2} g^{3}\right)} x^{3} - {\left(2 \, a b c^{2} d^{2} f^{3} - 3 \, a b d^{2} f g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{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^2*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^2*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^2*g^3 - 3/7*(-c^2*d*x^2 + d)^(7/2)*a^2*f^2*g/(c^2*d) + sqrt(d)*integrate(((b^2*c^4*d^2*g^3*x^7 + 3*b^2*c^4*d^2*f*g^2*x^6 + 3*b^2*d^2*f^2*g*x + b^2*d^2*f^3 + (3*b^2*c^4*d^2*f^2*g - 2*b^2*c^2*d^2*g^3)*x^5 + (b^2*c^4*d^2*f^3 - 6*b^2*c^2*d^2*f*g^2)*x^4 - (6*b^2*c^2*d^2*f^2*g - b^2*d^2*g^3)*x^3 - (2*b^2*c^2*d^2*f^3 - 3*b^2*d^2*f*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*g^3*x^7 + 3*a*b*c^4*d^2*f*g^2*x^6 + 3*a*b*d^2*f^2*g*x + a*b*d^2*f^3 + (3*a*b*c^4*d^2*f^2*g - 2*a*b*c^2*d^2*g^3)*x^5 + (a*b*c^4*d^2*f^3 - 6*a*b*c^2*d^2*f*g^2)*x^4 - (6*a*b*c^2*d^2*f^2*g - a*b*d^2*g^3)*x^3 - (2*a*b*c^2*d^2*f^3 - 3*a*b*d^2*f*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
67,0,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,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^{2} 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^{2} g^{2} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a^{2} f g}{7 \, c^{2} d} + \sqrt{d} \int {\left({\left(b^{2} c^{4} d^{2} g^{2} x^{6} + 2 \, b^{2} c^{4} d^{2} f g x^{5} - 4 \, b^{2} c^{2} d^{2} f g x^{3} + 2 \, b^{2} d^{2} f g x + b^{2} d^{2} f^{2} + {\left(b^{2} c^{4} d^{2} f^{2} - 2 \, b^{2} c^{2} d^{2} g^{2}\right)} x^{4} - {\left(2 \, b^{2} c^{2} d^{2} f^{2} - b^{2} d^{2} g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{4} d^{2} g^{2} x^{6} + 2 \, a b c^{4} d^{2} f g x^{5} - 4 \, a b c^{2} d^{2} f g x^{3} + 2 \, a b d^{2} f g x + a b d^{2} f^{2} + {\left(a b c^{4} d^{2} f^{2} - 2 \, a b c^{2} d^{2} g^{2}\right)} x^{4} - {\left(2 \, a b c^{2} d^{2} f^{2} - a b d^{2} g^{2}\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{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^2*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^2*g^2 - 2/7*(-c^2*d*x^2 + d)^(7/2)*a^2*f*g/(c^2*d) + sqrt(d)*integrate(((b^2*c^4*d^2*g^2*x^6 + 2*b^2*c^4*d^2*f*g*x^5 - 4*b^2*c^2*d^2*f*g*x^3 + 2*b^2*d^2*f*g*x + b^2*d^2*f^2 + (b^2*c^4*d^2*f^2 - 2*b^2*c^2*d^2*g^2)*x^4 - (2*b^2*c^2*d^2*f^2 - b^2*d^2*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*g^2*x^6 + 2*a*b*c^4*d^2*f*g*x^5 - 4*a*b*c^2*d^2*f*g*x^3 + 2*a*b*d^2*f*g*x + a*b*d^2*f^2 + (a*b*c^4*d^2*f^2 - 2*a*b*c^2*d^2*g^2)*x^4 - (2*a*b*c^2*d^2*f^2 - a*b*d^2*g^2)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
68,0,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,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^{2} f - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a^{2} g}{7 \, c^{2} d} + \sqrt{d} \int {\left({\left(b^{2} c^{4} d^{2} g x^{5} + b^{2} c^{4} d^{2} f x^{4} - 2 \, b^{2} c^{2} d^{2} g x^{3} - 2 \, b^{2} c^{2} d^{2} f x^{2} + b^{2} d^{2} g x + b^{2} d^{2} f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{4} d^{2} g x^{5} + a b c^{4} d^{2} f x^{4} - 2 \, a b c^{2} d^{2} g x^{3} - 2 \, a b c^{2} d^{2} f x^{2} + a b d^{2} g x + a b d^{2} f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{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^2*f - 1/7*(-c^2*d*x^2 + d)^(7/2)*a^2*g/(c^2*d) + sqrt(d)*integrate(((b^2*c^4*d^2*g*x^5 + b^2*c^4*d^2*f*x^4 - 2*b^2*c^2*d^2*g*x^3 - 2*b^2*c^2*d^2*f*x^2 + b^2*d^2*g*x + b^2*d^2*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*g*x^5 + a*b*c^4*d^2*f*x^4 - 2*a*b*c^2*d^2*g*x^3 - 2*a*b*c^2*d^2*f*x^2 + a*b*d^2*g*x + a*b*d^2*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
69,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^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
70,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} 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^{2} 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 b f^{3} \arcsin\left(c x\right)^{2}}{c \sqrt{d}} + \frac{6 \, a b f^{2} g x}{c \sqrt{d}} + \frac{a^{2} f^{3} \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{6 \, \sqrt{-c^{2} d x^{2} + d} a b f^{2} g \arcsin\left(c x\right)}{c^{2} d} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} a^{2} f^{2} g}{c^{2} d} - \sqrt{d} \int \frac{{\left({\left(b^{2} g^{3} x^{3} + 3 \, b^{2} f g^{2} x^{2} + 3 \, b^{2} f^{2} g x + b^{2} f^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{3} x^{3} + 3 \, a b f g^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-1/3*a^2*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^2*f*g^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + a*b*f^3*arcsin(c*x)^2/(c*sqrt(d)) + 6*a*b*f^2*g*x/(c*sqrt(d)) + a^2*f^3*arcsin(c*x)/(c*sqrt(d)) - 6*sqrt(-c^2*d*x^2 + d)*a*b*f^2*g*arcsin(c*x)/(c^2*d) - 3*sqrt(-c^2*d*x^2 + d)*a^2*f^2*g/(c^2*d) - sqrt(d)*integrate(((b^2*g^3*x^3 + 3*b^2*f*g^2*x^2 + 3*b^2*f^2*g*x + b^2*f^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^3*x^3 + 3*a*b*f*g^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^2 - d), x)","F",0
71,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} 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 b f^{2} \arcsin\left(c x\right)^{2}}{c \sqrt{d}} + \frac{4 \, a b f g x}{c \sqrt{d}} + \frac{a^{2} f^{2} \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{4 \, \sqrt{-c^{2} d x^{2} + d} a b f g \arcsin\left(c x\right)}{c^{2} d} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a^{2} f g}{c^{2} d} - \sqrt{d} \int \frac{{\left(2 \, a b g^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(b^{2} g^{2} x^{2} + 2 \, b^{2} f g x + b^{2} f^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-1/2*a^2*g^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + a*b*f^2*arcsin(c*x)^2/(c*sqrt(d)) + 4*a*b*f*g*x/(c*sqrt(d)) + a^2*f^2*arcsin(c*x)/(c*sqrt(d)) - 4*sqrt(-c^2*d*x^2 + d)*a*b*f*g*arcsin(c*x)/(c^2*d) - 2*sqrt(-c^2*d*x^2 + d)*a^2*f*g/(c^2*d) - sqrt(d)*integrate((2*a*b*g^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (b^2*g^2*x^2 + 2*b^2*f*g*x + b^2*f^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^2 - d), x)","F",0
72,1,184,0,0.472263," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} f \arcsin\left(c x\right)^{3}}{3 \, c \sqrt{d}} + 2 \, b^{2} g {\left(\frac{x \arcsin\left(c x\right)}{c \sqrt{d}} + \frac{\sqrt{-c^{2} x^{2} + 1}}{c^{2} \sqrt{d}}\right)} + \frac{a b f \arcsin\left(c x\right)^{2}}{c \sqrt{d}} + \frac{2 \, a b g x}{c \sqrt{d}} + \frac{a^{2} f \arcsin\left(c x\right)}{c \sqrt{d}} - \frac{\sqrt{-c^{2} d x^{2} + d} b^{2} g \arcsin\left(c x\right)^{2}}{c^{2} d} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b g \arcsin\left(c x\right)}{c^{2} d} - \frac{\sqrt{-c^{2} d x^{2} + d} a^{2} g}{c^{2} d}"," ",0,"1/3*b^2*f*arcsin(c*x)^3/(c*sqrt(d)) + 2*b^2*g*(x*arcsin(c*x)/(c*sqrt(d)) + sqrt(-c^2*x^2 + 1)/(c^2*sqrt(d))) + a*b*f*arcsin(c*x)^2/(c*sqrt(d)) + 2*a*b*g*x/(c*sqrt(d)) + a^2*f*arcsin(c*x)/(c*sqrt(d)) - sqrt(-c^2*d*x^2 + d)*b^2*g*arcsin(c*x)^2/(c^2*d) - 2*sqrt(-c^2*d*x^2 + d)*a*b*g*arcsin(c*x)/(c^2*d) - sqrt(-c^2*d*x^2 + d)*a^2*g/(c^2*d)","A",0
73,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}{\sqrt{-c^{2} d x^{2} + d} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2/(sqrt(-c^2*d*x^2 + d)*(g*x + f)), x)","F",0
74,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}{\sqrt{-c^{2} d x^{2} + d} {\left(g x + f\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2/(sqrt(-c^2*d*x^2 + d)*(g*x + f)^2), x)","F",0
75,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a^{2} 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^{2} 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{2 \, a b f^{3} x \arcsin\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a^{2} f^{3} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{a b f^{3} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{c d^{\frac{3}{2}}} + \frac{3 \, a^{2} f^{2} g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \sqrt{d} \int \frac{{\left(b^{2} g^{3} x^{3} + 3 \, b^{2} f g^{2} x^{2} + 3 \, b^{2} f^{2} g x + b^{2} f^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{3} x^{3} + 3 \, a b f g^{2} x^{2} + 3 \, a b f^{2} g x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c^{2} d^{2} x^{2} - d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x}"," ",0,"-a^2*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^2*f*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + 2*a*b*f^3*x*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a^2*f^3*x/(sqrt(-c^2*d*x^2 + d)*d) - a*b*f^3*log(x^2 - 1/c^2)/(c*d^(3/2)) + 3*a^2*f^2*g/(sqrt(-c^2*d*x^2 + d)*c^2*d) - sqrt(d)*integrate(((b^2*g^3*x^3 + 3*b^2*f*g^2*x^2 + 3*b^2*f^2*g*x + b^2*f^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^3*x^3 + 3*a*b*f*g^2*x^2 + 3*a*b*f^2*g*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/((c^2*d^2*x^2 - d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
76,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a^{2} 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{2 \, a b f^{2} x \arcsin\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a^{2} f^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{a b f^{2} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{c d^{\frac{3}{2}}} - \sqrt{d} \int \frac{{\left(b^{2} g^{2} x^{2} + 2 \, b^{2} f g x + b^{2} f^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{2} x^{2} + 2 \, a b f g x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c^{2} d^{2} x^{2} - d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + \frac{2 \, a^{2} f g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"a^2*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + 2*a*b*f^2*x*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a^2*f^2*x/(sqrt(-c^2*d*x^2 + d)*d) - a*b*f^2*log(x^2 - 1/c^2)/(c*d^(3/2)) - sqrt(d)*integrate(((b^2*g^2*x^2 + 2*b^2*f*g*x + b^2*f^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^2*x^2 + 2*a*b*f*g*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/((c^2*d^2*x^2 - d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 2*a^2*f*g/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
77,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{2 \, a b f x \arcsin\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a^{2} f x}{\sqrt{-c^{2} d x^{2} + d} d} - \sqrt{d} \int \frac{2 \, a b g x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(b^{2} g x + b^{2} f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c^{2} d^{2} x^{2} - d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} - \frac{a b f \log\left(x^{2} - \frac{1}{c^{2}}\right)}{c d^{\frac{3}{2}}} + \frac{a^{2} g}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"2*a*b*f*x*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a^2*f*x/(sqrt(-c^2*d*x^2 + d)*d) - sqrt(d)*integrate((2*a*b*g*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (b^2*g*x + b^2*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/((c^2*d^2*x^2 - d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) - a*b*f*log(x^2 - 1/c^2)/(c*d^(3/2)) + a^2*g/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
78,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(g x + f\right)}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2/((-c^2*d*x^2 + d)^(3/2)*(g*x + f)), x)","F",0
79,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c f^{3} {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b f^{3} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} f^{3} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \frac{1}{3} \, a^{2} g^{3} {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} - a^{2} f g^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} + \sqrt{d} \int \frac{{\left(b^{2} g^{3} x^{3} + 3 \, b^{2} f g^{2} x^{2} + 3 \, b^{2} f^{2} g x + b^{2} f^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{3} x^{3} + 3 \, a b f g^{2} x^{2} + 3 \, a b f^{2} g x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + \frac{a^{2} f^{2} g}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"1/3*a*b*c*f^3*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 2/3*a*b*f^3*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a^2*f^3*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) + 1/3*a^2*g^3*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) - a^2*f*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d)) + sqrt(d)*integrate(((b^2*g^3*x^3 + 3*b^2*f*g^2*x^2 + 3*b^2*f^2*g*x + b^2*f^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^3*x^3 + 3*a*b*f*g^2*x^2 + 3*a*b*f^2*g*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/((c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + a^2*f^2*g/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
80,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c f^{2} {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b f^{2} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} f^{2} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} - \frac{1}{3} \, a^{2} g^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} + \sqrt{d} \int \frac{{\left(b^{2} g^{2} x^{2} + 2 \, b^{2} f g x + b^{2} f^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b g^{2} x^{2} + 2 \, a b f g x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + \frac{2 \, a^{2} f g}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"1/3*a*b*c*f^2*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 2/3*a*b*f^2*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a^2*f^2*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) - 1/3*a^2*g^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d)) + sqrt(d)*integrate(((b^2*g^2*x^2 + 2*b^2*f*g*x + b^2*f^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*g^2*x^2 + 2*a*b*f*g*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/((c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 2/3*a^2*f*g/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
81,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c f {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b f {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} f {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \sqrt{d} \int \frac{2 \, a b g x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(b^{2} g x + b^{2} f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + \frac{a^{2} g}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"1/3*a*b*c*f*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 2/3*a*b*f*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a^2*f*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) + sqrt(d)*integrate((2*a*b*g*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (b^2*g*x + b^2*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/((c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/3*a^2*g/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
82,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^n*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\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*arcsin(c*x) + a)^n*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","F",0
83,-1,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^3*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\frac{1}{3} \, b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{3} \log\left(h\right) + a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(h\right) + b^{2} c \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left({\left(g x + f\right)}^{m}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + 2 \, a b c \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left({\left(g x + f\right)}^{m}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + a^{2} c \int \frac{\log\left({\left(g x + f\right)}^{m}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + a^{2} \arctan\left(c x, \sqrt{-c^{2} x^{2} + 1}\right) \log\left(h\right)}{c}"," ",0,"(b^2*c*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)*log(h) + 2*a*b*c*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)*log(h) + b^2*c*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log((g*x + f)^m)/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 2*a*b*c*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log((g*x + f)^m)/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + a^2*c*integrate(log((g*x + f)^m)/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + a^2*arctan2(c*x, sqrt(-c^2*x^2 + 1))*log(h))/c","F",0
85,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\frac{1}{2} \, b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(h\right) + b c \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left({\left(g x + f\right)}^{m}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + a c \int \frac{\log\left({\left(g x + f\right)}^{m}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + a \arctan\left(c x, \sqrt{-c^{2} x^{2} + 1}\right) \log\left(h\right)}{c}"," ",0,"(b*c*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)*log(h) + b*c*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log((g*x + f)^m)/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + a*c*integrate(log((g*x + f)^m)/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + a*arctan2(c*x, sqrt(-c^2*x^2 + 1))*log(h))/c","F",0
86,0,0,0,0.000000," ","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
87,0,0,0,0.000000," ","integrate(log(h*(g*x+f)^m)/(a+b*arcsin(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 \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(log((g*x + f)^m*h)/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
88,1,528,0,1.249048," ","integrate((e*x+d)^3*(g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{3} g x^{5} + \frac{1}{4} \, a e^{3} f x^{4} + \frac{3}{4} \, a d e^{2} g x^{4} + a d e^{2} f x^{3} + a d^{2} e g x^{3} + \frac{3}{2} \, a d^{2} e f x^{2} + \frac{1}{2} \, a d^{3} g x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} e f + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\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} f + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{3} f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{3} g + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} e g + \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d e^{2} g + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{3} g + a d^{3} f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{3} f}{c}"," ",0,"1/5*a*e^3*g*x^5 + 1/4*a*e^3*f*x^4 + 3/4*a*d*e^2*g*x^4 + a*d*e^2*f*x^3 + a*d^2*e*g*x^3 + 3/2*a*d^2*e*f*x^2 + 1/2*a*d^3*g*x^2 + 3/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*e*f + 1/3*(3*x^3*arcsin(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*f + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^3*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^3*g + 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2*e*g + 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*e^2*g + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^3*g + a*d^3*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^3*f/c","A",0
89,1,353,0,0.489532," ","integrate((e*x+d)^2*(g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{2} g x^{4} + \frac{1}{3} \, a e^{2} f x^{3} + \frac{2}{3} \, a d e g x^{3} + a d e f x^{2} + \frac{1}{2} \, a d^{2} g x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d e f + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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} f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} g + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 g + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{2} g + a d^{2} f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{2} f}{c}"," ",0,"1/4*a*e^2*g*x^4 + 1/3*a*e^2*f*x^3 + 2/3*a*d*e*g*x^3 + a*d*e*f*x^2 + 1/2*a*d^2*g*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*e*f + 1/9*(3*x^3*arcsin(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*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*g + 2/9*(3*x^3*arcsin(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*g + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^2*g + a*d^2*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2*f/c","A",0
90,1,199,0,1.823138," ","integrate((e*x+d)*(g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e g x^{3} + \frac{1}{2} \, a e f x^{2} + \frac{1}{2} \, a d g x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b e f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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 g + a d f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d f}{c}"," ",0,"1/3*a*e*g*x^3 + 1/2*a*e*f*x^2 + 1/2*a*d*g*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*e*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e*g + a*d*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d*f/c","A",0
91,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x, algorithm=""maxima"")","a g {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} + \frac{a f \log\left(e x + d\right)}{e} + \int \frac{{\left(b g x + b f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x + d}\,{d x}"," ",0,"a*g*(x/e - d*log(e*x + d)/e^2) + a*f*log(e*x + d)/e + integrate((b*g*x + b*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x + d), x)","F",0
92,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(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
93,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(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
94,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","-\frac{{\left(3 \, e x + d\right)} a g}{6 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{a f}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}} - \frac{{\left(3 \, b e g x + 2 \, b e f + b d g\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)} \int \frac{{\left(3 \, b c e g x + 2 \, b c e f + b c d g\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{5} x^{7} + 3 \, c^{4} d e^{4} x^{6} - 3 \, c^{2} d^{2} e^{3} x^{3} - c^{2} d^{3} e^{2} x^{2} + {\left(3 \, c^{4} d^{2} e^{3} - c^{2} e^{5}\right)} x^{5} + {\left(c^{4} d^{3} e^{2} - 3 \, c^{2} d e^{4}\right)} x^{4} - {\left(c^{2} e^{5} x^{5} + 3 \, c^{2} d e^{4} x^{4} - 3 \, d^{2} e^{3} x - d^{3} e^{2} + {\left(3 \, c^{2} d^{2} e^{3} - e^{5}\right)} x^{3} + {\left(c^{2} d^{3} e^{2} - 3 \, d e^{4}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}}{6 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}"," ",0,"-1/6*(3*e*x + d)*a*g/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2) - 1/3*a*f/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e) - 1/6*((3*b*e*g*x + 2*b*e*f + b*d*g)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 6*(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)*integrate(1/6*(3*b*c*e*g*x + 2*b*c*e*f + b*c*d*g)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^5*x^7 + 3*c^4*d*e^4*x^6 - 3*c^2*d^2*e^3*x^3 - c^2*d^3*e^2*x^2 + (3*c^4*d^2*e^3 - c^2*e^5)*x^5 + (c^4*d^3*e^2 - 3*c^2*d*e^4)*x^4 + (c^2*e^5*x^5 + 3*c^2*d*e^4*x^4 - 3*d^2*e^3*x - d^3*e^2 + (3*c^2*d^2*e^3 - e^5)*x^3 + (c^2*d^3*e^2 - 3*d*e^4)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)","F",0
95,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^5,x, algorithm=""maxima"")","-\frac{{\left(4 \, e x + d\right)} a g}{12 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{a f}{4 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}} - \frac{{\left(4 \, b e g x + 3 \, b e f + b d g\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)} \int \frac{{\left(4 \, b c e g x + 3 \, b c e f + b c d g\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{6} x^{8} + 4 \, c^{4} d e^{5} x^{7} - 4 \, c^{2} d^{3} e^{3} x^{3} - c^{2} d^{4} e^{2} x^{2} + {\left(6 \, c^{4} d^{2} e^{4} - c^{2} e^{6}\right)} x^{6} + 4 \, {\left(c^{4} d^{3} e^{3} - c^{2} d e^{5}\right)} x^{5} + {\left(c^{4} d^{4} e^{2} - 6 \, c^{2} d^{2} e^{4}\right)} x^{4} - {\left(c^{2} e^{6} x^{6} + 4 \, c^{2} d e^{5} x^{5} - 4 \, d^{3} e^{3} x - d^{4} e^{2} + {\left(6 \, c^{2} d^{2} e^{4} - e^{6}\right)} x^{4} + 4 \, {\left(c^{2} d^{3} e^{3} - d e^{5}\right)} x^{3} + {\left(c^{2} d^{4} e^{2} - 6 \, d^{2} e^{4}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}}{12 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}}"," ",0,"-1/12*(4*e*x + d)*a*g/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2) - 1/4*a*f/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e) - 1/12*((4*b*e*g*x + 3*b*e*f + b*d*g)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 12*(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2)*integrate(1/12*(4*b*c*e*g*x + 3*b*c*e*f + b*c*d*g)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^6*x^8 + 4*c^4*d*e^5*x^7 - 4*c^2*d^3*e^3*x^3 - c^2*d^4*e^2*x^2 + (6*c^4*d^2*e^4 - c^2*e^6)*x^6 + 4*(c^4*d^3*e^3 - c^2*d*e^5)*x^5 + (c^4*d^4*e^2 - 6*c^2*d^2*e^4)*x^4 + (c^2*e^6*x^6 + 4*c^2*d*e^5*x^5 - 4*d^3*e^3*x - d^4*e^2 + (6*c^2*d^2*e^4 - e^6)*x^4 + 4*(c^2*d^3*e^3 - d*e^5)*x^3 + (c^2*d^4*e^2 - 6*d^2*e^4)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2)","F",0
96,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^6,x, algorithm=""maxima"")","-\frac{{\left(5 \, e x + d\right)} a g}{20 \, {\left(e^{7} x^{5} + 5 \, d e^{6} x^{4} + 10 \, d^{2} e^{5} x^{3} + 10 \, d^{3} e^{4} x^{2} + 5 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} - \frac{a f}{5 \, {\left(e^{6} x^{5} + 5 \, d e^{5} x^{4} + 10 \, d^{2} e^{4} x^{3} + 10 \, d^{3} e^{3} x^{2} + 5 \, d^{4} e^{2} x + d^{5} e\right)}} - \frac{{\left(5 \, b e g x + 4 \, b e f + b d g\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{7} x^{5} + 5 \, d e^{6} x^{4} + 10 \, d^{2} e^{5} x^{3} + 10 \, d^{3} e^{4} x^{2} + 5 \, d^{4} e^{3} x + d^{5} e^{2}\right)} \int \frac{{\left(5 \, b c e g x + 4 \, b c e f + b c d g\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{7} x^{9} + 5 \, c^{4} d e^{6} x^{8} - 5 \, c^{2} d^{4} e^{3} x^{3} - c^{2} d^{5} e^{2} x^{2} + {\left(10 \, c^{4} d^{2} e^{5} - c^{2} e^{7}\right)} x^{7} + 5 \, {\left(2 \, c^{4} d^{3} e^{4} - c^{2} d e^{6}\right)} x^{6} + 5 \, {\left(c^{4} d^{4} e^{3} - 2 \, c^{2} d^{2} e^{5}\right)} x^{5} + {\left(c^{4} d^{5} e^{2} - 10 \, c^{2} d^{3} e^{4}\right)} x^{4} - {\left(c^{2} e^{7} x^{7} + 5 \, c^{2} d e^{6} x^{6} - 5 \, d^{4} e^{3} x - d^{5} e^{2} + {\left(10 \, c^{2} d^{2} e^{5} - e^{7}\right)} x^{5} + 5 \, {\left(2 \, c^{2} d^{3} e^{4} - d e^{6}\right)} x^{4} + 5 \, {\left(c^{2} d^{4} e^{3} - 2 \, d^{2} e^{5}\right)} x^{3} + {\left(c^{2} d^{5} e^{2} - 10 \, d^{3} e^{4}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}}{20 \, {\left(e^{7} x^{5} + 5 \, d e^{6} x^{4} + 10 \, d^{2} e^{5} x^{3} + 10 \, d^{3} e^{4} x^{2} + 5 \, d^{4} e^{3} x + d^{5} e^{2}\right)}}"," ",0,"-1/20*(5*e*x + d)*a*g/(e^7*x^5 + 5*d*e^6*x^4 + 10*d^2*e^5*x^3 + 10*d^3*e^4*x^2 + 5*d^4*e^3*x + d^5*e^2) - 1/5*a*f/(e^6*x^5 + 5*d*e^5*x^4 + 10*d^2*e^4*x^3 + 10*d^3*e^3*x^2 + 5*d^4*e^2*x + d^5*e) - 1/20*((5*b*e*g*x + 4*b*e*f + b*d*g)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 20*(e^7*x^5 + 5*d*e^6*x^4 + 10*d^2*e^5*x^3 + 10*d^3*e^4*x^2 + 5*d^4*e^3*x + d^5*e^2)*integrate(1/20*(5*b*c*e*g*x + 4*b*c*e*f + b*c*d*g)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^7*x^9 + 5*c^4*d*e^6*x^8 - 5*c^2*d^4*e^3*x^3 - c^2*d^5*e^2*x^2 + (10*c^4*d^2*e^5 - c^2*e^7)*x^7 + 5*(2*c^4*d^3*e^4 - c^2*d*e^6)*x^6 + 5*(c^4*d^4*e^3 - 2*c^2*d^2*e^5)*x^5 + (c^4*d^5*e^2 - 10*c^2*d^3*e^4)*x^4 + (c^2*e^7*x^7 + 5*c^2*d*e^6*x^6 - 5*d^4*e^3*x - d^5*e^2 + (10*c^2*d^2*e^5 - e^7)*x^5 + 5*(2*c^2*d^3*e^4 - d*e^6)*x^4 + 5*(c^2*d^4*e^3 - 2*d^2*e^5)*x^3 + (c^2*d^5*e^2 - 10*d^3*e^4)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))/(e^7*x^5 + 5*d*e^6*x^4 + 10*d^2*e^5*x^3 + 10*d^3*e^4*x^2 + 5*d^4*e^3*x + d^5*e^2)","F",0
97,1,859,0,0.451750," ","integrate((e*x+d)^3*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{3} h x^{6} + \frac{1}{5} \, a e^{3} g x^{5} + \frac{3}{5} \, a d e^{2} h x^{5} + \frac{1}{4} \, a e^{3} f x^{4} + \frac{3}{4} \, a d e^{2} g x^{4} + \frac{3}{4} \, a d^{2} e h x^{4} + a d e^{2} f x^{3} + a d^{2} e g x^{3} + \frac{1}{3} \, a d^{3} h x^{3} + \frac{3}{2} \, a d^{2} e f x^{2} + \frac{1}{2} \, a d^{3} g x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} e f + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\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} f + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{3} f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{3} g + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} e g + \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d e^{2} g + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{3} g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3} h + \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2} e h + \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d e^{2} h + \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b e^{3} h + a d^{3} f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{3} f}{c}"," ",0,"1/6*a*e^3*h*x^6 + 1/5*a*e^3*g*x^5 + 3/5*a*d*e^2*h*x^5 + 1/4*a*e^3*f*x^4 + 3/4*a*d*e^2*g*x^4 + 3/4*a*d^2*e*h*x^4 + a*d*e^2*f*x^3 + a*d^2*e*g*x^3 + 1/3*a*d^3*h*x^3 + 3/2*a*d^2*e*f*x^2 + 1/2*a*d^3*g*x^2 + 3/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*e*f + 1/3*(3*x^3*arcsin(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*f + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^3*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^3*g + 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2*e*g + 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*e^2*g + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^3*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^3*h + 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^2*e*h + 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d*e^2*h + 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*e^3*h + a*d^3*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^3*f/c","A",0
