1,1,310,0,0.337091," ","integrate((e*x+d)^3*(a+b*arcsin(c*x)),x, algorithm=""giac"")","b d^{3} x \arcsin\left(c x\right) + \frac{1}{4} \, a x^{4} e^{3} + a d x^{3} e^{2} + a d^{3} x + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3}}{c} + \frac{b d x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a d^{2} e}{2 \, c^{2}} + \frac{3 \, b d^{2} \arcsin\left(c x\right) e}{4 \, c^{2}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b x e^{3}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d e^{2}}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b \arcsin\left(c x\right) e^{3}}{4 \, c^{4}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b x e^{3}}{32 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d e^{2}}{c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b \arcsin\left(c x\right) e^{3}}{2 \, c^{4}} + \frac{5 \, b \arcsin\left(c x\right) e^{3}}{32 \, c^{4}}"," ",0,"b*d^3*x*arcsin(c*x) + 1/4*a*x^4*e^3 + a*d*x^3*e^2 + a*d^3*x + 3/4*sqrt(-c^2*x^2 + 1)*b*d^2*x*e/c + (c^2*x^2 - 1)*b*d*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*b*d^2*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d^3/c + b*d*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*a*d^2*e/c^2 + 3/4*b*d^2*arcsin(c*x)*e/c^2 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*x*e^3/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d*e^2/c^3 + 1/4*(c^2*x^2 - 1)^2*b*arcsin(c*x)*e^3/c^4 + 5/32*sqrt(-c^2*x^2 + 1)*b*x*e^3/c^3 + sqrt(-c^2*x^2 + 1)*b*d*e^2/c^3 + 1/2*(c^2*x^2 - 1)*b*arcsin(c*x)*e^3/c^4 + 5/32*b*arcsin(c*x)*e^3/c^4","A",0
2,1,193,0,0.265090," ","integrate((e*x+d)^2*(a+b*arcsin(c*x)),x, algorithm=""giac"")","b d^{2} x \arcsin\left(c x\right) + \frac{1}{3} \, a x^{3} e^{2} + a d^{2} x + \frac{\sqrt{-c^{2} x^{2} + 1} b d x e}{2 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d \arcsin\left(c x\right) e}{c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2}}{c} + \frac{b x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d e}{c^{2}} + \frac{b d \arcsin\left(c x\right) e}{2 \, c^{2}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b e^{2}}{9 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b e^{2}}{3 \, c^{3}}"," ",0,"b*d^2*x*arcsin(c*x) + 1/3*a*x^3*e^2 + a*d^2*x + 1/2*sqrt(-c^2*x^2 + 1)*b*d*x*e/c + 1/3*(c^2*x^2 - 1)*b*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*b*d*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d^2/c + 1/3*b*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*a*d*e/c^2 + 1/2*b*d*arcsin(c*x)*e/c^2 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*e^2/c^3 + 1/3*sqrt(-c^2*x^2 + 1)*b*e^2/c^3","A",0
3,1,102,0,0.372271," ","integrate((e*x+d)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","b d x \arcsin\left(c x\right) + a d x + \frac{\sqrt{-c^{2} x^{2} + 1} b x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d}{c} + \frac{{\left(c^{2} x^{2} - 1\right)} a e}{2 \, c^{2}} + \frac{b \arcsin\left(c x\right) e}{4 \, c^{2}}"," ",0,"b*d*x*arcsin(c*x) + a*d*x + 1/4*sqrt(-c^2*x^2 + 1)*b*x*e/c + 1/2*(c^2*x^2 - 1)*b*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d/c + 1/2*(c^2*x^2 - 1)*a*e/c^2 + 1/4*b*arcsin(c*x)*e/c^2","A",0
4,1,29,0,0.294796," ","integrate(a+b*arcsin(c*x),x, algorithm=""giac"")","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=""giac"")","\int \frac{b \arcsin\left(c x\right) + a}{e x + d}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)/(e*x + d), x)","F",0
6,1,204,0,0.391279," ","integrate((a+b*arcsin(c*x))/(e*x+d)^2,x, algorithm=""giac"")","-\frac{{\left(\frac{2 \, c^{2} \arctan\left(\frac{\frac{c d {\left(\sqrt{-{\left(x e + d\right)}^{2} {\left(c - \frac{c d}{x e + d}\right)}^{2} e^{\left(-2\right)} + 1} - 1\right)} e}{{\left(x e + d\right)} {\left(c - \frac{c d}{x e + d}\right)}} - e}{\sqrt{c^{2} d^{2} - e^{2}}}\right) e^{\left(-3\right)}}{\sqrt{c^{2} d^{2} - e^{2}}} + \frac{c^{2} \arcsin\left({\left({\left(\frac{{\left(x e + d\right)} {\left(c - \frac{c d}{x e + d}\right)} e}{c} + d e\right)} e^{\left(-1\right)} - d\right)} c e^{\left(-1\right)}\right) e^{\left(-3\right)}}{{\left(x e + d\right)} {\left(c - \frac{c d}{x e + d}\right)} + c d}\right)} b e^{2}}{c} - \frac{a e^{\left(-1\right)}}{x e + d}"," ",0,"-(2*c^2*arctan((c*d*(sqrt(-(x*e + d)^2*(c - c*d/(x*e + d))^2*e^(-2) + 1) - 1)*e/((x*e + d)*(c - c*d/(x*e + d))) - e)/sqrt(c^2*d^2 - e^2))*e^(-3)/sqrt(c^2*d^2 - e^2) + c^2*arcsin((((x*e + d)*(c - c*d/(x*e + d))*e/c + d*e)*e^(-1) - d)*c*e^(-1))*e^(-3)/((x*e + d)*(c - c*d/(x*e + d)) + c*d))*b*e^2/c - a*e^(-1)/(x*e + d)","B",0
7,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x\right) + a}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)/(e*x + d)^3, x)","F",0
8,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x\right) + a}{{\left(e x + d\right)}^{4}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)/(e*x + d)^4, x)","F",0
9,1,800,0,0.478053," ","integrate((e*x+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","b^{2} d^{3} x \arcsin\left(c x\right)^{2} + 2 \, a b d^{3} x \arcsin\left(c x\right) + \frac{1}{4} \, a^{2} x^{4} e^{3} + a^{2} d x^{3} e^{2} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d^{2} x \arcsin\left(c x\right) e}{2 \, c} + a^{2} d^{3} x - 2 \, b^{2} d^{3} x + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d x \arcsin\left(c x\right)^{2} e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d^{2} \arcsin\left(c x\right)^{2} e}{2 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d^{3} \arcsin\left(c x\right)}{c} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} a b d^{2} x e}{2 \, c} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b d x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{b^{2} d x \arcsin\left(c x\right)^{2} e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a b d^{2} \arcsin\left(c x\right) e}{c^{2}} + \frac{3 \, b^{2} d^{2} \arcsin\left(c x\right)^{2} e}{4 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d^{3}}{c} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d x e^{2}}{9 \, c^{2}} + \frac{2 \, a b d x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a^{2} d^{2} e}{2 \, c^{2}} - \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d^{2} e}{4 \, c^{2}} + \frac{3 \, a b d^{2} \arcsin\left(c x\right) e}{2 \, c^{2}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} x \arcsin\left(c x\right) e^{3}}{8 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} d \arcsin\left(c x\right) e^{2}}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} \arcsin\left(c x\right)^{2} e^{3}}{4 \, c^{4}} - \frac{14 \, b^{2} d x e^{2}}{9 \, c^{2}} - \frac{3 \, b^{2} d^{2} e}{8 \, c^{2}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b x e^{3}}{8 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b^{2} x \arcsin\left(c x\right) e^{3}}{16 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b d e^{2}}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d \arcsin\left(c x\right) e^{2}}{c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a b \arcsin\left(c x\right) e^{3}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} \arcsin\left(c x\right)^{2} e^{3}}{2 \, c^{4}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} a b x e^{3}}{16 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d e^{2}}{c^{3}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} e^{3}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b \arcsin\left(c x\right) e^{3}}{c^{4}} + \frac{5 \, b^{2} \arcsin\left(c x\right)^{2} e^{3}}{32 \, c^{4}} - \frac{5 \, {\left(c^{2} x^{2} - 1\right)} b^{2} e^{3}}{32 \, c^{4}} + \frac{5 \, a b \arcsin\left(c x\right) e^{3}}{16 \, c^{4}} - \frac{17 \, b^{2} e^{3}}{256 \, c^{4}}"," ",0,"b^2*d^3*x*arcsin(c*x)^2 + 2*a*b*d^3*x*arcsin(c*x) + 1/4*a^2*x^4*e^3 + a^2*d*x^3*e^2 + 3/2*sqrt(-c^2*x^2 + 1)*b^2*d^2*x*arcsin(c*x)*e/c + a^2*d^3*x - 2*b^2*d^3*x + (c^2*x^2 - 1)*b^2*d*x*arcsin(c*x)^2*e^2/c^2 + 3/2*(c^2*x^2 - 1)*b^2*d^2*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*b^2*d^3*arcsin(c*x)/c + 3/2*sqrt(-c^2*x^2 + 1)*a*b*d^2*x*e/c + 2*(c^2*x^2 - 1)*a*b*d*x*arcsin(c*x)*e^2/c^2 + b^2*d*x*arcsin(c*x)^2*e^2/c^2 + 3*(c^2*x^2 - 1)*a*b*d^2*arcsin(c*x)*e/c^2 + 3/4*b^2*d^2*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*a*b*d^3/c - 2/9*(c^2*x^2 - 1)*b^2*d*x*e^2/c^2 + 2*a*b*d*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*a^2*d^2*e/c^2 - 3/4*(c^2*x^2 - 1)*b^2*d^2*e/c^2 + 3/2*a*b*d^2*arcsin(c*x)*e/c^2 - 1/8*(-c^2*x^2 + 1)^(3/2)*b^2*x*arcsin(c*x)*e^3/c^3 - 2/3*(-c^2*x^2 + 1)^(3/2)*b^2*d*arcsin(c*x)*e^2/c^3 + 1/4*(c^2*x^2 - 1)^2*b^2*arcsin(c*x)^2*e^3/c^4 - 14/9*b^2*d*x*e^2/c^2 - 3/8*b^2*d^2*e/c^2 - 1/8*(-c^2*x^2 + 1)^(3/2)*a*b*x*e^3/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*b^2*x*arcsin(c*x)*e^3/c^3 - 2/3*(-c^2*x^2 + 1)^(3/2)*a*b*d*e^2/c^3 + 2*sqrt(-c^2*x^2 + 1)*b^2*d*arcsin(c*x)*e^2/c^3 + 1/2*(c^2*x^2 - 1)^2*a*b*arcsin(c*x)*e^3/c^4 + 1/2*(c^2*x^2 - 1)*b^2*arcsin(c*x)^2*e^3/c^4 + 5/16*sqrt(-c^2*x^2 + 1)*a*b*x*e^3/c^3 + 2*sqrt(-c^2*x^2 + 1)*a*b*d*e^2/c^3 - 1/32*(c^2*x^2 - 1)^2*b^2*e^3/c^4 + (c^2*x^2 - 1)*a*b*arcsin(c*x)*e^3/c^4 + 5/32*b^2*arcsin(c*x)^2*e^3/c^4 - 5/32*(c^2*x^2 - 1)*b^2*e^3/c^4 + 5/16*a*b*arcsin(c*x)*e^3/c^4 - 17/256*b^2*e^3/c^4","B",0
10,1,485,0,0.358477," ","integrate((e*x+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","b^{2} d^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b d^{2} x \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} x^{3} e^{2} + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} d x \arcsin\left(c x\right) e}{c} + a^{2} d^{2} x - 2 \, b^{2} d^{2} x + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} x \arcsin\left(c x\right)^{2} e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d \arcsin\left(c x\right)^{2} e}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d^{2} \arcsin\left(c x\right)}{c} + \frac{\sqrt{-c^{2} x^{2} + 1} a b d x e}{c} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{b^{2} x \arcsin\left(c x\right)^{2} e^{2}}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b d \arcsin\left(c x\right) e}{c^{2}} + \frac{b^{2} d \arcsin\left(c x\right)^{2} e}{2 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d^{2}}{c} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} x e^{2}}{27 \, c^{2}} + \frac{2 \, a b x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} d e}{c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d e}{2 \, c^{2}} + \frac{a b d \arcsin\left(c x\right) e}{c^{2}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} \arcsin\left(c x\right) e^{2}}{9 \, c^{3}} - \frac{14 \, b^{2} x e^{2}}{27 \, c^{2}} - \frac{b^{2} d e}{4 \, c^{2}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b e^{2}}{9 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} \arcsin\left(c x\right) e^{2}}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b e^{2}}{3 \, c^{3}}"," ",0,"b^2*d^2*x*arcsin(c*x)^2 + 2*a*b*d^2*x*arcsin(c*x) + 1/3*a^2*x^3*e^2 + sqrt(-c^2*x^2 + 1)*b^2*d*x*arcsin(c*x)*e/c + a^2*d^2*x - 2*b^2*d^2*x + 1/3*(c^2*x^2 - 1)*b^2*x*arcsin(c*x)^2*e^2/c^2 + (c^2*x^2 - 1)*b^2*d*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*b^2*d^2*arcsin(c*x)/c + sqrt(-c^2*x^2 + 1)*a*b*d*x*e/c + 2/3*(c^2*x^2 - 1)*a*b*x*arcsin(c*x)*e^2/c^2 + 1/3*b^2*x*arcsin(c*x)^2*e^2/c^2 + 2*(c^2*x^2 - 1)*a*b*d*arcsin(c*x)*e/c^2 + 1/2*b^2*d*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*a*b*d^2/c - 2/27*(c^2*x^2 - 1)*b^2*x*e^2/c^2 + 2/3*a*b*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*a^2*d*e/c^2 - 1/2*(c^2*x^2 - 1)*b^2*d*e/c^2 + a*b*d*arcsin(c*x)*e/c^2 - 2/9*(-c^2*x^2 + 1)^(3/2)*b^2*arcsin(c*x)*e^2/c^3 - 14/27*b^2*x*e^2/c^2 - 1/4*b^2*d*e/c^2 - 2/9*(-c^2*x^2 + 1)^(3/2)*a*b*e^2/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b^2*arcsin(c*x)*e^2/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*a*b*e^2/c^3","B",0
11,1,253,0,0.428950," ","integrate((e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","b^{2} d x \arcsin\left(c x\right)^{2} + 2 \, a b d x \arcsin\left(c x\right) + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} x \arcsin\left(c x\right) e}{2 \, c} + a^{2} d x - 2 \, b^{2} d x + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} \arcsin\left(c x\right)^{2} e}{2 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d \arcsin\left(c x\right)}{c} + \frac{\sqrt{-c^{2} x^{2} + 1} a b x e}{2 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} a b \arcsin\left(c x\right) e}{c^{2}} + \frac{b^{2} \arcsin\left(c x\right)^{2} e}{4 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d}{c} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} e}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} e}{4 \, c^{2}} + \frac{a b \arcsin\left(c x\right) e}{2 \, c^{2}} - \frac{b^{2} e}{8 \, c^{2}}"," ",0,"b^2*d*x*arcsin(c*x)^2 + 2*a*b*d*x*arcsin(c*x) + 1/2*sqrt(-c^2*x^2 + 1)*b^2*x*arcsin(c*x)*e/c + a^2*d*x - 2*b^2*d*x + 1/2*(c^2*x^2 - 1)*b^2*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*b^2*d*arcsin(c*x)/c + 1/2*sqrt(-c^2*x^2 + 1)*a*b*x*e/c + (c^2*x^2 - 1)*a*b*arcsin(c*x)*e/c^2 + 1/4*b^2*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*a*b*d/c + 1/2*(c^2*x^2 - 1)*a^2*e/c^2 - 1/4*(c^2*x^2 - 1)*b^2*e/c^2 + 1/2*a*b*arcsin(c*x)*e/c^2 - 1/8*b^2*e/c^2","A",0
12,1,75,0,0.320508," ","integrate((a+b*arcsin(c*x))^2,x, algorithm=""giac"")","b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x - 2 \, b^{2} x + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} \arcsin\left(c x\right)}{c} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b}{c}"," ",0,"b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x - 2*b^2*x + 2*sqrt(-c^2*x^2 + 1)*b^2*arcsin(c*x)/c + 2*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=""giac"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}{e x + d}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2/(e*x + d), x)","F",0
14,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2/(e*x + d)^2, x)","F",0
15,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2/(e*x + d)^3, x)","F",0
16,1,598,0,0.477460," ","integrate((e*x+d)^3/(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{d^{3} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} - \frac{3 \, d^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e \sin\left(\frac{a}{b}\right)}{b c^{2}} + \frac{3 \, d^{2} \cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b c^{2}} + \frac{d^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} - \frac{3 \, d \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2}}{b c^{3}} - \frac{3 \, d \cos\left(\frac{a}{b}\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{b c^{3}} + \frac{\cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(c x\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b c^{4}} - \frac{\cos\left(\frac{a}{b}\right)^{4} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(c x\right)\right)}{b c^{4}} - \frac{3 \, d^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{2 \, b c^{2}} + \frac{9 \, d \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2}}{4 \, b c^{3}} + \frac{3 \, d \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) e^{2}}{4 \, b c^{3}} + \frac{3 \, d e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{4 \, b c^{3}} + \frac{3 \, d e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{4 \, b c^{3}} - \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(c x\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{2 \, b c^{4}} - \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{2 \, b c^{4}} + \frac{\cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(c x\right)\right)}{b c^{4}} + \frac{\cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{2 \, b c^{4}} - \frac{e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(c x\right)\right)}{8 \, b c^{4}} - \frac{e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{4 \, b c^{4}}"," ",0,"d^3*cos(a/b)*cos_integral(a/b + arcsin(c*x))/(b*c) - 3*d^2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(c*x))*e*sin(a/b)/(b*c^2) + 3*d^2*cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^2) + d^3*sin(a/b)*sin_integral(a/b + arcsin(c*x))/(b*c) - 3*d*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(c*x))*e^2/(b*c^3) - 3*d*cos(a/b)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(c*x))/(b*c^3) + cos(a/b)^3*cos_integral(4*a/b + 4*arcsin(c*x))*e^3*sin(a/b)/(b*c^4) - cos(a/b)^4*e^3*sin_integral(4*a/b + 4*arcsin(c*x))/(b*c^4) - 3/2*d^2*e*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^2) + 9/4*d*cos(a/b)*cos_integral(3*a/b + 3*arcsin(c*x))*e^2/(b*c^3) + 3/4*d*cos(a/b)*cos_integral(a/b + arcsin(c*x))*e^2/(b*c^3) + 3/4*d*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(c*x))/(b*c^3) + 3/4*d*e^2*sin(a/b)*sin_integral(a/b + arcsin(c*x))/(b*c^3) - 1/2*cos(a/b)*cos_integral(4*a/b + 4*arcsin(c*x))*e^3*sin(a/b)/(b*c^4) - 1/2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(c*x))*e^3*sin(a/b)/(b*c^4) + cos(a/b)^2*e^3*sin_integral(4*a/b + 4*arcsin(c*x))/(b*c^4) + 1/2*cos(a/b)^2*e^3*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^4) - 1/8*e^3*sin_integral(4*a/b + 4*arcsin(c*x))/(b*c^4) - 1/4*e^3*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^4)","A",0
17,1,334,0,0.371376," ","integrate((e*x+d)^2/(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{d^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} - \frac{2 \, d \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e \sin\left(\frac{a}{b}\right)}{b c^{2}} + \frac{2 \, d \cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b c^{2}} + \frac{d^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} - \frac{\cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2}}{b c^{3}} - \frac{\cos\left(\frac{a}{b}\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{b c^{3}} - \frac{d e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b c^{2}} + \frac{3 \, \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2}}{4 \, b c^{3}} + \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) e^{2}}{4 \, b c^{3}} + \frac{e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{4 \, b c^{3}} + \frac{e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{4 \, b c^{3}}"," ",0,"d^2*cos(a/b)*cos_integral(a/b + arcsin(c*x))/(b*c) - 2*d*cos(a/b)*cos_integral(2*a/b + 2*arcsin(c*x))*e*sin(a/b)/(b*c^2) + 2*d*cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^2) + d^2*sin(a/b)*sin_integral(a/b + arcsin(c*x))/(b*c) - cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(c*x))*e^2/(b*c^3) - cos(a/b)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(c*x))/(b*c^3) - d*e*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^2) + 3/4*cos(a/b)*cos_integral(3*a/b + 3*arcsin(c*x))*e^2/(b*c^3) + 1/4*cos(a/b)*cos_integral(a/b + arcsin(c*x))*e^2/(b*c^3) + 1/4*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(c*x))/(b*c^3) + 1/4*e^2*sin(a/b)*sin_integral(a/b + arcsin(c*x))/(b*c^3)","A",0
18,1,142,0,0.412402," ","integrate((e*x+d)/(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{d \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} - \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e \sin\left(\frac{a}{b}\right)}{b c^{2}} + \frac{\cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b c^{2}} + \frac{d \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} - \frac{e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{2 \, b c^{2}}"," ",0,"d*cos(a/b)*cos_integral(a/b + arcsin(c*x))/(b*c) - cos(a/b)*cos_integral(2*a/b + 2*arcsin(c*x))*e*sin(a/b)/(b*c^2) + cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^2) + d*sin(a/b)*sin_integral(a/b + arcsin(c*x))/(b*c) - 1/2*e*sin_integral(2*a/b + 2*arcsin(c*x))/(b*c^2)","A",0
19,1,49,0,0.354679," ","integrate(1/(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c} + \frac{\sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b c}"," ",0,"cos(a/b)*cos_integral(a/b + arcsin(c*x))/(b*c) + sin(a/b)*sin_integral(a/b + arcsin(c*x))/(b*c)","A",0
20,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arcsin(c*x)),x, algorithm=""giac"")","\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=""giac"")","\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