98,1,581,0,0.436343," ","integrate((e*x+d)^2*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} h x^{5} + \frac{1}{4} \, a e^{2} g x^{4} + \frac{1}{2} \, a d e h x^{4} + \frac{1}{3} \, a e^{2} f x^{3} + \frac{2}{3} \, a d e g x^{3} + \frac{1}{3} \, a d^{2} h x^{3} + a d e f x^{2} + \frac{1}{2} \, a d^{2} g x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d e f + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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} f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} g + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 g + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{2} g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} h + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d e h + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{2} h + a d^{2} f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{2} f}{c}"," ",0,"1/5*a*e^2*h*x^5 + 1/4*a*e^2*g*x^4 + 1/2*a*d*e*h*x^4 + 1/3*a*e^2*f*x^3 + 2/3*a*d*e*g*x^3 + 1/3*a*d^2*h*x^3 + a*d*e*f*x^2 + 1/2*a*d^2*g*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*e*f + 1/9*(3*x^3*arcsin(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*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*g + 2/9*(3*x^3*arcsin(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*g + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^2*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2*h + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*e*h + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^2*h + a*d^2*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2*f/c","A",0
99,1,334,0,0.440364," ","integrate((e*x+d)*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e h x^{4} + \frac{1}{3} \, a e g x^{3} + \frac{1}{3} \, a d h x^{3} + \frac{1}{2} \, a e f x^{2} + \frac{1}{2} \, a d g x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b e f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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 g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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 h + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e h + a d f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d f}{c}"," ",0,"1/4*a*e*h*x^4 + 1/3*a*e*g*x^3 + 1/3*a*d*h*x^3 + 1/2*a*e*f*x^2 + 1/2*a*d*g*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*e*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d*h + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e*h + a*d*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d*f/c","A",0
100,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x, algorithm=""maxima"")","a g {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} + \frac{1}{2} \, a h {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + \frac{a f \log\left(e x + d\right)}{e} + \int \frac{{\left(b h x^{2} + b g x + b f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x + d}\,{d x}"," ",0,"a*g*(x/e - d*log(e*x + d)/e^2) + 1/2*a*h*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + a*f*log(e*x + d)/e + integrate((b*h*x^2 + b*g*x + b*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x + d), x)","F",0
101,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(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
102,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(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
103,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","-\frac{{\left(3 \, e x + d\right)} a g}{6 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{{\left(3 \, e^{2} x^{2} + 3 \, d e x + d^{2}\right)} a h}{3 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{a f}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}} - \frac{{\left(6 \, b e^{2} h x^{2} + 2 \, b e^{2} f + b d e g + 2 \, b d^{2} h + 3 \, {\left(b e^{2} g + 2 \, b d e h\right)} x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)} \int \frac{{\left(6 \, b c e^{2} h x^{2} + 2 \, b c e^{2} f + b c d e g + 2 \, b c d^{2} h + 3 \, {\left(b c e^{2} g + 2 \, b c d e h\right)} x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{6} x^{7} + 3 \, c^{4} d e^{5} x^{6} - 3 \, c^{2} d^{2} e^{4} x^{3} - c^{2} d^{3} e^{3} x^{2} + {\left(3 \, c^{4} d^{2} e^{4} - c^{2} e^{6}\right)} x^{5} + {\left(c^{4} d^{3} e^{3} - 3 \, c^{2} d e^{5}\right)} x^{4} - {\left(c^{2} e^{6} x^{5} + 3 \, c^{2} d e^{5} x^{4} - 3 \, d^{2} e^{4} x - d^{3} e^{3} + {\left(3 \, c^{2} d^{2} e^{4} - e^{6}\right)} x^{3} + {\left(c^{2} d^{3} e^{3} - 3 \, d e^{5}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}}{6 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/6*(3*e*x + d)*a*g/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2) - 1/3*(3*e^2*x^2 + 3*d*e*x + d^2)*a*h/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3) - 1/3*a*f/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e) - 1/6*((6*b*e^2*h*x^2 + 2*b*e^2*f + b*d*e*g + 2*b*d^2*h + 3*(b*e^2*g + 2*b*d*e*h)*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 6*(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)*integrate(1/6*(6*b*c*e^2*h*x^2 + 2*b*c*e^2*f + b*c*d*e*g + 2*b*c*d^2*h + 3*(b*c*e^2*g + 2*b*c*d*e*h)*x)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^6*x^7 + 3*c^4*d*e^5*x^6 - 3*c^2*d^2*e^4*x^3 - c^2*d^3*e^3*x^2 + (3*c^4*d^2*e^4 - c^2*e^6)*x^5 + (c^4*d^3*e^3 - 3*c^2*d*e^5)*x^4 + (c^2*e^6*x^5 + 3*c^2*d*e^5*x^4 - 3*d^2*e^4*x - d^3*e^3 + (3*c^2*d^2*e^4 - e^6)*x^3 + (c^2*d^3*e^3 - 3*d*e^5)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","F",0
104,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^5,x, algorithm=""maxima"")","-\frac{{\left(4 \, e x + d\right)} a g}{12 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}} - \frac{{\left(6 \, e^{2} x^{2} + 4 \, d e x + d^{2}\right)} a h}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}} - \frac{a f}{4 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}} - \frac{{\left(6 \, b e^{2} h x^{2} + 3 \, b e^{2} f + b d e g + b d^{2} h + 4 \, {\left(b e^{2} g + b d e h\right)} x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)} \int \frac{{\left(6 \, b c e^{2} h x^{2} + 3 \, b c e^{2} f + b c d e g + b c d^{2} h + 4 \, {\left(b c e^{2} g + b c d e h\right)} x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{7} x^{8} + 4 \, c^{4} d e^{6} x^{7} - 4 \, c^{2} d^{3} e^{4} x^{3} - c^{2} d^{4} e^{3} x^{2} + {\left(6 \, c^{4} d^{2} e^{5} - c^{2} e^{7}\right)} x^{6} + 4 \, {\left(c^{4} d^{3} e^{4} - c^{2} d e^{6}\right)} x^{5} + {\left(c^{4} d^{4} e^{3} - 6 \, c^{2} d^{2} e^{5}\right)} x^{4} - {\left(c^{2} e^{7} x^{6} + 4 \, c^{2} d e^{6} x^{5} - 4 \, d^{3} e^{4} x - d^{4} e^{3} + {\left(6 \, c^{2} d^{2} e^{5} - e^{7}\right)} x^{4} + 4 \, {\left(c^{2} d^{3} e^{4} - d e^{6}\right)} x^{3} + {\left(c^{2} d^{4} e^{3} - 6 \, d^{2} e^{5}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(4*e*x + d)*a*g/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2) - 1/12*(6*e^2*x^2 + 4*d*e*x + d^2)*a*h/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3) - 1/4*a*f/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e) - 1/12*((6*b*e^2*h*x^2 + 3*b*e^2*f + b*d*e*g + b*d^2*h + 4*(b*e^2*g + b*d*e*h)*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 12*(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)*integrate(1/12*(6*b*c*e^2*h*x^2 + 3*b*c*e^2*f + b*c*d*e*g + b*c*d^2*h + 4*(b*c*e^2*g + b*c*d*e*h)*x)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^7*x^8 + 4*c^4*d*e^6*x^7 - 4*c^2*d^3*e^4*x^3 - c^2*d^4*e^3*x^2 + (6*c^4*d^2*e^5 - c^2*e^7)*x^6 + 4*(c^4*d^3*e^4 - c^2*d*e^6)*x^5 + (c^4*d^4*e^3 - 6*c^2*d^2*e^5)*x^4 + (c^2*e^7*x^6 + 4*c^2*d*e^6*x^5 - 4*d^3*e^4*x - d^4*e^3 + (6*c^2*d^2*e^5 - e^7)*x^4 + 4*(c^2*d^3*e^4 - d*e^6)*x^3 + (c^2*d^4*e^3 - 6*d^2*e^5)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","F",0
105,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^6,x, algorithm=""maxima"")","-\frac{{\left(5 \, e x + d\right)} a g}{20 \, {\left(e^{7} x^{5} + 5 \, d e^{6} x^{4} + 10 \, d^{2} e^{5} x^{3} + 10 \, d^{3} e^{4} x^{2} + 5 \, d^{4} e^{3} x + d^{5} e^{2}\right)}} - \frac{{\left(10 \, e^{2} x^{2} + 5 \, d e x + d^{2}\right)} a h}{30 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}} - \frac{a f}{5 \, {\left(e^{6} x^{5} + 5 \, d e^{5} x^{4} + 10 \, d^{2} e^{4} x^{3} + 10 \, d^{3} e^{3} x^{2} + 5 \, d^{4} e^{2} x + d^{5} e\right)}} - \frac{{\left(20 \, b e^{2} h x^{2} + 12 \, b e^{2} f + 3 \, b d e g + 2 \, b d^{2} h + 5 \, {\left(3 \, b e^{2} g + 2 \, b d e h\right)} x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)} \int \frac{{\left(20 \, b c e^{2} h x^{2} + 12 \, b c e^{2} f + 3 \, b c d e g + 2 \, b c d^{2} h + 5 \, {\left(3 \, b c e^{2} g + 2 \, b c d e h\right)} x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{8} x^{9} + 5 \, c^{4} d e^{7} x^{8} - 5 \, c^{2} d^{4} e^{4} x^{3} - c^{2} d^{5} e^{3} x^{2} + {\left(10 \, c^{4} d^{2} e^{6} - c^{2} e^{8}\right)} x^{7} + 5 \, {\left(2 \, c^{4} d^{3} e^{5} - c^{2} d e^{7}\right)} x^{6} + 5 \, {\left(c^{4} d^{4} e^{4} - 2 \, c^{2} d^{2} e^{6}\right)} x^{5} + {\left(c^{4} d^{5} e^{3} - 10 \, c^{2} d^{3} e^{5}\right)} x^{4} - {\left(c^{2} e^{8} x^{7} + 5 \, c^{2} d e^{7} x^{6} - 5 \, d^{4} e^{4} x - d^{5} e^{3} + {\left(10 \, c^{2} d^{2} e^{6} - e^{8}\right)} x^{5} + 5 \, {\left(2 \, c^{2} d^{3} e^{5} - d e^{7}\right)} x^{4} + 5 \, {\left(c^{2} d^{4} e^{4} - 2 \, d^{2} e^{6}\right)} x^{3} + {\left(c^{2} d^{5} e^{3} - 10 \, d^{3} e^{5}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}}{60 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/20*(5*e*x + d)*a*g/(e^7*x^5 + 5*d*e^6*x^4 + 10*d^2*e^5*x^3 + 10*d^3*e^4*x^2 + 5*d^4*e^3*x + d^5*e^2) - 1/30*(10*e^2*x^2 + 5*d*e*x + d^2)*a*h/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3) - 1/5*a*f/(e^6*x^5 + 5*d*e^5*x^4 + 10*d^2*e^4*x^3 + 10*d^3*e^3*x^2 + 5*d^4*e^2*x + d^5*e) - 1/60*((20*b*e^2*h*x^2 + 12*b*e^2*f + 3*b*d*e*g + 2*b*d^2*h + 5*(3*b*e^2*g + 2*b*d*e*h)*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 60*(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)*integrate(1/60*(20*b*c*e^2*h*x^2 + 12*b*c*e^2*f + 3*b*c*d*e*g + 2*b*c*d^2*h + 5*(3*b*c*e^2*g + 2*b*c*d*e*h)*x)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^8*x^9 + 5*c^4*d*e^7*x^8 - 5*c^2*d^4*e^4*x^3 - c^2*d^5*e^3*x^2 + (10*c^4*d^2*e^6 - c^2*e^8)*x^7 + 5*(2*c^4*d^3*e^5 - c^2*d*e^7)*x^6 + 5*(c^4*d^4*e^4 - 2*c^2*d^2*e^6)*x^5 + (c^4*d^5*e^3 - 10*c^2*d^3*e^5)*x^4 + (c^2*e^8*x^7 + 5*c^2*d*e^7*x^6 - 5*d^4*e^4*x - d^5*e^3 + (10*c^2*d^2*e^6 - e^8)*x^5 + 5*(2*c^2*d^3*e^5 - d*e^7)*x^4 + 5*(c^2*d^4*e^4 - 2*d^2*e^6)*x^3 + (c^2*d^5*e^3 - 10*d^3*e^5)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","F",0
106,1,1231,0,0.467767," ","integrate((e*x+d)^3*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{3} i x^{7} + \frac{1}{6} \, a e^{3} h x^{6} + \frac{1}{2} \, a d e^{2} i x^{6} + \frac{1}{5} \, a e^{3} g x^{5} + \frac{3}{5} \, a d e^{2} h x^{5} + \frac{3}{5} \, a d^{2} e i x^{5} + \frac{1}{4} \, a e^{3} f x^{4} + \frac{3}{4} \, a d e^{2} g x^{4} + \frac{3}{4} \, a d^{2} e h x^{4} + \frac{1}{4} \, a d^{3} i x^{4} + a d e^{2} f x^{3} + a d^{2} e g x^{3} + \frac{1}{3} \, a d^{3} h x^{3} + \frac{3}{2} \, a d^{2} e f x^{2} + \frac{1}{2} \, a d^{3} g x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} e f + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\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} f + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{3} f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{3} g + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} e g + \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d e^{2} g + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{3} g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3} h + \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2} e h + \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d e^{2} h + \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b e^{3} h + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{3} i + \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2} e i + \frac{1}{96} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b d e^{2} i + \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b e^{3} i + a d^{3} f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{3} f}{c}"," ",0,"1/7*a*e^3*i*x^7 + 1/6*a*e^3*h*x^6 + 1/2*a*d*e^2*i*x^6 + 1/5*a*e^3*g*x^5 + 3/5*a*d*e^2*h*x^5 + 3/5*a*d^2*e*i*x^5 + 1/4*a*e^3*f*x^4 + 3/4*a*d*e^2*g*x^4 + 3/4*a*d^2*e*h*x^4 + 1/4*a*d^3*i*x^4 + a*d*e^2*f*x^3 + a*d^2*e*g*x^3 + 1/3*a*d^3*h*x^3 + 3/2*a*d^2*e*f*x^2 + 1/2*a*d^3*g*x^2 + 3/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*e*f + 1/3*(3*x^3*arcsin(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*f + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^3*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^3*g + 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2*e*g + 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*e^2*g + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^3*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^3*h + 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^2*e*h + 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d*e^2*h + 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*e^3*h + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^3*i + 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^2*e*i + 1/96*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*d*e^2*i + 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*e^3*i + a*d^3*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^3*f/c","A",0
107,1,840,0,0.456473," ","integrate((e*x+d)^2*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{2} i x^{6} + \frac{1}{5} \, a e^{2} h x^{5} + \frac{2}{5} \, a d e i x^{5} + \frac{1}{4} \, a e^{2} g x^{4} + \frac{1}{2} \, a d e h x^{4} + \frac{1}{4} \, a d^{2} i x^{4} + \frac{1}{3} \, a e^{2} f x^{3} + \frac{2}{3} \, a d e g x^{3} + \frac{1}{3} \, a d^{2} h x^{3} + a d e f x^{2} + \frac{1}{2} \, a d^{2} g x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d e f + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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} f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} g + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 g + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e^{2} g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} h + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d e h + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{2} h + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2} i + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d e i + \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b e^{2} i + a d^{2} f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{2} f}{c}"," ",0,"1/6*a*e^2*i*x^6 + 1/5*a*e^2*h*x^5 + 2/5*a*d*e*i*x^5 + 1/4*a*e^2*g*x^4 + 1/2*a*d*e*h*x^4 + 1/4*a*d^2*i*x^4 + 1/3*a*e^2*f*x^3 + 2/3*a*d*e*g*x^3 + 1/3*a*d^2*h*x^3 + a*d*e*f*x^2 + 1/2*a*d^2*g*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*e*f + 1/9*(3*x^3*arcsin(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*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2*g + 2/9*(3*x^3*arcsin(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*g + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e^2*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2*h + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*e*h + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^2*h + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^2*i + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d*e*i + 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*e^2*i + a*d^2*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2*f/c","A",0
108,1,490,0,0.512902," ","integrate((e*x+d)*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e i x^{5} + \frac{1}{4} \, a e h x^{4} + \frac{1}{4} \, a d i x^{4} + \frac{1}{3} \, a e g x^{3} + \frac{1}{3} \, a d h x^{3} + \frac{1}{2} \, a e f x^{2} + \frac{1}{2} \, a d g x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b e f + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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 g + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\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 h + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e h + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d i + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e i + a d f x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d f}{c}"," ",0,"1/5*a*e*i*x^5 + 1/4*a*e*h*x^4 + 1/4*a*d*i*x^4 + 1/3*a*e*g*x^3 + 1/3*a*d*h*x^3 + 1/2*a*e*f*x^2 + 1/2*a*d*g*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*e*f + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e*g + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d*h + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e*h + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*i + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e*i + a*d*f*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d*f/c","A",0
109,0,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x, algorithm=""maxima"")","a g {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} - \frac{1}{6} \, a i {\left(\frac{6 \, d^{3} \log\left(e x + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{3} - 3 \, d e x^{2} + 6 \, d^{2} x}{e^{3}}\right)} + \frac{1}{2} \, a h {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + \frac{a f \log\left(e x + d\right)}{e} + \int \frac{{\left(b i x^{3} + b h x^{2} + b g x + b f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x + d}\,{d x}"," ",0,"a*g*(x/e - d*log(e*x + d)/e^2) - 1/6*a*i*(6*d^3*log(e*x + d)/e^4 - (2*e^2*x^3 - 3*d*e*x^2 + 6*d^2*x)/e^3) + 1/2*a*h*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + a*f*log(e*x + d)/e + integrate((b*i*x^3 + b*h*x^2 + b*g*x + b*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x + d), x)","F",0
110,-2,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(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
111,-2,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(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
112,0,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","\frac{1}{6} \, a i {\left(\frac{18 \, d e^{2} x^{2} + 27 \, d^{2} e x + 11 \, d^{3}}{e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}} + \frac{6 \, \log\left(e x + d\right)}{e^{4}}\right)} - \frac{{\left(3 \, e x + d\right)} a g}{6 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}} - \frac{{\left(3 \, e^{2} x^{2} + 3 \, d e x + d^{2}\right)} a h}{3 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}} - \frac{a f}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}} + \int \frac{{\left(b i x^{3} + b h x^{2} + b g x + b f\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}\,{d x}"," ",0,"1/6*a*i*((18*d*e^2*x^2 + 27*d^2*e*x + 11*d^3)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4) + 6*log(e*x + d)/e^4) - 1/6*(3*e*x + d)*a*g/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2) - 1/3*(3*e^2*x^2 + 3*d*e*x + d^2)*a*h/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3) - 1/3*a*f/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e) + integrate((b*i*x^3 + b*h*x^2 + b*g*x + b*f)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
113,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(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
114,-2,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(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
115,0,0,0,0.000000," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} f h^{3} x^{6} + \frac{3}{5} \, a^{2} f g h^{2} x^{5} + \frac{1}{5} \, a^{2} e h^{3} x^{5} + \frac{3}{4} \, a^{2} f g^{2} h x^{4} + \frac{3}{4} \, a^{2} e g h^{2} x^{4} + \frac{1}{4} \, a^{2} d h^{3} x^{4} + \frac{1}{3} \, a^{2} f g^{3} x^{3} + a^{2} e g^{2} h x^{3} + a^{2} d g h^{2} x^{3} + b^{2} d g^{3} x \arcsin\left(c x\right)^{2} + \frac{1}{2} \, a^{2} e g^{3} x^{2} + \frac{3}{2} \, a^{2} d g^{2} h x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b e g^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 f g^{3} + \frac{3}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d g^{2} h + \frac{2}{3} \, {\left(3 \, x^{3} \arcsin\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 g^{2} h + \frac{3}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b f g^{2} h + \frac{2}{3} \, {\left(3 \, x^{3} \arcsin\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 g h^{2} + \frac{3}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b e g h^{2} + \frac{2}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b f g h^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b d h^{3} + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b e h^{3} + \frac{1}{144} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} a b f h^{3} - 2 \, b^{2} d g^{3} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d g^{3} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d g^{3}}{c} + \frac{1}{60} \, {\left(10 \, b^{2} f h^{3} x^{6} + 12 \, {\left(3 \, b^{2} f g h^{2} + b^{2} e h^{3}\right)} x^{5} + 15 \, {\left(3 \, b^{2} f g^{2} h + 3 \, b^{2} e g h^{2} + b^{2} d h^{3}\right)} x^{4} + 20 \, {\left(b^{2} f g^{3} + 3 \, b^{2} e g^{2} h + 3 \, b^{2} d g h^{2}\right)} x^{3} + 30 \, {\left(b^{2} e g^{3} + 3 \, b^{2} d g^{2} h\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{{\left(10 \, b^{2} c f h^{3} x^{6} + 12 \, {\left(3 \, b^{2} c f g h^{2} + b^{2} c e h^{3}\right)} x^{5} + 15 \, {\left(3 \, b^{2} c f g^{2} h + 3 \, b^{2} c e g h^{2} + b^{2} c d h^{3}\right)} x^{4} + 20 \, {\left(b^{2} c f g^{3} + 3 \, b^{2} c e g^{2} h + 3 \, b^{2} c d g h^{2}\right)} x^{3} + 30 \, {\left(b^{2} c e g^{3} + 3 \, b^{2} c d g^{2} h\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{30 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/6*a^2*f*h^3*x^6 + 3/5*a^2*f*g*h^2*x^5 + 1/5*a^2*e*h^3*x^5 + 3/4*a^2*f*g^2*h*x^4 + 3/4*a^2*e*g*h^2*x^4 + 1/4*a^2*d*h^3*x^4 + 1/3*a^2*f*g^3*x^3 + a^2*e*g^2*h*x^3 + a^2*d*g*h^2*x^3 + b^2*d*g^3*x*arcsin(c*x)^2 + 1/2*a^2*e*g^3*x^2 + 3/2*a^2*d*g^2*h*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*e*g^3 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*f*g^3 + 3/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d*g^2*h + 2/3*(3*x^3*arcsin(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*g^2*h + 3/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*f*g^2*h + 2/3*(3*x^3*arcsin(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*g*h^2 + 3/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*e*g*h^2 + 2/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*f*g*h^2 + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*d*h^3 + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*e*h^3 + 1/144*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*a*b*f*h^3 - 2*b^2*d*g^3*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d*g^3*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d*g^3/c + 1/60*(10*b^2*f*h^3*x^6 + 12*(3*b^2*f*g*h^2 + b^2*e*h^3)*x^5 + 15*(3*b^2*f*g^2*h + 3*b^2*e*g*h^2 + b^2*d*h^3)*x^4 + 20*(b^2*f*g^3 + 3*b^2*e*g^2*h + 3*b^2*d*g*h^2)*x^3 + 30*(b^2*e*g^3 + 3*b^2*d*g^2*h)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(1/30*(10*b^2*c*f*h^3*x^6 + 12*(3*b^2*c*f*g*h^2 + b^2*c*e*h^3)*x^5 + 15*(3*b^2*c*f*g^2*h + 3*b^2*c*e*g*h^2 + b^2*c*d*h^3)*x^4 + 20*(b^2*c*f*g^3 + 3*b^2*c*e*g^2*h + 3*b^2*c*d*g*h^2)*x^3 + 30*(b^2*c*e*g^3 + 3*b^2*c*d*g^2*h)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
116,0,0,0,0.000000," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} f h^{2} x^{5} + \frac{1}{2} \, a^{2} f g h x^{4} + \frac{1}{4} \, a^{2} e h^{2} x^{4} + \frac{1}{3} \, a^{2} f g^{2} x^{3} + \frac{2}{3} \, a^{2} e g h x^{3} + \frac{1}{3} \, a^{2} d h^{2} x^{3} + b^{2} d g^{2} x \arcsin\left(c x\right)^{2} + \frac{1}{2} \, a^{2} e g^{2} x^{2} + a^{2} d g h x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b e g^{2} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 f g^{2} + {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d g h + \frac{4}{9} \, {\left(3 \, x^{3} \arcsin\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 g h + \frac{1}{8} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b f g h + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 h^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b e h^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b f h^{2} - 2 \, b^{2} d g^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d g^{2} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d g^{2}}{c} + \frac{1}{60} \, {\left(12 \, b^{2} f h^{2} x^{5} + 15 \, {\left(2 \, b^{2} f g h + b^{2} e h^{2}\right)} x^{4} + 20 \, {\left(b^{2} f g^{2} + 2 \, b^{2} e g h + b^{2} d h^{2}\right)} x^{3} + 30 \, {\left(b^{2} e g^{2} + 2 \, b^{2} d g h\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{{\left(12 \, b^{2} c f h^{2} x^{5} + 15 \, {\left(2 \, b^{2} c f g h + b^{2} c e h^{2}\right)} x^{4} + 20 \, {\left(b^{2} c f g^{2} + 2 \, b^{2} c e g h + b^{2} c d h^{2}\right)} x^{3} + 30 \, {\left(b^{2} c e g^{2} + 2 \, b^{2} c d g h\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{30 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/5*a^2*f*h^2*x^5 + 1/2*a^2*f*g*h*x^4 + 1/4*a^2*e*h^2*x^4 + 1/3*a^2*f*g^2*x^3 + 2/3*a^2*e*g*h*x^3 + 1/3*a^2*d*h^2*x^3 + b^2*d*g^2*x*arcsin(c*x)^2 + 1/2*a^2*e*g^2*x^2 + a^2*d*g*h*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*e*g^2 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*f*g^2 + (2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d*g*h + 4/9*(3*x^3*arcsin(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*g*h + 1/8*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*f*g*h + 2/9*(3*x^3*arcsin(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*h^2 + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*e*h^2 + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*f*h^2 - 2*b^2*d*g^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d*g^2*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d*g^2/c + 1/60*(12*b^2*f*h^2*x^5 + 15*(2*b^2*f*g*h + b^2*e*h^2)*x^4 + 20*(b^2*f*g^2 + 2*b^2*e*g*h + b^2*d*h^2)*x^3 + 30*(b^2*e*g^2 + 2*b^2*d*g*h)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(1/30*(12*b^2*c*f*h^2*x^5 + 15*(2*b^2*c*f*g*h + b^2*c*e*h^2)*x^4 + 20*(b^2*c*f*g^2 + 2*b^2*c*e*g*h + b^2*c*d*h^2)*x^3 + 30*(b^2*c*e*g^2 + 2*b^2*c*d*g*h)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
117,0,0,0,0.000000," ","integrate((h*x+g)*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} f h x^{4} + \frac{1}{3} \, a^{2} f g x^{3} + \frac{1}{3} \, a^{2} e h x^{3} + b^{2} d g x \arcsin\left(c x\right)^{2} + \frac{1}{2} \, a^{2} e g x^{2} + \frac{1}{2} \, a^{2} d h x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b e g + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 f g + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d h + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\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 h + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\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 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b f h - 2 \, b^{2} d g {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d g x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d g}{c} + \frac{1}{12} \, {\left(3 \, b^{2} f h x^{4} + 4 \, {\left(b^{2} f g + b^{2} e h\right)} x^{3} + 6 \, {\left(b^{2} e g + b^{2} d h\right)} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{{\left(3 \, b^{2} c f h x^{4} + 4 \, {\left(b^{2} c f g + b^{2} c e h\right)} x^{3} + 6 \, {\left(b^{2} c e g + b^{2} c d h\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{6 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/4*a^2*f*h*x^4 + 1/3*a^2*f*g*x^3 + 1/3*a^2*e*h*x^3 + b^2*d*g*x*arcsin(c*x)^2 + 1/2*a^2*e*g*x^2 + 1/2*a^2*d*h*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*e*g + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*f*g + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d*h + 2/9*(3*x^3*arcsin(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*h + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*f*h - 2*b^2*d*g*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d*g*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d*g/c + 1/12*(3*b^2*f*h*x^4 + 4*(b^2*f*g + b^2*e*h)*x^3 + 6*(b^2*e*g + b^2*d*h)*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(1/6*(3*b^2*c*f*h*x^4 + 4*(b^2*c*f*g + b^2*c*e*h)*x^3 + 6*(b^2*c*e*g + b^2*c*d*h)*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
118,0,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g),x, algorithm=""maxima"")","a^{2} e {\left(\frac{x}{h} - \frac{g \log\left(h x + g\right)}{h^{2}}\right)} + \frac{1}{2} \, a^{2} f {\left(\frac{2 \, g^{2} \log\left(h x + g\right)}{h^{3}} + \frac{h x^{2} - 2 \, g x}{h^{2}}\right)} + \frac{a^{2} d \log\left(h x + g\right)}{h} + \int \frac{{\left(b^{2} f x^{2} + b^{2} e x + b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b f x^{2} + a b e x + a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{h x + g}\,{d x}"," ",0,"a^2*e*(x/h - g*log(h*x + g)/h^2) + 1/2*a^2*f*(2*g^2*log(h*x + g)/h^3 + (h*x^2 - 2*g*x)/h^2) + a^2*d*log(h*x + g)/h + integrate(((b^2*f*x^2 + b^2*e*x + b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*f*x^2 + a*b*e*x + a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(h*x + g), x)","F",0
119,-2,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g)^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(h-c*g>0)', see `assume?` for more details)Is h-c*g positive, negative or zero?","F(-2)",0
120,-2,0,0,0.000000," ","integrate((e*h*x^2+2*d*h*x+e*f)*(a+b*arcsin(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
121,-2,0,0,0.000000," ","integrate((e*h*x^2+2*d*h*x+e*f)^2*(a+b*arcsin(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
122,1,333,0,0.456074," ","integrate(x^3*arcsin(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arcsin\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} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{5}} + \frac{35 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2} x}{b^{4}} - \frac{90 \, {\left(a^{2} - 1\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{5}} - \frac{105 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{3}}{b^{5}} - \frac{9 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)} x}{b^{4}} + \frac{9 \, {\left(a^{2} - 1\right)}^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{5}} + \frac{55 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)} a}{b^{5}}\right)} b"," ",0,"1/4*x^4*arcsin(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*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 + 35*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2*x/b^4 - 90*(a^2 - 1)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 - 105*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^3/b^5 - 9*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)*x/b^4 + 9*(a^2 - 1)^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 + 55*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)*a/b^5)*b","B",0
123,1,220,0,0.447586," ","integrate(x^2*arcsin(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arcsin\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} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{4}} - \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a x}{b^{3}} + \frac{9 \, {\left(a^{2} - 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{4}} + \frac{15 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{b^{4}} - \frac{4 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)}}{b^{4}}\right)}"," ",0,"1/3*x^3*arcsin(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*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 - 5*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*x/b^3 + 9*(a^2 - 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + 15*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/b^4 - 4*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)/b^4)","B",0
124,1,153,0,0.436685," ","integrate(x*arcsin(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arcsin\left(b x + a\right) + \frac{1}{4} \, b {\left(\frac{3 \, a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{b^{2}} - \frac{{\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{3}}\right)}"," ",0,"1/2*x^2*arcsin(b*x + a) + 1/4*b*(3*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b^2 - (a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^3)","B",0
125,1,30,0,0.439629," ","integrate(arcsin(b*x+a),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \arcsin\left(b x + a\right) + \sqrt{-{\left(b x + a\right)}^{2} + 1}}{b}"," ",0,"((b*x + a)*arcsin(b*x + a) + sqrt(-(b*x + a)^2 + 1))/b","A",0
126,0,0,0,0.000000," ","integrate(arcsin(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\arcsin\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arcsin(b*x + a)/x, x)","F",0
127,-2,0,0,0.000000," ","integrate(arcsin(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
128,-2,0,0,0.000000," ","integrate(arcsin(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
129,-2,0,0,0.000000," ","integrate(arcsin(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
130,-2,0,0,0.000000," ","integrate(arcsin(b*x+a)/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 positive, negative or zero?","F(-2)",0
131,0,0,0,0.000000," ","integrate(x^3*arcsin(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} + b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x^{4} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}\,{d x}"," ",0,"1/4*x^4*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2 + b*integrate(1/2*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x^4*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
132,0,0,0,0.000000," ","integrate(x^2*arcsin(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} + 2 \, b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x^{3} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2 + 2*b*integrate(1/3*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x^3*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
133,0,0,0,0.000000," ","integrate(x*arcsin(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} + b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\,{d x}"," ",0,"1/2*x^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2 + b*integrate(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
134,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2,x, algorithm=""maxima"")","x \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} + 2 \, b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\,{d x}"," ",0,"x*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2 + 2*b*integrate(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
135,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2/x,x, algorithm=""maxima"")","\int \frac{\arcsin\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^2/x, x)","F",0
136,-2,0,0,0.000000," ","integrate(arcsin(b*x+a)^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 positive, negative or zero?","F(-2)",0
137,-2,0,0,0.000000," ","integrate(arcsin(b*x+a)^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 positive, negative or zero?","F(-2)",0
138,0,0,0,0.000000," ","integrate(x^2*arcsin(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{3} + b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x^{3} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\,{d x}"," ",0,"1/3*x^3*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^3 + b*integrate(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x^3*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
139,0,0,0,0.000000," ","integrate(x*arcsin(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{3} + 3 \, b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}\,{d x}"," ",0,"1/2*x^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^3 + 3*b*integrate(1/2*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
140,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^3,x, algorithm=""maxima"")","x \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{3} + 3 \, b \int \frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} x \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\,{d x}"," ",0,"x*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^3 + 3*b*integrate(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*x*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2/(b^2*x^2 + 2*a*b*x + a^2 - 1), x)","F",0
141,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^3/x,x, algorithm=""maxima"")","\int \frac{\arcsin\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^3/x, x)","F",0
142,-2,0,0,0.000000," ","integrate(arcsin(b*x+a)^3/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
143,0,0,0,0.000000," ","integrate(x^2/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{x^{2}}{\arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(x^2/arcsin(b*x + a), x)","F",0
144,0,0,0,0.000000," ","integrate(x/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{x}{\arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(x/arcsin(b*x + a), x)","F",0
145,0,0,0,0.000000," ","integrate(1/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{1}{\arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/arcsin(b*x + a), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{1}{x \arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/(x*arcsin(b*x + a)), x)","F",0
147,-1,0,0,0.000000," ","integrate(x^2/arcsin(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate(x/arcsin(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,0,0,0,0.000000," ","integrate(1/arcsin(b*x+a)^2,x, algorithm=""maxima"")","\frac{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right) \int \frac{{\left(b x + a\right)} \sqrt{-b x - a + 1}}{\sqrt{b x + a + 1} {\left(b x + a - 1\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} - \sqrt{b x + a + 1} \sqrt{-b x - a + 1}}{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}"," ",0,"(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))*integrate(sqrt(b*x + a + 1)*(b*x + a)*sqrt(-b*x - a + 1)/((b^2*x^2 + 2*a*b*x + a^2 - 1)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))), x) - sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))/(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))","F",0
150,-1,0,0,0.000000," ","integrate(1/x/arcsin(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,0,0,0,0.000000," ","integrate(x^2/arcsin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x^{2} + \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} \int \frac{9 \, b^{2} x^{2} + 10 \, a b x + 2 \, a^{2} - 2}{\arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} - {\left(3 \, b^{2} x^{3} + 5 \, a b x^{2} + 2 \, {\left(a^{2} - 1\right)} x\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{2 \, b^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}"," ",0,"-1/2*(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x^2 + arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2*integrate((9*b^2*x^2 + 10*a*b*x + 2*a^2 - 2)/arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x) - (3*b^2*x^3 + 5*a*b*x^2 + 2*(a^2 - 1)*x)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))/(b^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2)","F",0
152,0,0,0,0.000000," ","integrate(x/arcsin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} \int \frac{4 \, b x + 3 \, a}{\arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x - {\left(2 \, b^{2} x^{2} + 3 \, a b x + a^{2} - 1\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{2 \, b^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}"," ",0,"-1/2*(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2*integrate((4*b*x + 3*a)/arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x) + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x - (2*b^2*x^2 + 3*a*b*x + a^2 - 1)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))/(b^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2)","F",0
153,0,0,0,0.000000," ","integrate(1/arcsin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} \int \frac{1}{\arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} - {\left(b x + a\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right) + \sqrt{b x + a + 1} \sqrt{-b x - a + 1}}{2 \, b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}"," ",0,"-1/2*(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2*integrate(1/arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x) - (b*x + a)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)) + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))/(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2)","F",0
154,0,0,0,0.000000," ","integrate(1/x/arcsin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{x^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2} \int \frac{a b x + 2 \, a^{2} - 2}{x^{3} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + {\left(a b x + a^{2} - 1\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}{2 \, b^{2} x^{2} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}"," ",0,"-1/2*(x^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2*integrate((a*b*x + 2*a^2 - 2)/(x^3*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))), x) + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + (a*b*x + a^2 - 1)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))/(b^2*x^2*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2)","F",0
155,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \arcsin\left(d x + c\right) + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(d*x + c) + a)*x^2, x)","F",0
156,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \arcsin\left(d x + c\right) + a} x\,{d x}"," ",0,"integrate(sqrt(b*arcsin(d*x + c) + a)*x, x)","F",0
157,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(d*x + c) + a), x)","F",0
158,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(3/2)*x, x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(3/2), x)","F",0
160,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}} x\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(5/2)*x, x)","F",0
161,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(5/2), x)","F",0
162,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(7/2), x)","F",0
163,0,0,0,0.000000," ","integrate(x^2/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(b*arcsin(d*x + c) + a), x)","F",0
164,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*arcsin(d*x + c) + a), x)","F",0
165,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsin(d*x + c) + a), x)","F",0
166,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
167,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(-3/2), x)","F",0
168,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(-5/2), x)","F",0
170,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x/(b*arcsin(d*x + c) + a)^(7/2), x)","F",0
171,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(-7/2), x)","F",0
172,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{n} x^{m}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^n*x^m, x)","F",0
173,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^n*x^2, x)","F",0
174,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^n*x, x)","F",0
175,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^n, x)","F",0
176,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^n/x, x)","F",0
177,1,1280,0,0.460065," ","integrate((d*e*x+c*e)^4*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} b c^{3} d e^{4} + \frac{1}{3} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} b c^{2} d^{2} e^{4} + \frac{1}{24} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} b c d^{3} e^{4} + \frac{1}{600} \, {\left(120 \, x^{5} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} - \frac{315 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3} x}{d^{5}} - \frac{32 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x^{2}}{d^{4}} + \frac{1050 \, {\left(c^{2} - 1\right)} c^{3} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} + \frac{945 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{4}}{d^{6}} + \frac{161 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c x}{d^{5}} - \frac{225 \, {\left(c^{2} - 1\right)}^{2} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} - \frac{735 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c^{2}}{d^{6}} + \frac{64 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}^{2}}{d^{6}}\right)} d\right)} b d^{4} e^{4} + a c^{4} e^{4} x + \frac{{\left({\left(d x + c\right)} \arcsin\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*b*c^3*d*e^4 + 1/3*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*b*c^2*d^2*e^4 + 1/24*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*b*c*d^3*e^4 + 1/600*(120*x^5*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 - 315*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3*x/d^5 - 32*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x^2/d^4 + 1050*(c^2 - 1)*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 + 945*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^4/d^6 + 161*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c*x/d^5 - 225*(c^2 - 1)^2*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 - 735*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c^2/d^6 + 64*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)^2/d^6)*d)*b*d^4*e^4 + a*c^4*e^4*x + ((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*b*c^4*e^4/d","B",0
178,1,816,0,0.433329," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} b c^{2} d e^{3} + \frac{1}{6} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} b c d^{2} e^{3} + \frac{1}{96} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} b d^{3} e^{3} + a c^{3} e^{3} x + \frac{{\left({\left(d x + c\right)} \arcsin\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*b*c^2*d*e^3 + 1/6*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*b*c*d^2*e^3 + 1/96*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*b*d^3*e^3 + a*c^3*e^3*x + ((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*b*c^3*e^3/d","B",0
179,1,457,0,0.420009," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} b c d e^{2} + \frac{1}{18} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} b d^{2} e^{2} + a c^{2} e^{2} x + \frac{{\left({\left(d x + c\right)} \arcsin\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*b*c*d*e^2 + 1/18*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*b*d^2*e^2 + a*c^2*e^2*x + ((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*b*c^2*e^2/d","B",0
180,1,204,0,0.418320," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a d e x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} b d e + a c e x + \frac{{\left({\left(d x + c\right)} \arcsin\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*b*d*e + a*c*e*x + ((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*b*c*e/d","B",0
181,1,35,0,0.411704," ","integrate(a+b*arcsin(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left({\left(d x + c\right)} \arcsin\left(d x + c\right) + \sqrt{-{\left(d x + c\right)}^{2} + 1}\right)} b}{d}"," ",0,"a*x + ((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*b/d","A",0
182,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e),x, algorithm=""maxima"")","b \int \frac{\arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d e x + c e}\,{d x} + \frac{a \log\left(d e x + c e\right)}{d e}"," ",0,"b*integrate(arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d*e*x + c*e), x) + a*log(d*e*x + c*e)/(d*e)","F",0
183,1,120,0,0.428281," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-b {\left(\frac{\arcsin\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}} + \frac{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*(arcsin(d*x + c)/(d^2*e^2*x + c*d*e^2) + log(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)/abs(d^2*e^2*x + c*d*e^2) + 2/abs(d^2*e^2*x + c*d*e^2))/(d*e^2)) - a/(d^2*e^2*x + c*d*e^2)","B",0
184,1,120,0,0.423520," ","integrate((a+b*arcsin(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{\arcsin\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) + arcsin(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
185,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\frac{{\left({\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{e^{\left(\frac{1}{2} \, \log\left(d x + c + 1\right) + \frac{1}{2} \, \log\left(-d x - c + 1\right)\right)}}{d^{7} e^{4} x^{7} + 7 \, c d^{6} e^{4} x^{6} + {\left(21 \, c^{2} - 1\right)} d^{5} e^{4} x^{5} + 5 \, {\left(7 \, c^{3} - c\right)} d^{4} e^{4} x^{4} + 5 \, {\left(7 \, c^{4} - 2 \, c^{2}\right)} d^{3} e^{4} x^{3} + {\left(21 \, c^{5} - 10 \, c^{3}\right)} d^{2} e^{4} x^{2} + {\left(7 \, c^{6} - 5 \, c^{4}\right)} d e^{4} x + {\left(c^{7} - c^{5}\right)} e^{4} - {\left(d^{5} e^{4} x^{5} + 5 \, c d^{4} e^{4} x^{4} + {\left(10 \, c^{2} - 1\right)} d^{3} e^{4} x^{3} + {\left(10 \, c^{3} - 3 \, c\right)} d^{2} e^{4} x^{2} + {\left(5 \, c^{4} - 3 \, c^{2}\right)} d e^{4} x + {\left(c^{5} - c^{3}\right)} e^{4}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)}}\,{d x} + \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)\right)} b}{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 \, {\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,"-1/3*(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(1/3*e^(1/2*log(d*x + c + 1) + 1/2*log(-d*x - c + 1))/(d^7*e^4*x^7 + 7*c*d^6*e^4*x^6 + (21*c^2 - 1)*d^5*e^4*x^5 + 5*(7*c^3 - c)*d^4*e^4*x^4 + 5*(7*c^4 - 2*c^2)*d^3*e^4*x^3 + (21*c^5 - 10*c^3)*d^2*e^4*x^2 + (7*c^6 - 5*c^4)*d*e^4*x + (c^7 - c^5)*e^4 + (d^5*e^4*x^5 + 5*c*d^4*e^4*x^4 + (10*c^2 - 1)*d^3*e^4*x^3 + (10*c^3 - 3*c)*d^2*e^4*x^2 + (5*c^4 - 3*c^2)*d*e^4*x + (c^5 - c^3)*e^4)*e^(log(d*x + c + 1) + log(-d*x - c + 1))), x) + arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))*b/(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/(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
186,1,263,0,0.463169," ","integrate((a+b*arcsin(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 \, \arcsin\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*arcsin(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
187,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^6,x, algorithm=""maxima"")","-\frac{{\left({\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)} \int \frac{e^{\left(\frac{1}{2} \, \log\left(d x + c + 1\right) + \frac{1}{2} \, \log\left(-d x - c + 1\right)\right)}}{d^{9} e^{6} x^{9} + 9 \, c d^{8} e^{6} x^{8} + {\left(36 \, c^{2} - 1\right)} d^{7} e^{6} x^{7} + 7 \, {\left(12 \, c^{3} - c\right)} d^{6} e^{6} x^{6} + 21 \, {\left(6 \, c^{4} - c^{2}\right)} d^{5} e^{6} x^{5} + 7 \, {\left(18 \, c^{5} - 5 \, c^{3}\right)} d^{4} e^{6} x^{4} + 7 \, {\left(12 \, c^{6} - 5 \, c^{4}\right)} d^{3} e^{6} x^{3} + 3 \, {\left(12 \, c^{7} - 7 \, c^{5}\right)} d^{2} e^{6} x^{2} + {\left(9 \, c^{8} - 7 \, c^{6}\right)} d e^{6} x + {\left(c^{9} - c^{7}\right)} e^{6} - {\left(d^{7} e^{6} x^{7} + 7 \, c d^{6} e^{6} x^{6} + {\left(21 \, c^{2} - 1\right)} d^{5} e^{6} x^{5} + 5 \, {\left(7 \, c^{3} - c\right)} d^{4} e^{6} x^{4} + 5 \, {\left(7 \, c^{4} - 2 \, c^{2}\right)} d^{3} e^{6} x^{3} + {\left(21 \, c^{5} - 10 \, c^{3}\right)} d^{2} e^{6} x^{2} + {\left(7 \, c^{6} - 5 \, c^{4}\right)} d e^{6} x + {\left(c^{7} - c^{5}\right)} e^{6}\right)} {\left(d x + c + 1\right)} {\left(d x + c - 1\right)}}\,{d x} + \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)\right)} b}{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)}} - \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,"-1/5*(5*(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)*integrate(1/5*e^(1/2*log(d*x + c + 1) + 1/2*log(-d*x - c + 1))/(d^9*e^6*x^9 + 9*c*d^8*e^6*x^8 + (36*c^2 - 1)*d^7*e^6*x^7 + 7*(12*c^3 - c)*d^6*e^6*x^6 + 21*(6*c^4 - c^2)*d^5*e^6*x^5 + 7*(18*c^5 - 5*c^3)*d^4*e^6*x^4 + 7*(12*c^6 - 5*c^4)*d^3*e^6*x^3 + 3*(12*c^7 - 7*c^5)*d^2*e^6*x^2 + (9*c^8 - 7*c^6)*d*e^6*x + (c^9 - c^7)*e^6 + (d^7*e^6*x^7 + 7*c*d^6*e^6*x^6 + (21*c^2 - 1)*d^5*e^6*x^5 + 5*(7*c^3 - c)*d^4*e^6*x^4 + 5*(7*c^4 - 2*c^2)*d^3*e^6*x^3 + (21*c^5 - 10*c^3)*d^2*e^6*x^2 + (7*c^6 - 5*c^4)*d*e^6*x + (c^7 - c^5)*e^6)*e^(log(d*x + c + 1) + log(-d*x - c + 1))), x) + arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))*b/(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) - 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
188,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a b c^{3} d e^{4} + \frac{2}{3} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a b c^{2} d^{2} e^{4} + \frac{1}{12} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} a b c d^{3} e^{4} + \frac{1}{300} \, {\left(120 \, x^{5} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} - \frac{315 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3} x}{d^{5}} - \frac{32 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x^{2}}{d^{4}} + \frac{1050 \, {\left(c^{2} - 1\right)} c^{3} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} + \frac{945 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{4}}{d^{6}} + \frac{161 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c x}{d^{5}} - \frac{225 \, {\left(c^{2} - 1\right)}^{2} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} - \frac{735 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c^{2}}{d^{6}} + \frac{64 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}^{2}}{d^{6}}\right)} d\right)} a b d^{4} e^{4} + a^{2} c^{4} e^{4} x + \frac{2 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + \int \frac{2 \, {\left(b^{2} d^{5} e^{4} x^{5} + 5 \, b^{2} c d^{4} e^{4} x^{4} + 10 \, b^{2} c^{2} d^{3} e^{4} x^{3} + 10 \, b^{2} c^{3} d^{2} e^{4} x^{2} + 5 \, b^{2} c^{4} d e^{4} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{5 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a*b*c^3*d*e^4 + 2/3*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a*b*c^2*d^2*e^4 + 1/12*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*a*b*c*d^3*e^4 + 1/300*(120*x^5*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 - 315*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3*x/d^5 - 32*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x^2/d^4 + 1050*(c^2 - 1)*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 + 945*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^4/d^6 + 161*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c*x/d^5 - 225*(c^2 - 1)^2*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 - 735*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c^2/d^6 + 64*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)^2/d^6)*d)*a*b*d^4*e^4 + a^2*c^4*e^4*x + 2*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + integrate(2/5*(b^2*d^5*e^4*x^5 + 5*b^2*c*d^4*e^4*x^4 + 10*b^2*c^2*d^3*e^4*x^3 + 10*b^2*c^3*d^2*e^4*x^2 + 5*b^2*c^4*d*e^4*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
189,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a b c^{2} d e^{3} + \frac{1}{3} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a b c d^{2} e^{3} + \frac{1}{48} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} a b d^{3} e^{3} + a^{2} c^{3} e^{3} x + \frac{2 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + \int \frac{{\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a*b*c^2*d*e^3 + 1/3*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a*b*c*d^2*e^3 + 1/48*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*a*b*d^3*e^3 + a^2*c^3*e^3*x + 2*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + integrate(1/2*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
190,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a b c d e^{2} + \frac{1}{9} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a b d^{2} e^{2} + a^{2} c^{2} e^{2} x + \frac{2 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + \int \frac{2 \, {\left(b^{2} d^{3} e^{2} x^{3} + 3 \, b^{2} c d^{2} e^{2} x^{2} + 3 \, b^{2} c^{2} d e^{2} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a*b*c*d*e^2 + 1/9*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a*b*d^2*e^2 + a^2*c^2*e^2*x + 2*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + integrate(2/3*(b^2*d^3*e^2*x^3 + 3*b^2*c*d^2*e^2*x^2 + 3*b^2*c^2*d*e^2*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
191,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} d e x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a b d e + a^{2} c e x + \frac{2 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + \int \frac{{\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}"," ",0,"1/2*a^2*d*e*x^2 + 1/2*(2*x^2*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a*b*d*e + a^2*c*e*x + 2*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + integrate((b^2*d^2*e*x^2 + 2*b^2*c*d*e*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
192,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","{\left(x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, d \int \frac{\sqrt{d x + c + 1} \sqrt{-d x - c + 1} x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} b^{2} + a^{2} x + \frac{2 \, {\left({\left(d x + c\right)} \arcsin\left(d x + c\right) + \sqrt{-{\left(d x + c\right)}^{2} + 1}\right)} a b}{d}"," ",0,"(x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*d*integrate(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x))*b^2 + a^2*x + 2*((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*a*b/d","F",0
193,0,0,0,0.000000," ","integrate((a+b*arcsin(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} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, a b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d e x + c e}\,{d x}"," ",0,"a^2*log(d*e*x + c*e)/(d*e) + integrate((b^2*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*a*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d*e*x + c*e), x)","F",0
194,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-2 \, a b {\left(\frac{\arcsin\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}} + \frac{2}{{\left| d^{2} e^{2} x + c d e^{2} \right|}}\right)}{d e^{2}}\right)} - \frac{{\left(\arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + \frac{2 \, {\left(d^{2} e^{2} x + c d e^{2}\right)} \int \frac{\sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{\sqrt{d x + c + 1} {\left(d x + c\right)} {\left(d x + c - 1\right)}}\,{d x}}{e^{2}}\right)} b^{2}}{d^{2} e^{2} x + c d e^{2}} - \frac{a^{2}}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-2*a*b*(arcsin(d*x + c)/(d^2*e^2*x + c*d*e^2) + log(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)/abs(d^2*e^2*x + c*d*e^2) + 2/abs(d^2*e^2*x + c*d*e^2))/(d*e^2)) - (arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*(d^2*e^2*x + c*d*e^2)*integrate(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))/(d^3*e^2*x^3 + 3*c*d^2*e^2*x^2 + (3*c^2 - 1)*d*e^2*x + (c^3 - c)*e^2), x))*b^2/(d^2*e^2*x + c*d*e^2) - a^2/(d^2*e^2*x + c*d*e^2)","F",0
195,1,236,0,0.449530," ","integrate((a+b*arcsin(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 \arcsin\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{\arcsin\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} \arcsin\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*arcsin(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) + arcsin(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*arcsin(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
196,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\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)}} - \frac{b^{2} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, {\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(b^{2} d x + b^{2} c\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) - 3 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - a b\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + {\left(15 \, c^{2} - 1\right)} d^{4} e^{4} x^{4} + 4 \, {\left(5 \, c^{3} - c\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, c^{4} - 2 \, c^{2}\right)} d^{2} e^{4} x^{2} + 2 \, {\left(3 \, c^{5} - 2 \, c^{3}\right)} d e^{4} x + {\left(c^{6} - c^{4}\right)} e^{4}}\,{d x}}{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,"-1/3*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) - 1/3*(b^2*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 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(2/3*((b^2*d*x + b^2*c)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) - 3*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - a*b)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + (15*c^2 - 1)*d^4*e^4*x^4 + 4*(5*c^3 - c)*d^3*e^4*x^3 + 3*(5*c^4 - 2*c^2)*d^2*e^4*x^2 + 2*(3*c^5 - 2*c^3)*d*e^4*x + (c^6 - c^4)*e^4), x))/(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