22,1,1269,0,0.460567," ","integrate((e*x+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\frac{4 \, b c d \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{b c^{2} d^{2} \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{4 \, b c d \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{b c^{2} d^{2} \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{4 \, a c d \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{a c^{2} d^{2} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{3 \, b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{3 \, b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{4 \, a c d \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{a c^{2} d^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b c^{2} d x e}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{2 \, b c d \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{3 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{3 \, a \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{\sqrt{-c^{2} x^{2} + 1} b c^{2} d^{2}}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{2 \, a c d \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} + \frac{3 \, b \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} + \frac{b \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} - \frac{9 \, b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} - \frac{b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} + \frac{3 \, a \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} + \frac{a \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} - \frac{9 \, a \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(c x\right)\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} - \frac{a \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{4 \, {\left(b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}\right)}} + \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b e^{2}}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}} - \frac{\sqrt{-c^{2} x^{2} + 1} b e^{2}}{b^{3} c^{3} \arcsin\left(c x\right) + a b^{2} c^{3}}"," ",0,"4*b*c*d*arcsin(c*x)*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + b*c^2*d^2*arcsin(c*x)*cos_integral(a/b + arcsin(c*x))*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 4*b*c*d*arcsin(c*x)*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - b*c^2*d^2*arcsin(c*x)*cos(a/b)*sin_integral(a/b + arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 4*a*c*d*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + a*c^2*d^2*cos_integral(a/b + arcsin(c*x))*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 3*b*arcsin(c*x)*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(c*x))*e^2*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 3*b*arcsin(c*x)*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 4*a*c*d*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - a*c^2*d^2*cos(a/b)*sin_integral(a/b + arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 2*sqrt(-c^2*x^2 + 1)*b*c^2*d*x*e/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 2*b*c*d*arcsin(c*x)*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 3*a*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(c*x))*e^2*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 3*a*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - sqrt(-c^2*x^2 + 1)*b*c^2*d^2/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 2*a*c*d*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 3/4*b*arcsin(c*x)*cos_integral(3*a/b + 3*arcsin(c*x))*e^2*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 1/4*b*arcsin(c*x)*cos_integral(a/b + arcsin(c*x))*e^2*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 9/4*b*arcsin(c*x)*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 1/4*b*arcsin(c*x)*cos(a/b)*e^2*sin_integral(a/b + arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 3/4*a*cos_integral(3*a/b + 3*arcsin(c*x))*e^2*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + 1/4*a*cos_integral(a/b + arcsin(c*x))*e^2*sin(a/b)/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 9/4*a*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - 1/4*a*cos(a/b)*e^2*sin_integral(a/b + arcsin(c*x))/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) + (-c^2*x^2 + 1)^(3/2)*b*e^2/(b^3*c^3*arcsin(c*x) + a*b^2*c^3) - sqrt(-c^2*x^2 + 1)*b*e^2/(b^3*c^3*arcsin(c*x) + a*b^2*c^3)","B",0
23,1,561,0,0.494130," ","integrate((e*x+d)/(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\frac{2 \, b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} + \frac{b c d \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} + \frac{2 \, b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} - \frac{b c d \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} + \frac{2 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} + \frac{a c d \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} + \frac{2 \, a \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right)}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} - \frac{a c d \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} - \frac{\sqrt{-c^{2} x^{2} + 1} b c x e}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} - \frac{b \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} - \frac{\sqrt{-c^{2} x^{2} + 1} b c d}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}} - \frac{a \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(c x\right)\right) e}{b^{3} c^{2} \arcsin\left(c x\right) + a b^{2} c^{2}}"," ",0,"2*b*arcsin(c*x)*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) + b*c*d*arcsin(c*x)*cos_integral(a/b + arcsin(c*x))*sin(a/b)/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) + 2*b*arcsin(c*x)*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(c*x))/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) - b*c*d*arcsin(c*x)*cos(a/b)*sin_integral(a/b + arcsin(c*x))/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) + 2*a*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) + a*c*d*cos_integral(a/b + arcsin(c*x))*sin(a/b)/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) + 2*a*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(c*x))/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) - a*c*d*cos(a/b)*sin_integral(a/b + arcsin(c*x))/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) - sqrt(-c^2*x^2 + 1)*b*c*x*e/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) - b*arcsin(c*x)*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) - sqrt(-c^2*x^2 + 1)*b*c*d/(b^3*c^2*arcsin(c*x) + a*b^2*c^2) - a*cos_integral(2*a/b + 2*arcsin(c*x))*e/(b^3*c^2*arcsin(c*x) + a*b^2*c^2)","B",0
24,1,192,0,0.413274," ","integrate(1/(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\frac{b \arcsin\left(c x\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} c \arcsin\left(c x\right) + a b^{2} c} - \frac{b \arcsin\left(c x\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b^{3} c \arcsin\left(c x\right) + a b^{2} c} + \frac{a \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(c x\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} c \arcsin\left(c x\right) + a b^{2} c} - \frac{a \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(c x\right)\right)}{b^{3} c \arcsin\left(c x\right) + a b^{2} c} - \frac{\sqrt{-c^{2} x^{2} + 1} b}{b^{3} c \arcsin\left(c x\right) + a b^{2} c}"," ",0,"b*arcsin(c*x)*cos_integral(a/b + arcsin(c*x))*sin(a/b)/(b^3*c*arcsin(c*x) + a*b^2*c) - b*arcsin(c*x)*cos(a/b)*sin_integral(a/b + arcsin(c*x))/(b^3*c*arcsin(c*x) + a*b^2*c) + a*cos_integral(a/b + arcsin(c*x))*sin(a/b)/(b^3*c*arcsin(c*x) + a*b^2*c) - a*cos(a/b)*sin_integral(a/b + arcsin(c*x))/(b^3*c*arcsin(c*x) + a*b^2*c) - sqrt(-c^2*x^2 + 1)*b/(b^3*c*arcsin(c*x) + a*b^2*c)","B",0
25,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(e x + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*x + d)*(b*arcsin(c*x) + a)^2), x)","F",0
26,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(e x + d\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*x + d)^2*(b*arcsin(c*x) + a)^2), x)","F",0
27,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x\right) + a\right)}^{2} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2*(e*x + d)^m, x)","F",0
28,0,0,0,0.000000," ","integrate((e*x+d)^m*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x\right) + a\right)} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*(e*x + d)^m, x)","F",0
29,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arcsin(c*x)),x, algorithm=""giac"")","\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
30,0,0,0,0.000000," ","integrate((e*x+d)^m/(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(b \arcsin\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(b*arcsin(c*x) + a)^2, x)","F",0
31,-2,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
32,-2,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
33,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
36,-2,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
37,-2,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
38,-2,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
40,-2,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
41,-2,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
42,-2,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","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=""giac"")","\int \frac{{\left(g x + f\right)}^{3} {\left(b \arcsin\left(c x\right) + a\right)}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((g*x + f)^3*(b*arcsin(c*x) + a)/sqrt(-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=""giac"")","\int \frac{{\left(g x + f\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((g*x + f)^2*(b*arcsin(c*x) + a)/sqrt(-c^2*d*x^2 + d), x)","F",0
46,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/sqrt(-c^2*d*x^2 + d), x)","F",0
47,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",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=""giac"")","\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,-2,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
50,-2,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
51,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
52,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",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=""giac"")","\int \frac{{\left(g x + f\right)}^{4} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)^4*(b*arcsin(c*x) + a)/(-c^2*d*x^2 + d)^(5/2), x)","F",0
54,0,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)}^{3} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)^3*(b*arcsin(c*x) + a)/(-c^2*d*x^2 + d)^(5/2), x)","F",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=""giac"")","\int \frac{{\left(g x + f\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)^2*(b*arcsin(c*x) + a)/(-c^2*d*x^2 + d)^(5/2), x)","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=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/(-c^2*d*x^2 + d)^(5/2), x)","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=""giac"")","\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,-2,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
59,-2,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
60,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
62,-2,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
63,-2,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
64,-2,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
66,-2,0,0,0.000000," ","integrate((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
67,-2,0,0,0.000000," ","integrate((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
68,-2,0,0,0.000000," ","integrate((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","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=""giac"")","\int \frac{{\left(g x + f\right)}^{3} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((g*x + f)^3*(b*arcsin(c*x) + a)^2/sqrt(-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=""giac"")","\int \frac{{\left(g x + f\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((g*x + f)^2*(b*arcsin(c*x) + a)^2/sqrt(-c^2*d*x^2 + d), x)","F",0
72,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)^2/sqrt(-c^2*d*x^2 + d), x)","F",0
73,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",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=""giac"")","\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,-2,0,0,0.000000," ","integrate((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
76,-2,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
77,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
78,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^4-1)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",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=""giac"")","\int \frac{{\left(g x + f\right)}^{3} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)^3*(b*arcsin(c*x) + a)^2/(-c^2*d*x^2 + d)^(5/2), x)","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=""giac"")","\int \frac{{\left(g x + f\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)^2*(b*arcsin(c*x) + a)^2/(-c^2*d*x^2 + d)^(5/2), x)","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=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)^2/(-c^2*d*x^2 + d)^(5/2), x)","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=""giac"")","\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
83,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^3*log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{3} \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)^3*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","F",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=""giac"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} \log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","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=""giac"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} \log\left({\left(g x + f\right)}^{m} h\right)}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*log((g*x + f)^m*h)/sqrt(-c^2*x^2 + 1), x)","F",0
86,0,0,0,0.000000," ","integrate(log(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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
88,1,769,0,0.418337," ","integrate((e*x+d)^3*(g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{5} \, a g x^{5} e^{3} + \frac{3}{4} \, a d g x^{4} e^{2} + a d^{2} g x^{3} e + b d^{3} f x \arcsin\left(c x\right) + \frac{1}{4} \, a f x^{4} e^{3} + a d f x^{3} e^{2} + a d^{3} f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} g x \arcsin\left(c x\right) e}{c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} g x}{4 \, c} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} f x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{3} g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d f x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{b d^{2} g x \arcsin\left(c x\right) e}{c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} f}{c} + \frac{{\left(c^{2} x^{2} - 1\right)} a d^{3} g}{2 \, c^{2}} + \frac{b d^{3} g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{b d f x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a d^{2} f e}{2 \, c^{2}} + \frac{3 \, b d^{2} f \arcsin\left(c x\right) e}{4 \, c^{2}} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d g x e^{2}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} g e}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d g \arcsin\left(c x\right) e^{2}}{4 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b f x e^{3}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d f e^{2}}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b d g x e^{2}}{32 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} g e}{c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b f \arcsin\left(c x\right) e^{3}}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d g \arcsin\left(c x\right) e^{2}}{2 \, c^{4}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b f x e^{3}}{32 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f e^{2}}{c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f \arcsin\left(c x\right) e^{3}}{2 \, c^{4}} + \frac{b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{15 \, b d g \arcsin\left(c x\right) e^{2}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b g e^{3}}{25 \, c^{5}} + \frac{5 \, b f \arcsin\left(c x\right) e^{3}}{32 \, c^{4}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g e^{3}}{15 \, c^{5}} + \frac{\sqrt{-c^{2} x^{2} + 1} b g e^{3}}{5 \, c^{5}}"," ",0,"1/5*a*g*x^5*e^3 + 3/4*a*d*g*x^4*e^2 + a*d^2*g*x^3*e + b*d^3*f*x*arcsin(c*x) + 1/4*a*f*x^4*e^3 + a*d*f*x^3*e^2 + a*d^3*f*x + (c^2*x^2 - 1)*b*d^2*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d^3*g*x/c + 3/4*sqrt(-c^2*x^2 + 1)*b*d^2*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d^3*g*arcsin(c*x)/c^2 + (c^2*x^2 - 1)*b*d*f*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*b*d^2*f*arcsin(c*x)*e/c^2 + b*d^2*g*x*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d^3*f/c + 1/2*(c^2*x^2 - 1)*a*d^3*g/c^2 + 1/4*b*d^3*g*arcsin(c*x)/c^2 + b*d*f*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*a*d^2*f*e/c^2 + 3/4*b*d^2*f*arcsin(c*x)*e/c^2 - 3/16*(-c^2*x^2 + 1)^(3/2)*b*d*g*x*e^2/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d^2*g*e/c^3 + 1/5*(c^2*x^2 - 1)^2*b*g*x*arcsin(c*x)*e^3/c^4 + 3/4*(c^2*x^2 - 1)^2*b*d*g*arcsin(c*x)*e^2/c^4 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*f*x*e^3/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d*f*e^2/c^3 + 15/32*sqrt(-c^2*x^2 + 1)*b*d*g*x*e^2/c^3 + sqrt(-c^2*x^2 + 1)*b*d^2*g*e/c^3 + 1/4*(c^2*x^2 - 1)^2*b*f*arcsin(c*x)*e^3/c^4 + 2/5*(c^2*x^2 - 1)*b*g*x*arcsin(c*x)*e^3/c^4 + 3/2*(c^2*x^2 - 1)*b*d*g*arcsin(c*x)*e^2/c^4 + 5/32*sqrt(-c^2*x^2 + 1)*b*f*x*e^3/c^3 + sqrt(-c^2*x^2 + 1)*b*d*f*e^2/c^3 + 1/2*(c^2*x^2 - 1)*b*f*arcsin(c*x)*e^3/c^4 + 1/5*b*g*x*arcsin(c*x)*e^3/c^4 + 15/32*b*d*g*arcsin(c*x)*e^2/c^4 + 1/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*g*e^3/c^5 + 5/32*b*f*arcsin(c*x)*e^3/c^4 - 2/15*(-c^2*x^2 + 1)^(3/2)*b*g*e^3/c^5 + 1/5*sqrt(-c^2*x^2 + 1)*b*g*e^3/c^5","B",0
89,1,489,0,0.437997," ","integrate((e*x+d)^2*(g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{4} \, a g x^{4} e^{2} + \frac{2}{3} \, a d g x^{3} e + b d^{2} f x \arcsin\left(c x\right) + \frac{1}{3} \, a f x^{3} e^{2} + a d^{2} f x + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b d g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} g x}{4 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f x e}{2 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d f \arcsin\left(c x\right) e}{c^{2}} + \frac{2 \, b d g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} f}{c} + \frac{{\left(c^{2} x^{2} - 1\right)} a d^{2} g}{2 \, c^{2}} + \frac{b d^{2} g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{b f x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d f e}{c^{2}} + \frac{b d f \arcsin\left(c x\right) e}{2 \, c^{2}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g x e^{2}}{16 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d g e}{9 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b g \arcsin\left(c x\right) e^{2}}{4 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b f e^{2}}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b g x e^{2}}{32 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b d g e}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b g \arcsin\left(c x\right) e^{2}}{2 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b f e^{2}}{3 \, c^{3}} + \frac{5 \, b g \arcsin\left(c x\right) e^{2}}{32 \, c^{4}}"," ",0,"1/4*a*g*x^4*e^2 + 2/3*a*d*g*x^3*e + b*d^2*f*x*arcsin(c*x) + 1/3*a*f*x^3*e^2 + a*d^2*f*x + 2/3*(c^2*x^2 - 1)*b*d*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d^2*g*x/c + 1/2*sqrt(-c^2*x^2 + 1)*b*d*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d^2*g*arcsin(c*x)/c^2 + 1/3*(c^2*x^2 - 1)*b*f*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*b*d*f*arcsin(c*x)*e/c^2 + 2/3*b*d*g*x*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d^2*f/c + 1/2*(c^2*x^2 - 1)*a*d^2*g/c^2 + 1/4*b*d^2*g*arcsin(c*x)/c^2 + 1/3*b*f*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*a*d*f*e/c^2 + 1/2*b*d*f*arcsin(c*x)*e/c^2 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*g*x*e^2/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b*d*g*e/c^3 + 1/4*(c^2*x^2 - 1)^2*b*g*arcsin(c*x)*e^2/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*f*e^2/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*g*x*e^2/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b*d*g*e/c^3 + 1/2*(c^2*x^2 - 1)*b*g*arcsin(c*x)*e^2/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*f*e^2/c^3 + 5/32*b*g*arcsin(c*x)*e^2/c^4","B",0
90,1,268,0,0.495273," ","integrate((e*x+d)*(g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{3} \, a g x^{3} e + b d f x \arcsin\left(c x\right) + a d f x + \frac{{\left(c^{2} x^{2} - 1\right)} b g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d g x}{4 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b f x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{b g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f}{c} + \frac{{\left(c^{2} x^{2} - 1\right)} a d g}{2 \, c^{2}} + \frac{b d g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a f e}{2 \, c^{2}} + \frac{b f \arcsin\left(c x\right) e}{4 \, c^{2}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g e}{9 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b g e}{3 \, c^{3}}"," ",0,"1/3*a*g*x^3*e + b*d*f*x*arcsin(c*x) + a*d*f*x + 1/3*(c^2*x^2 - 1)*b*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d*g*x/c + 1/4*sqrt(-c^2*x^2 + 1)*b*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d*g*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)*b*f*arcsin(c*x)*e/c^2 + 1/3*b*g*x*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d*f/c + 1/2*(c^2*x^2 - 1)*a*d*g/c^2 + 1/4*b*d*g*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)*a*f*e/c^2 + 1/4*b*f*arcsin(c*x)*e/c^2 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*g*e/c^3 + 1/3*sqrt(-c^2*x^2 + 1)*b*g*e/c^3","B",0
91,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{e x + d}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/(e*x + d), x)","F",0
92,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^2, x)","F",0
93,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^3, x)","F",0
94,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{4}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^4, x)","F",0
95,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 0.46sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
96,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^6,x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{6}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^6, x)","F",0