197,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b c^{3} d e^{4} + {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a^{2} b c^{2} d^{2} e^{4} + \frac{1}{8} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} a^{2} b c d^{3} e^{4} + \frac{1}{200} \, {\left(120 \, x^{5} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} - \frac{315 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3} x}{d^{5}} - \frac{32 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x^{2}}{d^{4}} + \frac{1050 \, {\left(c^{2} - 1\right)} c^{3} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} + \frac{945 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{4}}{d^{6}} + \frac{161 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c x}{d^{5}} - \frac{225 \, {\left(c^{2} - 1\right)}^{2} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{6}} - \frac{735 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c^{2}}{d^{6}} + \frac{64 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}^{2}}{d^{6}}\right)} d\right)} a^{2} b d^{4} e^{4} + a^{3} c^{4} e^{4} x + \frac{3 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + \int \frac{3 \, {\left({\left(b^{3} d^{5} e^{4} x^{5} + 5 \, b^{3} c d^{4} e^{4} x^{4} + 10 \, b^{3} c^{2} d^{3} e^{4} x^{3} + 10 \, b^{3} c^{3} d^{2} e^{4} x^{2} + 5 \, b^{3} c^{4} d e^{4} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 5 \, {\left(a b^{2} d^{6} e^{4} x^{6} + 6 \, a b^{2} c d^{5} e^{4} x^{5} + {\left(15 \, a b^{2} c^{2} - a b^{2}\right)} d^{4} e^{4} x^{4} + 4 \, {\left(5 \, a b^{2} c^{3} - a b^{2} c\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, a b^{2} c^{4} - 2 \, a b^{2} c^{2}\right)} d^{2} e^{4} x^{2} + 2 \, {\left(3 \, a b^{2} c^{5} - 2 \, a b^{2} c^{3}\right)} d e^{4} x + {\left(a b^{2} c^{6} - a b^{2} c^{4}\right)} e^{4}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{5 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^2*b*c^3*d*e^4 + (6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a^2*b*c^2*d^2*e^4 + 1/8*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*a^2*b*c*d^3*e^4 + 1/200*(120*x^5*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 - 315*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3*x/d^5 - 32*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x^2/d^4 + 1050*(c^2 - 1)*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 + 945*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^4/d^6 + 161*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c*x/d^5 - 225*(c^2 - 1)^2*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^6 - 735*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c^2/d^6 + 64*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)^2/d^6)*d)*a^2*b*d^4*e^4 + a^3*c^4*e^4*x + 3*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + integrate(3/5*((b^3*d^5*e^4*x^5 + 5*b^3*c*d^4*e^4*x^4 + 10*b^3*c^2*d^3*e^4*x^3 + 10*b^3*c^3*d^2*e^4*x^2 + 5*b^3*c^4*d*e^4*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 5*(a*b^2*d^6*e^4*x^6 + 6*a*b^2*c*d^5*e^4*x^5 + (15*a*b^2*c^2 - a*b^2)*d^4*e^4*x^4 + 4*(5*a*b^2*c^3 - a*b^2*c)*d^3*e^4*x^3 + 3*(5*a*b^2*c^4 - 2*a*b^2*c^2)*d^2*e^4*x^2 + 2*(3*a*b^2*c^5 - 2*a*b^2*c^3)*d*e^4*x + (a*b^2*c^6 - a*b^2*c^4)*e^4)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
198,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b c^{2} d e^{3} + \frac{1}{2} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a^{2} b c d^{2} e^{3} + \frac{1}{32} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} a^{2} b d^{3} e^{3} + a^{3} c^{3} e^{3} x + \frac{3 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + \int \frac{3 \, {\left({\left(b^{3} d^{4} e^{3} x^{4} + 4 \, b^{3} c d^{3} e^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{3} c^{3} d e^{3} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 4 \, {\left(a b^{2} d^{5} e^{3} x^{5} + 5 \, a b^{2} c d^{4} e^{3} x^{4} + {\left(10 \, a b^{2} c^{2} - a b^{2}\right)} d^{3} e^{3} x^{3} + {\left(10 \, a b^{2} c^{3} - 3 \, a b^{2} c\right)} d^{2} e^{3} x^{2} + {\left(5 \, a b^{2} c^{4} - 3 \, a b^{2} c^{2}\right)} d e^{3} x + {\left(a b^{2} c^{5} - a b^{2} c^{3}\right)} e^{3}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{4 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^2*b*c^2*d*e^3 + 1/2*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a^2*b*c*d^2*e^3 + 1/32*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*a^2*b*d^3*e^3 + a^3*c^3*e^3*x + 3*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + integrate(3/4*((b^3*d^4*e^3*x^4 + 4*b^3*c*d^3*e^3*x^3 + 6*b^3*c^2*d^2*e^3*x^2 + 4*b^3*c^3*d*e^3*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 4*(a*b^2*d^5*e^3*x^5 + 5*a*b^2*c*d^4*e^3*x^4 + (10*a*b^2*c^2 - a*b^2)*d^3*e^3*x^3 + (10*a*b^2*c^3 - 3*a*b^2*c)*d^2*e^3*x^2 + (5*a*b^2*c^4 - 3*a*b^2*c^2)*d*e^3*x + (a*b^2*c^5 - a*b^2*c^3)*e^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
199,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b c d e^{2} + \frac{1}{6} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a^{2} b d^{2} e^{2} + a^{3} c^{2} e^{2} x + \frac{3 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + \int \frac{{\left(b^{3} d^{3} e^{2} x^{3} + 3 \, b^{3} c d^{2} e^{2} x^{2} + 3 \, b^{3} c^{2} d e^{2} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 3 \, {\left(a b^{2} d^{4} e^{2} x^{4} + 4 \, a b^{2} c d^{3} e^{2} x^{3} + {\left(6 \, a b^{2} c^{2} - a b^{2}\right)} d^{2} e^{2} x^{2} + 2 \, {\left(2 \, a b^{2} c^{3} - a b^{2} c\right)} d e^{2} x + {\left(a b^{2} c^{4} - a b^{2} c^{2}\right)} e^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^2*b*c*d*e^2 + 1/6*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a^2*b*d^2*e^2 + a^3*c^2*e^2*x + 3*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + integrate(((b^3*d^3*e^2*x^3 + 3*b^3*c*d^2*e^2*x^2 + 3*b^3*c^2*d*e^2*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 3*(a*b^2*d^4*e^2*x^4 + 4*a*b^2*c*d^3*e^2*x^3 + (6*a*b^2*c^2 - a*b^2)*d^2*e^2*x^2 + 2*(2*a*b^2*c^3 - a*b^2*c)*d*e^2*x + (a*b^2*c^4 - a*b^2*c^2)*e^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
200,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} d e x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{2} b d e + a^{3} c e x + \frac{3 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + \int \frac{3 \, {\left({\left(b^{3} d^{2} e x^{2} + 2 \, b^{3} c d e x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, {\left(a b^{2} d^{3} e x^{3} + 3 \, a b^{2} c d^{2} e x^{2} + {\left(3 \, a b^{2} c^{2} - a b^{2}\right)} d e x + {\left(a b^{2} c^{3} - a b^{2} c\right)} e\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right)}}\,{d x}"," ",0,"1/2*a^3*d*e*x^2 + 3/4*(2*x^2*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^2*b*d*e + a^3*c*e*x + 3*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + integrate(3/2*((b^3*d^2*e*x^2 + 2*b^3*c*d*e*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*(a*b^2*d^3*e*x^3 + 3*a*b^2*c*d^2*e*x^2 + (3*a*b^2*c^2 - a*b^2)*d*e*x + (a*b^2*c^3 - a*b^2*c)*e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
201,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","b^{3} x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + a^{3} x + \frac{3 \, {\left({\left(d x + c\right)} \arcsin\left(d x + c\right) + \sqrt{-{\left(d x + c\right)}^{2} + 1}\right)} a^{2} b}{d} + \int \frac{3 \, {\left(\sqrt{d x + c + 1} \sqrt{-d x - c + 1} b^{3} d x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left(a b^{2} d^{2} x^{2} + 2 \, a b^{2} c d x + a b^{2} c^{2} - a b^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}"," ",0,"b^3*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + a^3*x + 3*((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*a^2*b/d + integrate(3*(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*b^3*d*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + (a*b^2*d^2*x^2 + 2*a*b^2*c*d*x + a*b^2*c^2 - a*b^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
202,0,0,0,0.000000," ","integrate((a+b*arcsin(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} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d e x + c e}\,{d x}"," ",0,"a^3*log(d*e*x + c*e)/(d*e) + integrate((b^3*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 3*a*b^2*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 3*a^2*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d*e*x + c*e), x)","F",0
203,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-3 \, a^{2} b {\left(\frac{\arcsin\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}} + \frac{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}} - \frac{b^{3} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} - \frac{3}{2} \, {\left(a b^{2} {\left(\frac{2 \, c^{2}}{d^{4} e^{2} x + c d^{3} e^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3} e^{2}} + \frac{4 \, c \log\left(d x + c\right)}{d^{3} e^{2}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3} e^{2}}\right)} d^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} - 2 \, a b^{2} c d {\left(\frac{2 \, c}{d^{3} e^{2} x + c d^{2} e^{2}} - \frac{{\left(c + 1\right)} \log\left(d x + c + 1\right)}{d^{2} e^{2}} + \frac{{\left(c - 1\right)} \log\left(d x + c - 1\right)}{d^{2} e^{2}} + \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} + a b^{2} c^{2} {\left(\frac{2}{d^{2} e^{2} x + c d e^{2}} - \frac{\log\left(d x + c + 1\right)}{d e^{2}} + \frac{\log\left(d x + c - 1\right)}{d e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} - a b^{2} {\left(\frac{2}{d^{2} e^{2} x + c d e^{2}} - \frac{\log\left(d x + c + 1\right)}{d e^{2}} + \frac{\log\left(d x + c - 1\right)}{d e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}\right)} {\left(d^{2} e^{2} x + c d e^{2}\right)}}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-3*a^2*b*(arcsin(d*x + c)/(d^2*e^2*x + c*d*e^2) + log(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)/abs(d^2*e^2*x + c*d*e^2) + 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) - (b^3*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + (d^2*e^2*x + c*d*e^2)*integrate(3*((b^3*d*x + b^3*c)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 - (a*b^2*d^2*x^2 + 2*a*b^2*c*d*x + a*b^2*c^2 - a*b^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + (6*c^2 - 1)*d^2*e^2*x^2 + 2*(2*c^3 - c)*d*e^2*x + (c^4 - c^2)*e^2), x))/(d^2*e^2*x + c*d*e^2)","F",0
204,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{3} b c^{2} d e^{3} + \frac{2}{3} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a^{3} b c d^{2} e^{3} + \frac{1}{24} \, {\left(24 \, x^{4} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{35 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2} x}{d^{4}} - \frac{90 \, {\left(c^{2} - 1\right)} c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} - \frac{105 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{3}}{d^{5}} - \frac{9 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} x}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)}^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{5}} + \frac{55 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)} c}{d^{5}}\right)} d\right)} a^{3} b d^{3} e^{3} + a^{4} c^{3} e^{3} x + \frac{4 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + \int \frac{{\left(b^{4} d^{4} e^{3} x^{4} + 4 \, b^{4} c d^{3} e^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{4} c^{3} d e^{3} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 4 \, {\left(a b^{3} d^{5} e^{3} x^{5} + 5 \, a b^{3} c d^{4} e^{3} x^{4} + {\left(10 \, a b^{3} c^{2} - a b^{3}\right)} d^{3} e^{3} x^{3} + {\left(10 \, a b^{3} c^{3} - 3 \, a b^{3} c\right)} d^{2} e^{3} x^{2} + {\left(5 \, a b^{3} c^{4} - 3 \, a b^{3} c^{2}\right)} d e^{3} x + {\left(a b^{3} c^{5} - a b^{3} c^{3}\right)} e^{3}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 6 \, {\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 \, a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} d^{3} e^{3} x^{3} + {\left(10 \, a^{2} b^{2} c^{3} - 3 \, a^{2} b^{2} c\right)} d^{2} e^{3} x^{2} + {\left(5 \, a^{2} b^{2} c^{4} - 3 \, a^{2} b^{2} c^{2}\right)} d e^{3} x + {\left(a^{2} b^{2} c^{5} - a^{2} b^{2} c^{3}\right)} e^{3}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^3*b*c^2*d*e^3 + 2/3*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a^3*b*c*d^2*e^3 + 1/24*(24*x^4*arcsin(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*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 35*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2*x/d^4 - 90*(c^2 - 1)*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 - 105*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^3/d^5 - 9*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*x/d^4 + 9*(c^2 - 1)^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^5 + 55*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)*c/d^5)*d)*a^3*b*d^3*e^3 + a^4*c^3*e^3*x + 4*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + integrate(((b^4*d^4*e^3*x^4 + 4*b^4*c*d^3*e^3*x^3 + 6*b^4*c^2*d^2*e^3*x^2 + 4*b^4*c^3*d*e^3*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 4*(a*b^3*d^5*e^3*x^5 + 5*a*b^3*c*d^4*e^3*x^4 + (10*a*b^3*c^2 - a*b^3)*d^3*e^3*x^3 + (10*a*b^3*c^3 - 3*a*b^3*c)*d^2*e^3*x^2 + (5*a*b^3*c^4 - 3*a*b^3*c^2)*d*e^3*x + (a*b^3*c^5 - a*b^3*c^3)*e^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 6*(a^2*b^2*d^5*e^3*x^5 + 5*a^2*b^2*c*d^4*e^3*x^4 + (10*a^2*b^2*c^2 - a^2*b^2)*d^3*e^3*x^3 + (10*a^2*b^2*c^3 - 3*a^2*b^2*c)*d^2*e^3*x^2 + (5*a^2*b^2*c^4 - 3*a^2*b^2*c^2)*d*e^3*x + (a^2*b^2*c^5 - a^2*b^2*c^3)*e^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
207,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(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} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{3} b c d e^{2} + \frac{2}{9} \, {\left(6 \, x^{3} \arcsin\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} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} - \frac{5 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c x}{d^{3}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)}\right)} a^{3} b d^{2} e^{2} + a^{4} c^{2} e^{2} x + \frac{4 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + \int \frac{2 \, {\left(2 \, {\left(b^{4} d^{3} e^{2} x^{3} + 3 \, b^{4} c d^{2} e^{2} x^{2} + 3 \, b^{4} c^{2} d e^{2} x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 6 \, {\left(a b^{3} d^{4} e^{2} x^{4} + 4 \, a b^{3} c d^{3} e^{2} x^{3} + {\left(6 \, a b^{3} c^{2} - a b^{3}\right)} d^{2} e^{2} x^{2} + 2 \, {\left(2 \, a b^{3} c^{3} - a b^{3} c\right)} d e^{2} x + {\left(a b^{3} c^{4} - a b^{3} c^{2}\right)} e^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 9 \, {\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 \, a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} d^{2} e^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} c^{3} - a^{2} b^{2} c\right)} d e^{2} x + {\left(a^{2} b^{2} c^{4} - a^{2} b^{2} c^{2}\right)} e^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} - 1\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*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^3*b*c*d*e^2 + 2/9*(6*x^3*arcsin(d*x + c) + d*(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x^2/d^2 - 15*c^3*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 - 5*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c*x/d^3 + 9*(c^2 - 1)*c*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(c^2 - 1)/d^4))*a^3*b*d^2*e^2 + a^4*c^2*e^2*x + 4*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + integrate(2/3*(2*(b^4*d^3*e^2*x^3 + 3*b^4*c*d^2*e^2*x^2 + 3*b^4*c^2*d*e^2*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 6*(a*b^3*d^4*e^2*x^4 + 4*a*b^3*c*d^3*e^2*x^3 + (6*a*b^3*c^2 - a*b^3)*d^2*e^2*x^2 + 2*(2*a*b^3*c^3 - a*b^3*c)*d*e^2*x + (a*b^3*c^4 - a*b^3*c^2)*e^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 9*(a^2*b^2*d^4*e^2*x^4 + 4*a^2*b^2*c*d^3*e^2*x^3 + (6*a^2*b^2*c^2 - a^2*b^2)*d^2*e^2*x^2 + 2*(2*a^2*b^2*c^3 - a^2*b^2*c)*d*e^2*x + (a^2*b^2*c^4 - a^2*b^2*c^2)*e^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
208,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\frac{1}{2} \, a^{4} d e x^{2} + {\left(2 \, x^{2} \arcsin\left(d x + c\right) + d {\left(\frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} + \frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} x}{d^{2}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} c}{d^{3}}\right)}\right)} a^{3} b d e + a^{4} c e x + \frac{4 \, {\left({\left(d x + c\right)} \arcsin\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)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + \int \frac{2 \, {\left({\left(b^{4} d^{2} e x^{2} + 2 \, b^{4} c d e x\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 2 \, {\left(a b^{3} d^{3} e x^{3} + 3 \, a b^{3} c d^{2} e x^{2} + {\left(3 \, a b^{3} c^{2} - a b^{3}\right)} d e x + {\left(a b^{3} c^{3} - a b^{3} c\right)} e\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 3 \, {\left(a^{2} b^{2} d^{3} e x^{3} + 3 \, a^{2} b^{2} c d^{2} e x^{2} + {\left(3 \, a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} d e x + {\left(a^{2} b^{2} c^{3} - a^{2} b^{2} c\right)} e\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}"," ",0,"1/2*a^4*d*e*x^2 + (2*x^2*arcsin(d*x + c) + d*(3*c^2*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 + sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*x/d^2 - (c^2 - 1)*arcsin(-(d^2*x + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*c/d^3))*a^3*b*d*e + a^4*c*e*x + 4*((d*x + c)*arcsin(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)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + integrate(2*((b^4*d^2*e*x^2 + 2*b^4*c*d*e*x)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 2*(a*b^3*d^3*e*x^3 + 3*a*b^3*c*d^2*e*x^2 + (3*a*b^3*c^2 - a*b^3)*d*e*x + (a*b^3*c^3 - a*b^3*c)*e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 3*(a^2*b^2*d^3*e*x^3 + 3*a^2*b^2*c*d^2*e*x^2 + (3*a^2*b^2*c^2 - a^2*b^2)*d*e*x + (a^2*b^2*c^3 - a^2*b^2*c)*e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
209,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","b^{4} x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + a^{4} x + \frac{4 \, {\left({\left(d x + c\right)} \arcsin\left(d x + c\right) + \sqrt{-{\left(d x + c\right)}^{2} + 1}\right)} a^{3} b}{d} + \int \frac{2 \, {\left(2 \, \sqrt{d x + c + 1} \sqrt{-d x - c + 1} b^{4} d x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 2 \, {\left(a b^{3} d^{2} x^{2} + 2 \, a b^{3} c d x + a b^{3} c^{2} - a b^{3}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 3 \, {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{2} b^{2} c d x + a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}"," ",0,"b^4*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + a^4*x + 4*((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*a^3*b/d + integrate(2*(2*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*b^4*d*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 2*(a*b^3*d^2*x^2 + 2*a*b^3*c*d*x + a*b^3*c^2 - a*b^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 3*(a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + a^2*b^2*c^2 - a^2*b^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
210,0,0,0,0.000000," ","integrate((a+b*arcsin(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} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + 4 \, a b^{3} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 6 \, a^{2} b^{2} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 4 \, a^{3} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d e x + c e}\,{d x}"," ",0,"a^4*log(d*e*x + c*e)/(d*e) + integrate((b^4*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + 4*a*b^3*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 6*a^2*b^2*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 4*a^3*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d*e*x + c*e), x)","F",0
211,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-4 \, a^{3} b {\left(\frac{\arcsin\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}{{\left| d^{2} e^{2} x + c d e^{2} \right|}} + \frac{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}} - \frac{b^{4} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} - {\left(2 \, a b^{3} {\left(\frac{2 \, c^{2}}{d^{4} e^{2} x + c d^{3} e^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3} e^{2}} + \frac{4 \, c \log\left(d x + c\right)}{d^{3} e^{2}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3} e^{2}}\right)} d^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3} - 4 \, a b^{3} c d {\left(\frac{2 \, c}{d^{3} e^{2} x + c d^{2} e^{2}} - \frac{{\left(c + 1\right)} \log\left(d x + c + 1\right)}{d^{2} e^{2}} + \frac{{\left(c - 1\right)} \log\left(d x + c - 1\right)}{d^{2} e^{2}} + \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3} + 2 \, a b^{3} c^{2} {\left(\frac{2}{d^{2} e^{2} x + c d e^{2}} - \frac{\log\left(d x + c + 1\right)}{d e^{2}} + \frac{\log\left(d x + c - 1\right)}{d e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3} + 3 \, a^{2} b^{2} {\left(\frac{2 \, c^{2}}{d^{4} e^{2} x + c d^{3} e^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3} e^{2}} + \frac{4 \, c \log\left(d x + c\right)}{d^{3} e^{2}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3} e^{2}}\right)} d^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} - 6 \, a^{2} b^{2} c d {\left(\frac{2 \, c}{d^{3} e^{2} x + c d^{2} e^{2}} - \frac{{\left(c + 1\right)} \log\left(d x + c + 1\right)}{d^{2} e^{2}} + \frac{{\left(c - 1\right)} \log\left(d x + c - 1\right)}{d^{2} e^{2}} + \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} + 3 \, a^{2} b^{2} c^{2} {\left(\frac{2}{d^{2} e^{2} x + c d e^{2}} - \frac{\log\left(d x + c + 1\right)}{d e^{2}} + \frac{\log\left(d x + c - 1\right)}{d e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} - \frac{4 \, \sqrt{d x + c + 1} \sqrt{-d x - c + 1} b^{4} c \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d^{2} e^{2} x + c d e^{2}} - 2 \, a b^{3} {\left(\frac{2}{d^{2} e^{2} x + c d e^{2}} - \frac{\log\left(d x + c + 1\right)}{d e^{2}} + \frac{\log\left(d x + c - 1\right)}{d e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3} - 3 \, a^{2} b^{2} {\left(\frac{2}{d^{2} e^{2} x + c d e^{2}} - \frac{\log\left(d x + c + 1\right)}{d e^{2}} + \frac{\log\left(d x + c - 1\right)}{d e^{2}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} + \frac{12 \, b^{4} c \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2} \log\left(d x + c\right)}{d e^{2}}\right)} {\left(d^{2} e^{2} x + c d e^{2}\right)}}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-4*a^3*b*(arcsin(d*x + c)/(d^2*e^2*x + c*d*e^2) + log(2*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)/abs(d^2*e^2*x + c*d*e^2) + 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) - (b^4*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + (d^2*e^2*x + c*d*e^2)*integrate(2*(2*(b^4*d*x + b^4*c)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 - 2*(a*b^3*d^2*x^2 + 2*a*b^3*c*d*x + a*b^3*c^2 - a*b^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 - 3*(a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + a^2*b^2*c^2 - a^2*b^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + (6*c^2 - 1)*d^2*e^2*x^2 + 2*(2*c^3 - c)*d*e^2*x + (c^4 - c^2)*e^2), x))/(d^2*e^2*x + c*d*e^2)","F",0
212,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^4,x, algorithm=""maxima"")","-\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)}} - \frac{b^{4} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + 2 \, {\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(b^{4} d x + b^{4} c\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} - 6 \, {\left(a b^{3} d^{2} x^{2} + 2 \, a b^{3} c d x + a b^{3} c^{2} - a b^{3}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} - 9 \, {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{2} b^{2} c d x + a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} - 6 \, {\left(a^{3} b d^{2} x^{2} + 2 \, a^{3} b c d x + a^{3} b c^{2} - a^{3} b\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + {\left(15 \, c^{2} - 1\right)} d^{4} e^{4} x^{4} + 4 \, {\left(5 \, c^{3} - c\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, c^{4} - 2 \, c^{2}\right)} d^{2} e^{4} x^{2} + 2 \, {\left(3 \, c^{5} - 2 \, c^{3}\right)} d e^{4} x + {\left(c^{6} - c^{4}\right)} e^{4}}\,{d x}}{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,"-1/3*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) - 1/3*(b^4*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + 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(2/3*(2*(b^4*d*x + b^4*c)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 - 6*(a*b^3*d^2*x^2 + 2*a*b^3*c*d*x + a*b^3*c^2 - a*b^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 - 9*(a^2*b^2*d^2*x^2 + 2*a^2*b^2*c*d*x + a^2*b^2*c^2 - a^2*b^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 - 6*(a^3*b*d^2*x^2 + 2*a^3*b*c*d*x + a^3*b*c^2 - a^3*b)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + (15*c^2 - 1)*d^4*e^4*x^4 + 4*(5*c^3 - c)*d^3*e^4*x^3 + 3*(5*c^4 - 2*c^2)*d^2*e^4*x^2 + 2*(3*c^5 - 2*c^3)*d*e^4*x + (c^6 - c^4)*e^4), x))/(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
214,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^5,x, algorithm=""maxima"")","b^{5} x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{5} + a^{5} x + \frac{5 \, {\left({\left(d x + c\right)} \arcsin\left(d x + c\right) + \sqrt{-{\left(d x + c\right)}^{2} + 1}\right)} a^{4} b}{d} + \int \frac{5 \, {\left(\sqrt{d x + c + 1} \sqrt{-d x - c + 1} b^{5} d x \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + {\left(a b^{4} d^{2} x^{2} + 2 \, a b^{4} c d x + a b^{4} c^{2} - a b^{4}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + 2 \, {\left(a^{2} b^{3} d^{2} x^{2} + 2 \, a^{2} b^{3} c d x + a^{2} b^{3} c^{2} - a^{2} b^{3}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 2 \, {\left(a^{3} b^{2} d^{2} x^{2} + 2 \, a^{3} b^{2} c d x + a^{3} b^{2} c^{2} - a^{3} b^{2}\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2}\right)}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}"," ",0,"b^5*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^5 + a^5*x + 5*((d*x + c)*arcsin(d*x + c) + sqrt(-(d*x + c)^2 + 1))*a^4*b/d + integrate(5*(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*b^5*d*x*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + (a*b^4*d^2*x^2 + 2*a*b^4*c*d*x + a*b^4*c^2 - a*b^4)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + 2*(a^2*b^3*d^2*x^2 + 2*a^2*b^3*c*d*x + a^2*b^3*c^2 - a^2*b^3)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 2*(a^3*b^2*d^2*x^2 + 2*a^3*b^2*c*d*x + a^3*b^2*c^2 - a^3*b^2)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
215,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arcsin(d*x + c) + a), x)","F",0
216,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsin(d*x + c) + a), x)","F",0
217,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsin(d*x + c) + a), x)","F",0
218,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{d e x + c e}{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsin(d*x + c) + a), x)","F",0
219,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsin(d*x + c) + a), x)","F",0
220,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)), x)","F",0
221,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a d x - \sqrt{d x + c + 1} \sqrt{-d x - c + 1} b + a c + {\left(b d x + b c\right)} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) - {\left(b^{4} d \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, a b^{3} d \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + a^{2} b^{2} d\right)} \int \frac{1}{b^{3} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + a b^{2}}\,{d x}}{2 \, {\left(b^{4} d \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, a b^{3} d \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + a^{2} b^{2} d\right)}}"," ",0,"1/2*(a*d*x - sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*b + a*c + (b*d*x + b*c)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) - 2*(b^4*d*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*a*b^3*d*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + a^2*b^2*d)*integrate(1/2/(b^3*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + a*b^2), x))/(b^4*d*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*a*b^3*d*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + a^2*b^2*d)","F",0
232,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} \sqrt{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*sqrt(b*arcsin(d*x + c) + a), x)","F",0
241,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} \sqrt{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*sqrt(b*arcsin(d*x + c) + a), x)","F",0
242,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} \sqrt{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)*sqrt(b*arcsin(d*x + c) + a), x)","F",0
243,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(d*x + c) + a), x)","F",0
244,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(1/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{d e x + c e}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(d*x + c) + a)/(d*e*x + c*e), x)","F",0
245,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
246,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