97,1,1313,0,0.504545," ","integrate((e*x+d)^3*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{6} \, a h x^{6} e^{3} + \frac{3}{5} \, a d h x^{5} e^{2} + \frac{3}{4} \, a d^{2} h x^{4} e + \frac{1}{3} \, a d^{3} h x^{3} + \frac{1}{5} \, a g x^{5} e^{3} + \frac{3}{4} \, a d g x^{4} e^{2} + a d^{2} g x^{3} e + b d^{3} f x \arcsin\left(c x\right) + \frac{1}{4} \, a f x^{4} e^{3} + a d f x^{3} e^{2} + a d^{3} f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{3} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} g x \arcsin\left(c x\right) e}{c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} g x}{4 \, c} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} f x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{3} g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{b d^{3} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d f x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{b d^{2} g x \arcsin\left(c x\right) e}{c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} f}{c} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} h x e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d^{3} g}{2 \, c^{2}} + \frac{b d^{3} g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{b d f x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a d^{2} f e}{2 \, c^{2}} + \frac{3 \, b d^{2} f \arcsin\left(c x\right) e}{4 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d^{2} h \arcsin\left(c x\right) e}{4 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{3} h}{9 \, c^{3}} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d g x e^{2}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} g e}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} h x e}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d g \arcsin\left(c x\right) e^{2}}{4 \, c^{4}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)} b d h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} h \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} h}{3 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b f x e^{3}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d f e^{2}}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b d g x e^{2}}{32 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} g e}{c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b f \arcsin\left(c x\right) e^{3}}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d g \arcsin\left(c x\right) e^{2}}{2 \, c^{4}} + \frac{3 \, b d h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{15 \, b d^{2} h \arcsin\left(c x\right) e}{32 \, c^{4}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b f x e^{3}}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b h x e^{3}}{36 \, c^{5}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f e^{2}}{c^{3}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b d h e^{2}}{25 \, c^{5}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f \arcsin\left(c x\right) e^{3}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b h \arcsin\left(c x\right) e^{3}}{6 \, c^{6}} + \frac{b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{15 \, b d g \arcsin\left(c x\right) e^{2}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b g e^{3}}{25 \, c^{5}} - \frac{13 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b h x e^{3}}{144 \, c^{5}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d h e^{2}}{5 \, c^{5}} + \frac{5 \, b f \arcsin\left(c x\right) e^{3}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b h \arcsin\left(c x\right) e^{3}}{2 \, c^{6}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g e^{3}}{15 \, c^{5}} + \frac{11 \, \sqrt{-c^{2} x^{2} + 1} b h x e^{3}}{96 \, c^{5}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d h e^{2}}{5 \, c^{5}} + \frac{{\left(c^{2} x^{2} - 1\right)} b h \arcsin\left(c x\right) e^{3}}{2 \, c^{6}} + \frac{\sqrt{-c^{2} x^{2} + 1} b g e^{3}}{5 \, c^{5}} + \frac{11 \, b h \arcsin\left(c x\right) e^{3}}{96 \, c^{6}}"," ",0,"1/6*a*h*x^6*e^3 + 3/5*a*d*h*x^5*e^2 + 3/4*a*d^2*h*x^4*e + 1/3*a*d^3*h*x^3 + 1/5*a*g*x^5*e^3 + 3/4*a*d*g*x^4*e^2 + a*d^2*g*x^3*e + b*d^3*f*x*arcsin(c*x) + 1/4*a*f*x^4*e^3 + a*d*f*x^3*e^2 + a*d^3*f*x + 1/3*(c^2*x^2 - 1)*b*d^3*h*x*arcsin(c*x)/c^2 + (c^2*x^2 - 1)*b*d^2*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d^3*g*x/c + 3/4*sqrt(-c^2*x^2 + 1)*b*d^2*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d^3*g*arcsin(c*x)/c^2 + 1/3*b*d^3*h*x*arcsin(c*x)/c^2 + (c^2*x^2 - 1)*b*d*f*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*b*d^2*f*arcsin(c*x)*e/c^2 + b*d^2*g*x*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d^3*f/c - 3/16*(-c^2*x^2 + 1)^(3/2)*b*d^2*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*a*d^3*g/c^2 + 1/4*b*d^3*g*arcsin(c*x)/c^2 + b*d*f*x*arcsin(c*x)*e^2/c^2 + 3/5*(c^2*x^2 - 1)^2*b*d*h*x*arcsin(c*x)*e^2/c^4 + 3/2*(c^2*x^2 - 1)*a*d^2*f*e/c^2 + 3/4*b*d^2*f*arcsin(c*x)*e/c^2 + 3/4*(c^2*x^2 - 1)^2*b*d^2*h*arcsin(c*x)*e/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*d^3*h/c^3 - 3/16*(-c^2*x^2 + 1)^(3/2)*b*d*g*x*e^2/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d^2*g*e/c^3 + 15/32*sqrt(-c^2*x^2 + 1)*b*d^2*h*x*e/c^3 + 1/5*(c^2*x^2 - 1)^2*b*g*x*arcsin(c*x)*e^3/c^4 + 3/4*(c^2*x^2 - 1)^2*b*d*g*arcsin(c*x)*e^2/c^4 + 6/5*(c^2*x^2 - 1)*b*d*h*x*arcsin(c*x)*e^2/c^4 + 3/2*(c^2*x^2 - 1)*b*d^2*h*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*d^3*h/c^3 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*f*x*e^3/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d*f*e^2/c^3 + 15/32*sqrt(-c^2*x^2 + 1)*b*d*g*x*e^2/c^3 + sqrt(-c^2*x^2 + 1)*b*d^2*g*e/c^3 + 1/4*(c^2*x^2 - 1)^2*b*f*arcsin(c*x)*e^3/c^4 + 2/5*(c^2*x^2 - 1)*b*g*x*arcsin(c*x)*e^3/c^4 + 3/2*(c^2*x^2 - 1)*b*d*g*arcsin(c*x)*e^2/c^4 + 3/5*b*d*h*x*arcsin(c*x)*e^2/c^4 + 15/32*b*d^2*h*arcsin(c*x)*e/c^4 + 5/32*sqrt(-c^2*x^2 + 1)*b*f*x*e^3/c^3 + 1/36*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*h*x*e^3/c^5 + sqrt(-c^2*x^2 + 1)*b*d*f*e^2/c^3 + 3/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*d*h*e^2/c^5 + 1/2*(c^2*x^2 - 1)*b*f*arcsin(c*x)*e^3/c^4 + 1/6*(c^2*x^2 - 1)^3*b*h*arcsin(c*x)*e^3/c^6 + 1/5*b*g*x*arcsin(c*x)*e^3/c^4 + 15/32*b*d*g*arcsin(c*x)*e^2/c^4 + 1/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*g*e^3/c^5 - 13/144*(-c^2*x^2 + 1)^(3/2)*b*h*x*e^3/c^5 - 2/5*(-c^2*x^2 + 1)^(3/2)*b*d*h*e^2/c^5 + 5/32*b*f*arcsin(c*x)*e^3/c^4 + 1/2*(c^2*x^2 - 1)^2*b*h*arcsin(c*x)*e^3/c^6 - 2/15*(-c^2*x^2 + 1)^(3/2)*b*g*e^3/c^5 + 11/96*sqrt(-c^2*x^2 + 1)*b*h*x*e^3/c^5 + 3/5*sqrt(-c^2*x^2 + 1)*b*d*h*e^2/c^5 + 1/2*(c^2*x^2 - 1)*b*h*arcsin(c*x)*e^3/c^6 + 1/5*sqrt(-c^2*x^2 + 1)*b*g*e^3/c^5 + 11/96*b*h*arcsin(c*x)*e^3/c^6","B",0
98,1,844,0,0.538678," ","integrate((e*x+d)^2*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{5} \, a h x^{5} e^{2} + \frac{1}{2} \, a d h x^{4} e + \frac{1}{3} \, a d^{2} h x^{3} + \frac{1}{4} \, a g x^{4} e^{2} + \frac{2}{3} \, a d g x^{3} e + b d^{2} f x \arcsin\left(c x\right) + \frac{1}{3} \, a f x^{3} e^{2} + a d^{2} f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b d g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} g x}{4 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f x e}{2 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{b d^{2} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d f \arcsin\left(c x\right) e}{c^{2}} + \frac{2 \, b d g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} f}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d h x e}{8 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d^{2} g}{2 \, c^{2}} + \frac{b d^{2} g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{b f x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d f e}{c^{2}} + \frac{b d f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b d h \arcsin\left(c x\right) e}{2 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} h}{9 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g x e^{2}}{16 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d g e}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b d h x e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b g \arcsin\left(c x\right) e^{2}}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d h \arcsin\left(c x\right) e}{c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} h}{3 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b f e^{2}}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b g x e^{2}}{32 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b d g e}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b g \arcsin\left(c x\right) e^{2}}{2 \, c^{4}} + \frac{b h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{5 \, b d h \arcsin\left(c x\right) e}{16 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b f e^{2}}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b h e^{2}}{25 \, c^{5}} + \frac{5 \, b g \arcsin\left(c x\right) e^{2}}{32 \, c^{4}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b h e^{2}}{15 \, c^{5}} + \frac{\sqrt{-c^{2} x^{2} + 1} b h e^{2}}{5 \, c^{5}}"," ",0,"1/5*a*h*x^5*e^2 + 1/2*a*d*h*x^4*e + 1/3*a*d^2*h*x^3 + 1/4*a*g*x^4*e^2 + 2/3*a*d*g*x^3*e + b*d^2*f*x*arcsin(c*x) + 1/3*a*f*x^3*e^2 + a*d^2*f*x + 1/3*(c^2*x^2 - 1)*b*d^2*h*x*arcsin(c*x)/c^2 + 2/3*(c^2*x^2 - 1)*b*d*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d^2*g*x/c + 1/2*sqrt(-c^2*x^2 + 1)*b*d*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d^2*g*arcsin(c*x)/c^2 + 1/3*b*d^2*h*x*arcsin(c*x)/c^2 + 1/3*(c^2*x^2 - 1)*b*f*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*b*d*f*arcsin(c*x)*e/c^2 + 2/3*b*d*g*x*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d^2*f/c - 1/8*(-c^2*x^2 + 1)^(3/2)*b*d*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*a*d^2*g/c^2 + 1/4*b*d^2*g*arcsin(c*x)/c^2 + 1/3*b*f*x*arcsin(c*x)*e^2/c^2 + 1/5*(c^2*x^2 - 1)^2*b*h*x*arcsin(c*x)*e^2/c^4 + (c^2*x^2 - 1)*a*d*f*e/c^2 + 1/2*b*d*f*arcsin(c*x)*e/c^2 + 1/2*(c^2*x^2 - 1)^2*b*d*h*arcsin(c*x)*e/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*d^2*h/c^3 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*g*x*e^2/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b*d*g*e/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*b*d*h*x*e/c^3 + 1/4*(c^2*x^2 - 1)^2*b*g*arcsin(c*x)*e^2/c^4 + 2/5*(c^2*x^2 - 1)*b*h*x*arcsin(c*x)*e^2/c^4 + (c^2*x^2 - 1)*b*d*h*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*d^2*h/c^3 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*f*e^2/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*g*x*e^2/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b*d*g*e/c^3 + 1/2*(c^2*x^2 - 1)*b*g*arcsin(c*x)*e^2/c^4 + 1/5*b*h*x*arcsin(c*x)*e^2/c^4 + 5/16*b*d*h*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*f*e^2/c^3 + 1/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*h*e^2/c^5 + 5/32*b*g*arcsin(c*x)*e^2/c^4 - 2/15*(-c^2*x^2 + 1)^(3/2)*b*h*e^2/c^5 + 1/5*sqrt(-c^2*x^2 + 1)*b*h*e^2/c^5","B",0
99,1,463,0,0.376298," ","integrate((e*x+d)*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{4} \, a h x^{4} e + \frac{1}{3} \, a d h x^{3} + \frac{1}{3} \, a g x^{3} e + b d f x \arcsin\left(c x\right) + a d f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d g x}{4 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b f x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{b d h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{b g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b h x e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d g}{2 \, c^{2}} + \frac{b d g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a f e}{2 \, c^{2}} + \frac{b f \arcsin\left(c x\right) e}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b h \arcsin\left(c x\right) e}{4 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d h}{9 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g e}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b h x e}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b h \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d h}{3 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b g e}{3 \, c^{3}} + \frac{5 \, b h \arcsin\left(c x\right) e}{32 \, c^{4}}"," ",0,"1/4*a*h*x^4*e + 1/3*a*d*h*x^3 + 1/3*a*g*x^3*e + b*d*f*x*arcsin(c*x) + a*d*f*x + 1/3*(c^2*x^2 - 1)*b*d*h*x*arcsin(c*x)/c^2 + 1/3*(c^2*x^2 - 1)*b*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d*g*x/c + 1/4*sqrt(-c^2*x^2 + 1)*b*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d*g*arcsin(c*x)/c^2 + 1/3*b*d*h*x*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)*b*f*arcsin(c*x)*e/c^2 + 1/3*b*g*x*arcsin(c*x)*e/c^2 + sqrt(-c^2*x^2 + 1)*b*d*f/c - 1/16*(-c^2*x^2 + 1)^(3/2)*b*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*a*d*g/c^2 + 1/4*b*d*g*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)*a*f*e/c^2 + 1/4*b*f*arcsin(c*x)*e/c^2 + 1/4*(c^2*x^2 - 1)^2*b*h*arcsin(c*x)*e/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*d*h/c^3 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*g*e/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*b*h*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*d*h/c^3 + 1/3*sqrt(-c^2*x^2 + 1)*b*g*e/c^3 + 5/32*b*h*arcsin(c*x)*e/c^4","B",0
100,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{e x + d}\,{d x}"," ",0,"integrate((h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d), x)","F",0
101,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^2, x)","F",0
102,0,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^3, x)","F",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=""giac"")","\int \frac{{\left(h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{4}}\,{d x}"," ",0,"integrate((h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^4, x)","F",0
104,-2,0,0,0.000000," ","integrate((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 0.59sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",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=""giac"")","\int \frac{{\left(h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{6}}\,{d x}"," ",0,"integrate((h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^6, x)","F",0
106,1,1976,0,0.534194," ","integrate((e*x+d)^3*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{7} \, a i x^{7} e^{3} + \frac{1}{2} \, a d i x^{6} e^{2} + \frac{3}{5} \, a d^{2} i x^{5} e + \frac{1}{4} \, a d^{3} i x^{4} + \frac{1}{6} \, a h x^{6} e^{3} + \frac{3}{5} \, a d h x^{5} e^{2} + \frac{3}{4} \, a d^{2} h x^{4} e + \frac{1}{3} \, a d^{3} h x^{3} + \frac{1}{5} \, a g x^{5} e^{3} + \frac{3}{4} \, a d g x^{4} e^{2} + a d^{2} g x^{3} e + b d^{3} f x \arcsin\left(c x\right) + \frac{1}{4} \, a f x^{4} e^{3} + a d f x^{3} e^{2} + a d^{3} f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{3} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} g x \arcsin\left(c x\right) e}{c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} g x}{4 \, c} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} f x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{3} g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{b d^{3} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d f x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{b d^{2} g x \arcsin\left(c x\right) e}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d^{2} i x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} f}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{3} i x}{16 \, c^{3}} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} h x e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d^{3} g}{2 \, c^{2}} + \frac{b d^{3} g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b d^{3} i \arcsin\left(c x\right)}{4 \, c^{4}} + \frac{b d f x \arcsin\left(c x\right) e^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a d^{2} f e}{2 \, c^{2}} + \frac{3 \, b d^{2} f \arcsin\left(c x\right) e}{4 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d^{2} h \arcsin\left(c x\right) e}{4 \, c^{4}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} i x \arcsin\left(c x\right) e}{5 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{3} h}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b d^{3} i x}{32 \, c^{3}} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d g x e^{2}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} g e}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} h x e}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{3} i \arcsin\left(c x\right)}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d g \arcsin\left(c x\right) e^{2}}{4 \, c^{4}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)} b d h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d^{2} h \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{3 \, b d^{2} i x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{3} h}{3 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b f x e^{3}}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d f e^{2}}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b d g x e^{2}}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b d i x e^{2}}{12 \, c^{5}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} g e}{c^{3}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b d^{2} i e}{25 \, c^{5}} + \frac{5 \, b d^{3} i \arcsin\left(c x\right)}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b f \arcsin\left(c x\right) e^{3}}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b i x \arcsin\left(c x\right) e^{3}}{7 \, c^{6}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d g \arcsin\left(c x\right) e^{2}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b d i \arcsin\left(c x\right) e^{2}}{2 \, c^{6}} + \frac{3 \, b d h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{15 \, b d^{2} h \arcsin\left(c x\right) e}{32 \, c^{4}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b f x e^{3}}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b h x e^{3}}{36 \, c^{5}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f e^{2}}{c^{3}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b d h e^{2}}{25 \, c^{5}} - \frac{13 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d i x e^{2}}{48 \, c^{5}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} i e}{5 \, c^{5}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f \arcsin\left(c x\right) e^{3}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b h \arcsin\left(c x\right) e^{3}}{6 \, c^{6}} + \frac{b g x \arcsin\left(c x\right) e^{3}}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b i x \arcsin\left(c x\right) e^{3}}{7 \, c^{6}} + \frac{15 \, b d g \arcsin\left(c x\right) e^{2}}{32 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d i \arcsin\left(c x\right) e^{2}}{2 \, c^{6}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b g e^{3}}{25 \, c^{5}} - \frac{13 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b h x e^{3}}{144 \, c^{5}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d h e^{2}}{5 \, c^{5}} + \frac{11 \, \sqrt{-c^{2} x^{2} + 1} b d i x e^{2}}{32 \, c^{5}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} i e}{5 \, c^{5}} + \frac{5 \, b f \arcsin\left(c x\right) e^{3}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b h \arcsin\left(c x\right) e^{3}}{2 \, c^{6}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b i x \arcsin\left(c x\right) e^{3}}{7 \, c^{6}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b d i \arcsin\left(c x\right) e^{2}}{2 \, c^{6}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g e^{3}}{15 \, c^{5}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} \sqrt{-c^{2} x^{2} + 1} b i e^{3}}{49 \, c^{7}} + \frac{11 \, \sqrt{-c^{2} x^{2} + 1} b h x e^{3}}{96 \, c^{5}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d h e^{2}}{5 \, c^{5}} + \frac{{\left(c^{2} x^{2} - 1\right)} b h \arcsin\left(c x\right) e^{3}}{2 \, c^{6}} + \frac{b i x \arcsin\left(c x\right) e^{3}}{7 \, c^{6}} + \frac{11 \, b d i \arcsin\left(c x\right) e^{2}}{32 \, c^{6}} + \frac{\sqrt{-c^{2} x^{2} + 1} b g e^{3}}{5 \, c^{5}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b i e^{3}}{35 \, c^{7}} + \frac{11 \, b h \arcsin\left(c x\right) e^{3}}{96 \, c^{6}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b i e^{3}}{7 \, c^{7}} + \frac{\sqrt{-c^{2} x^{2} + 1} b i e^{3}}{7 \, c^{7}}"," ",0,"1/7*a*i*x^7*e^3 + 1/2*a*d*i*x^6*e^2 + 3/5*a*d^2*i*x^5*e + 1/4*a*d^3*i*x^4 + 1/6*a*h*x^6*e^3 + 3/5*a*d*h*x^5*e^2 + 3/4*a*d^2*h*x^4*e + 1/3*a*d^3*h*x^3 + 1/5*a*g*x^5*e^3 + 3/4*a*d*g*x^4*e^2 + a*d^2*g*x^3*e + b*d^3*f*x*arcsin(c*x) + 1/4*a*f*x^4*e^3 + a*d*f*x^3*e^2 + a*d^3*f*x + 1/3*(c^2*x^2 - 1)*b*d^3*h*x*arcsin(c*x)/c^2 + (c^2*x^2 - 1)*b*d^2*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d^3*g*x/c + 3/4*sqrt(-c^2*x^2 + 1)*b*d^2*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d^3*g*arcsin(c*x)/c^2 + 1/3*b*d^3*h*x*arcsin(c*x)/c^2 + (c^2*x^2 - 1)*b*d*f*x*arcsin(c*x)*e^2/c^2 + 3/2*(c^2*x^2 - 1)*b*d^2*f*arcsin(c*x)*e/c^2 + b*d^2*g*x*arcsin(c*x)*e/c^2 + 3/5*(c^2*x^2 - 1)^2*b*d^2*i*x*arcsin(c*x)*e/c^4 + sqrt(-c^2*x^2 + 1)*b*d^3*f/c - 1/16*(-c^2*x^2 + 1)^(3/2)*b*d^3*i*x/c^3 - 3/16*(-c^2*x^2 + 1)^(3/2)*b*d^2*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*a*d^3*g/c^2 + 1/4*b*d^3*g*arcsin(c*x)/c^2 + 1/4*(c^2*x^2 - 1)^2*b*d^3*i*arcsin(c*x)/c^4 + b*d*f*x*arcsin(c*x)*e^2/c^2 + 3/5*(c^2*x^2 - 1)^2*b*d*h*x*arcsin(c*x)*e^2/c^4 + 3/2*(c^2*x^2 - 1)*a*d^2*f*e/c^2 + 3/4*b*d^2*f*arcsin(c*x)*e/c^2 + 3/4*(c^2*x^2 - 1)^2*b*d^2*h*arcsin(c*x)*e/c^4 + 6/5*(c^2*x^2 - 1)*b*d^2*i*x*arcsin(c*x)*e/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*d^3*h/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*d^3*i*x/c^3 - 3/16*(-c^2*x^2 + 1)^(3/2)*b*d*g*x*e^2/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d^2*g*e/c^3 + 15/32*sqrt(-c^2*x^2 + 1)*b*d^2*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*b*d^3*i*arcsin(c*x)/c^4 + 1/5*(c^2*x^2 - 1)^2*b*g*x*arcsin(c*x)*e^3/c^4 + 3/4*(c^2*x^2 - 1)^2*b*d*g*arcsin(c*x)*e^2/c^4 + 6/5*(c^2*x^2 - 1)*b*d*h*x*arcsin(c*x)*e^2/c^4 + 3/2*(c^2*x^2 - 1)*b*d^2*h*arcsin(c*x)*e/c^4 + 3/5*b*d^2*i*x*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*d^3*h/c^3 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*f*x*e^3/c^3 - 1/3*(-c^2*x^2 + 1)^(3/2)*b*d*f*e^2/c^3 + 15/32*sqrt(-c^2*x^2 + 1)*b*d*g*x*e^2/c^3 + 1/12*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*d*i*x*e^2/c^5 + sqrt(-c^2*x^2 + 1)*b*d^2*g*e/c^3 + 3/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*d^2*i*e/c^5 + 5/32*b*d^3*i*arcsin(c*x)/c^4 + 1/4*(c^2*x^2 - 1)^2*b*f*arcsin(c*x)*e^3/c^4 + 2/5*(c^2*x^2 - 1)*b*g*x*arcsin(c*x)*e^3/c^4 + 1/7*(c^2*x^2 - 1)^3*b*i*x*arcsin(c*x)*e^3/c^6 + 3/2*(c^2*x^2 - 1)*b*d*g*arcsin(c*x)*e^2/c^4 + 1/2*(c^2*x^2 - 1)^3*b*d*i*arcsin(c*x)*e^2/c^6 + 3/5*b*d*h*x*arcsin(c*x)*e^2/c^4 + 15/32*b*d^2*h*arcsin(c*x)*e/c^4 + 5/32*sqrt(-c^2*x^2 + 1)*b*f*x*e^3/c^3 + 1/36*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*h*x*e^3/c^5 + sqrt(-c^2*x^2 + 1)*b*d*f*e^2/c^3 + 3/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*d*h*e^2/c^5 - 13/48*(-c^2*x^2 + 1)^(3/2)*b*d*i*x*e^2/c^5 - 2/5*(-c^2*x^2 + 1)^(3/2)*b*d^2*i*e/c^5 + 1/2*(c^2*x^2 - 1)*b*f*arcsin(c*x)*e^3/c^4 + 1/6*(c^2*x^2 - 1)^3*b*h*arcsin(c*x)*e^3/c^6 + 1/5*b*g*x*arcsin(c*x)*e^3/c^4 + 3/7*(c^2*x^2 - 1)^2*b*i*x*arcsin(c*x)*e^3/c^6 + 15/32*b*d*g*arcsin(c*x)*e^2/c^4 + 3/2*(c^2*x^2 - 1)^2*b*d*i*arcsin(c*x)*e^2/c^6 + 1/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*g*e^3/c^5 - 13/144*(-c^2*x^2 + 1)^(3/2)*b*h*x*e^3/c^5 - 2/5*(-c^2*x^2 + 1)^(3/2)*b*d*h*e^2/c^5 + 11/32*sqrt(-c^2*x^2 + 1)*b*d*i*x*e^2/c^5 + 3/5*sqrt(-c^2*x^2 + 1)*b*d^2*i*e/c^5 + 5/32*b*f*arcsin(c*x)*e^3/c^4 + 1/2*(c^2*x^2 - 1)^2*b*h*arcsin(c*x)*e^3/c^6 + 3/7*(c^2*x^2 - 1)*b*i*x*arcsin(c*x)*e^3/c^6 + 3/2*(c^2*x^2 - 1)*b*d*i*arcsin(c*x)*e^2/c^6 - 2/15*(-c^2*x^2 + 1)^(3/2)*b*g*e^3/c^5 + 1/49*(c^2*x^2 - 1)^3*sqrt(-c^2*x^2 + 1)*b*i*e^3/c^7 + 11/96*sqrt(-c^2*x^2 + 1)*b*h*x*e^3/c^5 + 3/5*sqrt(-c^2*x^2 + 1)*b*d*h*e^2/c^5 + 1/2*(c^2*x^2 - 1)*b*h*arcsin(c*x)*e^3/c^6 + 1/7*b*i*x*arcsin(c*x)*e^3/c^6 + 11/32*b*d*i*arcsin(c*x)*e^2/c^6 + 1/5*sqrt(-c^2*x^2 + 1)*b*g*e^3/c^5 + 3/35*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*i*e^3/c^7 + 11/96*b*h*arcsin(c*x)*e^3/c^6 - 1/7*(-c^2*x^2 + 1)^(3/2)*b*i*e^3/c^7 + 1/7*sqrt(-c^2*x^2 + 1)*b*i*e^3/c^7","B",0