247,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(3/2), x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(3/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(3/2)/(d*e*x + c*e), x)","F",0
250,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{3} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3*(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
251,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
252,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
253,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(5/2), x)","F",0
254,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(5/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(5/2)/(d*e*x + c*e), x)","F",0
255,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)}^{2} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2*(b*arcsin(d*x + c) + a)^(7/2), x)","F",0
256,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^(7/2), x)","F",0
257,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(7/2), x)","F",0
258,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(7/2)/(d*e*x+c*e),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(7/2)/(d*e*x + c*e), x)","F",0
259,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/sqrt(b*arcsin(d*x + c) + a), x)","F",0
260,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/sqrt(b*arcsin(d*x + c) + a), x)","F",0
261,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/sqrt(b*arcsin(d*x + c) + a), x)","F",0
262,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/sqrt(b*arcsin(d*x + c) + a), x)","F",0
263,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsin(d*x + c) + a), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} \sqrt{b \arcsin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*sqrt(b*arcsin(d*x + c) + a)), x)","F",0
265,0,0,0,0.000000," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{4}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^4/(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
266,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
268,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsin(d*x + c) + a)^(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(-3/2), x)","F",0
270,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^(3/2)), x)","F",0
271,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
272,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
273,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsin(d*x + c) + a)^(5/2), x)","F",0
274,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(-5/2), x)","F",0
275,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^(5/2)), x)","F",0
276,0,0,0,0.000000," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{3}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^3/(b*arcsin(d*x + c) + a)^(7/2), x)","F",0
277,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{2}}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^2/(b*arcsin(d*x + c) + a)^(7/2), x)","F",0
278,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{d e x + c e}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*e*x + c*e)/(b*arcsin(d*x + c) + a)^(7/2), x)","F",0
279,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^(-7/2), x)","F",0
280,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^(7/2)), x)","F",0
281,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(b d^{4} e^{3} x^{4} + 4 \, b c d^{3} e^{3} x^{3} + 6 \, b c^{2} d^{2} e^{3} x^{2} + 4 \, b c^{3} d e^{3} x + b c^{4} e^{3}\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{9}{2}} a e^{3} + d \int \frac{{\left(b d^{4} e^{3} x^{4} + 4 \, b c d^{3} e^{3} x^{3} + 6 \, b c^{2} d^{2} e^{3} x^{2} + 4 \, b c^{3} d e^{3} x + b c^{4} e^{3}\right)} \sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} \sqrt{e}}{9 \, d}"," ",0,"1/9*(2*(b*d^4*e^3*x^4 + 4*b*c*d^3*e^3*x^3 + 6*b*c^2*d^2*e^3*x^2 + 4*b*c^3*d*e^3*x + b*c^4*e^3)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (2*(d*x + c)^(9/2)*a*e^3 + 9*d*integrate(2/9*(b*d^4*e^3*x^4 + 4*b*c*d^3*e^3*x^3 + 6*b*c^2*d^2*e^3*x^2 + 4*b*c^3*d*e^3*x + b*c^4*e^3)*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x))*sqrt(e))/d","F",0
282,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(b d^{3} e^{2} x^{3} + 3 \, b c d^{2} e^{2} x^{2} + 3 \, b c^{2} d e^{2} x + b c^{3} e^{2}\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{7}{2}} a e^{2} + d \int \frac{{\left(b d^{3} e^{2} x^{3} + 3 \, b c d^{2} e^{2} x^{2} + 3 \, b c^{2} d e^{2} x + b c^{3} e^{2}\right)} \sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} \sqrt{e}}{7 \, d}"," ",0,"1/7*(2*(b*d^3*e^2*x^3 + 3*b*c*d^2*e^2*x^2 + 3*b*c^2*d*e^2*x + b*c^3*e^2)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (2*(d*x + c)^(7/2)*a*e^2 + 7*d*integrate(2/7*(b*d^3*e^2*x^3 + 3*b*c*d^2*e^2*x^2 + 3*b*c^2*d*e^2*x + b*c^3*e^2)*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x))*sqrt(e))/d","F",0
283,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(b d^{2} e x^{2} + 2 \, b c d e x + b c^{2} e\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{5}{2}} a e + d \int \frac{{\left(b d^{2} e x^{2} + 2 \, b c d e x + b c^{2} e\right)} \sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} \sqrt{e}}{5 \, d}"," ",0,"1/5*(2*(b*d^2*e*x^2 + 2*b*c*d*e*x + b*c^2*e)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (2*(d*x + c)^(5/2)*a*e + 5*d*integrate(2/5*(b*d^2*e*x^2 + 2*b*c*d*e*x + b*c^2*e)*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x))*sqrt(e))/d","F",0
284,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(b d x + b c\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} a + d \int \frac{{\left(b d x + b c\right)} \sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} \sqrt{e}}{3 \, d}"," ",0,"1/3*(2*(b*d*x + b*c)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (2*(d*x + c)^(3/2)*a + 3*d*integrate(2/3*(b*d*x + b*c)*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x))*sqrt(e))/d","F",0
285,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b d \int \frac{\sqrt{d x + c} \sqrt{-d x - c + 1}}{\sqrt{d x + c + 1} d x + \sqrt{d x + c + 1} c - \sqrt{d x + c + 1}}\,{d x} + \sqrt{d x + c} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + \sqrt{d x + c} a\right)}}{d \sqrt{e}}"," ",0,"2*(b*d*e*integrate(sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^2*e*x^2 + 2*c*d*e*x + (c^2 - 1)*e), x) + sqrt(d*x + c)*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + sqrt(d*x + c)*a)/(d*sqrt(e))","F",0
286,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{d x + c} b \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + {\left(\sqrt{d x + c} b d \int \frac{\sqrt{-d x - c + 1}}{\sqrt{d x + c + 1} \sqrt{d x + c} d x + \sqrt{d x + c + 1} \sqrt{d x + c} c - \sqrt{d x + c + 1} \sqrt{d x + c}}\,{d x} + a\right)} \sqrt{d x + c} \sqrt{e}\right)}}{{\left(d x + c\right)} d e^{2}}"," ",0,"-2*(sqrt(d*x + c)*b*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (sqrt(d*x + c)*b*d*e^2*integrate(sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^3*e^2*x^3 + 3*c*d^2*e^2*x^2 + (3*c^2 - 1)*d*e^2*x + (c^3 - c)*e^2), x) + a)*sqrt(d*x + c)*sqrt(e))/((d*x + c)*d*e^2)","F",0
287,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + {\left({\left(b d^{2} e^{3} x + b c d e^{3}\right)} {\left(d x + c\right)}^{\frac{3}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{4} e^{3} x^{4} + 4 \, c d^{3} e^{3} x^{3} + {\left(6 \, c^{2} - 1\right)} d^{2} e^{3} x^{2} + 2 \, {\left(2 \, c^{3} - c\right)} d e^{3} x + {\left(c^{4} - c^{2}\right)} e^{3}}\,{d x} + a d x + a c\right)} \sqrt{d x + c}\right)}}{3 \, {\left(d^{2} e^{2} x + c d e^{2}\right)} {\left(d x + c\right)}^{2} \sqrt{e}}"," ",0,"-2/3*((d*x + c)^(3/2)*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (3*(b*d^2*e^3*x + b*c*d*e^3)*(d*x + c)^(3/2)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^4*e^3*x^4 + 4*c*d^3*e^3*x^3 + (6*c^2 - 1)*d^2*e^3*x^2 + 2*(2*c^3 - c)*d*e^3*x + (c^4 - c^2)*e^3), x) + a*d*x + a*c)*sqrt(d*x + c))/((d^2*e^2*x + c*d*e^2)*(d*x + c)^2*sqrt(e))","F",0
288,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(d x + c\right)}^{\frac{5}{2}} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + {\left(a d^{2} x^{2} + {\left(b d^{3} e^{4} x^{2} + 2 \, b c d^{2} e^{4} x + b c^{2} d e^{4}\right)} {\left(d x + c\right)}^{\frac{5}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{5} e^{4} x^{5} + 5 \, c d^{4} e^{4} x^{4} + {\left(10 \, c^{2} - 1\right)} d^{3} e^{4} x^{3} + {\left(10 \, c^{3} - 3 \, c\right)} d^{2} e^{4} x^{2} + {\left(5 \, c^{4} - 3 \, c^{2}\right)} d e^{4} x + {\left(c^{5} - c^{3}\right)} e^{4}}\,{d x} + 2 \, a c d x + a c^{2}\right)} \sqrt{d x + c}\right)}}{5 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)} {\left(d x + c\right)}^{3} \sqrt{e}}"," ",0,"-2/5*((d*x + c)^(5/2)*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (a*d^2*x^2 + 5*(b*d^3*e^4*x^2 + 2*b*c*d^2*e^4*x + b*c^2*d*e^4)*(d*x + c)^(5/2)*integrate(1/5*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^5*e^4*x^5 + 5*c*d^4*e^4*x^4 + (10*c^2 - 1)*d^3*e^4*x^3 + (10*c^3 - 3*c)*d^2*e^4*x^2 + (5*c^4 - 3*c^2)*d*e^4*x + (c^5 - c^3)*e^4), x) + 2*a*c*d*x + a*c^2)*sqrt(d*x + c))/((d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)*(d*x + c)^3*sqrt(e))","F",0
289,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(9/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(d x + c\right)}^{\frac{7}{2}} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + {\left(a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + {\left(b d^{4} e^{5} x^{3} + 3 \, b c d^{3} e^{5} x^{2} + 3 \, b c^{2} d^{2} e^{5} x + b c^{3} d e^{5}\right)} {\left(d x + c\right)}^{\frac{7}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{6} e^{5} x^{6} + 6 \, c d^{5} e^{5} x^{5} + {\left(15 \, c^{2} - 1\right)} d^{4} e^{5} x^{4} + 4 \, {\left(5 \, c^{3} - c\right)} d^{3} e^{5} x^{3} + 3 \, {\left(5 \, c^{4} - 2 \, c^{2}\right)} d^{2} e^{5} x^{2} + 2 \, {\left(3 \, c^{5} - 2 \, c^{3}\right)} d e^{5} x + {\left(c^{6} - c^{4}\right)} e^{5}}\,{d x} + 3 \, a c^{2} d x + a c^{3}\right)} \sqrt{d x + c}\right)}}{7 \, {\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)} {\left(d x + c\right)}^{4} \sqrt{e}}"," ",0,"-2/7*((d*x + c)^(7/2)*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (a*d^3*x^3 + 3*a*c*d^2*x^2 + 7*(b*d^4*e^5*x^3 + 3*b*c*d^3*e^5*x^2 + 3*b*c^2*d^2*e^5*x + b*c^3*d*e^5)*(d*x + c)^(7/2)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^6*e^5*x^6 + 6*c*d^5*e^5*x^5 + (15*c^2 - 1)*d^4*e^5*x^4 + 4*(5*c^3 - c)*d^3*e^5*x^3 + 3*(5*c^4 - 2*c^2)*d^2*e^5*x^2 + 2*(3*c^5 - 2*c^3)*d*e^5*x + (c^6 - c^4)*e^5), x) + 3*a*c^2*d*x + a*c^3)*sqrt(d*x + 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)*(d*x + c)^4*sqrt(e))","F",0
290,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(11/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(d x + c\right)}^{\frac{9}{2}} b \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right) + {\left(a d^{4} x^{4} + 4 \, a c d^{3} x^{3} + 6 \, a c^{2} d^{2} x^{2} + {\left(b d^{5} e^{6} x^{4} + 4 \, b c d^{4} e^{6} x^{3} + 6 \, b c^{2} d^{3} e^{6} x^{2} + 4 \, b c^{3} d^{2} e^{6} x + b c^{4} d e^{6}\right)} {\left(d x + c\right)}^{\frac{9}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1}}{d^{7} e^{6} x^{7} + 7 \, c d^{6} e^{6} x^{6} + {\left(21 \, c^{2} - 1\right)} d^{5} e^{6} x^{5} + 5 \, {\left(7 \, c^{3} - c\right)} d^{4} e^{6} x^{4} + 5 \, {\left(7 \, c^{4} - 2 \, c^{2}\right)} d^{3} e^{6} x^{3} + {\left(21 \, c^{5} - 10 \, c^{3}\right)} d^{2} e^{6} x^{2} + {\left(7 \, c^{6} - 5 \, c^{4}\right)} d e^{6} x + {\left(c^{7} - c^{5}\right)} e^{6}}\,{d x} + 4 \, a c^{3} d x + a c^{4}\right)} \sqrt{d x + c}\right)}}{9 \, {\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)} {\left(d x + c\right)}^{5} \sqrt{e}}"," ",0,"-2/9*((d*x + c)^(9/2)*b*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + (a*d^4*x^4 + 4*a*c*d^3*x^3 + 6*a*c^2*d^2*x^2 + 9*(b*d^5*e^6*x^4 + 4*b*c*d^4*e^6*x^3 + 6*b*c^2*d^3*e^6*x^2 + 4*b*c^3*d^2*e^6*x + b*c^4*d*e^6)*(d*x + c)^(9/2)*integrate(1/9*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)/(d^7*e^6*x^7 + 7*c*d^6*e^6*x^6 + (21*c^2 - 1)*d^5*e^6*x^5 + 5*(7*c^3 - c)*d^4*e^6*x^4 + 5*(7*c^4 - 2*c^2)*d^3*e^6*x^3 + (21*c^5 - 10*c^3)*d^2*e^6*x^2 + (7*c^6 - 5*c^4)*d*e^6*x + (c^7 - c^5)*e^6), x) + 4*a*c^3*d*x + a*c^4)*sqrt(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)*(d*x + c)^5*sqrt(e))","F",0
291,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)*(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\frac{140 \, {\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x + b^{2} c^{4} e^{3}\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left(1260 \, a b d^{5} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x^{5} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 6300 \, a b c d^{4} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x^{4} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 12600 \, a b c^{2} d^{3} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x^{3} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 12600 \, a b c^{3} d^{2} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 6300 \, a b c^{4} d e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 1260 \, a b c^{5} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{315 \, a^{2} c^{5} e^{\frac{7}{2}} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + 280 \, b^{2} d^{4} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x^{4} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 1120 \, b^{2} c d^{3} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x^{3} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 1680 \, b^{2} c^{2} d^{2} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 1120 \, b^{2} c^{3} d e^{\frac{7}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 280 \, b^{2} c^{4} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - \frac{1575 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} c^{4} e^{\frac{7}{2}}}{d} - 1260 \, a b d^{3} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x^{3} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 3780 \, a b c d^{2} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 3780 \, a b c^{2} d e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 1260 \, a b c^{3} e^{\frac{7}{2}} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{1050 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} c^{3} e^{\frac{7}{2}}}{d} - \frac{315 \, a^{2} c^{3} e^{\frac{7}{2}} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + \frac{630 \, {\left(4 \, {\left(d x + c\right)}^{\frac{5}{2}} - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} c - 10 \, {\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) + 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) - 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 20 \, {\left(3 \, c^{2} + 1\right)} \sqrt{d x + c}\right)} a^{2} c^{2} e^{\frac{7}{2}}}{d} + \frac{945 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} c^{2} e^{\frac{7}{2}}}{d} + \frac{15 \, {\left(60 \, {\left(d x + c\right)}^{\frac{7}{2}} - 336 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 140 \, {\left(6 \, c^{2} + 1\right)} {\left(d x + c\right)}^{\frac{3}{2}} + 210 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 105 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 105 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 1680 \, {\left(c^{3} + c\right)} \sqrt{d x + c}\right)} a^{2} c e^{\frac{7}{2}}}{d} - \frac{315 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} c e^{\frac{7}{2}}}{d} + \frac{{\left(140 \, {\left(d x + c\right)}^{\frac{9}{2}} - 900 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 252 \, {\left(10 \, c^{2} + 1\right)} {\left(d x + c\right)}^{\frac{5}{2}} - 2100 \, {\left(2 \, c^{3} + c\right)} {\left(d x + c\right)}^{\frac{3}{2}} - 630 \, {\left(c^{5} + 5 \, c^{4} + 10 \, c^{3} + 10 \, c^{2} + 5 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) + 315 \, {\left(c^{5} - 5 \, c^{4} + 10 \, c^{3} - 10 \, c^{2} + 5 \, c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) - 315 \, {\left(c^{5} - 5 \, c^{4} + 10 \, c^{3} - 10 \, c^{2} + 5 \, c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 1260 \, {\left(5 \, c^{4} + 10 \, c^{2} + 1\right)} \sqrt{d x + c}\right)} a^{2} e^{\frac{7}{2}}}{d} - \frac{63 \, {\left(4 \, {\left(d x + c\right)}^{\frac{5}{2}} - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} c - 10 \, {\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) + 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) - 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 20 \, {\left(3 \, c^{2} + 1\right)} \sqrt{d x + c}\right)} a^{2} e^{\frac{7}{2}}}{d}\right)} d}{630 \, d}"," ",0,"1/630*(140*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x + b^2*c^4*e^3)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + (11340*a*b*d^5*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x^5*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 56700*a*b*c*d^4*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x^4*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 113400*a*b*c^2*d^3*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x^3*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 113400*a*b*c^3*d^2*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 56700*a*b*c^4*d*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 11340*a*b*c^5*e^(7/2)*integrate(1/9*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 315*a^2*c^5*e^(7/2)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 2520*b^2*d^4*e^(7/2)*integrate(1/9*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x^4*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 10080*b^2*c*d^3*e^(7/2)*integrate(1/9*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x^3*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 15120*b^2*c^2*d^2*e^(7/2)*integrate(1/9*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 10080*b^2*c^3*d*e^(7/2)*integrate(1/9*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 2520*b^2*c^4*e^(7/2)*integrate(1/9*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 1575*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*c^4*e^(7/2)/d - 11340*a*b*d^3*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x^3*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 34020*a*b*c*d^2*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 34020*a*b*c^2*d*e^(7/2)*integrate(1/9*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 11340*a*b*c^3*e^(7/2)*integrate(1/9*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 1050*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^2*c^3*e^(7/2)/d - 315*a^2*c^3*e^(7/2)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 630*(4*(d*x + c)^(5/2) - 20*(d*x + c)^(3/2)*c - 10*(c^3 + 3*c^2 + 3*c + 1)*arctan(sqrt(d*x + c)) + 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) + 1) - 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) - 1) + 20*(3*c^2 + 1)*sqrt(d*x + c))*a^2*c^2*e^(7/2)/d + 945*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*c^2*e^(7/2)/d + 15*(60*(d*x + c)^(7/2) - 336*(d*x + c)^(5/2)*c + 140*(6*c^2 + 1)*(d*x + c)^(3/2) + 210*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*arctan(sqrt(d*x + c)) - 105*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(sqrt(d*x + c) + 1) + 105*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(sqrt(d*x + c) - 1) - 1680*(c^3 + c)*sqrt(d*x + c))*a^2*c*e^(7/2)/d - 315*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^2*c*e^(7/2)/d + (140*(d*x + c)^(9/2) - 900*(d*x + c)^(7/2)*c + 252*(10*c^2 + 1)*(d*x + c)^(5/2) - 2100*(2*c^3 + c)*(d*x + c)^(3/2) - 630*(c^5 + 5*c^4 + 10*c^3 + 10*c^2 + 5*c + 1)*arctan(sqrt(d*x + c)) + 315*(c^5 - 5*c^4 + 10*c^3 - 10*c^2 + 5*c - 1)*log(sqrt(d*x + c) + 1) - 315*(c^5 - 5*c^4 + 10*c^3 - 10*c^2 + 5*c - 1)*log(sqrt(d*x + c) - 1) + 1260*(5*c^4 + 10*c^2 + 1)*sqrt(d*x + c))*a^2*e^(7/2)/d - 63*(4*(d*x + c)^(5/2) - 20*(d*x + c)^(3/2)*c - 10*(c^3 + 3*c^2 + 3*c + 1)*arctan(sqrt(d*x + c)) + 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) + 1) - 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) - 1) + 20*(3*c^2 + 1)*sqrt(d*x + c))*a^2*e^(7/2)/d)*d)/d","F",0
292,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\frac{60 \, {\left(b^{2} d^{3} e^{2} x^{3} + 3 \, b^{2} c d^{2} e^{2} x^{2} + 3 \, b^{2} c^{2} d e^{2} x + b^{2} c^{3} e^{2}\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left(420 \, a b d^{4} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} x^{4} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 1680 \, a b c d^{3} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} x^{3} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 2520 \, a b c^{2} d^{2} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 1680 \, a b c^{3} d e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 420 \, a b c^{4} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{105 \, a^{2} c^{4} e^{\frac{5}{2}} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + 120 \, b^{2} d^{3} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x^{3} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 360 \, b^{2} c d^{2} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 360 \, b^{2} c^{2} d e^{\frac{5}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 120 \, b^{2} c^{3} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - \frac{420 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} c^{3} e^{\frac{5}{2}}}{d} - 420 \, a b d^{2} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 840 \, a b c d e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 420 \, a b c^{2} e^{\frac{5}{2}} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{210 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} c^{2} e^{\frac{5}{2}}}{d} - \frac{105 \, a^{2} c^{2} e^{\frac{5}{2}} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + \frac{84 \, {\left(4 \, {\left(d x + c\right)}^{\frac{5}{2}} - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} c - 10 \, {\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) + 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) - 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 20 \, {\left(3 \, c^{2} + 1\right)} \sqrt{d x + c}\right)} a^{2} c e^{\frac{5}{2}}}{d} + \frac{210 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} c e^{\frac{5}{2}}}{d} + \frac{{\left(60 \, {\left(d x + c\right)}^{\frac{7}{2}} - 336 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 140 \, {\left(6 \, c^{2} + 1\right)} {\left(d x + c\right)}^{\frac{3}{2}} + 210 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 105 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 105 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 1680 \, {\left(c^{3} + c\right)} \sqrt{d x + c}\right)} a^{2} e^{\frac{5}{2}}}{d} - \frac{35 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} e^{\frac{5}{2}}}{d}\right)} d}{210 \, d}"," ",0,"1/210*(60*(b^2*d^3*e^2*x^3 + 3*b^2*c*d^2*e^2*x^2 + 3*b^2*c^2*d*e^2*x + b^2*c^3*e^2)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + (2940*a*b*d^4*e^(5/2)*integrate(1/7*sqrt(d*x + c)*x^4*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 11760*a*b*c*d^3*e^(5/2)*integrate(1/7*sqrt(d*x + c)*x^3*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 17640*a*b*c^2*d^2*e^(5/2)*integrate(1/7*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 11760*a*b*c^3*d*e^(5/2)*integrate(1/7*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 2940*a*b*c^4*e^(5/2)*integrate(1/7*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 105*a^2*c^4*e^(5/2)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 840*b^2*d^3*e^(5/2)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x^3*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 2520*b^2*c*d^2*e^(5/2)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 2520*b^2*c^2*d*e^(5/2)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 840*b^2*c^3*e^(5/2)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 420*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*c^3*e^(5/2)/d - 2940*a*b*d^2*e^(5/2)*integrate(1/7*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 5880*a*b*c*d*e^(5/2)*integrate(1/7*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 2940*a*b*c^2*e^(5/2)*integrate(1/7*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 210*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^2*c^2*e^(5/2)/d - 105*a^2*c^2*e^(5/2)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 84*(4*(d*x + c)^(5/2) - 20*(d*x + c)^(3/2)*c - 10*(c^3 + 3*c^2 + 3*c + 1)*arctan(sqrt(d*x + c)) + 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) + 1) - 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) - 1) + 20*(3*c^2 + 1)*sqrt(d*x + c))*a^2*c*e^(5/2)/d + 210*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*c*e^(5/2)/d + (60*(d*x + c)^(7/2) - 336*(d*x + c)^(5/2)*c + 140*(6*c^2 + 1)*(d*x + c)^(3/2) + 210*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*arctan(sqrt(d*x + c)) - 105*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(sqrt(d*x + c) + 1) + 105*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(sqrt(d*x + c) - 1) - 1680*(c^3 + c)*sqrt(d*x + c))*a^2*e^(5/2)/d - 35*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^2*e^(5/2)/d)*d)/d","F",0
293,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x + b^{2} c^{2} e\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left(20 \, a b d^{3} e^{\frac{3}{2}} \int \frac{\sqrt{d x + c} x^{3} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 60 \, a b c d^{2} e^{\frac{3}{2}} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 60 \, a b c^{2} d e^{\frac{3}{2}} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 20 \, a b c^{3} e^{\frac{3}{2}} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{5 \, a^{2} c^{3} e^{\frac{3}{2}} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + 8 \, b^{2} d^{2} e^{\frac{3}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 16 \, b^{2} c d e^{\frac{3}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 8 \, b^{2} c^{2} e^{\frac{3}{2}} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - \frac{15 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} c^{2} e^{\frac{3}{2}}}{d} - 20 \, a b d e^{\frac{3}{2}} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - 20 \, a b c e^{\frac{3}{2}} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{5 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} c e^{\frac{3}{2}}}{d} - \frac{5 \, a^{2} c e^{\frac{3}{2}} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + \frac{{\left(4 \, {\left(d x + c\right)}^{\frac{5}{2}} - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} c - 10 \, {\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) + 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) - 5 \, {\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 20 \, {\left(3 \, c^{2} + 1\right)} \sqrt{d x + c}\right)} a^{2} e^{\frac{3}{2}}}{d} + \frac{5 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} e^{\frac{3}{2}}}{d}\right)} d}{10 \, d}"," ",0,"1/10*(4*(b^2*d^2*e*x^2 + 2*b^2*c*d*e*x + b^2*c^2*e)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + (100*a*b*d^3*e^(3/2)*integrate(1/5*sqrt(d*x + c)*x^3*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 300*a*b*c*d^2*e^(3/2)*integrate(1/5*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 300*a*b*c^2*d*e^(3/2)*integrate(1/5*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 100*a*b*c^3*e^(3/2)*integrate(1/5*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 5*a^2*c^3*e^(3/2)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 40*b^2*d^2*e^(3/2)*integrate(1/5*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 80*b^2*c*d*e^(3/2)*integrate(1/5*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 40*b^2*c^2*e^(3/2)*integrate(1/5*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 15*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*c^2*e^(3/2)/d - 100*a*b*d*e^(3/2)*integrate(1/5*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 100*a*b*c*e^(3/2)*integrate(1/5*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 5*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^2*c*e^(3/2)/d - 5*a^2*c*e^(3/2)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + (4*(d*x + c)^(5/2) - 20*(d*x + c)^(3/2)*c - 10*(c^3 + 3*c^2 + 3*c + 1)*arctan(sqrt(d*x + c)) + 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) + 1) - 5*(c^3 - 3*c^2 + 3*c - 1)*log(sqrt(d*x + c) - 1) + 20*(3*c^2 + 1)*sqrt(d*x + c))*a^2*e^(3/2)/d + 5*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*e^(3/2)/d)*d)/d","F",0
294,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(b^{2} d x + b^{2} c\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left(12 \, a b d^{2} \sqrt{e} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 24 \, a b c d \sqrt{e} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 12 \, a b c^{2} \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{3 \, a^{2} c^{2} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + 8 \, b^{2} d \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 8 \, b^{2} c \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - \frac{6 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} c \sqrt{e}}{d} - 12 \, a b \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{{\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} \sqrt{e}}{d} - \frac{3 \, a^{2} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d}\right)} d}{6 \, d}"," ",0,"1/6*(4*(b^2*d*x + b^2*c)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + (36*a*b*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 72*a*b*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 36*a*b*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 3*a^2*c^2*sqrt(e)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 24*b^2*d*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 24*b^2*c*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 6*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^2*c*sqrt(e)/d - 36*a*b*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + (6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^2*sqrt(e)/d - 3*a^2*sqrt(e)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d)*d)/d","F",0