107,1,1283,0,0.606222," ","integrate((e*x+d)^2*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{6} \, a i x^{6} e^{2} + \frac{2}{5} \, a d i x^{5} e + \frac{1}{4} \, a d^{2} i x^{4} + \frac{1}{5} \, a h x^{5} e^{2} + \frac{1}{2} \, a d h x^{4} e + \frac{1}{3} \, a d^{2} h x^{3} + \frac{1}{4} \, a g x^{4} e^{2} + \frac{2}{3} \, a d g x^{3} e + b d^{2} f x \arcsin\left(c x\right) + \frac{1}{3} \, a f x^{3} e^{2} + a d^{2} f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b d g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} g x}{4 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f x e}{2 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{b d^{2} h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d f \arcsin\left(c x\right) e}{c^{2}} + \frac{2 \, b d g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} b d i x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} f}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} i x}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d h x e}{8 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d^{2} g}{2 \, c^{2}} + \frac{b d^{2} g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b d^{2} i \arcsin\left(c x\right)}{4 \, c^{4}} + \frac{b f x \arcsin\left(c x\right) e^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d f e}{c^{2}} + \frac{b d f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b d h \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{4 \, {\left(c^{2} x^{2} - 1\right)} b d i x \arcsin\left(c x\right) e}{5 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d^{2} h}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b d^{2} i x}{32 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g x e^{2}}{16 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d g e}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b d h x e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d^{2} i \arcsin\left(c x\right)}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b g \arcsin\left(c x\right) e^{2}}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d h \arcsin\left(c x\right) e}{c^{4}} + \frac{2 \, b d i x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d^{2} h}{3 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b f e^{2}}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b g x e^{2}}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b i x e^{2}}{36 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b d g e}{3 \, c^{3}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b d i e}{25 \, c^{5}} + \frac{5 \, b d^{2} i \arcsin\left(c x\right)}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b g \arcsin\left(c x\right) e^{2}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b i \arcsin\left(c x\right) e^{2}}{6 \, c^{6}} + \frac{b h x \arcsin\left(c x\right) e^{2}}{5 \, c^{4}} + \frac{5 \, b d h \arcsin\left(c x\right) e}{16 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b f e^{2}}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b h e^{2}}{25 \, c^{5}} - \frac{13 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b i x e^{2}}{144 \, c^{5}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d i e}{15 \, c^{5}} + \frac{5 \, b g \arcsin\left(c x\right) e^{2}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b i \arcsin\left(c x\right) e^{2}}{2 \, c^{6}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b h e^{2}}{15 \, c^{5}} + \frac{11 \, \sqrt{-c^{2} x^{2} + 1} b i x e^{2}}{96 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b d i e}{5 \, c^{5}} + \frac{{\left(c^{2} x^{2} - 1\right)} b i \arcsin\left(c x\right) e^{2}}{2 \, c^{6}} + \frac{\sqrt{-c^{2} x^{2} + 1} b h e^{2}}{5 \, c^{5}} + \frac{11 \, b i \arcsin\left(c x\right) e^{2}}{96 \, c^{6}}"," ",0,"1/6*a*i*x^6*e^2 + 2/5*a*d*i*x^5*e + 1/4*a*d^2*i*x^4 + 1/5*a*h*x^5*e^2 + 1/2*a*d*h*x^4*e + 1/3*a*d^2*h*x^3 + 1/4*a*g*x^4*e^2 + 2/3*a*d*g*x^3*e + b*d^2*f*x*arcsin(c*x) + 1/3*a*f*x^3*e^2 + a*d^2*f*x + 1/3*(c^2*x^2 - 1)*b*d^2*h*x*arcsin(c*x)/c^2 + 2/3*(c^2*x^2 - 1)*b*d*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d^2*g*x/c + 1/2*sqrt(-c^2*x^2 + 1)*b*d*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d^2*g*arcsin(c*x)/c^2 + 1/3*b*d^2*h*x*arcsin(c*x)/c^2 + 1/3*(c^2*x^2 - 1)*b*f*x*arcsin(c*x)*e^2/c^2 + (c^2*x^2 - 1)*b*d*f*arcsin(c*x)*e/c^2 + 2/3*b*d*g*x*arcsin(c*x)*e/c^2 + 2/5*(c^2*x^2 - 1)^2*b*d*i*x*arcsin(c*x)*e/c^4 + sqrt(-c^2*x^2 + 1)*b*d^2*f/c - 1/16*(-c^2*x^2 + 1)^(3/2)*b*d^2*i*x/c^3 - 1/8*(-c^2*x^2 + 1)^(3/2)*b*d*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*a*d^2*g/c^2 + 1/4*b*d^2*g*arcsin(c*x)/c^2 + 1/4*(c^2*x^2 - 1)^2*b*d^2*i*arcsin(c*x)/c^4 + 1/3*b*f*x*arcsin(c*x)*e^2/c^2 + 1/5*(c^2*x^2 - 1)^2*b*h*x*arcsin(c*x)*e^2/c^4 + (c^2*x^2 - 1)*a*d*f*e/c^2 + 1/2*b*d*f*arcsin(c*x)*e/c^2 + 1/2*(c^2*x^2 - 1)^2*b*d*h*arcsin(c*x)*e/c^4 + 4/5*(c^2*x^2 - 1)*b*d*i*x*arcsin(c*x)*e/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*d^2*h/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*d^2*i*x/c^3 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*g*x*e^2/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b*d*g*e/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*b*d*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*b*d^2*i*arcsin(c*x)/c^4 + 1/4*(c^2*x^2 - 1)^2*b*g*arcsin(c*x)*e^2/c^4 + 2/5*(c^2*x^2 - 1)*b*h*x*arcsin(c*x)*e^2/c^4 + (c^2*x^2 - 1)*b*d*h*arcsin(c*x)*e/c^4 + 2/5*b*d*i*x*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*d^2*h/c^3 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*f*e^2/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*g*x*e^2/c^3 + 1/36*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*i*x*e^2/c^5 + 2/3*sqrt(-c^2*x^2 + 1)*b*d*g*e/c^3 + 2/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*d*i*e/c^5 + 5/32*b*d^2*i*arcsin(c*x)/c^4 + 1/2*(c^2*x^2 - 1)*b*g*arcsin(c*x)*e^2/c^4 + 1/6*(c^2*x^2 - 1)^3*b*i*arcsin(c*x)*e^2/c^6 + 1/5*b*h*x*arcsin(c*x)*e^2/c^4 + 5/16*b*d*h*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*f*e^2/c^3 + 1/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*h*e^2/c^5 - 13/144*(-c^2*x^2 + 1)^(3/2)*b*i*x*e^2/c^5 - 4/15*(-c^2*x^2 + 1)^(3/2)*b*d*i*e/c^5 + 5/32*b*g*arcsin(c*x)*e^2/c^4 + 1/2*(c^2*x^2 - 1)^2*b*i*arcsin(c*x)*e^2/c^6 - 2/15*(-c^2*x^2 + 1)^(3/2)*b*h*e^2/c^5 + 11/96*sqrt(-c^2*x^2 + 1)*b*i*x*e^2/c^5 + 2/5*sqrt(-c^2*x^2 + 1)*b*d*i*e/c^5 + 1/2*(c^2*x^2 - 1)*b*i*arcsin(c*x)*e^2/c^6 + 1/5*sqrt(-c^2*x^2 + 1)*b*h*e^2/c^5 + 11/96*b*i*arcsin(c*x)*e^2/c^6","B",0
108,1,714,0,0.483225," ","integrate((e*x+d)*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x, algorithm=""giac"")","\frac{1}{5} \, a i x^{5} e + \frac{1}{4} \, a d i x^{4} + \frac{1}{4} \, a h x^{4} e + \frac{1}{3} \, a d h x^{3} + \frac{1}{3} \, a g x^{3} e + b d f x \arcsin\left(c x\right) + a d f x + \frac{{\left(c^{2} x^{2} - 1\right)} b d h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d g x}{4 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b f x e}{4 \, c} + \frac{{\left(c^{2} x^{2} - 1\right)} b d g \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{b d h x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b f \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{b g x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b i x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d f}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d i x}{16 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b h x e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a d g}{2 \, c^{2}} + \frac{b d g \arcsin\left(c x\right)}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b d i \arcsin\left(c x\right)}{4 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a f e}{2 \, c^{2}} + \frac{b f \arcsin\left(c x\right) e}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b h \arcsin\left(c x\right) e}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b i x \arcsin\left(c x\right) e}{5 \, c^{4}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b d h}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b d i x}{32 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b g e}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b h x e}{32 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} b d i \arcsin\left(c x\right)}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b h \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{b i x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} b d h}{3 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} b g e}{3 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b i e}{25 \, c^{5}} + \frac{5 \, b d i \arcsin\left(c x\right)}{32 \, c^{4}} + \frac{5 \, b h \arcsin\left(c x\right) e}{32 \, c^{4}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b i e}{15 \, c^{5}} + \frac{\sqrt{-c^{2} x^{2} + 1} b i e}{5 \, c^{5}}"," ",0,"1/5*a*i*x^5*e + 1/4*a*d*i*x^4 + 1/4*a*h*x^4*e + 1/3*a*d*h*x^3 + 1/3*a*g*x^3*e + b*d*f*x*arcsin(c*x) + a*d*f*x + 1/3*(c^2*x^2 - 1)*b*d*h*x*arcsin(c*x)/c^2 + 1/3*(c^2*x^2 - 1)*b*g*x*arcsin(c*x)*e/c^2 + 1/4*sqrt(-c^2*x^2 + 1)*b*d*g*x/c + 1/4*sqrt(-c^2*x^2 + 1)*b*f*x*e/c + 1/2*(c^2*x^2 - 1)*b*d*g*arcsin(c*x)/c^2 + 1/3*b*d*h*x*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)*b*f*arcsin(c*x)*e/c^2 + 1/3*b*g*x*arcsin(c*x)*e/c^2 + 1/5*(c^2*x^2 - 1)^2*b*i*x*arcsin(c*x)*e/c^4 + sqrt(-c^2*x^2 + 1)*b*d*f/c - 1/16*(-c^2*x^2 + 1)^(3/2)*b*d*i*x/c^3 - 1/16*(-c^2*x^2 + 1)^(3/2)*b*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*a*d*g/c^2 + 1/4*b*d*g*arcsin(c*x)/c^2 + 1/4*(c^2*x^2 - 1)^2*b*d*i*arcsin(c*x)/c^4 + 1/2*(c^2*x^2 - 1)*a*f*e/c^2 + 1/4*b*f*arcsin(c*x)*e/c^2 + 1/4*(c^2*x^2 - 1)^2*b*h*arcsin(c*x)*e/c^4 + 2/5*(c^2*x^2 - 1)*b*i*x*arcsin(c*x)*e/c^4 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*d*h/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*d*i*x/c^3 - 1/9*(-c^2*x^2 + 1)^(3/2)*b*g*e/c^3 + 5/32*sqrt(-c^2*x^2 + 1)*b*h*x*e/c^3 + 1/2*(c^2*x^2 - 1)*b*d*i*arcsin(c*x)/c^4 + 1/2*(c^2*x^2 - 1)*b*h*arcsin(c*x)*e/c^4 + 1/5*b*i*x*arcsin(c*x)*e/c^4 + 1/3*sqrt(-c^2*x^2 + 1)*b*d*h/c^3 + 1/3*sqrt(-c^2*x^2 + 1)*b*g*e/c^3 + 1/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*i*e/c^5 + 5/32*b*d*i*arcsin(c*x)/c^4 + 5/32*b*h*arcsin(c*x)*e/c^4 - 2/15*(-c^2*x^2 + 1)^(3/2)*b*i*e/c^5 + 1/5*sqrt(-c^2*x^2 + 1)*b*i*e/c^5","B",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=""giac"")","\int \frac{{\left(i x^{3} + h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{e x + d}\,{d x}"," ",0,"integrate((i*x^3 + h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d), x)","F",0
110,0,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(i x^{3} + h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((i*x^3 + h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^2, x)","F",0
111,0,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(i x^{3} + h x^{2} + g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((i*x^3 + h*x^2 + g*x + f)*(b*arcsin(c*x) + a)/(e*x + d)^3, x)","F",0
112,-1,0,0,0.000000," ","integrate((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*arcsin(c*x))^2/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((g*x + f)*(b*arcsin(c*x) + a)^2/(e*x + d)^3, x)","F",0
114,0,0,0,0.000000," ","integrate((g*x+f)^2*(a+b*arcsin(c*x))^2/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(g x + f\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((g*x + f)^2*(b*arcsin(c*x) + a)^2/(e*x + d)^3, x)","F",0
115,1,3494,0,0.498735," ","integrate((h*x+g)^3*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\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} h^{3} x^{5} e + \frac{3}{4} \, a^{2} f g^{2} h x^{4} + \frac{1}{4} \, a^{2} d h^{3} x^{4} + \frac{3}{4} \, a^{2} g h^{2} x^{4} e + \frac{1}{3} \, a^{2} f g^{3} x^{3} + a^{2} d g h^{2} x^{3} + b^{2} d g^{3} x \arcsin\left(c x\right)^{2} + a^{2} g^{2} h x^{3} e + 2 \, a b d g^{3} x \arcsin\left(c x\right) + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} f g^{3} x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d g h^{2} x \arcsin\left(c x\right)^{2}}{c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g^{2} h x \arcsin\left(c x\right)^{2} e}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d g^{2} h x \arcsin\left(c x\right)}{2 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} g^{3} x \arcsin\left(c x\right) e}{2 \, c} + a^{2} d g^{3} x - 2 \, b^{2} d g^{3} x + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b f g^{3} x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b d g h^{2} x \arcsin\left(c x\right)}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d g^{2} h \arcsin\left(c x\right)^{2}}{2 \, c^{2}} + \frac{b^{2} f g^{3} x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{b^{2} d g h^{2} x \arcsin\left(c x\right)^{2}}{c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f g h^{2} x \arcsin\left(c x\right)^{2}}{5 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b g^{2} h x \arcsin\left(c x\right) e}{c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g^{3} \arcsin\left(c x\right)^{2} e}{2 \, c^{2}} + \frac{b^{2} g^{2} h x \arcsin\left(c x\right)^{2} e}{c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} h^{3} x \arcsin\left(c x\right)^{2} e}{5 \, c^{4}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} a b d g^{2} h x}{2 \, c} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d g^{3} \arcsin\left(c x\right)}{c} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f g^{2} h x \arcsin\left(c x\right)}{8 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} d h^{3} x \arcsin\left(c x\right)}{8 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} a b g^{3} x e}{2 \, c} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} g h^{2} x \arcsin\left(c x\right) e}{8 \, c^{3}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g^{3} x}{27 \, c^{2}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d g h^{2} x}{9 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a b d g^{2} h \arcsin\left(c x\right)}{c^{2}} + \frac{2 \, a b f g^{3} x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, a b d g h^{2} x \arcsin\left(c x\right)}{c^{2}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)}^{2} a b f g h^{2} x \arcsin\left(c x\right)}{5 \, c^{4}} + \frac{3 \, b^{2} d g^{2} h \arcsin\left(c x\right)^{2}}{4 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f g^{2} h \arcsin\left(c x\right)^{2}}{4 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} d h^{3} \arcsin\left(c x\right)^{2}}{4 \, c^{4}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g h^{2} x \arcsin\left(c x\right)^{2}}{5 \, c^{4}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} g^{2} h x e}{9 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b g^{3} \arcsin\left(c x\right) e}{c^{2}} + \frac{2 \, a b g^{2} h x \arcsin\left(c x\right) e}{c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} a b h^{3} x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{b^{2} g^{3} \arcsin\left(c x\right)^{2} e}{4 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} g h^{2} \arcsin\left(c x\right)^{2} e}{4 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} h^{3} x \arcsin\left(c x\right)^{2} e}{5 \, c^{4}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d g^{3}}{c} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f g^{2} h x}{8 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b d h^{3} x}{8 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f g^{3} \arcsin\left(c x\right)}{9 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} d g h^{2} \arcsin\left(c x\right)}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f g^{2} h x \arcsin\left(c x\right)}{16 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d h^{3} x \arcsin\left(c x\right)}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b^{2} f h^{3} x \arcsin\left(c x\right)}{18 \, c^{5}} - \frac{3 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b g h^{2} x e}{8 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} g^{2} h \arcsin\left(c x\right) e}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} b^{2} g h^{2} x \arcsin\left(c x\right) e}{16 \, c^{3}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a^{2} d g^{2} h}{2 \, c^{2}} - \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d g^{2} h}{4 \, c^{2}} - \frac{14 \, b^{2} f g^{3} x}{27 \, c^{2}} - \frac{14 \, b^{2} d g h^{2} x}{9 \, c^{2}} - \frac{6 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f g h^{2} x}{125 \, c^{4}} + \frac{3 \, a b d g^{2} h \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} a b f g^{2} h \arcsin\left(c x\right)}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a b d h^{3} \arcsin\left(c x\right)}{2 \, c^{4}} + \frac{12 \, {\left(c^{2} x^{2} - 1\right)} a b f g h^{2} x \arcsin\left(c x\right)}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g^{2} h \arcsin\left(c x\right)^{2}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d h^{3} \arcsin\left(c x\right)^{2}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b^{2} f h^{3} \arcsin\left(c x\right)^{2}}{6 \, c^{6}} + \frac{3 \, b^{2} f g h^{2} x \arcsin\left(c x\right)^{2}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} g^{3} e}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g^{3} e}{4 \, c^{2}} - \frac{14 \, b^{2} g^{2} h x e}{9 \, c^{2}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} h^{3} x e}{125 \, c^{4}} + \frac{a b g^{3} \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} a b g h^{2} \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{4 \, {\left(c^{2} x^{2} - 1\right)} a b h^{3} x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b^{2} g h^{2} \arcsin\left(c x\right)^{2} e}{2 \, c^{4}} + \frac{b^{2} h^{3} x \arcsin\left(c x\right)^{2} e}{5 \, c^{4}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f g^{3}}{9 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b d g h^{2}}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} a b f g^{2} h x}{16 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} a b d h^{3} x}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} a b f h^{3} x}{18 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f g^{3} \arcsin\left(c x\right)}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d g h^{2} \arcsin\left(c x\right)}{c^{3}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b^{2} f g h^{2} \arcsin\left(c x\right)}{25 \, c^{5}} - \frac{13 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f h^{3} x \arcsin\left(c x\right)}{72 \, c^{5}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b g^{2} h e}{3 \, c^{3}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} a b g h^{2} x e}{16 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} g^{2} h \arcsin\left(c x\right) e}{c^{3}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b^{2} h^{3} \arcsin\left(c x\right) e}{25 \, c^{5}} - \frac{3 \, b^{2} d g^{2} h}{8 \, c^{2}} - \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f g^{2} h}{32 \, c^{4}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} d h^{3}}{32 \, c^{4}} - \frac{76 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g h^{2} x}{375 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a b f g^{2} h \arcsin\left(c x\right)}{c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b d h^{3} \arcsin\left(c x\right)}{c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} a b f h^{3} \arcsin\left(c x\right)}{3 \, c^{6}} + \frac{6 \, a b f g h^{2} x \arcsin\left(c x\right)}{5 \, c^{4}} + \frac{15 \, b^{2} f g^{2} h \arcsin\left(c x\right)^{2}}{32 \, c^{4}} + \frac{5 \, b^{2} d h^{3} \arcsin\left(c x\right)^{2}}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f h^{3} \arcsin\left(c x\right)^{2}}{2 \, c^{6}} - \frac{b^{2} g^{3} e}{8 \, c^{2}} - \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} g h^{2} e}{32 \, c^{4}} - \frac{76 \, {\left(c^{2} x^{2} - 1\right)} b^{2} h^{3} x e}{1125 \, c^{4}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} a b g h^{2} \arcsin\left(c x\right) e}{c^{4}} + \frac{2 \, a b h^{3} x \arcsin\left(c x\right) e}{5 \, c^{4}} + \frac{15 \, b^{2} g h^{2} \arcsin\left(c x\right)^{2} e}{32 \, c^{4}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b f g^{3}}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d g h^{2}}{c^{3}} + \frac{6 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} a b f g h^{2}}{25 \, c^{5}} - \frac{13 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f h^{3} x}{72 \, c^{5}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f g h^{2} \arcsin\left(c x\right)}{5 \, c^{5}} + \frac{11 