295,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{4 \, b^{2} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} - {\left(d^{2} e^{3} x + c d e^{3}\right)} {\left(12 \, a b d^{2} \sqrt{e} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} + 24 \, a b c d \sqrt{e} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} + 12 \, a b c^{2} \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} - \frac{a^{2} c^{2} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d} - 8 \, b^{2} d \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} - 8 \, b^{2} c \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} + \frac{2 \, a^{2} c \sqrt{e} {\left(\frac{6 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(3 \, d x + 2 \, c\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d} - 12 \, a b \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} - \frac{a^{2} \sqrt{e} {\left(\frac{6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(6 \, {\left(d x + c\right)} c - c^{2}\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d} + \frac{a^{2} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d}\right)} \sqrt{d x + c}}{6 \, {\left(d^{2} e^{3} x + c d e^{3}\right)} \sqrt{d x + c}}"," ",0,"-1/6*(4*b^2*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 - (d^2*e^3*x + c*d*e^3)*(36*a*b*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 72*a*b*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 36*a*b*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - a^2*c^2*sqrt(e)*(6*arctan(sqrt(d*x + c))/e^3 + 3*log(sqrt(d*x + c) + 1)/e^3 - 3*log(sqrt(d*x + c) - 1)/e^3 - 4/((d*x + c)^(3/2)*e^3))/d - 24*b^2*d*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - 24*b^2*c*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 2*a^2*c*sqrt(e)*(6*(c + 1)*arctan(sqrt(d*x + c))/e^3 + 3*(c - 1)*log(sqrt(d*x + c) + 1)/e^3 - 3*(c - 1)*log(sqrt(d*x + c) - 1)/e^3 + 4*(3*d*x + 2*c)/((d*x + c)^(3/2)*e^3))/d - 36*a*b*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - a^2*sqrt(e)*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c))/e^3 + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1)/e^3 - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1)/e^3 + 4*(6*(d*x + c)*c - c^2)/((d*x + c)^(3/2)*e^3))/d + a^2*sqrt(e)*(6*arctan(sqrt(d*x + c))/e^3 + 3*log(sqrt(d*x + c) + 1)/e^3 - 3*log(sqrt(d*x + c) - 1)/e^3 - 4/((d*x + c)^(3/2)*e^3))/d)*sqrt(d*x + c))/((d^2*e^3*x + c*d*e^3)*sqrt(d*x + c))","F",0
298,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(7/2),x, algorithm=""maxima"")","-\frac{12 \, b^{2} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} - {\left(d^{3} e^{4} x^{2} + 2 \, c d^{2} e^{4} x + c^{2} d e^{4}\right)} {\left(60 \, a b d^{2} \sqrt{e} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + 15 \, c^{2} d^{4} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{4} d^{2} e^{4} x^{2} - d^{4} e^{4} x^{4} + 6 \, c^{5} d e^{4} x - 4 \, c d^{3} e^{4} x^{3} + c^{6} e^{4} - 6 \, c^{2} d^{2} e^{4} x^{2} - 4 \, c^{3} d e^{4} x - c^{4} e^{4}}\,{d x} + 120 \, a b c d \sqrt{e} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + 15 \, c^{2} d^{4} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{4} d^{2} e^{4} x^{2} - d^{4} e^{4} x^{4} + 6 \, c^{5} d e^{4} x - 4 \, c d^{3} e^{4} x^{3} + c^{6} e^{4} - 6 \, c^{2} d^{2} e^{4} x^{2} - 4 \, c^{3} d e^{4} x - c^{4} e^{4}}\,{d x} + 60 \, a b c^{2} \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + 15 \, c^{2} d^{4} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{4} d^{2} e^{4} x^{2} - d^{4} e^{4} x^{4} + 6 \, c^{5} d e^{4} x - 4 \, c d^{3} e^{4} x^{3} + c^{6} e^{4} - 6 \, c^{2} d^{2} e^{4} x^{2} - 4 \, c^{3} d e^{4} x - c^{4} e^{4}}\,{d x} + \frac{3 \, a^{2} c^{2} \sqrt{e} {\left(\frac{10 \, \arctan\left(\sqrt{d x + c}\right)}{e^{4}} - \frac{5 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{4}} + \frac{5 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{4}} + \frac{4 \, {\left(5 \, {\left(d x + c\right)}^{2} + 1\right)}}{{\left(d x + c\right)}^{\frac{5}{2}} e^{4}}\right)}}{d} - 24 \, b^{2} d \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + 15 \, c^{2} d^{4} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{4} d^{2} e^{4} x^{2} - d^{4} e^{4} x^{4} + 6 \, c^{5} d e^{4} x - 4 \, c d^{3} e^{4} x^{3} + c^{6} e^{4} - 6 \, c^{2} d^{2} e^{4} x^{2} - 4 \, c^{3} d e^{4} x - c^{4} e^{4}}\,{d x} - 24 \, b^{2} c \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + 15 \, c^{2} d^{4} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{4} d^{2} e^{4} x^{2} - d^{4} e^{4} x^{4} + 6 \, c^{5} d e^{4} x - 4 \, c d^{3} e^{4} x^{3} + c^{6} e^{4} - 6 \, c^{2} d^{2} e^{4} x^{2} - 4 \, c^{3} d e^{4} x - c^{4} e^{4}}\,{d x} - \frac{2 \, a^{2} c \sqrt{e} {\left(\frac{30 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{4}} - \frac{15 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{4}} + \frac{15 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{4}} + \frac{4 \, {\left(15 \, {\left(d x + c\right)}^{2} c - 5 \, d x - 2 \, c\right)}}{{\left(d x + c\right)}^{\frac{5}{2}} e^{4}}\right)}}{d} - 60 \, a b \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + 15 \, c^{2} d^{4} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{4} d^{2} e^{4} x^{2} - d^{4} e^{4} x^{4} + 6 \, c^{5} d e^{4} x - 4 \, c d^{3} e^{4} x^{3} + c^{6} e^{4} - 6 \, c^{2} d^{2} e^{4} x^{2} - 4 \, c^{3} d e^{4} x - c^{4} e^{4}}\,{d x} + \frac{a^{2} \sqrt{e} {\left(\frac{30 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{4}} - \frac{15 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{4}} + \frac{15 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{4}} + \frac{4 \, {\left(15 \, {\left(c^{2} + 1\right)} {\left(d x + c\right)}^{2} - 10 \, {\left(d x + c\right)} c + 3 \, c^{2}\right)}}{{\left(d x + c\right)}^{\frac{5}{2}} e^{4}}\right)}}{d} - \frac{3 \, a^{2} \sqrt{e} {\left(\frac{10 \, \arctan\left(\sqrt{d x + c}\right)}{e^{4}} - \frac{5 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{4}} + \frac{5 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{4}} + \frac{4 \, {\left(5 \, {\left(d x + c\right)}^{2} + 1\right)}}{{\left(d x + c\right)}^{\frac{5}{2}} e^{4}}\right)}}{d}\right)} \sqrt{d x + c}}{30 \, {\left(d^{3} e^{4} x^{2} + 2 \, c d^{2} e^{4} x + c^{2} d e^{4}\right)} \sqrt{d x + c}}"," ",0,"-1/30*(12*b^2*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 - (d^3*e^4*x^2 + 2*c*d^2*e^4*x + c^2*d*e^4)*(300*a*b*d^2*sqrt(e)*integrate(1/5*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + 15*c^2*d^4*e^4*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^4*d^2*e^4*x^2 - d^4*e^4*x^4 + 6*c^5*d*e^4*x - 4*c*d^3*e^4*x^3 + c^6*e^4 - 6*c^2*d^2*e^4*x^2 - 4*c^3*d*e^4*x - c^4*e^4), x) + 600*a*b*c*d*sqrt(e)*integrate(1/5*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + 15*c^2*d^4*e^4*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^4*d^2*e^4*x^2 - d^4*e^4*x^4 + 6*c^5*d*e^4*x - 4*c*d^3*e^4*x^3 + c^6*e^4 - 6*c^2*d^2*e^4*x^2 - 4*c^3*d*e^4*x - c^4*e^4), x) + 300*a*b*c^2*sqrt(e)*integrate(1/5*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + 15*c^2*d^4*e^4*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^4*d^2*e^4*x^2 - d^4*e^4*x^4 + 6*c^5*d*e^4*x - 4*c*d^3*e^4*x^3 + c^6*e^4 - 6*c^2*d^2*e^4*x^2 - 4*c^3*d*e^4*x - c^4*e^4), x) + 3*a^2*c^2*sqrt(e)*(10*arctan(sqrt(d*x + c))/e^4 - 5*log(sqrt(d*x + c) + 1)/e^4 + 5*log(sqrt(d*x + c) - 1)/e^4 + 4*(5*(d*x + c)^2 + 1)/((d*x + c)^(5/2)*e^4))/d - 120*b^2*d*sqrt(e)*integrate(1/5*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + 15*c^2*d^4*e^4*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^4*d^2*e^4*x^2 - d^4*e^4*x^4 + 6*c^5*d*e^4*x - 4*c*d^3*e^4*x^3 + c^6*e^4 - 6*c^2*d^2*e^4*x^2 - 4*c^3*d*e^4*x - c^4*e^4), x) - 120*b^2*c*sqrt(e)*integrate(1/5*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + 15*c^2*d^4*e^4*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^4*d^2*e^4*x^2 - d^4*e^4*x^4 + 6*c^5*d*e^4*x - 4*c*d^3*e^4*x^3 + c^6*e^4 - 6*c^2*d^2*e^4*x^2 - 4*c^3*d*e^4*x - c^4*e^4), x) - 2*a^2*c*sqrt(e)*(30*(c + 1)*arctan(sqrt(d*x + c))/e^4 - 15*(c - 1)*log(sqrt(d*x + c) + 1)/e^4 + 15*(c - 1)*log(sqrt(d*x + c) - 1)/e^4 + 4*(15*(d*x + c)^2*c - 5*d*x - 2*c)/((d*x + c)^(5/2)*e^4))/d - 300*a*b*sqrt(e)*integrate(1/5*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + 15*c^2*d^4*e^4*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^4*d^2*e^4*x^2 - d^4*e^4*x^4 + 6*c^5*d*e^4*x - 4*c*d^3*e^4*x^3 + c^6*e^4 - 6*c^2*d^2*e^4*x^2 - 4*c^3*d*e^4*x - c^4*e^4), x) + a^2*sqrt(e)*(30*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c))/e^4 - 15*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1)/e^4 + 15*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1)/e^4 + 4*(15*(c^2 + 1)*(d*x + c)^2 - 10*(d*x + c)*c + 3*c^2)/((d*x + c)^(5/2)*e^4))/d - 3*a^2*sqrt(e)*(10*arctan(sqrt(d*x + c))/e^4 - 5*log(sqrt(d*x + c) + 1)/e^4 + 5*log(sqrt(d*x + c) - 1)/e^4 + 4*(5*(d*x + c)^2 + 1)/((d*x + c)^(5/2)*e^4))/d)*sqrt(d*x + c))/((d^3*e^4*x^2 + 2*c*d^2*e^4*x + c^2*d*e^4)*sqrt(d*x + c))","F",0
299,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(9/2),x, algorithm=""maxima"")","-\frac{60 \, b^{2} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} - {\left(d^{4} e^{5} x^{3} + 3 \, c d^{3} e^{5} x^{2} + 3 \, c^{2} d^{2} e^{5} x + c^{3} d e^{5}\right)} {\left(420 \, a b d^{2} \sqrt{e} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + 21 \, c^{2} d^{5} e^{5} x^{5} + 35 \, c^{3} d^{4} e^{5} x^{4} + 35 \, c^{4} d^{3} e^{5} x^{3} - d^{5} e^{5} x^{5} + 21 \, c^{5} d^{2} e^{5} x^{2} - 5 \, c d^{4} e^{5} x^{4} + 7 \, c^{6} d e^{5} x - 10 \, c^{2} d^{3} e^{5} x^{3} + c^{7} e^{5} - 10 \, c^{3} d^{2} e^{5} x^{2} - 5 \, c^{4} d e^{5} x - c^{5} e^{5}}\,{d x} + 840 \, a b c d \sqrt{e} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + 21 \, c^{2} d^{5} e^{5} x^{5} + 35 \, c^{3} d^{4} e^{5} x^{4} + 35 \, c^{4} d^{3} e^{5} x^{3} - d^{5} e^{5} x^{5} + 21 \, c^{5} d^{2} e^{5} x^{2} - 5 \, c d^{4} e^{5} x^{4} + 7 \, c^{6} d e^{5} x - 10 \, c^{2} d^{3} e^{5} x^{3} + c^{7} e^{5} - 10 \, c^{3} d^{2} e^{5} x^{2} - 5 \, c^{4} d e^{5} x - c^{5} e^{5}}\,{d x} + 420 \, a b c^{2} \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + 21 \, c^{2} d^{5} e^{5} x^{5} + 35 \, c^{3} d^{4} e^{5} x^{4} + 35 \, c^{4} d^{3} e^{5} x^{3} - d^{5} e^{5} x^{5} + 21 \, c^{5} d^{2} e^{5} x^{2} - 5 \, c d^{4} e^{5} x^{4} + 7 \, c^{6} d e^{5} x - 10 \, c^{2} d^{3} e^{5} x^{3} + c^{7} e^{5} - 10 \, c^{3} d^{2} e^{5} x^{2} - 5 \, c^{4} d e^{5} x - c^{5} e^{5}}\,{d x} - \frac{5 \, a^{2} c^{2} \sqrt{e} {\left(\frac{42 \, \arctan\left(\sqrt{d x + c}\right)}{e^{5}} + \frac{21 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{5}} - \frac{21 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{5}} - \frac{4 \, {\left(7 \, {\left(d x + c\right)}^{2} + 3\right)}}{{\left(d x + c\right)}^{\frac{7}{2}} e^{5}}\right)}}{d} - 120 \, b^{2} d \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + 21 \, c^{2} d^{5} e^{5} x^{5} + 35 \, c^{3} d^{4} e^{5} x^{4} + 35 \, c^{4} d^{3} e^{5} x^{3} - d^{5} e^{5} x^{5} + 21 \, c^{5} d^{2} e^{5} x^{2} - 5 \, c d^{4} e^{5} x^{4} + 7 \, c^{6} d e^{5} x - 10 \, c^{2} d^{3} e^{5} x^{3} + c^{7} e^{5} - 10 \, c^{3} d^{2} e^{5} x^{2} - 5 \, c^{4} d e^{5} x - c^{5} e^{5}}\,{d x} - 120 \, b^{2} c \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + 21 \, c^{2} d^{5} e^{5} x^{5} + 35 \, c^{3} d^{4} e^{5} x^{4} + 35 \, c^{4} d^{3} e^{5} x^{3} - d^{5} e^{5} x^{5} + 21 \, c^{5} d^{2} e^{5} x^{2} - 5 \, c d^{4} e^{5} x^{4} + 7 \, c^{6} d e^{5} x - 10 \, c^{2} d^{3} e^{5} x^{3} + c^{7} e^{5} - 10 \, c^{3} d^{2} e^{5} x^{2} - 5 \, c^{4} d e^{5} x - c^{5} e^{5}}\,{d x} + \frac{2 \, a^{2} c \sqrt{e} {\left(\frac{210 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{5}} + \frac{105 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{5}} - \frac{105 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{5}} + \frac{4 \, {\left(105 \, {\left(d x + c\right)}^{3} - 35 \, {\left(d x + c\right)}^{2} c + 21 \, d x + 6 \, c\right)}}{{\left(d x + c\right)}^{\frac{7}{2}} e^{5}}\right)}}{d} - 420 \, a b \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + 21 \, c^{2} d^{5} e^{5} x^{5} + 35 \, c^{3} d^{4} e^{5} x^{4} + 35 \, c^{4} d^{3} e^{5} x^{3} - d^{5} e^{5} x^{5} + 21 \, c^{5} d^{2} e^{5} x^{2} - 5 \, c d^{4} e^{5} x^{4} + 7 \, c^{6} d e^{5} x - 10 \, c^{2} d^{3} e^{5} x^{3} + c^{7} e^{5} - 10 \, c^{3} d^{2} e^{5} x^{2} - 5 \, c^{4} d e^{5} x - c^{5} e^{5}}\,{d x} - \frac{a^{2} \sqrt{e} {\left(\frac{210 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{5}} + \frac{105 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{5}} - \frac{105 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{5}} + \frac{4 \, {\left(210 \, {\left(d x + c\right)}^{3} c - 35 \, {\left(c^{2} + 1\right)} {\left(d x + c\right)}^{2} + 42 \, {\left(d x + c\right)} c - 15 \, c^{2}\right)}}{{\left(d x + c\right)}^{\frac{7}{2}} e^{5}}\right)}}{d} + \frac{5 \, a^{2} \sqrt{e} {\left(\frac{42 \, \arctan\left(\sqrt{d x + c}\right)}{e^{5}} + \frac{21 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{5}} - \frac{21 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{5}} - \frac{4 \, {\left(7 \, {\left(d x + c\right)}^{2} + 3\right)}}{{\left(d x + c\right)}^{\frac{7}{2}} e^{5}}\right)}}{d}\right)} \sqrt{d x + c}}{210 \, {\left(d^{4} e^{5} x^{3} + 3 \, c d^{3} e^{5} x^{2} + 3 \, c^{2} d^{2} e^{5} x + c^{3} d e^{5}\right)} \sqrt{d x + c}}"," ",0,"-1/210*(60*b^2*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 - (d^4*e^5*x^3 + 3*c*d^3*e^5*x^2 + 3*c^2*d^2*e^5*x + c^3*d*e^5)*(2940*a*b*d^2*sqrt(e)*integrate(1/7*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + 21*c^2*d^5*e^5*x^5 + 35*c^3*d^4*e^5*x^4 + 35*c^4*d^3*e^5*x^3 - d^5*e^5*x^5 + 21*c^5*d^2*e^5*x^2 - 5*c*d^4*e^5*x^4 + 7*c^6*d*e^5*x - 10*c^2*d^3*e^5*x^3 + c^7*e^5 - 10*c^3*d^2*e^5*x^2 - 5*c^4*d*e^5*x - c^5*e^5), x) + 5880*a*b*c*d*sqrt(e)*integrate(1/7*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + 21*c^2*d^5*e^5*x^5 + 35*c^3*d^4*e^5*x^4 + 35*c^4*d^3*e^5*x^3 - d^5*e^5*x^5 + 21*c^5*d^2*e^5*x^2 - 5*c*d^4*e^5*x^4 + 7*c^6*d*e^5*x - 10*c^2*d^3*e^5*x^3 + c^7*e^5 - 10*c^3*d^2*e^5*x^2 - 5*c^4*d*e^5*x - c^5*e^5), x) + 2940*a*b*c^2*sqrt(e)*integrate(1/7*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + 21*c^2*d^5*e^5*x^5 + 35*c^3*d^4*e^5*x^4 + 35*c^4*d^3*e^5*x^3 - d^5*e^5*x^5 + 21*c^5*d^2*e^5*x^2 - 5*c*d^4*e^5*x^4 + 7*c^6*d*e^5*x - 10*c^2*d^3*e^5*x^3 + c^7*e^5 - 10*c^3*d^2*e^5*x^2 - 5*c^4*d*e^5*x - c^5*e^5), x) - 5*a^2*c^2*sqrt(e)*(42*arctan(sqrt(d*x + c))/e^5 + 21*log(sqrt(d*x + c) + 1)/e^5 - 21*log(sqrt(d*x + c) - 1)/e^5 - 4*(7*(d*x + c)^2 + 3)/((d*x + c)^(7/2)*e^5))/d - 840*b^2*d*sqrt(e)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + 21*c^2*d^5*e^5*x^5 + 35*c^3*d^4*e^5*x^4 + 35*c^4*d^3*e^5*x^3 - d^5*e^5*x^5 + 21*c^5*d^2*e^5*x^2 - 5*c*d^4*e^5*x^4 + 7*c^6*d*e^5*x - 10*c^2*d^3*e^5*x^3 + c^7*e^5 - 10*c^3*d^2*e^5*x^2 - 5*c^4*d*e^5*x - c^5*e^5), x) - 840*b^2*c*sqrt(e)*integrate(1/7*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + 21*c^2*d^5*e^5*x^5 + 35*c^3*d^4*e^5*x^4 + 35*c^4*d^3*e^5*x^3 - d^5*e^5*x^5 + 21*c^5*d^2*e^5*x^2 - 5*c*d^4*e^5*x^4 + 7*c^6*d*e^5*x - 10*c^2*d^3*e^5*x^3 + c^7*e^5 - 10*c^3*d^2*e^5*x^2 - 5*c^4*d*e^5*x - c^5*e^5), x) + 2*a^2*c*sqrt(e)*(210*(c + 1)*arctan(sqrt(d*x + c))/e^5 + 105*(c - 1)*log(sqrt(d*x + c) + 1)/e^5 - 105*(c - 1)*log(sqrt(d*x + c) - 1)/e^5 + 4*(105*(d*x + c)^3 - 35*(d*x + c)^2*c + 21*d*x + 6*c)/((d*x + c)^(7/2)*e^5))/d - 2940*a*b*sqrt(e)*integrate(1/7*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + 21*c^2*d^5*e^5*x^5 + 35*c^3*d^4*e^5*x^4 + 35*c^4*d^3*e^5*x^3 - d^5*e^5*x^5 + 21*c^5*d^2*e^5*x^2 - 5*c*d^4*e^5*x^4 + 7*c^6*d*e^5*x - 10*c^2*d^3*e^5*x^3 + c^7*e^5 - 10*c^3*d^2*e^5*x^2 - 5*c^4*d*e^5*x - c^5*e^5), x) - a^2*sqrt(e)*(210*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c))/e^5 + 105*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1)/e^5 - 105*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1)/e^5 + 4*(210*(d*x + c)^3*c - 35*(c^2 + 1)*(d*x + c)^2 + 42*(d*x + c)*c - 15*c^2)/((d*x + c)^(7/2)*e^5))/d + 5*a^2*sqrt(e)*(42*arctan(sqrt(d*x + c))/e^5 + 21*log(sqrt(d*x + c) + 1)/e^5 - 21*log(sqrt(d*x + c) - 1)/e^5 - 4*(7*(d*x + c)^2 + 3)/((d*x + c)^(7/2)*e^5))/d)*sqrt(d*x + c))/((d^4*e^5*x^3 + 3*c*d^3*e^5*x^2 + 3*c^2*d^2*e^5*x + c^3*d*e^5)*sqrt(d*x + c))","F",0
300,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\frac{4 \, {\left(b^{4} d x + b^{4} c\right)} \sqrt{d x + c} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + {\left(\frac{12 \, a b^{3} c^{2} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} + \frac{18 \, a^{2} b^{2} c^{2} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} - \frac{24 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a b^{3} c \sqrt{e} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} - \frac{36 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{2} b^{2} c \sqrt{e} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} + \frac{4 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a b^{3} \sqrt{e} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} - \frac{12 \, a b^{3} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} + 24 \, a^{3} b d^{2} \sqrt{e} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 48 \, a^{3} b c d \sqrt{e} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 24 \, a^{3} b c^{2} \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{3 \, a^{4} c^{2} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d} + \frac{6 \, {\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{2} b^{2} \sqrt{e} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} - \frac{18 \, a^{2} b^{2} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} + 16 \, b^{4} d \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + 16 \, b^{4} c \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} - \frac{6 \, {\left(2 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right) + {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right) - 4 \, \sqrt{d x + c}\right)} a^{4} c \sqrt{e}}{d} - 24 \, a^{3} b \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x} + \frac{{\left(6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right) - 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right) + 3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right) + 4 \, {\left(d x + c\right)}^{\frac{3}{2}} - 24 \, \sqrt{d x + c} c\right)} a^{4} \sqrt{e}}{d} - \frac{3 \, a^{4} \sqrt{e} {\left(2 \, \arctan\left(\sqrt{d x + c}\right) - \log\left(\sqrt{d x + c} + 1\right) + \log\left(\sqrt{d x + c} - 1\right)\right)}}{d}\right)} d}{6 \, d}"," ",0,"1/6*(4*(b^4*d*x + b^4*c)*sqrt(d*x + c)*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + (72*a*b^3*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 108*a^2*b^2*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 144*a*b^3*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 72*a^3*b*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 216*a^2*b^2*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 72*a*b^3*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 144*a^3*b*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 108*a^2*b^2*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 72*a^3*b*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 3*a^4*c^2*sqrt(e)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d + 48*b^4*d*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + 48*b^4*c*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 6*(2*(c + 1)*arctan(sqrt(d*x + c)) - (c - 1)*log(sqrt(d*x + c) + 1) + (c - 1)*log(sqrt(d*x + c) - 1) - 4*sqrt(d*x + c))*a^4*c*sqrt(e)/d - 72*a*b^3*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 108*a^2*b^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) - 72*a^3*b*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^2*x^2 + 2*c*d*x + c^2 - 1), x) + (6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c)) - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1) + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1) + 4*(d*x + c)^(3/2) - 24*sqrt(d*x + c)*c)*a^4*sqrt(e)/d - 3*a^4*sqrt(e)*(2*arctan(sqrt(d*x + c)) - log(sqrt(d*x + c) + 1) + log(sqrt(d*x + c) - 1))/d)*d)/d","F",0
305,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(5/2),x, algorithm=""maxima"")","-\frac{4 \, b^{4} \sqrt{e} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + {\left(\frac{4 \, a b^{3} c^{2} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} + \frac{6 \, a^{2} b^{2} c^{2} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} - \frac{8 \, a b^{3} c \sqrt{e} {\left(\frac{6 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(3 \, d x + 2 \, c\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} - \frac{12 \, a^{2} b^{2} c \sqrt{e} {\left(\frac{6 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(3 \, d x + 2 \, c\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} + \frac{4 \, a b^{3} \sqrt{e} {\left(\frac{6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(6 \, {\left(d x + c\right)} c - c^{2}\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} - \frac{4 \, a b^{3} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d} - 24 \, a^{3} b d^{2} \sqrt{e} \int \frac{\sqrt{d x + c} x^{2} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} - 48 \, a^{3} b c d \sqrt{e} \int \frac{\sqrt{d x + c} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} - 24 \, a^{3} b c^{2} \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} + \frac{a^{4} c^{2} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d} + \frac{6 \, a^{2} b^{2} \sqrt{e} {\left(\frac{6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(6 \, {\left(d x + c\right)} c - c^{2}\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} - \frac{6 \, a^{2} b^{2} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{2}}{d} + 16 \, b^{4} d \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} x \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} + 16 \, b^{4} c \sqrt{e} \int \frac{\sqrt{d x + c + 1} \sqrt{d x + c} \sqrt{-d x - c + 1} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)^{3}}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} - \frac{2 \, a^{4} c \sqrt{e} {\left(\frac{6 \, {\left(c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c - 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(3 \, d x + 2 \, c\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d} + 24 \, a^{3} b \sqrt{e} \int \frac{\sqrt{d x + c} \arctan\left(\frac{d x}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}} + \frac{c}{\sqrt{d x + c + 1} \sqrt{-d x - c + 1}}\right)}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + 10 \, c^{2} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{2} e^{3} x^{2} + 5 \, c^{4} d e^{3} x - d^{3} e^{3} x^{3} + c^{5} e^{3} - 3 \, c d^{2} e^{3} x^{2} - 3 \, c^{2} d e^{3} x - c^{3} e^{3}}\,{d x} + \frac{a^{4} \sqrt{e} {\left(\frac{6 \, {\left(c^{2} + 2 \, c + 1\right)} \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, {\left(c^{2} - 2 \, c + 1\right)} \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} + \frac{4 \, {\left(6 \, {\left(d x + c\right)} c - c^{2}\right)}}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d} - \frac{a^{4} \sqrt{e} {\left(\frac{6 \, \arctan\left(\sqrt{d x + c}\right)}{e^{3}} + \frac{3 \, \log\left(\sqrt{d x + c} + 1\right)}{e^{3}} - \frac{3 \, \log\left(\sqrt{d x + c} - 1\right)}{e^{3}} - \frac{4}{{\left(d x + c\right)}^{\frac{3}{2}} e^{3}}\right)}}{d}\right)} {\left(d^{2} e^{3} x + c d e^{3}\right)} \sqrt{d x + c}}{6 \, {\left(d^{2} e^{3} x + c d e^{3}\right)} \sqrt{d x + c}}"," ",0,"-1/6*(4*b^4*sqrt(e)*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 - (72*a*b^3*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 108*a^2*b^2*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 144*a*b^3*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 72*a^3*b*d^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x^2*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 216*a^2*b^2*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 72*a*b^3*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 144*a^3*b*c*d*sqrt(e)*integrate(1/3*sqrt(d*x + c)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 108*a^2*b^2*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 72*a^3*b*c^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - a^4*c^2*sqrt(e)*(6*arctan(sqrt(d*x + c))/e^3 + 3*log(sqrt(d*x + c) + 1)/e^3 - 3*log(sqrt(d*x + c) - 1)/e^3 - 4/((d*x + c)^(3/2)*e^3))/d - 48*b^4*d*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*x*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - 48*b^4*c*sqrt(e)*integrate(1/3*sqrt(d*x + c + 1)*sqrt(d*x + c)*sqrt(-d*x - c + 1)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) + 2*a^4*c*sqrt(e)*(6*(c + 1)*arctan(sqrt(d*x + c))/e^3 + 3*(c - 1)*log(sqrt(d*x + c) + 1)/e^3 - 3*(c - 1)*log(sqrt(d*x + c) - 1)/e^3 + 4*(3*d*x + 2*c)/((d*x + c)^(3/2)*e^3))/d - 72*a*b^3*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^3/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - 108*a^2*b^2*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))^2/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - 72*a^3*b*sqrt(e)*integrate(1/3*sqrt(d*x + c)*arctan(d*x/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + c/(sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + 10*c^2*d^3*e^3*x^3 + 10*c^3*d^2*e^3*x^2 + 5*c^4*d*e^3*x - d^3*e^3*x^3 + c^5*e^3 - 3*c*d^2*e^3*x^2 - 3*c^2*d*e^3*x - c^3*e^3), x) - a^4*sqrt(e)*(6*(c^2 + 2*c + 1)*arctan(sqrt(d*x + c))/e^3 + 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) + 1)/e^3 - 3*(c^2 - 2*c + 1)*log(sqrt(d*x + c) - 1)/e^3 + 4*(6*(d*x + c)*c - c^2)/((d*x + c)^(3/2)*e^3))/d + a^4*sqrt(e)*(6*arctan(sqrt(d*x + c))/e^3 + 3*log(sqrt(d*x + c) + 1)/e^3 - 3*log(sqrt(d*x + c) - 1)/e^3 - 4/((d*x + c)^(3/2)*e^3))/d)*(d^2*e^3*x + c*d*e^3)*sqrt(d*x + c))/((d^2*e^3*x + c*d*e^3)*sqrt(d*x + c))","F",0
308,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^4,x, algorithm=""maxima"")","\frac{{\left(d e x + c e\right)}^{m + 1} a^{4}}{d e {\left(m + 1\right)}} + \frac{{\left(b^{4} d e^{m} x + b^{4} c e^{m}\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{4} + 2 \, {\left(d m + d\right)} \int \frac{2 \, {\left(b^{4} d e^{m} x + b^{4} c e^{m}\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 2 \, {\left({\left(a b^{3} c^{2} - a b^{3}\right)} e^{m} m + {\left(a b^{3} d^{2} e^{m} m + a b^{3} d^{2} e^{m}\right)} x^{2} + {\left(a b^{3} c^{2} - a b^{3}\right)} e^{m} + 2 \, {\left(a b^{3} c d e^{m} m + a b^{3} c d e^{m}\right)} x\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 3 \, {\left({\left(a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} e^{m} m + {\left(a^{2} b^{2} d^{2} e^{m} m + a^{2} b^{2} d^{2} e^{m}\right)} x^{2} + {\left(a^{2} b^{2} c^{2} - a^{2} b^{2}\right)} e^{m} + 2 \, {\left(a^{2} b^{2} c d e^{m} m + a^{2} b^{2} c d e^{m}\right)} x\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + 2 \, {\left({\left(a^{3} b c^{2} - a^{3} b\right)} e^{m} m + {\left(a^{3} b d^{2} e^{m} m + a^{3} b d^{2} e^{m}\right)} x^{2} + {\left(a^{3} b c^{2} - a^{3} b\right)} e^{m} + 2 \, {\left(a^{3} b c d e^{m} m + a^{3} b c d e^{m}\right)} x\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{{\left(d^{2} m + d^{2}\right)} x^{2} + c^{2} + {\left(c^{2} - 1\right)} m + 2 \, {\left(c d m + c d\right)} x - 1}\,{d x}}{d m + d}"," ",0,"(d*e*x + c*e)^(m + 1)*a^4/(d*e*(m + 1)) + ((b^4*d*e^m*x + b^4*c*e^m)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^4 + (d*m + d)*integrate(2*(2*(b^4*d*e^m*x + b^4*c*e^m)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 2*((a*b^3*c^2 - a*b^3)*e^m*m + (a*b^3*d^2*e^m*m + a*b^3*d^2*e^m)*x^2 + (a*b^3*c^2 - a*b^3)*e^m + 2*(a*b^3*c*d*e^m*m + a*b^3*c*d*e^m)*x)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + 3*((a^2*b^2*c^2 - a^2*b^2)*e^m*m + (a^2*b^2*d^2*e^m*m + a^2*b^2*d^2*e^m)*x^2 + (a^2*b^2*c^2 - a^2*b^2)*e^m + 2*(a^2*b^2*c*d*e^m*m + a^2*b^2*c*d*e^m)*x)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + 2*((a^3*b*c^2 - a^3*b)*e^m*m + (a^3*b*d^2*e^m*m + a^3*b*d^2*e^m)*x^2 + (a^3*b*c^2 - a^3*b)*e^m + 2*(a^3*b*c*d*e^m*m + a^3*b*c*d*e^m)*x)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/((d^2*m + d^2)*x^2 + c^2 + (c^2 - 1)*m + 2*(c*d*m + c*d)*x - 1), x))/(d*m + d)","F",0
309,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(d e x + c e\right)}^{m + 1} a^{3}}{d e {\left(m + 1\right)}} + \frac{{\left(b^{3} d e^{m} x + b^{3} c e^{m}\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{3} + 3 \, {\left(d m + d\right)} \int \frac{{\left(b^{3} d e^{m} x + b^{3} c e^{m}\right)} \sqrt{d x + c + 1} \sqrt{-d x - c + 1} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left({\left(a b^{2} c^{2} - a b^{2}\right)} e^{m} m + {\left(a b^{2} d^{2} e^{m} m + a b^{2} d^{2} e^{m}\right)} x^{2} + {\left(a b^{2} c^{2} - a b^{2}\right)} e^{m} + 2 \, {\left(a b^{2} c d e^{m} m + a b^{2} c d e^{m}\right)} x\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} + {\left({\left(a^{2} b c^{2} - a^{2} b\right)} e^{m} m + {\left(a^{2} b d^{2} e^{m} m + a^{2} b d^{2} e^{m}\right)} x^{2} + {\left(a^{2} b c^{2} - a^{2} b\right)} e^{m} + 2 \, {\left(a^{2} b c d e^{m} m + a^{2} b c d e^{m}\right)} x\right)} {\left(d x + c\right)}^{m} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)}{{\left(d^{2} m + d^{2}\right)} x^{2} + c^{2} + {\left(c^{2} - 1\right)} m + 2 \, {\left(c d m + c d\right)} x - 1}\,{d x}}{d m + d}"," ",0,"(d*e*x + c*e)^(m + 1)*a^3/(d*e*(m + 1)) + ((b^3*d*e^m*x + b^3*c*e^m)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^3 + (d*m + d)*integrate(3*((b^3*d*e^m*x + b^3*c*e^m)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + ((a*b^2*c^2 - a*b^2)*e^m*m + (a*b^2*d^2*e^m*m + a*b^2*d^2*e^m)*x^2 + (a*b^2*c^2 - a*b^2)*e^m + 2*(a*b^2*c*d*e^m*m + a*b^2*c*d*e^m)*x)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + ((a^2*b*c^2 - a^2*b)*e^m*m + (a^2*b*d^2*e^m*m + a^2*b*d^2*e^m)*x^2 + (a^2*b*c^2 - a^2*b)*e^m + 2*(a^2*b*c*d*e^m*m + a^2*b*c*d*e^m)*x)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/((d^2*m + d^2)*x^2 + c^2 + (c^2 - 1)*m + 2*(c*d*m + c*d)*x - 1), x))/(d*m + d)","F",0