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f h^{3} x \arcsin\left(c x\right)}{48 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b g^{2} h e}{c^{3}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} a b h^{3} e}{25 \, c^{5}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} h^{3} \arcsin\left(c x\right) e}{15 \, c^{5}} - \frac{15 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g^{2} h}{32 \, c^{4}} - \frac{5 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d h^{3}}{32 \, c^{4}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b^{2} f h^{3}}{108 \, c^{6}} - \frac{298 \, b^{2} f g h^{2} x}{375 \, c^{4}} + \frac{15 \, a b f g^{2} h \arcsin\left(c x\right)}{16 \, c^{4}} + \frac{5 \, a b d h^{3} \arcsin\left(c x\right)}{16 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a b f h^{3} \arcsin\left(c x\right)}{c^{6}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} f h^{3} \arcsin\left(c x\right)^{2}}{2 \, c^{6}} - \frac{15 \, {\left(c^{2} x^{2} - 1\right)} b^{2} g h^{2} e}{32 \, c^{4}} - \frac{298 \, b^{2} h^{3} x e}{1125 \, c^{4}} + \frac{15 \, a b g h^{2} \arcsin\left(c x\right) e}{16 \, c^{4}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f g h^{2}}{5 \, c^{5}} + \frac{11 \, \sqrt{-c^{2} x^{2} + 1} a b f h^{3} x}{48 \, c^{5}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f g h^{2} \arcsin\left(c x\right)}{5 \, c^{5}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b h^{3} e}{15 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} h^{3} \arcsin\left(c x\right) e}{5 \, c^{5}} - \frac{51 \, b^{2} f g^{2} h}{256 \, c^{4}} - \frac{17 \, b^{2} d h^{3}}{256 \, c^{4}} - \frac{13 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f h^{3}}{288 \, c^{6}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b f h^{3} \arcsin\left(c x\right)}{c^{6}} + \frac{11 \, b^{2} f h^{3} \arcsin\left(c x\right)^{2}}{96 \, c^{6}} - \frac{51 \, b^{2} g h^{2} e}{256 \, c^{4}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} a b f g h^{2}}{5 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b h^{3} e}{5 \, c^{5}} - \frac{11 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f h^{3}}{96 \, c^{6}} + \frac{11 \, a b f h^{3} \arcsin\left(c x\right)}{48 \, c^{6}} - \frac{299 \, b^{2} f h^{3}}{6912 \, c^{6}}"," ",0,"1/6*a^2*f*h^3*x^6 + 3/5*a^2*f*g*h^2*x^5 + 1/5*a^2*h^3*x^5*e + 3/4*a^2*f*g^2*h*x^4 + 1/4*a^2*d*h^3*x^4 + 3/4*a^2*g*h^2*x^4*e + 1/3*a^2*f*g^3*x^3 + a^2*d*g*h^2*x^3 + b^2*d*g^3*x*arcsin(c*x)^2 + a^2*g^2*h*x^3*e + 2*a*b*d*g^3*x*arcsin(c*x) + 1/3*(c^2*x^2 - 1)*b^2*f*g^3*x*arcsin(c*x)^2/c^2 + (c^2*x^2 - 1)*b^2*d*g*h^2*x*arcsin(c*x)^2/c^2 + (c^2*x^2 - 1)*b^2*g^2*h*x*arcsin(c*x)^2*e/c^2 + 3/2*sqrt(-c^2*x^2 + 1)*b^2*d*g^2*h*x*arcsin(c*x)/c + 1/2*sqrt(-c^2*x^2 + 1)*b^2*g^3*x*arcsin(c*x)*e/c + a^2*d*g^3*x - 2*b^2*d*g^3*x + 2/3*(c^2*x^2 - 1)*a*b*f*g^3*x*arcsin(c*x)/c^2 + 2*(c^2*x^2 - 1)*a*b*d*g*h^2*x*arcsin(c*x)/c^2 + 3/2*(c^2*x^2 - 1)*b^2*d*g^2*h*arcsin(c*x)^2/c^2 + 1/3*b^2*f*g^3*x*arcsin(c*x)^2/c^2 + b^2*d*g*h^2*x*arcsin(c*x)^2/c^2 + 3/5*(c^2*x^2 - 1)^2*b^2*f*g*h^2*x*arcsin(c*x)^2/c^4 + 2*(c^2*x^2 - 1)*a*b*g^2*h*x*arcsin(c*x)*e/c^2 + 1/2*(c^2*x^2 - 1)*b^2*g^3*arcsin(c*x)^2*e/c^2 + b^2*g^2*h*x*arcsin(c*x)^2*e/c^2 + 1/5*(c^2*x^2 - 1)^2*b^2*h^3*x*arcsin(c*x)^2*e/c^4 + 3/2*sqrt(-c^2*x^2 + 1)*a*b*d*g^2*h*x/c + 2*sqrt(-c^2*x^2 + 1)*b^2*d*g^3*arcsin(c*x)/c - 3/8*(-c^2*x^2 + 1)^(3/2)*b^2*f*g^2*h*x*arcsin(c*x)/c^3 - 1/8*(-c^2*x^2 + 1)^(3/2)*b^2*d*h^3*x*arcsin(c*x)/c^3 + 1/2*sqrt(-c^2*x^2 + 1)*a*b*g^3*x*e/c - 3/8*(-c^2*x^2 + 1)^(3/2)*b^2*g*h^2*x*arcsin(c*x)*e/c^3 - 2/27*(c^2*x^2 - 1)*b^2*f*g^3*x/c^2 - 2/9*(c^2*x^2 - 1)*b^2*d*g*h^2*x/c^2 + 3*(c^2*x^2 - 1)*a*b*d*g^2*h*arcsin(c*x)/c^2 + 2/3*a*b*f*g^3*x*arcsin(c*x)/c^2 + 2*a*b*d*g*h^2*x*arcsin(c*x)/c^2 + 6/5*(c^2*x^2 - 1)^2*a*b*f*g*h^2*x*arcsin(c*x)/c^4 + 3/4*b^2*d*g^2*h*arcsin(c*x)^2/c^2 + 3/4*(c^2*x^2 - 1)^2*b^2*f*g^2*h*arcsin(c*x)^2/c^4 + 1/4*(c^2*x^2 - 1)^2*b^2*d*h^3*arcsin(c*x)^2/c^4 + 6/5*(c^2*x^2 - 1)*b^2*f*g*h^2*x*arcsin(c*x)^2/c^4 - 2/9*(c^2*x^2 - 1)*b^2*g^2*h*x*e/c^2 + (c^2*x^2 - 1)*a*b*g^3*arcsin(c*x)*e/c^2 + 2*a*b*g^2*h*x*arcsin(c*x)*e/c^2 + 2/5*(c^2*x^2 - 1)^2*a*b*h^3*x*arcsin(c*x)*e/c^4 + 1/4*b^2*g^3*arcsin(c*x)^2*e/c^2 + 3/4*(c^2*x^2 - 1)^2*b^2*g*h^2*arcsin(c*x)^2*e/c^4 + 2/5*(c^2*x^2 - 1)*b^2*h^3*x*arcsin(c*x)^2*e/c^4 + 2*sqrt(-c^2*x^2 + 1)*a*b*d*g^3/c - 3/8*(-c^2*x^2 + 1)^(3/2)*a*b*f*g^2*h*x/c^3 - 1/8*(-c^2*x^2 + 1)^(3/2)*a*b*d*h^3*x/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b^2*f*g^3*arcsin(c*x)/c^3 - 2/3*(-c^2*x^2 + 1)^(3/2)*b^2*d*g*h^2*arcsin(c*x)/c^3 + 15/16*sqrt(-c^2*x^2 + 1)*b^2*f*g^2*h*x*arcsin(c*x)/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*b^2*d*h^3*x*arcsin(c*x)/c^3 + 1/18*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b^2*f*h^3*x*arcsin(c*x)/c^5 - 3/8*(-c^2*x^2 + 1)^(3/2)*a*b*g*h^2*x*e/c^3 - 2/3*(-c^2*x^2 + 1)^(3/2)*b^2*g^2*h*arcsin(c*x)*e/c^3 + 15/16*sqrt(-c^2*x^2 + 1)*b^2*g*h^2*x*arcsin(c*x)*e/c^3 + 3/2*(c^2*x^2 - 1)*a^2*d*g^2*h/c^2 - 3/4*(c^2*x^2 - 1)*b^2*d*g^2*h/c^2 - 14/27*b^2*f*g^3*x/c^2 - 14/9*b^2*d*g*h^2*x/c^2 - 6/125*(c^2*x^2 - 1)^2*b^2*f*g*h^2*x/c^4 + 3/2*a*b*d*g^2*h*arcsin(c*x)/c^2 + 3/2*(c^2*x^2 - 1)^2*a*b*f*g^2*h*arcsin(c*x)/c^4 + 1/2*(c^2*x^2 - 1)^2*a*b*d*h^3*arcsin(c*x)/c^4 + 12/5*(c^2*x^2 - 1)*a*b*f*g*h^2*x*arcsin(c*x)/c^4 + 3/2*(c^2*x^2 - 1)*b^2*f*g^2*h*arcsin(c*x)^2/c^4 + 1/2*(c^2*x^2 - 1)*b^2*d*h^3*arcsin(c*x)^2/c^4 + 1/6*(c^2*x^2 - 1)^3*b^2*f*h^3*arcsin(c*x)^2/c^6 + 3/5*b^2*f*g*h^2*x*arcsin(c*x)^2/c^4 + 1/2*(c^2*x^2 - 1)*a^2*g^3*e/c^2 - 1/4*(c^2*x^2 - 1)*b^2*g^3*e/c^2 - 14/9*b^2*g^2*h*x*e/c^2 - 2/125*(c^2*x^2 - 1)^2*b^2*h^3*x*e/c^4 + 1/2*a*b*g^3*arcsin(c*x)*e/c^2 + 3/2*(c^2*x^2 - 1)^2*a*b*g*h^2*arcsin(c*x)*e/c^4 + 4/5*(c^2*x^2 - 1)*a*b*h^3*x*arcsin(c*x)*e/c^4 + 3/2*(c^2*x^2 - 1)*b^2*g*h^2*arcsin(c*x)^2*e/c^4 + 1/5*b^2*h^3*x*arcsin(c*x)^2*e/c^4 - 2/9*(-c^2*x^2 + 1)^(3/2)*a*b*f*g^3/c^3 - 2/3*(-c^2*x^2 + 1)^(3/2)*a*b*d*g*h^2/c^3 + 15/16*sqrt(-c^2*x^2 + 1)*a*b*f*g^2*h*x/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*a*b*d*h^3*x/c^3 + 1/18*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*a*b*f*h^3*x/c^5 + 2/3*sqrt(-c^2*x^2 + 1)*b^2*f*g^3*arcsin(c*x)/c^3 + 2*sqrt(-c^2*x^2 + 1)*b^2*d*g*h^2*arcsin(c*x)/c^3 + 6/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b^2*f*g*h^2*arcsin(c*x)/c^5 - 13/72*(-c^2*x^2 + 1)^(3/2)*b^2*f*h^3*x*arcsin(c*x)/c^5 - 2/3*(-c^2*x^2 + 1)^(3/2)*a*b*g^2*h*e/c^3 + 15/16*sqrt(-c^2*x^2 + 1)*a*b*g*h^2*x*e/c^3 + 2*sqrt(-c^2*x^2 + 1)*b^2*g^2*h*arcsin(c*x)*e/c^3 + 2/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b^2*h^3*arcsin(c*x)*e/c^5 - 3/8*b^2*d*g^2*h/c^2 - 3/32*(c^2*x^2 - 1)^2*b^2*f*g^2*h/c^4 - 1/32*(c^2*x^2 - 1)^2*b^2*d*h^3/c^4 - 76/375*(c^2*x^2 - 1)*b^2*f*g*h^2*x/c^4 + 3*(c^2*x^2 - 1)*a*b*f*g^2*h*arcsin(c*x)/c^4 + (c^2*x^2 - 1)*a*b*d*h^3*arcsin(c*x)/c^4 + 1/3*(c^2*x^2 - 1)^3*a*b*f*h^3*arcsin(c*x)/c^6 + 6/5*a*b*f*g*h^2*x*arcsin(c*x)/c^4 + 15/32*b^2*f*g^2*h*arcsin(c*x)^2/c^4 + 5/32*b^2*d*h^3*arcsin(c*x)^2/c^4 + 1/2*(c^2*x^2 - 1)^2*b^2*f*h^3*arcsin(c*x)^2/c^6 - 1/8*b^2*g^3*e/c^2 - 3/32*(c^2*x^2 - 1)^2*b^2*g*h^2*e/c^4 - 76/1125*(c^2*x^2 - 1)*b^2*h^3*x*e/c^4 + 3*(c^2*x^2 - 1)*a*b*g*h^2*arcsin(c*x)*e/c^4 + 2/5*a*b*h^3*x*arcsin(c*x)*e/c^4 + 15/32*b^2*g*h^2*arcsin(c*x)^2*e/c^4 + 2/3*sqrt(-c^2*x^2 + 1)*a*b*f*g^3/c^3 + 2*sqrt(-c^2*x^2 + 1)*a*b*d*g*h^2/c^3 + 6/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*a*b*f*g*h^2/c^5 - 13/72*(-c^2*x^2 + 1)^(3/2)*a*b*f*h^3*x/c^5 - 4/5*(-c^2*x^2 + 1)^(3/2)*b^2*f*g*h^2*arcsin(c*x)/c^5 + 11/48*sqrt(-c^2*x^2 + 1)*b^2*f*h^3*x*arcsin(c*x)/c^5 + 2*sqrt(-c^2*x^2 + 1)*a*b*g^2*h*e/c^3 + 2/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*a*b*h^3*e/c^5 - 4/15*(-c^2*x^2 + 1)^(3/2)*b^2*h^3*arcsin(c*x)*e/c^5 - 15/32*(c^2*x^2 - 1)*b^2*f*g^2*h/c^4 - 5/32*(c^2*x^2 - 1)*b^2*d*h^3/c^4 - 1/108*(c^2*x^2 - 1)^3*b^2*f*h^3/c^6 - 298/375*b^2*f*g*h^2*x/c^4 + 15/16*a*b*f*g^2*h*arcsin(c*x)/c^4 + 5/16*a*b*d*h^3*arcsin(c*x)/c^4 + (c^2*x^2 - 1)^2*a*b*f*h^3*arcsin(c*x)/c^6 + 1/2*(c^2*x^2 - 1)*b^2*f*h^3*arcsin(c*x)^2/c^6 - 15/32*(c^2*x^2 - 1)*b^2*g*h^2*e/c^4 - 298/1125*b^2*h^3*x*e/c^4 + 15/16*a*b*g*h^2*arcsin(c*x)*e/c^4 - 4/5*(-c^2*x^2 + 1)^(3/2)*a*b*f*g*h^2/c^5 + 11/48*sqrt(-c^2*x^2 + 1)*a*b*f*h^3*x/c^5 + 6/5*sqrt(-c^2*x^2 + 1)*b^2*f*g*h^2*arcsin(c*x)/c^5 - 4/15*(-c^2*x^2 + 1)^(3/2)*a*b*h^3*e/c^5 + 2/5*sqrt(-c^2*x^2 + 1)*b^2*h^3*arcsin(c*x)*e/c^5 - 51/256*b^2*f*g^2*h/c^4 - 17/256*b^2*d*h^3/c^4 - 13/288*(c^2*x^2 - 1)^2*b^2*f*h^3/c^6 + (c^2*x^2 - 1)*a*b*f*h^3*arcsin(c*x)/c^6 + 11/96*b^2*f*h^3*arcsin(c*x)^2/c^6 - 51/256*b^2*g*h^2*e/c^4 + 6/5*sqrt(-c^2*x^2 + 1)*a*b*f*g*h^2/c^5 + 2/5*sqrt(-c^2*x^2 + 1)*a*b*h^3*e/c^5 - 11/96*(c^2*x^2 - 1)*b^2*f*h^3/c^6 + 11/48*a*b*f*h^3*arcsin(c*x)/c^6 - 299/6912*b^2*f*h^3/c^6","B",0
116,1,2200,0,0.491928," ","integrate((h*x+g)^2*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\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} h^{2} x^{4} e + \frac{1}{3} \, a^{2} f g^{2} 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{2}{3} \, a^{2} g h x^{3} e + 2 \, a b d g^{2} x \arcsin\left(c x\right) + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} f g^{2} x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d h^{2} x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} g h x \arcsin\left(c x\right)^{2} e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} d g h x \arcsin\left(c x\right)}{c} + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} g^{2} x \arcsin\left(c x\right) e}{2 \, c} + a^{2} d g^{2} x - 2 \, b^{2} d g^{2} x + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b f g^{2} x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b d h^{2} x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d g h \arcsin\left(c x\right)^{2}}{c^{2}} + \frac{b^{2} f g^{2} x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{b^{2} d h^{2} x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f h^{2} x \arcsin\left(c x\right)^{2}}{5 \, c^{4}} + \frac{4 \, {\left(c^{2} x^{2} - 1\right)} a b g h x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g^{2} \arcsin\left(c x\right)^{2} e}{2 \, c^{2}} + \frac{2 \, b^{2} g h x \arcsin\left(c x\right)^{2} e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} a b d g h x}{c} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d g^{2} \arcsin\left(c x\right)}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f g h x \arcsin\left(c x\right)}{4 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} a b g^{2} x e}{2 \, c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} h^{2} x \arcsin\left(c x\right) e}{8 \, c^{3}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g^{2} x}{27 \, c^{2}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} d h^{2} x}{27 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b d g h \arcsin\left(c x\right)}{c^{2}} + \frac{2 \, a b f g^{2} x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, a b d h^{2} x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} a b f h^{2} x \arcsin\left(c x\right)}{5 \, c^{4}} + \frac{b^{2} d g h \arcsin\left(c x\right)^{2}}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f g h \arcsin\left(c x\right)^{2}}{2 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f h^{2} x \arcsin\left(c x\right)^{2}}{5 \, c^{4}} - \frac{4 \, {\left(c^{2} x^{2} - 1\right)} b^{2} g h x e}{27 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b g^{2} \arcsin\left(c x\right) e}{c^{2}} + \frac{4 \, a b g h x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{b^{2} g^{2} \arcsin\left(c x\right)^{2} e}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} h^{2} \arcsin\left(c x\right)^{2} e}{4 \, c^{4}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d g^{2}}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f g h x}{4 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f g^{2} \arcsin\left(c x\right)}{9 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} d h^{2} \arcsin\left(c x\right)}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f g h x \arcsin\left(c x\right)}{8 \, c^{3}} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b h^{2} x e}{8 \, c^{3}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} g h \arcsin\left(c x\right) e}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b^{2} h^{2} x \arcsin\left(c x\right) e}{16 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} d g h}{c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d g h}{2 \, c^{2}} - \frac{14 \, b^{2} f g^{2} x}{27 \, c^{2}} - \frac{14 \, b^{2} d h^{2} x}{27 \, c^{2}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f h^{2} x}{125 \, c^{4}} + \frac{a b d g h \arcsin\left(c x\right)}{c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a b f g h \arcsin\left(c x\right)}{c^{4}} + \frac{4 \, {\left(c^{2} x^{2} - 1\right)} a b f h^{2} x \arcsin\left(c x\right)}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} f g h \arcsin\left(c x\right)^{2}}{c^{4}} + \frac{b^{2} f h^{2} x \arcsin\left(c x\right)^{2}}{5 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} g^{2} e}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g^{2} e}{4 \, c^{2}} - \frac{28 \, b^{2} g h x e}{27 \, c^{2}} + \frac{a b g^{2} \arcsin\left(c x\right) e}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a b h^{2} \arcsin\left(c x\right) e}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} h^{2} \arcsin\left(c x\right)^{2} e}{2 \, c^{4}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f g^{2}}{9 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b d h^{2}}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} a b f g h x}{8 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f g^{2} \arcsin\left(c x\right)}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d h^{2} \arcsin\left(c x\right)}{3 \, c^{3}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b^{2} f h^{2} \arcsin\left(c x\right)}{25 \, c^{5}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b g h e}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} a b h^{2} x e}{16 \, c^{3}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} b^{2} g h \arcsin\left(c x\right) e}{3 \, c^{3}} - \frac{b^{2} d g h}{4 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f g h}{16 \, c^{4}} - \frac{76 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f h^{2} x}{1125 \, c^{4}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b f g h \arcsin\left(c x\right)}{c^{4}} + \frac{2 \, a b f h^{2} x \arcsin\left(c x\right)}{5 \, c^{4}} + \frac{5 \, b^{2} f g h \arcsin\left(c x\right)^{2}}{16 \, c^{4}} - \frac{b^{2} g^{2} e}{8 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} h^{2} e}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b h^{2} \arcsin\left(c x\right) e}{c^{4}} + \frac{5 \, b^{2} h^{2} \arcsin\left(c x\right)^{2} e}{32 \, c^{4}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b f g^{2}}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d h^{2}}{3 \, c^{3}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} a b f h^{2}}{25 \, c^{5}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f h^{2} \arcsin\left(c x\right)}{15 \, c^{5}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} a b g h e}{3 \, c^{3}} - \frac{5 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g h}{16 \, c^{4}} - \frac{298 \, b^{2} f h^{2} x}{1125 \, c^{4}} + \frac{5 \, a b f g h \arcsin\left(c x\right)}{8 \, c^{4}} - \frac{5 \, {\left(c^{2} x^{2} - 1\right)} b^{2} h^{2} e}{32 \, c^{4}} + \frac{5 \, a b h^{2} \arcsin\left(c x\right) e}{16 \, c^{4}} - \frac{4 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f h^{2}}{15 \, c^{5}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f h^{2} \arcsin\left(c x\right)}{5 \, c^{5}} - \frac{17 \, b^{2} f g h}{128 \, c^{4}} - \frac{17 \, b^{2} h^{2} e}{256 \, c^{4}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b f h^{2}}{5 \, c^{5}}"," ",0,"1/5*a^2*f*h^2*x^5 + 1/2*a^2*f*g*h*x^4 + 1/4*a^2*h^2*x^4*e + 1/3*a^2*f*g^2*x^3 + 1/3*a^2*d*h^2*x^3 + b^2*d*g^2*x*arcsin(c*x)^2 + 2/3*a^2*g*h*x^3*e + 2*a*b*d*g^2*x*arcsin(c*x) + 1/3*(c^2*x^2 - 1)*b^2*f*g^2*x*arcsin(c*x)^2/c^2 + 1/3*(c^2*x^2 - 1)*b^2*d*h^2*x*arcsin(c*x)^2/c^2 + 2/3*(c^2*x^2 - 1)*b^2*g*h*x*arcsin(c*x)^2*e/c^2 + sqrt(-c^2*x^2 + 1)*b^2*d*g*h*x*arcsin(c*x)/c + 1/2*sqrt(-c^2*x^2 + 1)*b^2*g^2*x*arcsin(c*x)*e/c + a^2*d*g^2*x - 2*b^2*d*g^2*x + 2/3*(c^2*x^2 - 1)*a*b*f*g^2*x*arcsin(c*x)/c^2 + 2/3*(c^2*x^2 - 1)*a*b*d*h^2*x*arcsin(c*x)/c^2 + (c^2*x^2 - 1)*b^2*d*g*h*arcsin(c*x)^2/c^2 + 1/3*b^2*f*g^2*x*arcsin(c*x)^2/c^2 + 1/3*b^2*d*h^2*x*arcsin(c*x)^2/c^2 + 1/5*(c^2*x^2 - 1)^2*b^2*f*h^2*x*arcsin(c*x)^2/c^4 + 4/3*(c^2*x^2 - 1)*a*b*g*h*x*arcsin(c*x)*e/c^2 + 1/2*(c^2*x^2 - 1)*b^2*g^2*arcsin(c*x)^2*e/c^2 + 2/3*b^2*g*h*x*arcsin(c*x)^2*e/c^2 + sqrt(-c^2*x^2 + 1)*a*b*d*g*h*x/c + 2*sqrt(-c^2*x^2 + 1)*b^2*d*g^2*arcsin(c*x)/c - 1/4*(-c^2*x^2 + 1)^(3/2)*b^2*f*g*h*x*arcsin(c*x)/c^3 + 1/2*sqrt(-c^2*x^2 + 1)*a*b*g^2*x*e/c - 1/8*(-c^2*x^2 + 1)^(3/2)*b^2*h^2*x*arcsin(c*x)*e/c^3 - 2/27*(c^2*x^2 - 1)*b^2*f*g^2*x/c^2 - 2/27*(c^2*x^2 - 1)*b^2*d*h^2*x/c^2 + 2*(c^2*x^2 - 1)*a*b*d*g*h*arcsin(c*x)/c^2 + 2/3*a*b*f*g^2*x*arcsin(c*x)/c^2 + 2/3*a*b*d*h^2*x*arcsin(c*x)/c^2 + 2/5*(c^2*x^2 - 1)^2*a*b*f*h^2*x*arcsin(c*x)/c^4 + 1/2*b^2*d*g*h*arcsin(c*x)^2/c^2 + 1/2*(c^2*x^2 - 1)^2*b^2*f*g*h*arcsin(c*x)^2/c^4 + 2/5*(c^2*x^2 - 1)*b^2*f*h^2*x*arcsin(c*x)^2/c^4 - 4/27*(c^2*x^2 - 1)*b^2*g*h*x*e/c^2 + (c^2*x^2 - 1)*a*b*g^2*arcsin(c*x)*e/c^2 + 4/3*a*b*g*h*x*arcsin(c*x)*e/c^2 + 1/4*b^2*g^2*arcsin(c*x)^2*e/c^2 + 1/4*(c^2*x^2 - 1)^2*b^2*h^2*arcsin(c*x)^2*e/c^4 + 2*sqrt(-c^2*x^2 + 1)*a*b*d*g^2/c - 1/4*(-c^2*x^2 + 1)^(3/2)*a*b*f*g*h*x/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b^2*f*g^2*arcsin(c*x)/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b^2*d*h^2*arcsin(c*x)/c^3 + 5/8*sqrt(-c^2*x^2 + 1)*b^2*f*g*h*x*arcsin(c*x)/c^3 - 1/8*(-c^2*x^2 + 1)^(3/2)*a*b*h^2*x*e/c^3 - 4/9*(-c^2*x^2 + 1)^(3/2)*b^2*g*h*arcsin(c*x)*e/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*b^2*h^2*x*arcsin(c*x)*e/c^3 + (c^2*x^2 - 1)*a^2*d*g*h/c^2 - 1/2*(c^2*x^2 - 1)*b^2*d*g*h/c^2 - 14/27*b^2*f*g^2*x/c^2 - 14/27*b^2*d*h^2*x/c^2 - 2/125*(c^2*x^2 - 1)^2*b^2*f*h^2*x/c^4 + a*b*d*g*h*arcsin(c*x)/c^2 + (c^2*x^2 - 1)^2*a*b*f*g*h*arcsin(c*x)/c^4 + 4/5*(c^2*x^2 - 1)*a*b*f*h^2*x*arcsin(c*x)/c^4 + (c^2*x^2 - 1)*b^2*f*g*h*arcsin(c*x)^2/c^4 + 1/5*b^2*f*h^2*x*arcsin(c*x)^2/c^4 + 1/2*(c^2*x^2 - 1)*a^2*g^2*e/c^2 - 1/4*(c^2*x^2 - 1)*b^2*g^2*e/c^2 - 28/27*b^2*g*h*x*e/c^2 + 1/2*a*b*g^2*arcsin(c*x)*e/c^2 + 1/2*(c^2*x^2 - 1)^2*a*b*h^2*arcsin(c*x)*e/c^4 + 1/2*(c^2*x^2 - 1)*b^2*h^2*arcsin(c*x)^2*e/c^4 - 2/9*(-c^2*x^2 + 1)^(3/2)*a*b*f*g^2/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*a*b*d*h^2/c^3 + 5/8*sqrt(-c^2*x^2 + 1)*a*b*f*g*h*x/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b^2*f*g^2*arcsin(c*x)/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b^2*d*h^2*arcsin(c*x)/c^3 + 2/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b^2*f*h^2*arcsin(c*x)/c^5 - 4/9*(-c^2*x^2 + 1)^(3/2)*a*b*g*h*e/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*a*b*h^2*x*e/c^3 + 4/3*sqrt(-c^2*x^2 + 1)*b^2*g*h*arcsin(c*x)*e/c^3 - 1/4*b^2*d*g*h/c^2 - 1/16*(c^2*x^2 - 1)^2*b^2*f*g*h/c^4 - 76/1125*(c^2*x^2 - 1)*b^2*f*h^2*x/c^4 + 2*(c^2*x^2 - 1)*a*b*f*g*h*arcsin(c*x)/c^4 + 2/5*a*b*f*h^2*x*arcsin(c*x)/c^4 + 5/16*b^2*f*g*h*arcsin(c*x)^2/c^4 - 1/8*b^2*g^2*e/c^2 - 1/32*(c^2*x^2 - 1)^2*b^2*h^2*e/c^4 + (c^2*x^2 - 1)*a*b*h^2*arcsin(c*x)*e/c^4 + 5/32*b^2*h^2*arcsin(c*x)^2*e/c^4 + 2/3*sqrt(-c^2*x^2 + 1)*a*b*f*g^2/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*a*b*d*h^2/c^3 + 2/25*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*a*b*f*h^2/c^5 - 4/15*(-c^2*x^2 + 1)^(3/2)*b^2*f*h^2*arcsin(c*x)/c^5 + 4/3*sqrt(-c^2*x^2 + 1)*a*b*g*h*e/c^3 - 5/16*(c^2*x^2 - 1)*b^2*f*g*h/c^4 - 298/1125*b^2*f*h^2*x/c^4 + 5/8*a*b*f*g*h*arcsin(c*x)/c^4 - 5/32*(c^2*x^2 - 1)*b^2*h^2*e/c^4 + 5/16*a*b*h^2*arcsin(c*x)*e/c^4 - 4/15*(-c^2*x^2 + 1)^(3/2)*a*b*f*h^2/c^5 + 2/5*sqrt(-c^2*x^2 + 1)*b^2*f*h^2*arcsin(c*x)/c^5 - 17/128*b^2*f*g*h/c^4 - 17/256*b^2*h^2*e/c^4 + 2/5*sqrt(-c^2*x^2 + 1)*a*b*f*h^2/c^5","B",0
117,1,1165,0,0.452527," ","integrate((h*x+g)*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x, algorithm=""giac"")","\frac{1}{4} \, a^{2} f h x^{4} + \frac{1}{3} \, a^{2} f g x^{3} + b^{2} d g x \arcsin\left(c x\right)^{2} + \frac{1}{3} \, a^{2} h x^{3} e + 2 \, a b d g x \arcsin\left(c x\right) + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} f g x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} h x \arcsin\left(c x\right)^{2} e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} d h x \arcsin\left(c x\right)}{2 \, c} + \frac{\sqrt{-c^{2} x^{2} + 1} b^{2} g x \arcsin\left(c x\right) e}{2 \, c} + a^{2} d g x - 2 \, b^{2} d g x + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b f g x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d h \arcsin\left(c x\right)^{2}}{2 \, c^{2}} + \frac{b^{2} f g x \arcsin\left(c x\right)^{2}}{3 \, c^{2}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a b h x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g \arcsin\left(c x\right)^{2} e}{2 \, c^{2}} + \frac{b^{2} h x \arcsin\left(c x\right)^{2} e}{3 \, c^{2}} + \frac{\sqrt{-c^{2} x^{2} + 1} a b d h x}{2 \, c} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} d g \arcsin\left(c x\right)}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f h x \arcsin\left(c x\right)}{8 \, c^{3}} + \frac{\sqrt{-c^{2} x^{2} + 1} a b g x e}{2 \, c} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f g x}{27 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b d h \arcsin\left(c x\right)}{c^{2}} + \frac{2 \, a b f g x \arcsin\left(c x\right)}{3 \, c^{2}} + \frac{b^{2} d h \arcsin\left(c x\right)^{2}}{4 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f h \arcsin\left(c x\right)^{2}}{4 \, c^{4}} - \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b^{2} h x e}{27 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b g \arcsin\left(c x\right) e}{c^{2}} + \frac{2 \, a b h x \arcsin\left(c x\right) e}{3 \, c^{2}} + \frac{b^{2} g \arcsin\left(c x\right)^{2} e}{4 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b d g}{c} - \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f h x}{8 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} f g \arcsin\left(c x\right)}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f h x \arcsin\left(c x\right)}{16 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b^{2} h \arcsin\left(c x\right) e}{9 \, c^{3}} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} d h}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} d h}{4 \, c^{2}} - \frac{14 \, b^{2} f g x}{27 \, c^{2}} + \frac{a b d h \arcsin\left(c x\right)}{2 \, c^{2}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a b f h \arcsin\left(c x\right)}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} f h \arcsin\left(c x\right)^{2}}{2 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a^{2} g e}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)} b^{2} g e}{4 \, c^{2}} - \frac{14 \, b^{2} h x e}{27 \, c^{2}} + \frac{a b g \arcsin\left(c x\right) e}{2 \, c^{2}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b f g}{9 \, c^{3}} + \frac{5 \, \sqrt{-c^{2} x^{2} + 1} a b f h x}{16 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} f g \arcsin\left(c x\right)}{3 \, c^{3}} - \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} a b h e}{9 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b^{2} h \arcsin\left(c x\right) e}{3 \, c^{3}} - \frac{b^{2} d h}{8 \, c^{2}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b^{2} f h}{32 \, c^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)} a b f h \arcsin\left(c x\right)}{c^{4}} + \frac{5 \, b^{2} f h \arcsin\left(c x\right)^{2}}{32 \, c^{4}} - \frac{b^{2} g e}{8 \, c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b f g}{3 \, c^{3}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1} a b h e}{3 \, c^{3}} - \frac{5 \, {\left(c^{2} x^{2} - 1\right)} b^{2} f h}{32 \, c^{4}} + \frac{5 \, a b f h \arcsin\left(c x\right)}{16 \, c^{4}} - \frac{17 \, b^{2} f h}{256 \, c^{4}}"," ",0,"1/4*a^2*f*h*x^4 + 1/3*a^2*f*g*x^3 + b^2*d*g*x*arcsin(c*x)^2 + 1/3*a^2*h*x^3*e + 2*a*b*d*g*x*arcsin(c*x) + 1/3*(c^2*x^2 - 1)*b^2*f*g*x*arcsin(c*x)^2/c^2 + 1/3*(c^2*x^2 - 1)*b^2*h*x*arcsin(c*x)^2*e/c^2 + 1/2*sqrt(-c^2*x^2 + 1)*b^2*d*h*x*arcsin(c*x)/c + 1/2*sqrt(-c^2*x^2 + 1)*b^2*g*x*arcsin(c*x)*e/c + a^2*d*g*x - 2*b^2*d*g*x + 2/3*(c^2*x^2 - 1)*a*b*f*g*x*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)*b^2*d*h*arcsin(c*x)^2/c^2 + 1/3*b^2*f*g*x*arcsin(c*x)^2/c^2 + 2/3*(c^2*x^2 - 1)*a*b*h*x*arcsin(c*x)*e/c^2 + 1/2*(c^2*x^2 - 1)*b^2*g*arcsin(c*x)^2*e/c^2 + 1/3*b^2*h*x*arcsin(c*x)^2*e/c^2 + 1/2*sqrt(-c^2*x^2 + 1)*a*b*d*h*x/c + 2*sqrt(-c^2*x^2 + 1)*b^2*d*g*arcsin(c*x)/c - 1/8*(-c^2*x^2 + 1)^(3/2)*b^2*f*h*x*arcsin(c*x)/c^3 + 1/2*sqrt(-c^2*x^2 + 1)*a*b*g*x*e/c - 2/27*(c^2*x^2 - 1)*b^2*f*g*x/c^2 + (c^2*x^2 - 1)*a*b*d*h*arcsin(c*x)/c^2 + 2/3*a*b*f*g*x*arcsin(c*x)/c^2 + 1/4*b^2*d*h*arcsin(c*x)^2/c^2 + 1/4*(c^2*x^2 - 1)^2*b^2*f*h*arcsin(c*x)^2/c^4 - 2/27*(c^2*x^2 - 1)*b^2*h*x*e/c^2 + (c^2*x^2 - 1)*a*b*g*arcsin(c*x)*e/c^2 + 2/3*a*b*h*x*arcsin(c*x)*e/c^2 + 1/4*b^2*g*arcsin(c*x)^2*e/c^2 + 2*sqrt(-c^2*x^2 + 1)*a*b*d*g/c - 1/8*(-c^2*x^2 + 1)^(3/2)*a*b*f*h*x/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b^2*f*g*arcsin(c*x)/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*b^2*f*h*x*arcsin(c*x)/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*b^2*h*arcsin(c*x)*e/c^3 + 1/2*(c^2*x^2 - 1)*a^2*d*h/c^2 - 1/4*(c^2*x^2 - 1)*b^2*d*h/c^2 - 14/27*b^2*f*g*x/c^2 + 1/2*a*b*d*h*arcsin(c*x)/c^2 + 1/2*(c^2*x^2 - 1)^2*a*b*f*h*arcsin(c*x)/c^4 + 1/2*(c^2*x^2 - 1)*b^2*f*h*arcsin(c*x)^2/c^4 + 1/2*(c^2*x^2 - 1)*a^2*g*e/c^2 - 1/4*(c^2*x^2 - 1)*b^2*g*e/c^2 - 14/27*b^2*h*x*e/c^2 + 1/2*a*b*g*arcsin(c*x)*e/c^2 - 2/9*(-c^2*x^2 + 1)^(3/2)*a*b*f*g/c^3 + 5/16*sqrt(-c^2*x^2 + 1)*a*b*f*h*x/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b^2*f*g*arcsin(c*x)/c^3 - 2/9*(-c^2*x^2 + 1)^(3/2)*a*b*h*e/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*b^2*h*arcsin(c*x)*e/c^3 - 1/8*b^2*d*h/c^2 - 1/32*(c^2*x^2 - 1)^2*b^2*f*h/c^4 + (c^2*x^2 - 1)*a*b*f*h*arcsin(c*x)/c^4 + 5/32*b^2*f*h*arcsin(c*x)^2/c^4 - 1/8*b^2*g*e/c^2 + 2/3*sqrt(-c^2*x^2 + 1)*a*b*f*g/c^3 + 2/3*sqrt(-c^2*x^2 + 1)*a*b*h*e/c^3 - 5/32*(c^2*x^2 - 1)*b^2*f*h/c^4 + 5/16*a*b*f*h*arcsin(c*x)/c^4 - 17/256*b^2*f*h/c^4","B",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=""giac"")","\int \frac{{\left(f x^{2} + e x + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{h x + g}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(b*arcsin(c*x) + a)^2/(h*x + g), x)","F",0
119,0,0,0,0.000000," ","integrate((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g)^2,x, algorithm=""giac"")","\int \frac{{\left(f x^{2} + e x + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(h x + g\right)}^{2}}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)*(b*arcsin(c*x) + a)^2/(h*x + g)^2, x)","F",0
120,0,0,0,0.000000," ","integrate((e*h*x^2+2*d*h*x+e*f)*(a+b*arcsin(c*x))^2/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(e h x^{2} + 2 \, d h x + e f\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((e*h*x^2 + 2*d*h*x + e*f)*(b*arcsin(c*x) + a)^2/(e*x + d)^2, x)","F",0
121,0,0,0,0.000000," ","integrate((e*h*x^2+2*d*h*x+e*f)^2*(a+b*arcsin(c*x))^2/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(e h x^{2} + 2 \, d h x + e f\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}^{2}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((e*h*x^2 + 2*d*h*x + e*f)^2*(b*arcsin(c*x) + a)^2/(e*x + d)^2, x)","F",0
122,1,284,0,0.276065," ","integrate(x^3*arcsin(b*x+a),x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a^{3} \arcsin\left(b x + a\right)}{b^{4}} - \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} a \arcsin\left(b x + a\right)}{b^{4}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a^{2} \arcsin\left(b x + a\right)}{2 \, b^{4}} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a^{2}}{4 \, b^{4}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a^{3}}{b^{4}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)}^{2} \arcsin\left(b x + a\right)}{4 \, b^{4}} - \frac{{\left(b x + a\right)} a \arcsin\left(b x + a\right)}{b^{4}} + \frac{3 \, a^{2} \arcsin\left(b x + a\right)}{4 \, b^{4}} - \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)}}{16 \, b^{4}} + \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} a}{3 \, b^{4}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} \arcsin\left(b x + a\right)}{2 \, b^{4}} + \frac{5 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)}}{32 \, b^{4}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a}{b^{4}} + \frac{5 \, \arcsin\left(b x + a\right)}{32 \, b^{4}}"," ",0,"-(b*x + a)*a^3*arcsin(b*x + a)/b^4 - ((b*x + a)^2 - 1)*(b*x + a)*a*arcsin(b*x + a)/b^4 + 3/2*((b*x + a)^2 - 1)*a^2*arcsin(b*x + a)/b^4 + 3/4*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a^2/b^4 - sqrt(-(b*x + a)^2 + 1)*a^3/b^4 + 1/4*((b*x + a)^2 - 1)^2*arcsin(b*x + a)/b^4 - (b*x + a)*a*arcsin(b*x + a)/b^4 + 3/4*a^2*arcsin(b*x + a)/b^4 - 1/16*(-(b*x + a)^2 + 1)^(3/2)*(b*x + a)/b^4 + 1/3*(-(b*x + a)^2 + 1)^(3/2)*a/b^4 + 1/2*((b*x + a)^2 - 1)*arcsin(b*x + a)/b^4 + 5/32*sqrt(-(b*x + a)^2 + 1)*(b*x + a)/b^4 - sqrt(-(b*x + a)^2 + 1)*a/b^4 + 5/32*arcsin(b*x + a)/b^4","B",0
123,1,173,0,0.275296," ","integrate(x^2*arcsin(b*x+a),x, algorithm=""giac"")","\frac{{\left(b x + a\right)} a^{2} \arcsin\left(b x + a\right)}{b^{3}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{3 \, b^{3}} - \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} a \arcsin\left(b x + a\right)}{b^{3}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a}{2 \, b^{3}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2}}{b^{3}} + \frac{{\left(b x + a\right)} \arcsin\left(b x + a\right)}{3 \, b^{3}} - \frac{a \arcsin\left(b x + a\right)}{2 \, b^{3}} - \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{9 \, b^{3}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{3 \, b^{3}}"," ",0,"(b*x + a)*a^2*arcsin(b*x + a)/b^3 + 1/3*((b*x + a)^2 - 1)*(b*x + a)*arcsin(b*x + a)/b^3 - ((b*x + a)^2 - 1)*a*arcsin(b*x + a)/b^3 - 1/2*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a/b^3 + sqrt(-(b*x + a)^2 + 1)*a^2/b^3 + 1/3*(b*x + a)*arcsin(b*x + a)/b^3 - 1/2*a*arcsin(b*x + a)/b^3 - 1/9*(-(b*x + a)^2 + 1)^(3/2)/b^3 + 1/3*sqrt(-(b*x + a)^2 + 1)/b^3","B",0
124,1,91,0,0.296361," ","integrate(x*arcsin(b*x+a),x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a \arcsin\left(b x + a\right)}{b^{2}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} \arcsin\left(b x + a\right)}{2 \, b^{2}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)}}{4 \, b^{2}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a}{b^{2}} + \frac{\arcsin\left(b x + a\right)}{4 \, b^{2}}"," ",0,"-(b*x + a)*a*arcsin(b*x + a)/b^2 + 1/2*((b*x + a)^2 - 1)*arcsin(b*x + a)/b^2 + 1/4*sqrt(-(b*x + a)^2 + 1)*(b*x + a)/b^2 - sqrt(-(b*x + a)^2 + 1)*a/b^2 + 1/4*arcsin(b*x + a)/b^2","A",0
125,1,30,0,0.285815," ","integrate(arcsin(b*x+a),x, algorithm=""giac"")","\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=""giac"")","\int \frac{\arcsin\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arcsin(b*x + a)/x, x)","F",0
127,1,79,0,0.340345," ","integrate(arcsin(b*x+a)/x^2,x, algorithm=""giac"")","\frac{2 \, b^{2} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left| b \right|}} - \frac{\arcsin\left(b x + a\right)}{x}"," ",0,"2*b^2*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*abs(b)) - arcsin(b*x + a)/x","A",0
128,1,243,0,0.355471," ","integrate(arcsin(b*x+a)/x^3,x, algorithm=""giac"")","-{\left(\frac{a b^{2} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{2} {\left| b \right|} - {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{a b^{2} - \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} b^{2}}{b^{2} x + a b}}{{\left(a^{3} {\left| b \right|} - a {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}}\right)} b - \frac{\arcsin\left(b x + a\right)}{2 \, x^{2}}"," ",0,"-(a*b^2*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^2*abs(b) - abs(b))*sqrt(a^2 - 1)) - (a*b^2 - (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*b^2/(b^2*x + a*b))/((a^3*abs(b) - a*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))))*b - 1/2*arcsin(b*x + a)/x^2","B",0
129,1,557,0,0.481492," ","integrate(arcsin(b*x+a)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, b {\left(\frac{{\left(2 \, a^{2} b^{3} + b^{3}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{4} {\left| b \right|} - 2 \, a^{2} {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{\frac{4 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + 4 \, a^{4} b^{3} - \frac{11 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{3}}{b^{2} x + a b} - \frac{5 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{7 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - a^{2} b^{3} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a b^{3}}{b^{2} x + a b} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}}}{{\left(a^{6} {\left| b \right|} - 2 \, a^{4} {\left| b \right|} + a^{2} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{2}}\right)} - \frac{\arcsin\left(b x + a\right)}{3 \, x^{3}}"," ",0,"1/3*b*((2*a^2*b^3 + b^3)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^4*abs(b) - 2*a^2*abs(b) + abs(b))*sqrt(a^2 - 1)) - (4*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^4*b^3/(b^2*x + a*b)^2 + 4*a^4*b^3 - 11*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^3*b^3/(b^2*x + a*b) - 5*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^3*b^3/(b^2*x + a*b)^3 + 7*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^2*b^3/(b^2*x + a*b)^2 - a^2*b^3 + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a*b^3/(b^2*x + a*b) + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a*b^3/(b^2*x + a*b)^3 - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*b^3/(b^2*x + a*b)^2)/((a^6*abs(b) - 2*a^4*abs(b) + a^2*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))^2)) - 1/3*arcsin(b*x + a)/x^3","B",0
130,1,1112,0,1.147866," ","integrate(arcsin(b*x+a)/x^5,x, algorithm=""giac"")","-\frac{1}{12} \, b {\left(\frac{3 \, {\left(2 \, a^{3} b^{4} + 3 \, a b^{4}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{6} {\left| b \right|} - 3 \, a^{4} {\left| b \right|} + 3 \, a^{2} {\left| b \right|} - {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{\frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + 18 \, a^{7} b^{4} - \frac{81 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{6} b^{4}}{b^{2} x + a b} - \frac{108 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{27 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + \frac{120 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{81 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - 5 \, a^{5} b^{4} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{4} b^{4}}{b^{2} x + a b} - \frac{42 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + 2 \, a^{3} b^{4} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{4}}{b^{2} x + a b} + \frac{8 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{8 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}}}{{\left(a^{9} {\left| b \right|} - 3 \, a^{7} {\left| b \right|} + 3 \, a^{5} {\left| b \right|} - a^{3} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{3}}\right)} - \frac{\arcsin\left(b x + a\right)}{4 \, x^{4}}"," ",0,"-1/12*b*(3*(2*a^3*b^4 + 3*a*b^4)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^6*abs(b) - 3*a^4*abs(b) + 3*a^2*abs(b) - abs(b))*sqrt(a^2 - 1)) - (36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^7*b^4/(b^2*x + a*b)^2 + 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^7*b^4/(b^2*x + a*b)^4 + 18*a^7*b^4 - 81*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^6*b^4/(b^2*x + a*b) - 108*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^6*b^4/(b^2*x + a*b)^3 - 27*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^6*b^4/(b^2*x + a*b)^5 + 120*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^5*b^4/(b^2*x + a*b)^2 + 81*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^5*b^4/(b^2*x + a*b)^4 - 5*a^5*b^4 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^4*b^4/(b^2*x + a*b) - 42*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^4*b^4/(b^2*x + a*b)^3 + 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^4*b^4/(b^2*x + a*b)^5 - 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^3*b^4/(b^2*x + a*b)^2 - 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^3*b^4/(b^2*x + a*b)^4 + 2*a^3*b^4 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^2*b^4/(b^2*x + a*b) + 8*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^2*b^4/(b^2*x + a*b)^3 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^2*b^4/(b^2*x + a*b)^5 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a*b^4/(b^2*x + a*b)^2 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a*b^4/(b^2*x + a*b)^4 - 8*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*b^4/(b^2*x + a*b)^3)/((a^9*abs(b) - 3*a^7*abs(b) + 3*a^5*abs(b) - a^3*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))^3)) - 1/4*arcsin(b*x + a)/x^4","B",0
131,1,440,0,2.797567," ","integrate(x^3*arcsin(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a^{3} \arcsin\left(b x + a\right)^{2}}{b^{4}} - \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} a \arcsin\left(b x + a\right)^{2}}{b^{4}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a^{2} \arcsin\left(b x + a\right)^{2}}{2 \, b^{4}} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a^{2} \arcsin\left(b x + a\right)}{2 \, b^{4}} - \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a^{3} \arcsin\left(b x + a\right)}{b^{4}} + \frac{2 \, {\left(b x + a\right)} a^{3}}{b^{4}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)}^{2} \arcsin\left(b x + a\right)^{2}}{4 \, b^{4}} - \frac{{\left(b x + a\right)} a \arcsin\left(b x + a\right)^{2}}{b^{4}} + \frac{3 \, a^{2} \arcsin\left(b x + a\right)^{2}}{4 \, b^{4}} - \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{8 \, b^{4}} + \frac{2 \, {\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} a \arcsin\left(b x + a\right)}{3 \, b^{4}} + \frac{2 \, {\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} a}{9 \, b^{4}} - \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a^{2}}{4 \, b^{4}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} \arcsin\left(b x + a\right)^{2}}{2 \, b^{4}} + \frac{5 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{16 \, b^{4}} - \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a \arcsin\left(b x + a\right)}{b^{4}} - \frac{{\left({\left(b x + a\right)}^{2} - 1\right)}^{2}}{32 \, b^{4}} + \frac{14 \, {\left(b x + a\right)} a}{9 \, b^{4}} - \frac{3 \, a^{2}}{8 \, b^{4}} + \frac{5 \, \arcsin\left(b x + a\right)^{2}}{32 \, b^{4}} - \frac{5 \, {\left({\left(b x + a\right)}^{2} - 1\right)}}{32 \, b^{4}} - \frac{17}{256 \, b^{4}}"," ",0,"-(b*x + a)*a^3*arcsin(b*x + a)^2/b^4 - ((b*x + a)^2 - 1)*(b*x + a)*a*arcsin(b*x + a)^2/b^4 + 3/2*((b*x + a)^2 - 1)*a^2*arcsin(b*x + a)^2/b^4 + 3/2*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a^2*arcsin(b*x + a)/b^4 - 2*sqrt(-(b*x + a)^2 + 1)*a^3*arcsin(b*x + a)/b^4 + 2*(b*x + a)*a^3/b^4 + 1/4*((b*x + a)^2 - 1)^2*arcsin(b*x + a)^2/b^4 - (b*x + a)*a*arcsin(b*x + a)^2/b^4 + 3/4*a^2*arcsin(b*x + a)^2/b^4 - 1/8*(-(b*x + a)^2 + 1)^(3/2)*(b*x + a)*arcsin(b*x + a)/b^4 + 2/3*(-(b*x + a)^2 + 1)^(3/2)*a*arcsin(b*x + a)/b^4 + 2/9*((b*x + a)^2 - 1)*(b*x + a)*a/b^4 - 3/4*((b*x + a)^2 - 1)*a^2/b^4 + 1/2*((b*x + a)^2 - 1)*arcsin(b*x + a)^2/b^4 + 5/16*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*arcsin(b*x + a)/b^4 - 2*sqrt(-(b*x + a)^2 + 1)*a*arcsin(b*x + a)/b^4 - 1/32*((b*x + a)^2 - 1)^2/b^4 + 14/9*(b*x + a)*a/b^4 - 3/8*a^2/b^4 + 5/32*arcsin(b*x + a)^2/b^4 - 5/32*((b*x + a)^2 - 1)/b^4 - 17/256/b^4","A",0
132,1,271,0,2.812986," ","integrate(x^2*arcsin(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)} a^{2} \arcsin\left(b x + a\right)^{2}}{b^{3}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{3 \, b^{3}} - \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} a \arcsin\left(b x + a\right)^{2}}{b^{3}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a \arcsin\left(b x + a\right)}{b^{3}} + \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2} \arcsin\left(b x + a\right)}{b^{3}} - \frac{2 \, {\left(b x + a\right)} a^{2}}{b^{3}} + \frac{{\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{3 \, b^{3}} - \frac{a \arcsin\left(b x + a\right)^{2}}{2 \, b^{3}} - \frac{2 \, {\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} \arcsin\left(b x + a\right)}{9 \, b^{3}} - \frac{2 \, {\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)}}{27 \, b^{3}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} a}{2 \, b^{3}} + \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} \arcsin\left(b x + a\right)}{3 \, b^{3}} - \frac{14 \, {\left(b x + a\right)}}{27 \, b^{3}} + \frac{a}{4 \, b^{3}}"," ",0,"(b*x + a)*a^2*arcsin(b*x + a)^2/b^3 + 1/3*((b*x + a)^2 - 1)*(b*x + a)*arcsin(b*x + a)^2/b^3 - ((b*x + a)^2 - 1)*a*arcsin(b*x + a)^2/b^3 - sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a*arcsin(b*x + a)/b^3 + 2*sqrt(-(b*x + a)^2 + 1)*a^2*arcsin(b*x + a)/b^3 - 2*(b*x + a)*a^2/b^3 + 1/3*(b*x + a)*arcsin(b*x + a)^2/b^3 - 1/2*a*arcsin(b*x + a)^2/b^3 - 2/9*(-(b*x + a)^2 + 1)^(3/2)*arcsin(b*x + a)/b^3 - 2/27*((b*x + a)^2 - 1)*(b*x + a)/b^3 + 1/2*((b*x + a)^2 - 1)*a/b^3 + 2/3*sqrt(-(b*x + a)^2 + 1)*arcsin(b*x + a)/b^3 - 14/27*(b*x + a)/b^3 + 1/4*a/b^3","A",0
133,1,139,0,1.925470," ","integrate(x*arcsin(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a \arcsin\left(b x + a\right)^{2}}{b^{2}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} \arcsin\left(b x + a\right)^{2}}{2 \, b^{2}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{2 \, b^{2}} - \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a \arcsin\left(b x + a\right)}{b^{2}} + \frac{2 \, {\left(b x + a\right)} a}{b^{2}} + \frac{\arcsin\left(b x + a\right)^{2}}{4 \, b^{2}} - \frac{{\left(b x + a\right)}^{2} - 1}{4 \, b^{2}} - \frac{1}{8 \, b^{2}}"," ",0,"-(b*x + a)*a*arcsin(b*x + a)^2/b^2 + 1/2*((b*x + a)^2 - 1)*arcsin(b*x + a)^2/b^2 + 1/2*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*arcsin(b*x + a)/b^2 - 2*sqrt(-(b*x + a)^2 + 1)*a*arcsin(b*x + a)/b^2 + 2*(b*x + a)*a/b^2 + 1/4*arcsin(b*x + a)^2/b^2 - 1/4*((b*x + a)^2 - 1)/b^2 - 1/8/b^2","A",0
134,1,52,0,0.989815," ","integrate(arcsin(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{b} + \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} \arcsin\left(b x + a\right)}{b} - \frac{2 \, {\left(b x + a\right)}}{b}"," ",0,"(b*x + a)*arcsin(b*x + a)^2/b + 2*sqrt(-(b*x + a)^2 + 1)*arcsin(b*x + a)/b - 2*(b*x + a)/b","A",0
135,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2/x,x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^2/x, x)","F",0
136,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2/x^2,x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^2/x^2, x)","F",0
137,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^2/x^3,x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^2/x^3, x)","F",0