310,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(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} \arctan\left(d x + c, \sqrt{d x + c + 1} \sqrt{-d x - c + 1}\right)^{2} - 2 \, {\left(a b d e^{m} x + a b c e^{m}\right)} {\left(d x + c\right)}^{m} \arctan\left(\sqrt{d x + c + 1} {\left(d x + c\right)} \sqrt{-d x - c + 1}, d^{2} x^{2} + 2 \, c d x + c^{2} - 1\right) - 2 \, {\left(d m + d\right)} \int \frac{{\left(a b d e^{m} x + a b c e^{m}\right)} e^{\left(m \log\left(d x + c\right) + \frac{1}{2} \, \log\left(d x + c + 1\right) + \frac{1}{2} \, \log\left(-d x - c + 1\right)\right)}}{{\left(d^{4} m + d^{4}\right)} x^{4} + c^{4} + 4 \, {\left(c d^{3} m + c d^{3}\right)} x^{3} + 2 \, {\left({\left(3 \, c^{2} - 1\right)} d^{2} m + {\left(3 \, c^{2} - 1\right)} d^{2}\right)} x^{2} - 2 \, c^{2} + {\left(c^{4} - 2 \, c^{2} + 1\right)} m + 4 \, {\left({\left(c^{3} - c\right)} d m + {\left(c^{3} - c\right)} d\right)} x + {\left(c^{2} m + {\left(d^{2} m + d^{2}\right)} x^{2} + c^{2} + 2 \, {\left(c d m + c d\right)} x\right)} e^{\left(\log\left(d x + c + 1\right) + \log\left(-d x - c + 1\right)\right)} + 1}\,{d x}}{d m + d} + \frac{{\left(d e x + c e\right)}^{m + 1} a^{2}}{d e {\left(m + 1\right)}}"," ",0,"((b^2*d*e^m*x + b^2*c*e^m)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1))^2 + (d*m + d)*integrate(2*((b^2*d*e^m*x + b^2*c*e^m)*sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)) + ((a*b*c^2 - a*b)*e^m*m + (a*b*d^2*e^m*m + a*b*d^2*e^m)*x^2 + (a*b*c^2 - a*b)*e^m + 2*(a*b*c*d*e^m*m + a*b*c*d*e^m)*x)*(d*x + c)^m*arctan2(d*x + c, sqrt(d*x + c + 1)*sqrt(-d*x - c + 1)))/((d^2*m + d^2)*x^2 + c^2 + (c^2 - 1)*m + 2*(c*d*m + c*d)*x - 1), x))/(d*m + d) + (d*e*x + c*e)^(m + 1)*a^2/(d*e*(m + 1))","F",0
311,-1,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m/(a+b*arcsin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(d e x + c e\right)}^{m}}{b \arcsin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((d*e*x + c*e)^m/(b*arcsin(d*x + c) + a), x)","F",0
313,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} \arcsin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*arcsin(b*x + a)^3, x)","F",0
314,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} \arcsin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*arcsin(b*x + a)^2, x)","F",0
315,1,240,0,0.420080," ","integrate(arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(x^{2} + \frac{2 \, a x}{b} - \frac{2 \, \arcsin\left(b x + a\right) \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{2}} - \frac{\arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{2}}{b^{2}}\right)} b - \frac{1}{2} \, {\left(\frac{a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b} - \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x - \frac{{\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b}\right)} \arcsin\left(b x + a\right)"," ",0,"-1/4*(x^2 + 2*a*x/b - 2*arcsin(b*x + a)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 - arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^2/b^2)*b - 1/2*(a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x - (a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b)*arcsin(b*x + a)","B",0
316,0,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{\arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/arcsin(b*x + a), x)","F",0
317,0,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^2,x, algorithm=""maxima"")","\frac{b^{2} x^{2} + 2 \, a b x - 2 \, b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right) \int \frac{b x + a}{\arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} + a^{2} - 1}{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}"," ",0,"(b^2*x^2 + 2*a*b*x - b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))*integrate(2*(b*x + a)/arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x) + a^2 - 1)/(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))","F",0
318,-1,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-1,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,0,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} \arcsin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*arcsin(b*x + a)^3, x)","F",0
321,0,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} \arcsin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*arcsin(b*x + a)^2, x)","F",0
322,1,402,0,0.981746," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a),x, algorithm=""maxima"")","\frac{1}{16} \, {\left(b^{2} x^{4} + 4 \, a b x^{3} + 6 \, a^{2} x^{2} + \frac{4 \, a^{3} x}{b} - 5 \, x^{2} - \frac{10 \, a x}{b} + \frac{6 \, \arcsin\left(b x + a\right) \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{2}} + \frac{3 \, \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{2}}{b^{2}}\right)} b + \frac{1}{8} \, {\left(2 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} x + \frac{2 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{b} - \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} + \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{b^{2}} + \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} {\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} + \frac{3 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{3}}\right)} \arcsin\left(b x + a\right)"," ",0,"1/16*(b^2*x^4 + 4*a*b*x^3 + 6*a^2*x^2 + 4*a^3*x/b - 5*x^2 - 10*a*x/b + 6*arcsin(b*x + a)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 + 3*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^2/b^2)*b + 1/8*(2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*x + 2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/b - 3*(a^2*b^2 - (a^2 - 1)*b^2)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 3*(a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b^2 + 3*(a^2*b^2 - (a^2 - 1)*b^2)*(a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 3*(a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^3)*arcsin(b*x + a)","B",0
323,0,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{\arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate((-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/arcsin(b*x + a), x)","F",0
324,0,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 2 \, {\left(3 \, a^{2} - 1\right)} b^{2} x^{2} + a^{4} + 4 \, {\left(a^{3} - a\right)} b x - 4 \, b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right) \int \frac{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a}{\arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} - 2 \, a^{2} + 1}{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}"," ",0,"-(b^4*x^4 + 4*a*b^3*x^3 + 2*(3*a^2 - 1)*b^2*x^2 + a^4 + 4*(a^3 - a)*b*x - b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))*integrate(4*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a)/arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x) - 2*a^2 + 1)/(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))","F",0
325,-1,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-2,0,0,0.000000," ","integrate(arcsin(b*x+a)^n/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
328,1,130,0,0.440003," ","integrate(arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(b x + a\right)^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b} - \frac{\arcsin\left(b x + a\right) \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{2}}{b} - \frac{\arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{3}}{3 \, b}"," ",0,"-arcsin(b*x + a)^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b - arcsin(b*x + a)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^2/b - 1/3*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^3/b","B",0
329,1,83,0,0.423587," ","integrate(arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(b x + a\right) \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b} - \frac{\arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{2}}{2 \, b}"," ",0,"-arcsin(b*x + a)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b - 1/2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^2/b","B",0
330,0,0,0,0.000000," ","integrate(1/arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} \arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*arcsin(b*x + a)), x)","F",0
331,1,33,0,0.877832," ","integrate(1/arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}"," ",0,"-1/(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))","B",0
332,1,33,0,25.345369," ","integrate(1/arcsin(b*x+a)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2 \, b \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)^{2}}"," ",0,"-1/2/(b*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))^2)","B",0
333,1,137,0,0.668970," ","integrate(arcsin(b*x+a)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x, algorithm=""maxima"")","\frac{3}{2} \, b {\left(\frac{\log\left(b x + a + 1\right)}{b^{2}} + \frac{\log\left(b x + a - 1\right)}{b^{2}}\right)} \arcsin\left(b x + a\right)^{2} + {\left(\frac{b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{a b}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}\right)} \arcsin\left(b x + a\right)^{3}"," ",0,"3/2*b*(log(b*x + a + 1)/b^2 + log(b*x + a - 1)/b^2)*arcsin(b*x + a)^2 + (b^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + a*b/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)))*arcsin(b*x + a)^3","A",0
334,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(b x + a\right)^{2}}{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^2/(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2), x)","F",0
335,1,160,0,0.417332," ","integrate(arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(a {\left(\frac{\log\left(b x + a + 1\right)}{b^{2}} - \frac{\log\left(b x + a - 1\right)}{b^{2}}\right)} - \frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{2}} + \frac{{\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{2}}\right)} b + {\left(\frac{b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{a b}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}\right)} \arcsin\left(b x + a\right)"," ",0,"-1/2*(a*(log(b*x + a + 1)/b^2 - log(b*x + a - 1)/b^2) - (a + 1)*log(b*x + a + 1)/b^2 + (a - 1)*log(b*x + a - 1)/b^2)*b + (b^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + a*b/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)))*arcsin(b*x + a)","B",0
336,0,0,0,0.000000," ","integrate(1/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a),x, algorithm=""maxima"")","\int \frac{1}{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} \arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/((-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*arcsin(b*x + a)), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + {\left(a^{2} - 1\right)} b\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right) \int \frac{b x + a}{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 2 \, {\left(3 \, a^{2} - 1\right)} b^{2} x^{2} + a^{4} + 4 \, {\left(a^{3} - a\right)} b x - 2 \, a^{2} + 1\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}\,{d x} + 1}{{\left(b^{3} x^{2} + 2 \, a b^{2} x + {\left(a^{2} - 1\right)} b\right)} \arctan\left(b x + a, \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}"," ",0,"((b^3*x^2 + 2*a*b^2*x + (a^2 - 1)*b)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))*integrate(2*(b*x + a)/((b^4*x^4 + 4*a*b^3*x^3 + 2*(3*a^2 - 1)*b^2*x^2 + a^4 + 4*(a^3 - a)*b*x - 2*a^2 + 1)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1))), x) + 1)/((b^3*x^2 + 2*a*b^2*x + (a^2 - 1)*b)*arctan2(b*x + a, sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)))","F",0
338,1,206,0,0.436980," ","integrate(arcsin(b*x+a)/(c-c*(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{2}}{2 \, \sqrt{a^{2} b^{2} c^{2} - {\left(a^{2} c - c\right)} b^{2} c}} - \frac{\arcsin\left(b x + a\right) \arcsin\left(-\frac{b^{2} c x + a b c}{\sqrt{a^{2} b^{2} c^{2} - {\left(a^{2} c - c\right)} b^{2} c}}\right)}{b \sqrt{c}} - \frac{\arcsin\left(-\frac{b^{2} c x + a b c}{\sqrt{a^{2} b^{2} c^{2} - {\left(a^{2} c - c\right)} b^{2} c}}\right) \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b \sqrt{c}}"," ",0,"1/2*sqrt(c)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^2/sqrt(a^2*b^2*c^2 - (a^2*c - c)*b^2*c) - arcsin(b*x + a)*arcsin(-(b^2*c*x + a*b*c)/sqrt(a^2*b^2*c^2 - (a^2*c - c)*b^2*c))/(b*sqrt(c)) - arcsin(-(b^2*c*x + a*b*c)/sqrt(a^2*b^2*c^2 - (a^2*c - c)*b^2*c))*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/(b*sqrt(c))","B",0
339,1,200,0,0.433245," ","integrate(arcsin(b*x+a)/((-a^2+1)*c-2*a*b*c*x-c*x^2*b^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)^{2}}{2 \, \sqrt{a^{2} b^{2} c^{2} - {\left(a^{2} - 1\right)} b^{2} c^{2}}} - \frac{\arcsin\left(b x + a\right) \arcsin\left(-\frac{b^{2} c x + a b c}{\sqrt{a^{2} b^{2} c^{2} - {\left(a^{2} - 1\right)} b^{2} c^{2}}}\right)}{b \sqrt{c}} - \frac{\arcsin\left(-\frac{b^{2} c x + a b c}{\sqrt{a^{2} b^{2} c^{2} - {\left(a^{2} - 1\right)} b^{2} c^{2}}}\right) \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b \sqrt{c}}"," ",0,"1/2*sqrt(c)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))^2/sqrt(a^2*b^2*c^2 - (a^2 - 1)*b^2*c^2) - arcsin(b*x + a)*arcsin(-(b^2*c*x + a*b*c)/sqrt(a^2*b^2*c^2 - (a^2 - 1)*b^2*c^2))/(b*sqrt(c)) - arcsin(-(b^2*c*x + a*b*c)/sqrt(a^2*b^2*c^2 - (a^2 - 1)*b^2*c^2))*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/(b*sqrt(c))","B",0
340,1,76,0,0.414573," ","integrate(x^9*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{10} \, a x^{10} + \frac{1}{150} \, {\left(15 \, x^{10} \arcsin\left(c x^{2}\right) + c {\left(\frac{3 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{5}{2}}}{c^{6}} - \frac{10 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{c^{6}} + \frac{15 \, \sqrt{-c^{2} x^{4} + 1}}{c^{6}}\right)}\right)} b"," ",0,"1/10*a*x^10 + 1/150*(15*x^10*arcsin(c*x^2) + c*(3*(-c^2*x^4 + 1)^(5/2)/c^6 - 10*(-c^2*x^4 + 1)^(3/2)/c^6 + 15*sqrt(-c^2*x^4 + 1)/c^6))*b","A",0
341,1,130,0,0.416598," ","integrate(x^7*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{8} \, a x^{8} + \frac{1}{64} \, {\left(8 \, x^{8} \arcsin\left(c x^{2}\right) + c {\left(\frac{\frac{5 \, \sqrt{-c^{2} x^{4} + 1} c^{2}}{x^{2}} + \frac{3 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{x^{6}}}{c^{8} - \frac{2 \, {\left(c^{2} x^{4} - 1\right)} c^{6}}{x^{4}} + \frac{{\left(c^{2} x^{4} - 1\right)}^{2} c^{4}}{x^{8}}} + \frac{3 \, \arctan\left(\frac{\sqrt{-c^{2} x^{4} + 1}}{c x^{2}}\right)}{c^{5}}\right)}\right)} b"," ",0,"1/8*a*x^8 + 1/64*(8*x^8*arcsin(c*x^2) + c*((5*sqrt(-c^2*x^4 + 1)*c^2/x^2 + 3*(-c^2*x^4 + 1)^(3/2)/x^6)/(c^8 - 2*(c^2*x^4 - 1)*c^6/x^4 + (c^2*x^4 - 1)^2*c^4/x^8) + 3*arctan(sqrt(-c^2*x^4 + 1)/(c*x^2))/c^5))*b","A",0
342,1,59,0,0.416620," ","integrate(x^5*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{18} \, {\left(3 \, x^{6} \arcsin\left(c x^{2}\right) - c {\left(\frac{{\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{c^{4}} - \frac{3 \, \sqrt{-c^{2} x^{4} + 1}}{c^{4}}\right)}\right)} b"," ",0,"1/6*a*x^6 + 1/18*(3*x^6*arcsin(c*x^2) - c*((-c^2*x^4 + 1)^(3/2)/c^4 - 3*sqrt(-c^2*x^4 + 1)/c^4))*b","A",0
343,1,88,0,0.419416," ","integrate(x^3*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{8} \, {\left(2 \, x^{4} \arcsin\left(c x^{2}\right) + c {\left(\frac{\arctan\left(\frac{\sqrt{-c^{2} x^{4} + 1}}{c x^{2}}\right)}{c^{3}} + \frac{\sqrt{-c^{2} x^{4} + 1}}{{\left(c^{4} - \frac{{\left(c^{2} x^{4} - 1\right)} c^{2}}{x^{4}}\right)} x^{2}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/8*(2*x^4*arcsin(c*x^2) + c*(arctan(sqrt(-c^2*x^4 + 1)/(c*x^2))/c^3 + sqrt(-c^2*x^4 + 1)/((c^4 - (c^2*x^4 - 1)*c^2/x^4)*x^2)))*b","A",0
344,1,37,0,0.416166," ","integrate(x*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{{\left(c x^{2} \arcsin\left(c x^{2}\right) + \sqrt{-c^{2} x^{4} + 1}\right)} b}{2 \, c}"," ",0,"1/2*a*x^2 + 1/2*(c*x^2*arcsin(c*x^2) + sqrt(-c^2*x^4 + 1))*b/c","A",0
345,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x,x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1))/x, x) + a*log(x)","F",0
346,1,57,0,0.417012," ","integrate((a+b*arcsin(c*x^2))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c {\left(\log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right) - \log\left(\sqrt{-c^{2} x^{4} + 1} - 1\right)\right)} + \frac{2 \, \arcsin\left(c x^{2}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*(c*(log(sqrt(-c^2*x^4 + 1) + 1) - log(sqrt(-c^2*x^4 + 1) - 1)) + 2*arcsin(c*x^2)/x^2)*b - 1/2*a/x^2","A",0
347,1,38,0,0.411439," ","integrate((a+b*arcsin(c*x^2))/x^5,x, algorithm=""maxima"")","-\frac{1}{4} \, b {\left(\frac{\sqrt{-c^{2} x^{4} + 1} c}{x^{2}} + \frac{\arcsin\left(c x^{2}\right)}{x^{4}}\right)} - \frac{a}{4 \, x^{4}}"," ",0,"-1/4*b*(sqrt(-c^2*x^4 + 1)*c/x^2 + arcsin(c*x^2)/x^4) - 1/4*a/x^4","A",0
348,1,81,0,0.408018," ","integrate((a+b*arcsin(c*x^2))/x^7,x, algorithm=""maxima"")","-\frac{1}{24} \, {\left({\left(c^{2} \log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right) - c^{2} \log\left(\sqrt{-c^{2} x^{4} + 1} - 1\right) + \frac{2 \, \sqrt{-c^{2} x^{4} + 1}}{x^{4}}\right)} c + \frac{4 \, \arcsin\left(c x^{2}\right)}{x^{6}}\right)} b - \frac{a}{6 \, x^{6}}"," ",0,"-1/24*((c^2*log(sqrt(-c^2*x^4 + 1) + 1) - c^2*log(sqrt(-c^2*x^4 + 1) - 1) + 2*sqrt(-c^2*x^4 + 1)/x^4)*c + 4*arcsin(c*x^2)/x^6)*b - 1/6*a/x^6","A",0
349,1,61,0,0.414813," ","integrate((a+b*arcsin(c*x^2))/x^9,x, algorithm=""maxima"")","-\frac{1}{24} \, {\left(c {\left(\frac{3 \, \sqrt{-c^{2} x^{4} + 1} c^{2}}{x^{2}} + \frac{{\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{x^{6}}\right)} + \frac{3 \, \arcsin\left(c x^{2}\right)}{x^{8}}\right)} b - \frac{a}{8 \, x^{8}}"," ",0,"-1/24*(c*(3*sqrt(-c^2*x^4 + 1)*c^2/x^2 + (-c^2*x^4 + 1)^(3/2)/x^6) + 3*arcsin(c*x^2)/x^8)*b - 1/8*a/x^8","A",0
350,1,125,0,0.411503," ","integrate((a+b*arcsin(c*x^2))/x^11,x, algorithm=""maxima"")","-\frac{1}{160} \, {\left({\left(3 \, c^{4} \log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right) - 3 \, c^{4} \log\left(\sqrt{-c^{2} x^{4} + 1} - 1\right) - \frac{2 \, {\left(3 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}} c^{4} - 5 \, \sqrt{-c^{2} x^{4} + 1} c^{4}\right)}}{2 \, c^{2} x^{4} + {\left(c^{2} x^{4} - 1\right)}^{2} - 1}\right)} c + \frac{16 \, \arcsin\left(c x^{2}\right)}{x^{10}}\right)} b - \frac{a}{10 \, x^{10}}"," ",0,"-1/160*((3*c^4*log(sqrt(-c^2*x^4 + 1) + 1) - 3*c^4*log(sqrt(-c^2*x^4 + 1) - 1) - 2*(3*(-c^2*x^4 + 1)^(3/2)*c^4 - 5*sqrt(-c^2*x^4 + 1)*c^4)/(2*c^2*x^4 + (c^2*x^4 - 1)^2 - 1))*c + 16*arcsin(c*x^2)/x^10)*b - 1/10*a/x^10","A",0
351,1,82,0,0.419368," ","integrate((a+b*arcsin(c*x^2))/x^13,x, algorithm=""maxima"")","-\frac{1}{180} \, {\left({\left(\frac{15 \, \sqrt{-c^{2} x^{4} + 1} c^{4}}{x^{2}} + \frac{10 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}} c^{2}}{x^{6}} + \frac{3 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{5}{2}}}{x^{10}}\right)} c + \frac{15 \, \arcsin\left(c x^{2}\right)}{x^{12}}\right)} b - \frac{a}{12 \, x^{12}}"," ",0,"-1/180*((15*sqrt(-c^2*x^4 + 1)*c^4/x^2 + 10*(-c^2*x^4 + 1)^(3/2)*c^2/x^6 + 3*(-c^2*x^4 + 1)^(5/2)/x^10)*c + 15*arcsin(c*x^2)/x^12)*b - 1/12*a/x^12","A",0
352,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{7} \, a x^{7} + \frac{1}{7} \, {\left(x^{7} \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right) + 14 \, c \int \frac{x^{8} e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{7 \, {\left(c^{4} x^{8} - c^{2} x^{4} + {\left(c^{2} x^{4} - 1\right)} e^{\left(\log\left(c x^{2} + 1\right) + \log\left(-c x^{2} + 1\right)\right)}\right)}}\,{d x}\right)} b"," ",0,"1/7*a*x^7 + 1/7*(x^7*arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)) + 14*c*integrate(1/7*x^8*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^8 - c^2*x^4 + (c^2*x^4 - 1)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x))*b","F",0
353,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{5} \, {\left(x^{5} \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right) + 10 \, c \int \frac{x^{6} e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{5 \, {\left(c^{4} x^{8} - c^{2} x^{4} + {\left(c^{2} x^{4} - 1\right)} e^{\left(\log\left(c x^{2} + 1\right) + \log\left(-c x^{2} + 1\right)\right)}\right)}}\,{d x}\right)} b"," ",0,"1/5*a*x^5 + 1/5*(x^5*arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)) + 10*c*integrate(1/5*x^6*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^8 - c^2*x^4 + (c^2*x^4 - 1)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x))*b","F",0
354,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x^2)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{3} \, {\left(x^{3} \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right) + 6 \, c \int \frac{x^{4} e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{3 \, {\left(c^{4} x^{8} - c^{2} x^{4} + {\left(c^{2} x^{4} - 1\right)} e^{\left(\log\left(c x^{2} + 1\right) + \log\left(-c x^{2} + 1\right)\right)}\right)}}\,{d x}\right)} b"," ",0,"1/3*a*x^3 + 1/3*(x^3*arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)) + 6*c*integrate(1/3*x^4*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^8 - c^2*x^4 + (c^2*x^4 - 1)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x))*b","F",0
355,0,0,0,0.000000," ","integrate(a+b*arcsin(c*x^2),x, algorithm=""maxima"")","{\left(x \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right) + 2 \, c \int \frac{x^{2} e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{c^{4} x^{8} - c^{2} x^{4} + {\left(c^{2} x^{4} - 1\right)} e^{\left(\log\left(c x^{2} + 1\right) + \log\left(-c x^{2} + 1\right)\right)}}\,{d x}\right)} b + a x"," ",0,"(x*arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)) + 2*c*integrate(x^2*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^8 - c^2*x^4 + (c^2*x^4 - 1)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x))*b + a*x","F",0
356,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, c x \int \frac{\sqrt{-c x^{2} + 1}}{\sqrt{c x^{2} + 1} {\left(c x^{2} - 1\right)}}\,{d x} + \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right)\right)} b}{x} - \frac{a}{x}"," ",0,"-(2*c*x*integrate(e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^8 - c^2*x^4 + (c^2*x^4 - 1)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x) + arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)))*b/x - a/x","F",0
357,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^4,x, algorithm=""maxima"")","-\frac{{\left(2 \, c x^{3} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{c^{4} x^{10} - c^{2} x^{6} - {\left(c^{2} x^{6} - x^{2}\right)} {\left(c x^{2} + 1\right)} {\left(c x^{2} - 1\right)}}\,{d x} + \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right)\right)} b}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"-1/3*(6*c*x^3*integrate(1/3*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^10 - c^2*x^6 + (c^2*x^6 - x^2)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x) + arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)))*b/x^3 - 1/3*a/x^3","F",0
358,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^6,x, algorithm=""maxima"")","-\frac{{\left(2 \, c x^{5} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{c^{4} x^{12} - c^{2} x^{8} - {\left(c^{2} x^{8} - x^{4}\right)} {\left(c x^{2} + 1\right)} {\left(c x^{2} - 1\right)}}\,{d x} + \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right)\right)} b}{5 \, x^{5}} - \frac{a}{5 \, x^{5}}"," ",0,"-1/5*(10*c*x^5*integrate(1/5*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^12 - c^2*x^8 + (c^2*x^8 - x^4)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x) + arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)))*b/x^5 - 1/5*a/x^5","F",0
359,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^8,x, algorithm=""maxima"")","-\frac{{\left(2 \, c x^{7} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x^{2} + 1\right) + \frac{1}{2} \, \log\left(-c x^{2} + 1\right)\right)}}{c^{4} x^{14} - c^{2} x^{10} - {\left(c^{2} x^{10} - x^{6}\right)} {\left(c x^{2} + 1\right)} {\left(c x^{2} - 1\right)}}\,{d x} + \arctan\left(c x^{2}, \sqrt{c x^{2} + 1} \sqrt{-c x^{2} + 1}\right)\right)} b}{7 \, x^{7}} - \frac{a}{7 \, x^{7}}"," ",0,"-1/7*(14*c*x^7*integrate(1/7*e^(1/2*log(c*x^2 + 1) + 1/2*log(-c*x^2 + 1))/(c^4*x^14 - c^2*x^10 + (c^2*x^10 - x^6)*e^(log(c*x^2 + 1) + log(-c*x^2 + 1))), x) + arctan2(c*x^2, sqrt(c*x^2 + 1)*sqrt(-c*x^2 + 1)))*b/x^7 - 1/7*a/x^7","F",0
360,0,0,0,0.000000," ","integrate(arcsin(a*x^5)/x,x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arcsin(a*x^5)/x, x)","F",0
361,1,52,0,0.414039," ","integrate(x^2*arcsin(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arcsin\left(\sqrt{x}\right) + \frac{1}{18} \, x^{\frac{5}{2}} \sqrt{-x + 1} + \frac{5}{72} \, x^{\frac{3}{2}} \sqrt{-x + 1} + \frac{5}{48} \, \sqrt{x} \sqrt{-x + 1} - \frac{5}{48} \, \arcsin\left(\sqrt{x}\right)"," ",0,"1/3*x^3*arcsin(sqrt(x)) + 1/18*x^(5/2)*sqrt(-x + 1) + 5/72*x^(3/2)*sqrt(-x + 1) + 5/48*sqrt(x)*sqrt(-x + 1) - 5/48*arcsin(sqrt(x))","A",0
362,1,40,0,0.404806," ","integrate(x*arcsin(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arcsin\left(\sqrt{x}\right) + \frac{1}{8} \, x^{\frac{3}{2}} \sqrt{-x + 1} + \frac{3}{16} \, \sqrt{x} \sqrt{-x + 1} - \frac{3}{16} \, \arcsin\left(\sqrt{x}\right)"," ",0,"1/2*x^2*arcsin(sqrt(x)) + 1/8*x^(3/2)*sqrt(-x + 1) + 3/16*sqrt(x)*sqrt(-x + 1) - 3/16*arcsin(sqrt(x))","A",0
363,1,25,0,0.405994," ","integrate(arcsin(x^(1/2)),x, algorithm=""maxima"")","x \arcsin\left(\sqrt{x}\right) + \frac{1}{2} \, \sqrt{x} \sqrt{-x + 1} - \frac{1}{2} \, \arcsin\left(\sqrt{x}\right)"," ",0,"x*arcsin(sqrt(x)) + 1/2*sqrt(x)*sqrt(-x + 1) - 1/2*arcsin(sqrt(x))","A",0
364,0,0,0,0.000000," ","integrate(arcsin(x^(1/2))/x,x, algorithm=""maxima"")","\int \frac{\arcsin\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arcsin(sqrt(x))/x, x)","F",0
365,1,22,0,0.412108," ","integrate(arcsin(x^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\sqrt{-x + 1}}{\sqrt{x}} - \frac{\arcsin\left(\sqrt{x}\right)}{x}"," ",0,"-sqrt(-x + 1)/sqrt(x) - arcsin(sqrt(x))/x","A",0
366,1,34,0,0.418879," ","integrate(arcsin(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{\arcsin\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*arcsin(sqrt(x))/x^2","A",0
367,1,46,0,0.416833," ","integrate(arcsin(x^(1/2))/x^4,x, algorithm=""maxima"")","-\frac{8 \, \sqrt{-x + 1}}{45 \, \sqrt{x}} - \frac{4 \, \sqrt{-x + 1}}{45 \, x^{\frac{3}{2}}} - \frac{\sqrt{-x + 1}}{15 \, x^{\frac{5}{2}}} - \frac{\arcsin\left(\sqrt{x}\right)}{3 \, x^{3}}"," ",0,"-8/45*sqrt(-x + 1)/sqrt(x) - 4/45*sqrt(-x + 1)/x^(3/2) - 1/15*sqrt(-x + 1)/x^(5/2) - 1/3*arcsin(sqrt(x))/x^3","A",0
368,1,58,0,0.411406," ","integrate(arcsin(x^(1/2))/x^5,x, algorithm=""maxima"")","-\frac{4 \, \sqrt{-x + 1}}{35 \, \sqrt{x}} - \frac{2 \, \sqrt{-x + 1}}{35 \, x^{\frac{3}{2}}} - \frac{3 \, \sqrt{-x + 1}}{70 \, x^{\frac{5}{2}}} - \frac{\sqrt{-x + 1}}{28 \, x^{\frac{7}{2}}} - \frac{\arcsin\left(\sqrt{x}\right)}{4 \, x^{4}}"," ",0,"-4/35*sqrt(-x + 1)/sqrt(x) - 2/35*sqrt(-x + 1)/x^(3/2) - 3/70*sqrt(-x + 1)/x^(5/2) - 1/28*sqrt(-x + 1)/x^(7/2) - 1/4*arcsin(sqrt(x))/x^4","A",0
369,1,125,0,0.609421," ","integrate(x^4*(a+b*arcsin(c/x)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{80} \, {\left(16 \, x^{5} \arcsin\left(\frac{c}{x}\right) + {\left(3 \, c^{4} \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right) - 3 \, c^{4} \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} - 1\right) - \frac{2 \, {\left(3 \, c^{4} {\left(-\frac{c^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}} - 5 \, c^{4} \sqrt{-\frac{c^{2}}{x^{2}} + 1}\right)}}{{\left(\frac{c^{2}}{x^{2}} - 1\right)}^{2} + \frac{2 \, c^{2}}{x^{2}} - 1}\right)} c\right)} b"," ",0,"1/5*a*x^5 + 1/80*(16*x^5*arcsin(c/x) + (3*c^4*log(sqrt(-c^2/x^2 + 1) + 1) - 3*c^4*log(sqrt(-c^2/x^2 + 1) - 1) - 2*(3*c^4*(-c^2/x^2 + 1)^(3/2) - 5*c^4*sqrt(-c^2/x^2 + 1))/((c^2/x^2 - 1)^2 + 2*c^2/x^2 - 1))*c)*b","A",0
370,1,59,0,1.086445," ","integrate(x^3*(a+b*arcsin(c/x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \arcsin\left(\frac{c}{x}\right) + {\left(x^{3} {\left(-\frac{c^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, c^{2} x \sqrt{-\frac{c^{2}}{x^{2}} + 1}\right)} c\right)} b"," ",0,"1/4*a*x^4 + 1/12*(3*x^4*arcsin(c/x) + (x^3*(-c^2/x^2 + 1)^(3/2) + 3*c^2*x*sqrt(-c^2/x^2 + 1))*c)*b","A",0
371,1,81,0,0.635798," ","integrate(x^2*(a+b*arcsin(c/x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{12} \, {\left(4 \, x^{3} \arcsin\left(\frac{c}{x}\right) + {\left(c^{2} \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right) - c^{2} \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} - 1\right) + 2 \, x^{2} \sqrt{-\frac{c^{2}}{x^{2}} + 1}\right)} c\right)} b"," ",0,"1/3*a*x^3 + 1/12*(4*x^3*arcsin(c/x) + (c^2*log(sqrt(-c^2/x^2 + 1) + 1) - c^2*log(sqrt(-c^2/x^2 + 1) - 1) + 2*x^2*sqrt(-c^2/x^2 + 1))*c)*b","A",0
372,1,36,0,0.658692," ","integrate(x*(a+b*arcsin(c/x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(x^{2} \arcsin\left(\frac{c}{x}\right) + c x \sqrt{-\frac{c^{2}}{x^{2}} + 1}\right)} b"," ",0,"1/2*a*x^2 + 1/2*(x^2*arcsin(c/x) + c*x*sqrt(-c^2/x^2 + 1))*b","A",0
373,1,52,0,0.926229," ","integrate(a+b*arcsin(c/x),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right) - \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} - 1\right)\right)} + 2 \, x \arcsin\left(\frac{c}{x}\right)\right)} b + a x"," ",0,"1/2*(c*(log(sqrt(-c^2/x^2 + 1) + 1) - log(sqrt(-c^2/x^2 + 1) - 1)) + 2*x*arcsin(c/x))*b + a*x","A",0
374,0,0,0,0.000000," ","integrate((a+b*arcsin(c/x))/x,x, algorithm=""maxima"")","{\left(c \int -\frac{\sqrt{c + x} \sqrt{-c + x} \log\left(x\right)}{c^{2} x - x^{3}}\,{d x} + \arctan\left(c, \sqrt{c + x} \sqrt{-c + x}\right) \log\left(x\right)\right)} b + a \log\left(x\right)"," ",0,"(c*integrate(-sqrt(c + x)*sqrt(-c + x)*log(x)/(c^2*x - x^3), x) + arctan2(c, sqrt(c + x)*sqrt(-c + x))*log(x))*b + a*log(x)","F",0