138,1,389,0,0.355321," ","integrate(x^2*arcsin(b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(b x + a\right)} a^{2} \arcsin\left(b x + a\right)^{3}}{b^{3}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{3}}{3 \, b^{3}} - \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} a \arcsin\left(b x + a\right)^{3}}{b^{3}} - \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a \arcsin\left(b x + a\right)^{2}}{2 \, b^{3}} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2} \arcsin\left(b x + a\right)^{2}}{b^{3}} - \frac{6 \, {\left(b x + a\right)} a^{2} \arcsin\left(b x + a\right)}{b^{3}} + \frac{{\left(b x + a\right)} \arcsin\left(b x + a\right)^{3}}{3 \, b^{3}} - \frac{a \arcsin\left(b x + a\right)^{3}}{2 \, b^{3}} - \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} \arcsin\left(b x + a\right)^{2}}{3 \, b^{3}} - \frac{2 \, {\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{9 \, b^{3}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a \arcsin\left(b x + a\right)}{2 \, b^{3}} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a}{4 \, b^{3}} - \frac{6 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2}}{b^{3}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} \arcsin\left(b x + a\right)^{2}}{b^{3}} - \frac{14 \, {\left(b x + a\right)} \arcsin\left(b x + a\right)}{9 \, b^{3}} + \frac{3 \, a \arcsin\left(b x + a\right)}{4 \, b^{3}} + \frac{2 \, {\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{27 \, b^{3}} - \frac{14 \, \sqrt{-{\left(b x + a\right)}^{2} + 1}}{9 \, b^{3}}"," ",0,"(b*x + a)*a^2*arcsin(b*x + a)^3/b^3 + 1/3*((b*x + a)^2 - 1)*(b*x + a)*arcsin(b*x + a)^3/b^3 - ((b*x + a)^2 - 1)*a*arcsin(b*x + a)^3/b^3 - 3/2*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a*arcsin(b*x + a)^2/b^3 + 3*sqrt(-(b*x + a)^2 + 1)*a^2*arcsin(b*x + a)^2/b^3 - 6*(b*x + a)*a^2*arcsin(b*x + a)/b^3 + 1/3*(b*x + a)*arcsin(b*x + a)^3/b^3 - 1/2*a*arcsin(b*x + a)^3/b^3 - 1/3*(-(b*x + a)^2 + 1)^(3/2)*arcsin(b*x + a)^2/b^3 - 2/9*((b*x + a)^2 - 1)*(b*x + a)*arcsin(b*x + a)/b^3 + 3/2*((b*x + a)^2 - 1)*a*arcsin(b*x + a)/b^3 + 3/4*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a/b^3 - 6*sqrt(-(b*x + a)^2 + 1)*a^2/b^3 + sqrt(-(b*x + a)^2 + 1)*arcsin(b*x + a)^2/b^3 - 14/9*(b*x + a)*arcsin(b*x + a)/b^3 + 3/4*a*arcsin(b*x + a)/b^3 + 2/27*(-(b*x + a)^2 + 1)^(3/2)/b^3 - 14/9*sqrt(-(b*x + a)^2 + 1)/b^3","A",0
139,1,203,0,0.414319," ","integrate(x*arcsin(b*x+a)^3,x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a \arcsin\left(b x + a\right)^{3}}{b^{2}} + \frac{{\left({\left(b x + a\right)}^{2} - 1\right)} \arcsin\left(b x + a\right)^{3}}{2 \, b^{2}} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{4 \, b^{2}} - \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a \arcsin\left(b x + a\right)^{2}}{b^{2}} + \frac{6 \, {\left(b x + a\right)} a \arcsin\left(b x + a\right)}{b^{2}} + \frac{\arcsin\left(b x + a\right)^{3}}{4 \, b^{2}} - \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} \arcsin\left(b x + a\right)}{4 \, b^{2}} - \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)}}{8 \, b^{2}} + \frac{6 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a}{b^{2}} - \frac{3 \, \arcsin\left(b x + a\right)}{8 \, b^{2}}"," ",0,"-(b*x + a)*a*arcsin(b*x + a)^3/b^2 + 1/2*((b*x + a)^2 - 1)*arcsin(b*x + a)^3/b^2 + 3/4*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*arcsin(b*x + a)^2/b^2 - 3*sqrt(-(b*x + a)^2 + 1)*a*arcsin(b*x + a)^2/b^2 + 6*(b*x + a)*a*arcsin(b*x + a)/b^2 + 1/4*arcsin(b*x + a)^3/b^2 - 3/4*((b*x + a)^2 - 1)*arcsin(b*x + a)/b^2 - 3/8*sqrt(-(b*x + a)^2 + 1)*(b*x + a)/b^2 + 6*sqrt(-(b*x + a)^2 + 1)*a/b^2 - 3/8*arcsin(b*x + a)/b^2","A",0
140,1,78,0,0.368261," ","integrate(arcsin(b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(b x + a\right)} \arcsin\left(b x + a\right)^{3}}{b} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} \arcsin\left(b x + a\right)^{2}}{b} - \frac{6 \, {\left(b x + a\right)} \arcsin\left(b x + a\right)}{b} - \frac{6 \, \sqrt{-{\left(b x + a\right)}^{2} + 1}}{b}"," ",0,"(b*x + a)*arcsin(b*x + a)^3/b + 3*sqrt(-(b*x + a)^2 + 1)*arcsin(b*x + a)^2/b - 6*(b*x + a)*arcsin(b*x + a)/b - 6*sqrt(-(b*x + a)^2 + 1)/b","A",0
141,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^3/x,x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^3/x, x)","F",0
142,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^3/x^2,x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^3/x^2, x)","F",0
143,1,56,0,0.344075," ","integrate(x^2/arcsin(b*x+a),x, algorithm=""giac"")","\frac{a^{2} \operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{b^{3}} - \frac{a \operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{b^{3}} - \frac{\operatorname{Ci}\left(3 \, \arcsin\left(b x + a\right)\right)}{4 \, b^{3}} + \frac{\operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{4 \, b^{3}}"," ",0,"a^2*cos_integral(arcsin(b*x + a))/b^3 - a*sin_integral(2*arcsin(b*x + a))/b^3 - 1/4*cos_integral(3*arcsin(b*x + a))/b^3 + 1/4*cos_integral(arcsin(b*x + a))/b^3","A",0
144,1,28,0,0.555296," ","integrate(x/arcsin(b*x+a),x, algorithm=""giac"")","-\frac{a \operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{b^{2}} + \frac{\operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{2 \, b^{2}}"," ",0,"-a*cos_integral(arcsin(b*x + a))/b^2 + 1/2*sin_integral(2*arcsin(b*x + a))/b^2","A",0
145,1,11,0,0.330490," ","integrate(1/arcsin(b*x+a),x, algorithm=""giac"")","\frac{\operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{b}"," ",0,"cos_integral(arcsin(b*x + a))/b","A",0
146,0,0,0,0.000000," ","integrate(1/x/arcsin(b*x+a),x, algorithm=""giac"")","\int \frac{1}{x \arcsin\left(b x + a\right)}\,{d x}"," ",0,"integrate(1/(x*arcsin(b*x + a)), x)","F",0
147,1,169,0,0.389684," ","integrate(x^2/arcsin(b*x+a)^2,x, algorithm=""giac"")","-\frac{a^{2} \operatorname{Si}\left(\arcsin\left(b x + a\right)\right)}{b^{3}} - \frac{2 \, a \operatorname{Ci}\left(2 \, \arcsin\left(b x + a\right)\right)}{b^{3}} + \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a}{b^{3} \arcsin\left(b x + a\right)} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2}}{b^{3} \arcsin\left(b x + a\right)} + \frac{3 \, \operatorname{Si}\left(3 \, \arcsin\left(b x + a\right)\right)}{4 \, b^{3}} - \frac{\operatorname{Si}\left(\arcsin\left(b x + a\right)\right)}{4 \, b^{3}} + \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{b^{3} \arcsin\left(b x + a\right)} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{b^{3} \arcsin\left(b x + a\right)}"," ",0,"-a^2*sin_integral(arcsin(b*x + a))/b^3 - 2*a*cos_integral(2*arcsin(b*x + a))/b^3 + 2*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a/(b^3*arcsin(b*x + a)) - sqrt(-(b*x + a)^2 + 1)*a^2/(b^3*arcsin(b*x + a)) + 3/4*sin_integral(3*arcsin(b*x + a))/b^3 - 1/4*sin_integral(arcsin(b*x + a))/b^3 + (-(b*x + a)^2 + 1)^(3/2)/(b^3*arcsin(b*x + a)) - sqrt(-(b*x + a)^2 + 1)/(b^3*arcsin(b*x + a))","B",0
148,1,83,0,1.576090," ","integrate(x/arcsin(b*x+a)^2,x, algorithm=""giac"")","\frac{a \operatorname{Si}\left(\arcsin\left(b x + a\right)\right)}{b^{2}} + \frac{\operatorname{Ci}\left(2 \, \arcsin\left(b x + a\right)\right)}{b^{2}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)}}{b^{2} \arcsin\left(b x + a\right)} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a}{b^{2} \arcsin\left(b x + a\right)}"," ",0,"a*sin_integral(arcsin(b*x + a))/b^2 + cos_integral(2*arcsin(b*x + a))/b^2 - sqrt(-(b*x + a)^2 + 1)*(b*x + a)/(b^2*arcsin(b*x + a)) + sqrt(-(b*x + a)^2 + 1)*a/(b^2*arcsin(b*x + a))","A",0
149,1,39,0,0.353907," ","integrate(1/arcsin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\operatorname{Si}\left(\arcsin\left(b x + a\right)\right)}{b} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{b \arcsin\left(b x + a\right)}"," ",0,"-sin_integral(arcsin(b*x + a))/b - sqrt(-(b*x + a)^2 + 1)/(b*arcsin(b*x + a))","A",0
150,0,0,0,0.000000," ","integrate(1/x/arcsin(b*x+a)^2,x, algorithm=""giac"")","\int \frac{1}{x \arcsin\left(b x + a\right)^{2}}\,{d x}"," ",0,"integrate(1/(x*arcsin(b*x + a)^2), x)","F",0
151,1,272,0,0.418550," ","integrate(x^2/arcsin(b*x+a)^3,x, algorithm=""giac"")","-\frac{a^{2} \operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{2 \, b^{3}} + \frac{{\left(b x + a\right)} a^{2}}{2 \, b^{3} \arcsin\left(b x + a\right)} + \frac{2 \, a \operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{b^{3}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)}}{2 \, b^{3} \arcsin\left(b x + a\right)} - \frac{2 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a}{b^{3} \arcsin\left(b x + a\right)} + \frac{9 \, \operatorname{Ci}\left(3 \, \arcsin\left(b x + a\right)\right)}{8 \, b^{3}} - \frac{\operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{8 \, b^{3}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a}{b^{3} \arcsin\left(b x + a\right)^{2}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2}}{2 \, b^{3} \arcsin\left(b x + a\right)^{2}} + \frac{b x + a}{2 \, b^{3} \arcsin\left(b x + a\right)} - \frac{a}{b^{3} \arcsin\left(b x + a\right)} + \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{2 \, b^{3} \arcsin\left(b x + a\right)^{2}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{2 \, b^{3} \arcsin\left(b x + a\right)^{2}}"," ",0,"-1/2*a^2*cos_integral(arcsin(b*x + a))/b^3 + 1/2*(b*x + a)*a^2/(b^3*arcsin(b*x + a)) + 2*a*sin_integral(2*arcsin(b*x + a))/b^3 + 3/2*((b*x + a)^2 - 1)*(b*x + a)/(b^3*arcsin(b*x + a)) - 2*((b*x + a)^2 - 1)*a/(b^3*arcsin(b*x + a)) + 9/8*cos_integral(3*arcsin(b*x + a))/b^3 - 1/8*cos_integral(arcsin(b*x + a))/b^3 + sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a/(b^3*arcsin(b*x + a)^2) - 1/2*sqrt(-(b*x + a)^2 + 1)*a^2/(b^3*arcsin(b*x + a)^2) + 1/2*(b*x + a)/(b^3*arcsin(b*x + a)) - a/(b^3*arcsin(b*x + a)) + 1/2*(-(b*x + a)^2 + 1)^(3/2)/(b^3*arcsin(b*x + a)^2) - 1/2*sqrt(-(b*x + a)^2 + 1)/(b^3*arcsin(b*x + a)^2)","A",0
152,1,139,0,0.489464," ","integrate(x/arcsin(b*x+a)^3,x, algorithm=""giac"")","\frac{a \operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{2 \, b^{2}} - \frac{{\left(b x + a\right)} a}{2 \, b^{2} \arcsin\left(b x + a\right)} - \frac{\operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{b^{2}} + \frac{{\left(b x + a\right)}^{2} - 1}{b^{2} \arcsin\left(b x + a\right)} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)}}{2 \, b^{2} \arcsin\left(b x + a\right)^{2}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a}{2 \, b^{2} \arcsin\left(b x + a\right)^{2}} + \frac{1}{2 \, b^{2} \arcsin\left(b x + a\right)}"," ",0,"1/2*a*cos_integral(arcsin(b*x + a))/b^2 - 1/2*(b*x + a)*a/(b^2*arcsin(b*x + a)) - sin_integral(2*arcsin(b*x + a))/b^2 + ((b*x + a)^2 - 1)/(b^2*arcsin(b*x + a)) - 1/2*sqrt(-(b*x + a)^2 + 1)*(b*x + a)/(b^2*arcsin(b*x + a)^2) + 1/2*sqrt(-(b*x + a)^2 + 1)*a/(b^2*arcsin(b*x + a)^2) + 1/2/(b^2*arcsin(b*x + a))","A",0
153,1,57,0,0.388330," ","integrate(1/arcsin(b*x+a)^3,x, algorithm=""giac"")","-\frac{\operatorname{Ci}\left(\arcsin\left(b x + a\right)\right)}{2 \, b} + \frac{b x + a}{2 \, b \arcsin\left(b x + a\right)} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{2 \, b \arcsin\left(b x + a\right)^{2}}"," ",0,"-1/2*cos_integral(arcsin(b*x + a))/b + 1/2*(b*x + a)/(b*arcsin(b*x + a)) - 1/2*sqrt(-(b*x + a)^2 + 1)/(b*arcsin(b*x + a)^2)","A",0
154,0,0,0,0.000000," ","integrate(1/x/arcsin(b*x+a)^3,x, algorithm=""giac"")","\int \frac{1}{x \arcsin\left(b x + a\right)^{3}}\,{d x}"," ",0,"integrate(1/(x*arcsin(b*x + a)^3), x)","F",0
155,1,2330,0,6.207163," ","integrate(x^2*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} b^{3} c^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{2} \sqrt{\pi} b^{3} c^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{2} \sqrt{\pi} a b^{2} c^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} c^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{\pi} a b^{\frac{3}{2}} c i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{3}} + \frac{\sqrt{2} \sqrt{\pi} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{2} \sqrt{\pi} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{\pi} a b^{\frac{3}{2}} c i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{3}} - \frac{\sqrt{\pi} a b c^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{\pi} a b c^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{\pi} a b c i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{2 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{3}} - \frac{\sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b}\right)}}{24 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d^{3}} + \frac{\sqrt{\pi} b^{\frac{5}{2}} c \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{3}} + \frac{\sqrt{\pi} a \sqrt{b} c i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{3}} + \frac{\sqrt{2} \sqrt{\pi} a b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{\pi} b^{\frac{5}{2}} c \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{3}} - \frac{\sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b}\right)}}{24 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d^{3}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} c^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d^{3}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} c^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d^{3}} - \frac{\sqrt{\pi} a b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d^{3}} + \frac{\sqrt{\pi} a b^{\frac{3}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d^{3}} + \frac{\sqrt{\pi} a b \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d^{3}} - \frac{\sqrt{\pi} a b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{\pi} a b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{\pi} a b \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d^{3}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(3 \, i \arcsin\left(d x + c\right)\right)}}{24 \, d^{3}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} c e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{4 \, d^{3}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d^{3}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d^{3}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} c e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{4 \, d^{3}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(-3 \, i \arcsin\left(d x + c\right)\right)}}{24 \, d^{3}}"," ",0,"1/4*sqrt(2)*sqrt(pi)*b^3*c^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^3) + 1/4*sqrt(2)*sqrt(pi)*b^3*c^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^3) + 1/2*sqrt(2)*sqrt(pi)*a*b^2*c^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^3) - 1/2*sqrt(2)*sqrt(pi)*a*b^2*c^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^3) - 1/2*sqrt(pi)*a*b^(3/2)*c*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^3) + 1/16*sqrt(2)*sqrt(pi)*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^3) + 1/16*sqrt(2)*sqrt(pi)*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^3) - 1/2*sqrt(pi)*a*b^(3/2)*c*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^3) - sqrt(pi)*a*b*c^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d^3) + sqrt(pi)*a*b*c^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d^3) + 1/2*sqrt(pi)*a*b*c*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^3) - 1/24*sqrt(pi)*b^(5/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d^3) + 1/8*sqrt(pi)*b^(5/2)*c*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^3) + 1/2*sqrt(pi)*a*sqrt(b)*c*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^3) + 1/8*sqrt(2)*sqrt(pi)*a*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^3) - 1/8*sqrt(2)*sqrt(pi)*a*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^3) - 1/8*sqrt(pi)*b^(5/2)*c*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^3) - 1/24*sqrt(pi)*b^(5/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d^3) - 1/2*sqrt(b*arcsin(d*x + c) + a)*c^2*i*e^(i*arcsin(d*x + c))/d^3 + 1/2*sqrt(b*arcsin(d*x + c) + a)*c^2*i*e^(-i*arcsin(d*x + c))/d^3 - 1/4*sqrt(pi)*a*b^(3/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d^3) + 1/4*sqrt(pi)*a*b^(3/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d^3) + 1/4*sqrt(pi)*a*b*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d^3) - 1/4*sqrt(pi)*a*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d^3) + 1/4*sqrt(pi)*a*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d^3) - 1/4*sqrt(pi)*a*b*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d^3) + 1/24*sqrt(b*arcsin(d*x + c) + a)*i*e^(3*i*arcsin(d*x + c))/d^3 + 1/4*sqrt(b*arcsin(d*x + c) + a)*c*e^(2*i*arcsin(d*x + c))/d^3 - 1/8*sqrt(b*arcsin(d*x + c) + a)*i*e^(i*arcsin(d*x + c))/d^3 + 1/8*sqrt(b*arcsin(d*x + c) + a)*i*e^(-i*arcsin(d*x + c))/d^3 + 1/4*sqrt(b*arcsin(d*x + c) + a)*c*e^(-2*i*arcsin(d*x + c))/d^3 - 1/24*sqrt(b*arcsin(d*x + c) + a)*i*e^(-3*i*arcsin(d*x + c))/d^3","B",0
156,1,1118,0,2.629012," ","integrate(x*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{\pi} b^{3} c i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{2} \sqrt{\pi} b^{3} c i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{2} \sqrt{\pi} a b^{2} c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{\pi} a b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{2}} + \frac{\sqrt{\pi} a b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{2}} + \frac{\sqrt{\pi} a b c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} a b c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} a b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{2}} - \frac{\sqrt{\pi} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{2}} - \frac{\sqrt{\pi} a \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{2}} + \frac{\sqrt{\pi} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{2}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} c i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} c i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}}"," ",0,"-1/4*sqrt(2)*sqrt(pi)*b^3*c*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^2) - 1/4*sqrt(2)*sqrt(pi)*b^3*c*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^2) - 1/2*sqrt(2)*sqrt(pi)*a*b^2*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^2) + 1/2*sqrt(2)*sqrt(pi)*a*b^2*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^2) + 1/4*sqrt(pi)*a*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^2) + 1/4*sqrt(pi)*a*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^2) + sqrt(pi)*a*b*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d^2) - sqrt(pi)*a*b*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d^2) - 1/4*sqrt(pi)*a*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^2) - 1/16*sqrt(pi)*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^2) - 1/4*sqrt(pi)*a*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^2) + 1/16*sqrt(pi)*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^2) + 1/2*sqrt(b*arcsin(d*x + c) + a)*c*i*e^(i*arcsin(d*x + c))/d^2 - 1/2*sqrt(b*arcsin(d*x + c) + a)*c*i*e^(-i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*e^(2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*e^(-2*i*arcsin(d*x + c))/d^2","B",0
157,1,579,0,4.831021," ","integrate((a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{\pi} a \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d}"," ",0,"1/4*sqrt(2)*sqrt(pi)*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 1/4*sqrt(2)*sqrt(pi)*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*i*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*i*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + sqrt(pi)*a*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d)","B",0
158,1,2058,0,2.977436," ","integrate(x*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{\pi} a b^{3} c i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{2} \sqrt{\pi} a b^{3} c i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{2} \sqrt{\pi} a b^{2} c i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{2} \sqrt{\pi} a b^{2} c i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{2}} - \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{2}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b c i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b c i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} + \frac{\sqrt{\pi} a^{2} b c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} a^{2} b c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} a^{2} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{2}} - \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{2}} - \frac{\sqrt{\pi} a^{2} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{2}} + \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{2}} + \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{2}} + \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d^{2}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a c i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a c i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} + \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d^{2}} - \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{2}} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{32 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b c e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b c e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{32 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}}"," ",0,"-1/2*sqrt(2)*sqrt(pi)*a*b^3*c*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^2) - 1/2*sqrt(2)*sqrt(pi)*a*b^3*c*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^2) - 1/2*sqrt(2)*sqrt(pi)*a^2*b^2*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^2) + 1/2*sqrt(2)*sqrt(pi)*a*b^2*c*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d^2) + 1/2*sqrt(2)*sqrt(pi)*a^2*b^2*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^2) + 1/2*sqrt(2)*sqrt(pi)*a*b^2*c*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d^2) + 1/4*sqrt(pi)*a^2*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^2) - 3/8*sqrt(2)*sqrt(pi)*b^3*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d^2) + 3/8*sqrt(2)*sqrt(pi)*b^3*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d^2) + 1/4*sqrt(pi)*a^2*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^2) + 1/2*sqrt(b*arcsin(d*x + c) + a)*b*c*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d^2 - 1/2*sqrt(b*arcsin(d*x + c) + a)*b*c*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d^2 + sqrt(pi)*a^2*b*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d^2) - sqrt(pi)*a^2*b*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d^2) - 1/4*sqrt(pi)*a^2*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^2) - 1/8*sqrt(pi)*a*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^2) - 1/4*sqrt(pi)*a^2*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^2) + 3/64*sqrt(pi)*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^2) + 1/8*sqrt(pi)*a*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^2) + 3/64*sqrt(pi)*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^2*i/abs(b) - b)*d^2) + 1/2*sqrt(b*arcsin(d*x + c) + a)*a*c*i*e^(i*arcsin(d*x + c))/d^2 - 1/2*sqrt(b*arcsin(d*x + c) + a)*a*c*i*e^(-i*arcsin(d*x + c))/d^2 + 1/8*sqrt(pi)*a*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^(5/2)*i/abs(b) + b^(3/2))*d^2) - 1/8*sqrt(pi)*a*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^2) - 3/32*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c))/d^2 - 3/4*sqrt(b*arcsin(d*x + c) + a)*b*c*e^(i*arcsin(d*x + c))/d^2 - 3/4*sqrt(b*arcsin(d*x + c) + a)*b*c*e^(-i*arcsin(d*x + c))/d^2 + 3/32*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(-2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*e^(2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*e^(-2*i*arcsin(d*x + c))/d^2","B",0