375,1,37,0,0.562486," ","integrate((a+b*arcsin(c/x))/x^2,x, algorithm=""maxima"")","-\frac{b {\left(\frac{c \arcsin\left(\frac{c}{x}\right)}{x} + \sqrt{-\frac{c^{2}}{x^{2}} + 1}\right)}}{c} - \frac{a}{x}"," ",0,"-b*(c*arcsin(c/x)/x + sqrt(-c^2/x^2 + 1))/c - a/x","A",0
376,1,86,0,0.588080," ","integrate((a+b*arcsin(c/x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{x \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c^{2} x^{2} {\left(\frac{c^{2}}{x^{2}} - 1\right)} - c^{4}} - \frac{\arctan\left(\frac{x \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c}\right)}{c^{3}}\right)} - \frac{2 \, \arcsin\left(\frac{c}{x}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/4*(c*(x*sqrt(-c^2/x^2 + 1)/(c^2*x^2*(c^2/x^2 - 1) - c^4) - arctan(x*sqrt(-c^2/x^2 + 1)/c)/c^3) - 2*arcsin(c/x)/x^2)*b - 1/2*a/x^2","A",0
377,1,58,0,0.619588," ","integrate((a+b*arcsin(c/x))/x^4,x, algorithm=""maxima"")","\frac{1}{9} \, {\left(c {\left(\frac{{\left(-\frac{c^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}}}{c^{4}} - \frac{3 \, \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c^{4}}\right)} - \frac{3 \, \arcsin\left(\frac{c}{x}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"1/9*(c*((-c^2/x^2 + 1)^(3/2)/c^4 - 3*sqrt(-c^2/x^2 + 1)/c^4) - 3*arcsin(c/x)/x^3)*b - 1/3*a/x^3","A",0
378,1,126,0,1.061176," ","integrate((a+b*arcsin(c/x))/x^5,x, algorithm=""maxima"")","-\frac{1}{32} \, {\left(c {\left(\frac{3 \, x^{3} {\left(-\frac{c^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}} + 5 \, c^{2} x \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c^{4} x^{4} {\left(\frac{c^{2}}{x^{2}} - 1\right)}^{2} - 2 \, c^{6} x^{2} {\left(\frac{c^{2}}{x^{2}} - 1\right)} + c^{8}} + \frac{3 \, \arctan\left(\frac{x \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c}\right)}{c^{5}}\right)} + \frac{8 \, \arcsin\left(\frac{c}{x}\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"-1/32*(c*((3*x^3*(-c^2/x^2 + 1)^(3/2) + 5*c^2*x*sqrt(-c^2/x^2 + 1))/(c^4*x^4*(c^2/x^2 - 1)^2 - 2*c^6*x^2*(c^2/x^2 - 1) + c^8) + 3*arctan(x*sqrt(-c^2/x^2 + 1)/c)/c^5) + 8*arcsin(c/x)/x^4)*b - 1/4*a/x^4","A",0
379,-1,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x^n)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{3} \, {\left(x^{3} \arctan\left(c x^{n}, \sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1}\right) + 3 \, c n \int \frac{\sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1} x^{2} x^{n}}{3 \, {\left(c^{2} x^{2 \, n} - 1\right)}}\,{d x}\right)} b"," ",0,"1/3*a*x^3 + 1/3*(x^3*arctan2(c*x^n, sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)) + 3*c*n*integrate(1/3*sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)*x^2*x^n/(c^2*x^(2*n) - 1), x))*b","F",0
381,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x^n)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(x^{2} \arctan\left(c x^{n}, \sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1}\right) + 2 \, c n \int \frac{\sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1} x x^{n}}{2 \, {\left(c^{2} x^{2 \, n} - 1\right)}}\,{d x}\right)} b"," ",0,"1/2*a*x^2 + 1/2*(x^2*arctan2(c*x^n, sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)) + 2*c*n*integrate(1/2*sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)*x*x^n/(c^2*x^(2*n) - 1), x))*b","F",0
382,0,0,0,0.000000," ","integrate(a+b*arcsin(c*x^n),x, algorithm=""maxima"")","{\left(c n \int \frac{\sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1} x^{n}}{c^{2} x^{2 \, n} - 1}\,{d x} + x \arctan\left(c x^{n}, \sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1}\right)\right)} b + a x"," ",0,"(c*n*integrate(sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)*x^n/(c^2*x^(2*n) - 1), x) + x*arctan2(c*x^n, sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)))*b + a*x","F",0
383,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^n))/x,x, algorithm=""maxima"")","{\left(c n \int \frac{\sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1} x^{n} \log\left(x\right)}{c^{2} x x^{2 \, n} - x}\,{d x} + \arctan\left(c x^{n}, \sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1}\right) \log\left(x\right)\right)} b + a \log\left(x\right)"," ",0,"(c*n*integrate(sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)*x^n*log(x)/(c^2*x*x^(2*n) - x), x) + arctan2(c*x^n, sqrt(c*x^n + 1)*sqrt(-c*x^n + 1))*log(x))*b + a*log(x)","F",0
384,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^n))/x^2,x, algorithm=""maxima"")","-\frac{{\left(c n x \int \frac{\sqrt{-c x^{n} + 1} x^{n}}{\sqrt{c x^{n} + 1} {\left(c x^{n} - 1\right)} x^{2}}\,{d x} + \arctan\left(c x^{n}, \sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1}\right)\right)} b}{x} - \frac{a}{x}"," ",0,"-(c*n*x*integrate(sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)*x^n/(c^2*x^2*x^(2*n) - x^2), x) + arctan2(c*x^n, sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)))*b/x - a/x","F",0
385,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^n))/x^3,x, algorithm=""maxima"")","-\frac{{\left(c n x^{2} \int \frac{\sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1} x^{n}}{c^{2} x^{2 \, n + 3} - x^{3}}\,{d x} + \arctan\left(c x^{n}, \sqrt{c x^{n} + 1} \sqrt{-c x^{n} + 1}\right)\right)} b}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"-1/2*(2*c*n*x^2*integrate(1/2*sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)*x^n/(c^2*x^3*x^(2*n) - x^3), x) + arctan2(c*x^n, sqrt(c*x^n + 1)*sqrt(-c*x^n + 1)))*b/x^2 - 1/2*a/x^2","F",0
386,1,245,0,0.410523," ","integrate(x^5*(a+b*arcsin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{36} \, {\left(6 \, x^{6} \arcsin\left(d x^{2} + c\right) + {\left(\frac{2 \, \sqrt{-d^{2} x^{4} - 2 \, c d x^{2} - c^{2} + 1} x^{4}}{d^{2}} - \frac{5 \, \sqrt{-d^{2} x^{4} - 2 \, c d x^{2} - c^{2} + 1} c x^{2}}{d^{3}} - \frac{15 \, c^{3} \arcsin\left(-\frac{d^{2} x^{2} + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{9 \, {\left(c^{2} - 1\right)} c \arcsin\left(-\frac{d^{2} x^{2} + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{4}} + \frac{15 \, \sqrt{-d^{2} x^{4} - 2 \, c d x^{2} - c^{2} + 1} c^{2}}{d^{4}} - \frac{4 \, \sqrt{-d^{2} x^{4} - 2 \, c d x^{2} - c^{2} + 1} {\left(c^{2} - 1\right)}}{d^{4}}\right)} d\right)} b"," ",0,"1/6*a*x^6 + 1/36*(6*x^6*arcsin(d*x^2 + c) + (2*sqrt(-d^2*x^4 - 2*c*d*x^2 - c^2 + 1)*x^4/d^2 - 5*sqrt(-d^2*x^4 - 2*c*d*x^2 - c^2 + 1)*c*x^2/d^3 - 15*c^3*arcsin(-(d^2*x^2 + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 9*(c^2 - 1)*c*arcsin(-(d^2*x^2 + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^4 + 15*sqrt(-d^2*x^4 - 2*c*d*x^2 - c^2 + 1)*c^2/d^4 - 4*sqrt(-d^2*x^4 - 2*c*d*x^2 - c^2 + 1)*(c^2 - 1)/d^4)*d)*b","B",0
387,1,174,0,0.413111," ","integrate(x^3*(a+b*arcsin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{8} \, {\left(2 \, x^{4} \arcsin\left(d x^{2} + c\right) + d {\left(\frac{\sqrt{-d^{2} x^{4} - 2 \, c d x^{2} - c^{2} + 1} x^{2}}{d^{2}} + \frac{3 \, c^{2} \arcsin\left(-\frac{d^{2} x^{2} + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{{\left(c^{2} - 1\right)} \arcsin\left(-\frac{d^{2} x^{2} + c d}{\sqrt{c^{2} d^{2} - {\left(c^{2} - 1\right)} d^{2}}}\right)}{d^{3}} - \frac{3 \, \sqrt{-d^{2} x^{4} - 2 \, c d x^{2} - c^{2} + 1} c}{d^{3}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/8*(2*x^4*arcsin(d*x^2 + c) + d*(sqrt(-d^2*x^4 - 2*c*d*x^2 - c^2 + 1)*x^2/d^2 + 3*c^2*arcsin(-(d^2*x^2 + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - (c^2 - 1)*arcsin(-(d^2*x^2 + c*d)/sqrt(c^2*d^2 - (c^2 - 1)*d^2))/d^3 - 3*sqrt(-d^2*x^4 - 2*c*d*x^2 - c^2 + 1)*c/d^3))*b","A",0
388,1,45,0,0.402135," ","integrate(x*(a+b*arcsin(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{{\left({\left(d x^{2} + c\right)} \arcsin\left(d x^{2} + c\right) + \sqrt{-{\left(d x^{2} + c\right)}^{2} + 1}\right)} b}{2 \, d}"," ",0,"1/2*a*x^2 + 1/2*((d*x^2 + c)*arcsin(d*x^2 + c) + sqrt(-(d*x^2 + c)^2 + 1))*b/d","A",0
389,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x,x, algorithm=""maxima"")","b \int \frac{\arctan\left(d x^{2} + c, \sqrt{d x^{2} + c + 1} \sqrt{-d x^{2} - c + 1}\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(arctan2(d*x^2 + c, sqrt(d*x^2 + c + 1)*sqrt(-d*x^2 - c + 1))/x, x) + a*log(x)","F",0
390,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/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(c-1>0)', see `assume?` for more details)Is c-1 positive, negative or zero?","F(-2)",0
391,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/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(c-1>0)', see `assume?` for more details)Is c-1 positive, negative or zero?","F(-2)",0
392,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^7,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(c-1>0)', see `assume?` for more details)Is c-1 positive, negative or zero?","F(-2)",0
393,-2,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(d*x^2+c)),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(c-1>0)', see `assume?` for more details)Is c-1 positive or negative?","F(-2)",0
394,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(d*x^2+c)),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(c-1>0)', see `assume?` for more details)Is c-1 positive or negative?","F(-2)",0
395,-2,0,0,0.000000," ","integrate(a+b*arcsin(d*x^2+c),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(c-1>0)', see `assume?` for more details)Is c-1 positive or negative?","F(-2)",0
396,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/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(c-1>0)', see `assume?` for more details)Is c-1 positive or negative?","F(-2)",0
397,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/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(c-1>0)', see `assume?` for more details)Is c-1 positive or negative?","F(-2)",0
398,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^6,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(c-1>0)', see `assume?` for more details)Is c-1 positive or negative?","F(-2)",0
399,1,37,0,0.418580," ","integrate(x^3*arcsin(b*x^4+a),x, algorithm=""maxima"")","\frac{{\left(b x^{4} + a\right)} \arcsin\left(b x^{4} + a\right) + \sqrt{-{\left(b x^{4} + a\right)}^{2} + 1}}{4 \, b}"," ",0,"1/4*((b*x^4 + a)*arcsin(b*x^4 + a) + sqrt(-(b*x^4 + a)^2 + 1))/b","A",0
400,1,39,0,0.416878," ","integrate(x^(-1+n)*arcsin(a+b*x^n),x, algorithm=""maxima"")","\frac{{\left(b x^{n} + a\right)} \arcsin\left(b x^{n} + a\right) + \sqrt{-{\left(b x^{n} + a\right)}^{2} + 1}}{b n}"," ",0,"((b*x^n + a)*arcsin(b*x^n + a) + sqrt(-(b*x^n + a)^2 + 1))/(b*n)","A",0
401,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
402,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
403,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
404,1,45,0,0.423844," ","integrate(a+b*arcsin(d*x^2+1),x, algorithm=""maxima"")","{\left(x \arcsin\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*arcsin(d*x^2 + 1) - 2*(d^(3/2)*x^2 + 2*sqrt(d))/(sqrt(-d*x^2 - 2)*d))*b + a*x","A",0
405,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
406,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
407,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
408,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^4,x, algorithm=""maxima"")","b^{4} x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{4} + 4 \, {\left(x \arcsin\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{2 \, {\left(4 \, \sqrt{-d x^{2} + 2} b^{4} \sqrt{d} x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{3} + 2 \, {\left(a b^{3} d x^{2} - 2 \, a b^{3}\right)} \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{3} + 3 \, {\left(a^{2} b^{2} d x^{2} - 2 \, a^{2} b^{2}\right)} \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{2}\right)}}{d x^{2} - 2}\,{d x}"," ",0,"b^4*x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^4 + 4*(x*arcsin(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(2*(4*sqrt(-d*x^2 + 2)*b^4*sqrt(d)*x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^3 + 2*(a*b^3*d*x^2 - 2*a*b^3)*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^3 + 3*(a^2*b^2*d*x^2 - 2*a^2*b^2)*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^2)/(d*x^2 - 2), x)","F",0
409,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^3,x, algorithm=""maxima"")","b^{3} x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{3} + 3 \, {\left(x \arcsin\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 + a^{3} x + \int \frac{3 \, {\left(2 \, \sqrt{-d x^{2} + 2} b^{3} \sqrt{d} x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{2} + {\left(a b^{2} d x^{2} - 2 \, a b^{2}\right)} \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{2}\right)}}{d x^{2} - 2}\,{d x}"," ",0,"b^3*x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^3 + 3*(x*arcsin(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(-d*x^2 + 2)*d))*a^2*b + a^3*x + integrate(3*(2*sqrt(-d*x^2 + 2)*b^3*sqrt(d)*x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^2 + (a*b^2*d*x^2 - 2*a*b^2)*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^2)/(d*x^2 - 2), x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^2,x, algorithm=""maxima"")","2 \, {\left(x \arcsin\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 + {\left(x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{2} + 4 \, \sqrt{d} \int \frac{\sqrt{-d x^{2} + 2} x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)}{d x^{2} - 2}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"2*(x*arcsin(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(-d*x^2 + 2)*d))*a*b + (x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^2 + 4*sqrt(d)*integrate(sqrt(-d*x^2 + 2)*x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)/(d*x^2 - 2), x))*b^2 + a^2*x","F",0
411,1,45,0,0.420331," ","integrate(a+b*arcsin(d*x^2-1),x, algorithm=""maxima"")","{\left(x \arcsin\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*arcsin(d*x^2 - 1) - 2*(d^(3/2)*x^2 - 2*sqrt(d))/(sqrt(-d*x^2 + 2)*d))*b + a*x","A",0
412,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1)),x, algorithm=""maxima"")","\int \frac{1}{b \arcsin\left(d x^{2} - 1\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsin(d*x^2 - 1) + a), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} d \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right) + a b d\right)} \sqrt{d} \int \frac{\sqrt{-d x^{2} + 2} x}{a b d x^{2} - 2 \, a b + {\left(b^{2} d x^{2} - 2 \, b^{2}\right)} \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)}\,{d x} - \sqrt{-d x^{2} + 2} \sqrt{d}}{2 \, {\left(b^{2} d \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right) + a b d\right)}}"," ",0,"1/2*(2*(b^2*d*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x) + a*b*d)*sqrt(d)*integrate(1/2*sqrt(-d*x^2 + 2)*x/(a*b*d*x^2 - 2*a*b + (b^2*d*x^2 - 2*b^2)*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)), x) - sqrt(-d*x^2 + 2)*sqrt(d))/(b^2*d*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x) + a*b*d)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^3,x, algorithm=""maxima"")","\frac{b d x \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right) + a d x - 2 \, \sqrt{-d x^{2} + 2} b \sqrt{d} - {\left(b^{4} d \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{2} + 2 \, a b^{3} d \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right) + a^{2} b^{2} d\right)} \int \frac{1}{b^{3} \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right) + a b^{2}}\,{d x}}{8 \, {\left(b^{4} d \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right)^{2} + 2 \, a b^{3} d \arctan\left(d x^{2} - 1, \sqrt{-d x^{2} + 2} \sqrt{d} x\right) + a^{2} b^{2} d\right)}}"," ",0,"1/8*(b*d*x*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x) + a*d*x - 2*sqrt(-d*x^2 + 2)*b*sqrt(d) - 8*(b^4*d*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^2 + 2*a*b^3*d*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x) + a^2*b^2*d)*integrate(1/8/(b^3*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x) + a*b^2), x))/(b^4*d*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x)^2 + 2*a*b^3*d*arctan2(d*x^2 - 1, sqrt(-d*x^2 + 2)*sqrt(d)*x) + a^2*b^2*d)","F",0
415,-2,0,0,0.000000," ","integrate(arcsin(x^2+1)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_x^2)-2)","F(-2)",0
416,0,0,0,0.000000," ","integrate(arcsin(x^2-1)^2,x, algorithm=""maxima"")","x \arctan\left(x^{2} - 1, \sqrt{-x^{2} + 2} x\right)^{2} + 4 \, \int \frac{\sqrt{-x^{2} + 2} x \arctan\left(x^{2} - 1, \sqrt{-x^{2} + 2} x\right)}{x^{2} - 2}\,{d x}"," ",0,"x*arctan2(x^2 - 1, sqrt(-x^2 + 2)*x)^2 + 4*integrate(sqrt(-x^2 + 2)*x*arctan2(x^2 - 1, sqrt(-x^2 + 2)*x)/(x^2 - 2), x)","F",0
417,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
418,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
419,-2,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
420,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
421,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
422,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
423,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt((-_SAGE_VAR_d*_SAGE_VAR_x^2)-2)","F(-2)",0
424,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^(5/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(5/2), x)","F",0
425,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^(3/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \arcsin\left(d x^{2} - 1\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(d*x^2 - 1) + a), x)","F",0
427,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \arcsin\left(d x^{2} - 1\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsin(d*x^2 - 1) + a), x)","F",0
428,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(-3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(-5/2), x)","F",0
430,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(-7/2), x)","F",0
431,0,0,0,0.000000," ","integrate((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(b \arcsin\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((b*arcsin(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
432,0,0,0,0.000000," ","integrate((a+b*arcsin((-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)} - \int \frac{b^{3} \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)^{3} + 3 \, a b^{2} \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)^{2} + 3 \, a^{2} b \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)}{c^{2} x^{2} - 1}\,{d x}"," ",0,"1/2*a^3*(log(c*x + 1)/c - log(c*x - 1)/c) - integrate((b^3*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x))^3 + 3*a*b^2*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x))^2 + 3*a^2*b*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x)))/(c^2*x^2 - 1), x)","F",0
433,0,0,0,0.000000," ","integrate((a+b*arcsin((-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)} - \int \frac{b^{2} \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)^{2} + 2 \, a b \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)}{c^{2} x^{2} - 1}\,{d x}"," ",0,"1/2*a^2*(log(c*x + 1)/c - log(c*x - 1)/c) - integrate((b^2*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x))^2 + 2*a*b*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x)))/(c^2*x^2 - 1), x)","F",0
434,0,0,0,0.000000," ","integrate((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} - b \int \frac{\arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)}{c^{2} x^{2} - 1}\,{d x}"," ",0,"1/2*a*(log(c*x + 1)/c - log(c*x - 1)/c) - b*integrate(arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x))/(c^2*x^2 - 1), x)","F",0
435,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arcsin((-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 \arcsin\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}}\,{d x}"," ",0,"-integrate(1/((c^2*x^2 - 1)*(b*arcsin(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)), x)","F",0
436,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""maxima"")","-\frac{\frac{1}{2} \, {\left(\sqrt{2} a b c^{2} x - \sqrt{2} a b c + {\left(\sqrt{2} b^{2} c^{2} x - \sqrt{2} b^{2} c\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)\right)} \sqrt{c} \int \frac{\sqrt{-c x + 1} \sqrt{x}}{a b c^{3} x^{3} - 2 \, a b c^{2} x^{2} + a b c x + {\left(b^{2} c^{3} x^{3} - 2 \, b^{2} c^{2} x^{2} + b^{2} c x\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)}\,{d x} + \sqrt{2} \sqrt{-c x + 1} \sqrt{c} \sqrt{x}}{a b c^{2} x - a b c + {\left(b^{2} c^{2} x - b^{2} c\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{2} \sqrt{c} \sqrt{x}\right)}"," ",0,"-((sqrt(2)*a*b*c^2*x - sqrt(2)*a*b*c + (sqrt(2)*b^2*c^2*x - sqrt(2)*b^2*c)*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x)))*sqrt(c)*integrate(1/2*sqrt(-c*x + 1)*sqrt(x)/(a*b*c^3*x^3 - 2*a*b*c^2*x^2 + a*b*c*x + (b^2*c^3*x^3 - 2*b^2*c^2*x^2 + b^2*c*x)*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x))), x) + sqrt(2)*sqrt(-c*x + 1)*sqrt(c)*sqrt(x))/(a*b*c^2*x - a*b*c + (b^2*c^2*x - b^2*c)*arctan2(sqrt(-c*x + 1), sqrt(2)*sqrt(c)*sqrt(x)))","F",0
437,1,17,0,0.401627," ","integrate(exp(x)*arcsin(exp(x)),x, algorithm=""maxima"")","\arcsin\left(e^{x}\right) e^{x} + \sqrt{-e^{\left(2 \, x\right)} + 1}"," ",0,"arcsin(e^x)*e^x + sqrt(-e^(2*x) + 1)","A",0
438,0,0,0,0.000000," ","integrate(arcsin(c*exp(b*x+a)),x, algorithm=""maxima"")","\frac{-i \, b^{2} c^{2} {\left(\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)}{b^{2} c^{2}} + \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)}{b^{2} c^{2}}\right)} + 2 \, b^{2} c e^{a} \int \frac{\sqrt{-c e^{\left(b x + a\right)} + 1} x e^{\left(b x\right)}}{\sqrt{c e^{\left(b x + a\right)} + 1} c e^{\left(b x + a\right)} - \sqrt{c e^{\left(b x + a\right)} + 1}}\,{d x} + 2 \, b x \arctan\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) + i \, b x \log\left(c e^{\left(b x + a\right)} + 1\right) + i \, b x \log\left(-c e^{\left(b x + a\right)} + 1\right) + i \, {\rm Li}_2\left(c e^{\left(b x + a\right)}\right) + i \, {\rm Li}_2\left(-c e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(-2*I*b^2*c^2*integrate(x*e^(2*b*x + 2*a)/(c^4*e^(4*b*x + 4*a) - c^2*e^(2*b*x + 2*a) + (c^2*e^(2*b*x + 2*a) - 1)*e^(log(c*e^(b*x + a) + 1) + log(-c*e^(b*x + a) + 1))), x) + 2*b^2*c*integrate(x*e^(b*x + a + 1/2*log(c*e^(b*x + a) + 1) + 1/2*log(-c*e^(b*x + a) + 1))/(c^4*e^(4*b*x + 4*a) - c^2*e^(2*b*x + 2*a) + (c^2*e^(2*b*x + 2*a) - 1)*e^(log(c*e^(b*x + a) + 1) + log(-c*e^(b*x + a) + 1))), x) + 2*b*x*arctan2(c*e^(b*x + a), sqrt(c*e^(b*x + a) + 1)*sqrt(-c*e^(b*x + a) + 1)) + I*b*x*log(c*e^(b*x + a) + 1) + I*b*x*log(-c*e^(b*x + a) + 1) + I*dilog(c*e^(b*x + a)) + I*dilog(-c*e^(b*x + a)))/b","F",0
439,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^3*e^(arcsin(a*x)), x)","F",0
440,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^2*e^(arcsin(a*x)), x)","F",0
441,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))*x,x, algorithm=""maxima"")","\int x e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x*e^(arcsin(a*x)), x)","F",0
442,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)),x, algorithm=""maxima"")","\int e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(arcsin(a*x)), x)","F",0
443,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(a x\right)\right)}}{x}\,{d x}"," ",0,"integrate(e^(arcsin(a*x))/x, x)","F",0
444,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(a x\right)\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arcsin(a*x))/x^2, x)","F",0
445,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)^2)*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(\arcsin\left(a x\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^3*e^(arcsin(a*x)^2), x)","F",0
446,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)^2)*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\arcsin\left(a x\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^2*e^(arcsin(a*x)^2), x)","F",0
447,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)^2)*x,x, algorithm=""maxima"")","\int x e^{\left(\arcsin\left(a x\right)^{2}\right)}\,{d x}"," ",0,"integrate(x*e^(arcsin(a*x)^2), x)","F",0
448,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)^2),x, algorithm=""maxima"")","\int e^{\left(\arcsin\left(a x\right)^{2}\right)}\,{d x}"," ",0,"integrate(e^(arcsin(a*x)^2), x)","F",0
449,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)^2)/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(a x\right)^{2}\right)}}{x}\,{d x}"," ",0,"integrate(e^(arcsin(a*x)^2)/x, x)","F",0
450,0,0,0,0.000000," ","integrate(exp(arcsin(a*x)^2)/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(a x\right)^{2}\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arcsin(a*x)^2)/x^2, x)","F",0
451,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a))*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(\arcsin\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x^3*e^(arcsin(b*x + a)), x)","F",0
452,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a))*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\arcsin\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x^2*e^(arcsin(b*x + a)), x)","F",0
453,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a))*x,x, algorithm=""maxima"")","\int x e^{\left(\arcsin\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x*e^(arcsin(b*x + a)), x)","F",0
454,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)),x, algorithm=""maxima"")","\int e^{\left(\arcsin\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(e^(arcsin(b*x + a)), x)","F",0
455,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(b x + a\right)\right)}}{x}\,{d x}"," ",0,"integrate(e^(arcsin(b*x + a))/x, x)","F",0
456,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a))/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(b x + a\right)\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arcsin(b*x + a))/x^2, x)","F",0
457,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)^2)*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(\arcsin\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^3*e^(arcsin(b*x + a)^2), x)","F",0
458,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)^2)*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\arcsin\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x^2*e^(arcsin(b*x + a)^2), x)","F",0
459,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)^2)*x,x, algorithm=""maxima"")","\int x e^{\left(\arcsin\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(x*e^(arcsin(b*x + a)^2), x)","F",0
460,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)^2),x, algorithm=""maxima"")","\int e^{\left(\arcsin\left(b x + a\right)^{2}\right)}\,{d x}"," ",0,"integrate(e^(arcsin(b*x + a)^2), x)","F",0
461,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)^2)/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(b x + a\right)^{2}\right)}}{x}\,{d x}"," ",0,"integrate(e^(arcsin(b*x + a)^2)/x, x)","F",0
462,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a)^2)/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(b x + a\right)^{2}\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arcsin(b*x + a)^2)/x^2, x)","F",0
463,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))*(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(5/2)*e^(arcsin(a*x)), x)","F",0
464,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*e^(arcsin(a*x)), x)","F",0
465,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} e^{\left(\arcsin\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*e^(arcsin(a*x)), x)","F",0
466,1,9,0,0.402535," ","integrate(exp(arcsin(a*x))/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{e^{\left(\arcsin\left(a x\right)\right)}}{a}"," ",0,"e^(arcsin(a*x))/a","A",0
467,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(a x\right)\right)}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(e^(arcsin(a*x))/(-a^2*x^2 + 1)^(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))/(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\int \frac{e^{\left(\arcsin\left(a x\right)\right)}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(e^(arcsin(a*x))/(-a^2*x^2 + 1)^(5/2), x)","F",0
469,0,0,0,0.000000," ","integrate(arcsin(c/(b*x+a)),x, algorithm=""maxima"")","x \arctan\left(c, \sqrt{b x + a + c} \sqrt{b x + a - c}\right) + \int \frac{{\left(b^{2} c x^{2} + a b c x\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + c\right) + \frac{1}{2} \, \log\left(b x + a - c\right)\right)}}{b^{2} c^{2} x^{2} + 2 \, a b c^{2} x + a^{2} c^{2} - c^{4} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - c^{2}\right)} e^{\left(\log\left(b x + a + c\right) + \log\left(b x + a - c\right)\right)}}\,{d x}"," ",0,"x*arctan2(c, sqrt(b*x + a + c)*sqrt(b*x + a - c)) + integrate((b^2*c*x^2 + a*b*c*x)*e^(1/2*log(b*x + a + c) + 1/2*log(b*x + a - c))/(b^2*c^2*x^2 + 2*a*b*c^2*x + a^2*c^2 - c^4 + (b^2*x^2 + 2*a*b*x + a^2 - c^2)*e^(log(b*x + a + c) + log(b*x + a - c))), x)","F",0
470,1,1,0,0.409283," ","integrate(x/arcsin(sin(x)),x, algorithm=""maxima"")","x"," ",0,"x","A",0
471,-2,0,0,0.000000," ","integrate(arcsin((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_b)","F(-2)",0
472,-2,0,0,0.000000," ","integrate(1/arcsin((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_b)","F(-2)",0
473,1,12,0,0.409590," ","integrate(x/(-x^2+1)+1/arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(x^{2} - 1\right) + \log\left(\arcsin\left(x\right)\right)"," ",0,"-1/2*log(x^2 - 1) + log(arcsin(x))","A",0
474,0,0,0,0.000000," ","integrate((x*arcsin(x)+(-x^2+1)^(1/2))/(arcsin(x)-x^2*arcsin(x)),x, algorithm=""maxima"")","-\int \frac{\sqrt{x + 1} \sqrt{-x + 1}}{{\left(x^{2} - 1\right)} \arctan\left(x, \sqrt{x + 1} \sqrt{-x + 1}\right)}\,{d x} - \frac{1}{2} \, \log\left(x + 1\right) - \frac{1}{2} \, \log\left(x - 1\right)"," ",0,"-integrate(sqrt(x + 1)*sqrt(-x + 1)/((x^2 - 1)*arctan2(x, sqrt(x + 1)*sqrt(-x + 1))), x) - 1/2*log(x + 1) - 1/2*log(x - 1)","F",0