159,1,1091,0,3.868721," ","integrate((a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/2*sqrt(2)*sqrt(pi)*a*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a^2*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a^2*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 3/8*sqrt(2)*sqrt(pi)*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 3/8*sqrt(2)*sqrt(pi)*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a^2*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + sqrt(pi)*a^2*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(-i*arcsin(d*x + c))/d + 3/4*sqrt(b*arcsin(d*x + c) + a)*b*e^(i*arcsin(d*x + c))/d + 3/4*sqrt(b*arcsin(d*x + c) + a)*b*e^(-i*arcsin(d*x + c))/d","B",0
160,1,2820,0,10.984278," ","integrate(x*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} c i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} c i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} c i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} c i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} c i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} c i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d^{2}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} c i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} c i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{2}} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{2}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b c i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b c i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{d^{2}} - \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{64 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d^{2}} + \frac{\sqrt{\pi} a^{3} b c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} a^{3} b c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} a^{3} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{2}} - \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{64 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{2}} - \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d^{2}} - \frac{\sqrt{\pi} a^{3} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{2}} + \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{2}} + \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d^{2}} + \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d^{2}} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{32 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} c i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} - \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} c i e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} c \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} c i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d^{2}} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} c i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} c \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{32 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} + \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d^{2}} - \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d^{2}} + \frac{15 \, \sqrt{\pi} b^{\frac{7}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{256 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d^{2}} - \frac{15 \, \sqrt{\pi} b^{\frac{7}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{256 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d^{2}} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{32 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b c e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b c e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{32 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{4 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(2 \, i \arcsin\left(d x + c\right)\right)}}{128 \, d^{2}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{8 \, d^{2}} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right)\right)}}{128 \, d^{2}}"," ",0,"-1/2*sqrt(2)*sqrt(pi)*a^3*b^3*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d^2) - 3/2*sqrt(2)*sqrt(pi)*a^2*b^3*c*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d^2) + 1/2*sqrt(2)*sqrt(pi)*a^3*b^3*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d^2) - 3/2*sqrt(2)*sqrt(pi)*a^2*b^3*c*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d^2) + 3/2*sqrt(2)*sqrt(pi)*a^2*b^2*c*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d^2) + 15/16*sqrt(2)*sqrt(pi)*b^4*c*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d^2) + 3/2*sqrt(2)*sqrt(pi)*a^2*b^2*c*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d^2) + 15/16*sqrt(2)*sqrt(pi)*b^4*c*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d^2) + 1/2*sqrt(b*arcsin(d*x + c) + a)*b^2*c*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d^2 - 1/2*sqrt(b*arcsin(d*x + c) + a)*b^2*c*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d^2 + 1/4*sqrt(pi)*a^3*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^2) + 1/4*sqrt(pi)*a^3*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^2) + sqrt(b*arcsin(d*x + c) + a)*a*b*c*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d^2 - sqrt(b*arcsin(d*x + c) + a)*a*b*c*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d^2 - 9/64*sqrt(pi)*a*b^3*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^(5/2)*i/abs(b) + b^(3/2))*d^2) + sqrt(pi)*a^3*b*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d^2) - sqrt(pi)*a^3*b*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d^2) - 1/4*sqrt(pi)*a^3*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^2) - 9/64*sqrt(pi)*a*b^3*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^2) - 3/8*sqrt(pi)*a^2*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^3*i/abs(b) + b^2)*d^2) - 1/4*sqrt(pi)*a^3*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^2) + 9/64*sqrt(pi)*a*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^2) + 3/8*sqrt(pi)*a^2*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^3*i/abs(b) - b^2)*d^2) + 9/64*sqrt(pi)*a*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^2*i/abs(b) - b)*d^2) - 5/32*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(2*i*arcsin(d*x + c))/d^2 + 1/2*sqrt(b*arcsin(d*x + c) + a)*a^2*c*i*e^(i*arcsin(d*x + c))/d^2 - 15/8*sqrt(b*arcsin(d*x + c) + a)*b^2*c*i*e^(i*arcsin(d*x + c))/d^2 - 5/4*sqrt(b*arcsin(d*x + c) + a)*b^2*c*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d^2 - 1/2*sqrt(b*arcsin(d*x + c) + a)*a^2*c*i*e^(-i*arcsin(d*x + c))/d^2 + 15/8*sqrt(b*arcsin(d*x + c) + a)*b^2*c*i*e^(-i*arcsin(d*x + c))/d^2 - 5/4*sqrt(b*arcsin(d*x + c) + a)*b^2*c*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d^2 + 5/32*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(-2*i*arcsin(d*x + c))/d^2 + 3/8*sqrt(pi)*a^2*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^(5/2)*i/abs(b) + b^(3/2))*d^2) - 3/8*sqrt(pi)*a^2*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(5/2)*i/abs(b) - b^(3/2))*d^2) + 15/256*sqrt(pi)*b^(7/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/((b^2*i/abs(b) + b)*d^2) - 15/256*sqrt(pi)*b^(7/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^2*i/abs(b) - b)*d^2) - 5/32*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(2*i*arcsin(d*x + c))/d^2 - 1/4*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c))/d^2 - 5/4*sqrt(b*arcsin(d*x + c) + a)*a*b*c*e^(i*arcsin(d*x + c))/d^2 - 5/4*sqrt(b*arcsin(d*x + c) + a)*a*b*c*e^(-i*arcsin(d*x + c))/d^2 + 5/32*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(-2*i*arcsin(d*x + c))/d^2 - 1/4*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(2*i*arcsin(d*x + c))/d^2 + 15/128*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(2*i*arcsin(d*x + c))/d^2 - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(-2*i*arcsin(d*x + c))/d^2 + 15/128*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(-2*i*arcsin(d*x + c))/d^2","B",0
161,1,1317,0,6.880631," ","integrate((a+b*arcsin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{d} - \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/2*sqrt(2)*sqrt(pi)*a^3*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 3/2*sqrt(2)*sqrt(pi)*a^2*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a^3*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 3/2*sqrt(2)*sqrt(pi)*a^2*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 3/2*sqrt(2)*sqrt(pi)*a^2*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 15/16*sqrt(2)*sqrt(pi)*b^4*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 3/2*sqrt(2)*sqrt(pi)*a^2*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 15/16*sqrt(2)*sqrt(pi)*b^4*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d - sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a^3*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + sqrt(pi)*a^3*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(i*arcsin(d*x + c))/d + 15/8*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(-i*arcsin(d*x + c))/d - 15/8*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(-i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(-i*arcsin(d*x + c))/d","B",0
162,1,2541,0,5.546834," ","integrate((a+b*arcsin(d*x+c))^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{\pi} a^{4} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{5} i}{\sqrt{{\left| b \right|}}} + b^{4} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{4} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{5} i}{\sqrt{{\left| b \right|}}} - b^{4} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{4} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{2 \, \sqrt{2} \sqrt{\pi} a^{4} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{4 \, \sqrt{2} \sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{2 \, \sqrt{2} \sqrt{\pi} a^{4} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{4 \, \sqrt{2} \sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{105 \, \sqrt{2} \sqrt{\pi} b^{5} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{32 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{105 \, \sqrt{2} \sqrt{\pi} b^{5} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{32 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d} - \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(i \arcsin\left(d x + c\right)\right)}}{16 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{16 \, d}"," ",0,"-1/2*sqrt(2)*sqrt(pi)*a^4*b^4*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^5*i/sqrt(abs(b)) + b^4*sqrt(abs(b)))*d) - sqrt(2)*sqrt(pi)*a^3*b^4*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a^4*b^4*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^5*i/sqrt(abs(b)) - b^4*sqrt(abs(b)))*d) - sqrt(2)*sqrt(pi)*a^3*b^4*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 2*sqrt(2)*sqrt(pi)*a^4*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 4*sqrt(2)*sqrt(pi)*a^3*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 2*sqrt(2)*sqrt(pi)*a^4*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 4*sqrt(2)*sqrt(pi)*a^3*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(-i*arcsin(d*x + c))/d - sqrt(2)*sqrt(pi)*a^4*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) + 9/4*sqrt(2)*sqrt(pi)*a^2*b^4*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 3*sqrt(2)*sqrt(pi)*a^3*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + sqrt(2)*sqrt(pi)*a^4*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 9/4*sqrt(2)*sqrt(pi)*a^2*b^4*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 3*sqrt(2)*sqrt(pi)*a^3*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 3/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d + 3/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d - 9/4*sqrt(2)*sqrt(pi)*a^2*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 105/32*sqrt(2)*sqrt(pi)*b^5*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 9/4*sqrt(2)*sqrt(pi)*a^2*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 105/32*sqrt(2)*sqrt(pi)*b^5*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 3/2*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 35/8*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d + 3/2*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d - 35/8*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a^4*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + sqrt(pi)*a^4*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(i*arcsin(d*x + c))/d + 35/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(i*arcsin(d*x + c))/d + 7/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(-i*arcsin(d*x + c))/d - 35/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(-i*arcsin(d*x + c))/d + 7/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(i*arcsin(d*x + c))/d - 105/16*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(-i*arcsin(d*x + c))/d - 105/16*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(-i*arcsin(d*x + c))/d","B",0
163,1,665,0,2.195566," ","integrate(x^2/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} c^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{\pi} c^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{\pi} c i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{2 \, {\left(\frac{b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{b}\right)} d^{3}} + \frac{\sqrt{\pi} c i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{2 \, \sqrt{b} d^{3} {\left(\frac{b i}{{\left| b \right|}} + 1\right)}} + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{3}{2}} i}{{\left| b \right|}} + \sqrt{6} \sqrt{b}\right)} d^{3}} - \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d^{3}} + \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d^{3}} - \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b}\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{6} \sqrt{b}\right)} d^{3}}"," ",0,"-sqrt(pi)*c^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d^3) + sqrt(pi)*c^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d^3) + 1/2*sqrt(pi)*c*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(3/2)*i/abs(b) - sqrt(b))*d^3) + 1/2*sqrt(pi)*c*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/(sqrt(b)*d^3*(b*i/abs(b) + 1)) + 1/4*sqrt(pi)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b)/((sqrt(6)*b^(3/2)*i/abs(b) + sqrt(6)*sqrt(b))*d^3) - 1/4*sqrt(pi)*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d^3) + 1/4*sqrt(pi)*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d^3) - 1/4*sqrt(pi)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b)/((sqrt(6)*b^(3/2)*i/abs(b) - sqrt(6)*sqrt(b))*d^3)","A",0
164,1,318,0,5.973047," ","integrate(x/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} c \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} c \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d^{2}} - \frac{\sqrt{\pi} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b}\right)}}{4 \, {\left(\frac{b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{b}\right)} d^{2}} - \frac{\sqrt{\pi} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b}\right)}}{4 \, \sqrt{b} d^{2} {\left(\frac{b i}{{\left| b \right|}} + 1\right)}}"," ",0,"sqrt(pi)*c*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d^2) - sqrt(pi)*c*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d^2) - 1/4*sqrt(pi)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b)/((b^(3/2)*i/abs(b) - sqrt(b))*d^2) - 1/4*sqrt(pi)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b)/(sqrt(b)*d^2*(b*i/abs(b) + 1))","A",0
165,1,170,0,5.005055," ","integrate(1/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d}"," ",0,"-sqrt(pi)*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + sqrt(pi)*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d)","A",0
166,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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,-1,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(d*x+c))^n,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(d*x+c))^n,x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
177,1,167,0,0.380541," ","integrate((d*e*x+c*e)^4*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{5} a e^{4}}{5 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{4}}{5 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{4}}{5 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b e^{4}}{25 \, d} + \frac{{\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b e^{4}}{15 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b e^{4}}{5 \, d}"," ",0,"1/5*(d*x + c)^5*a*e^4/d + 1/5*((d*x + c)^2 - 1)^2*(d*x + c)*b*arcsin(d*x + c)*e^4/d + 2/5*((d*x + c)^2 - 1)*(d*x + c)*b*arcsin(d*x + c)*e^4/d + 1/25*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b*e^4/d + 1/5*(d*x + c)*b*arcsin(d*x + c)*e^4/d - 2/15*(-(d*x + c)^2 + 1)^(3/2)*b*e^4/d + 1/5*sqrt(-(d*x + c)^2 + 1)*b*e^4/d","A",0
178,1,130,0,0.407355," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{4} a e^{3}}{4 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b \arcsin\left(d x + c\right) e^{3}}{4 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b e^{3}}{16 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b \arcsin\left(d x + c\right) e^{3}}{2 \, d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b e^{3}}{32 \, d} + \frac{5 \, b \arcsin\left(d x + c\right) e^{3}}{32 \, d}"," ",0,"1/4*(d*x + c)^4*a*e^3/d + 1/4*((d*x + c)^2 - 1)^2*b*arcsin(d*x + c)*e^3/d - 1/16*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b*e^3/d + 1/2*((d*x + c)^2 - 1)*b*arcsin(d*x + c)*e^3/d + 5/32*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b*e^3/d + 5/32*b*arcsin(d*x + c)*e^3/d","A",0
179,1,105,0,0.757270," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{3} a e^{2}}{3 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{2}}{3 \, d} + \frac{{\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{2}}{3 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b e^{2}}{9 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b e^{2}}{3 \, d}"," ",0,"1/3*(d*x + c)^3*a*e^2/d + 1/3*((d*x + c)^2 - 1)*(d*x + c)*b*arcsin(d*x + c)*e^2/d + 1/3*(d*x + c)*b*arcsin(d*x + c)*e^2/d - 1/9*(-(d*x + c)^2 + 1)^(3/2)*b*e^2/d + 1/3*sqrt(-(d*x + c)^2 + 1)*b*e^2/d","A",0
180,1,81,0,0.636049," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b \arcsin\left(d x + c\right) e}{2 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b e}{4 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a e}{2 \, d} + \frac{b \arcsin\left(d x + c\right) e}{4 \, d}"," ",0,"1/2*((d*x + c)^2 - 1)*b*arcsin(d*x + c)*e/d + 1/4*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b*e/d + 1/2*((d*x + c)^2 - 1)*a*e/d + 1/4*b*arcsin(d*x + c)*e/d","A",0
181,1,35,0,0.572634," ","integrate(a+b*arcsin(d*x+c),x, algorithm=""giac"")","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=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/(d*e*x + c*e), x)","F",0
183,1,110,0,0.508985," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""giac"")","-\frac{1}{2} \, b d {\left(\frac{{\left(\log\left(\sqrt{-{\left(d x e + c e\right)}^{2} e^{\left(-2\right)} + 1} + 1\right) - \log\left(-\sqrt{-{\left(d x e + c e\right)}^{2} e^{\left(-2\right)} + 1} + 1\right)\right)} e^{\left(-4\right)}}{d^{2}} + \frac{2 \, \arcsin\left(d x + c\right) e^{\left(-3\right)}}{{\left(d x e + c e\right)} d^{2}}\right)} e^{2} - \frac{a e^{\left(-1\right)}}{{\left(d x e + c e\right)} d}"," ",0,"-1/2*b*d*((log(sqrt(-(d*x*e + c*e)^2*e^(-2) + 1) + 1) - log(-sqrt(-(d*x*e + c*e)^2*e^(-2) + 1) + 1))*e^(-4)/d^2 + 2*arcsin(d*x + c)*e^(-3)/((d*x*e + c*e)*d^2))*e^2 - a*e^(-1)/((d*x*e + c*e)*d)","B",0
184,1,223,0,0.498945," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^3,x, algorithm=""giac"")","-\frac{b \arcsin\left(d x + c\right) e^{\left(-3\right)}}{4 \, d} - \frac{{\left(d x + c\right)}^{2} b \arcsin\left(d x + c\right) e^{\left(-3\right)}}{8 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} \arcsin\left(d x + c\right) e^{\left(-3\right)}}{8 \, {\left(d x + c\right)}^{2} d} - \frac{a e^{\left(-3\right)}}{4 \, d} - \frac{{\left(d x + c\right)}^{2} a e^{\left(-3\right)}}{8 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} + \frac{{\left(d x + c\right)} b e^{\left(-3\right)}}{4 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} e^{\left(-3\right)}}{4 \, {\left(d x + c\right)} d} - \frac{a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} e^{\left(-3\right)}}{8 \, {\left(d x + c\right)}^{2} d}"," ",0,"-1/4*b*arcsin(d*x + c)*e^(-3)/d - 1/8*(d*x + c)^2*b*arcsin(d*x + c)*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) - 1/8*b*(sqrt(-(d*x + c)^2 + 1) + 1)^2*arcsin(d*x + c)*e^(-3)/((d*x + c)^2*d) - 1/4*a*e^(-3)/d - 1/8*(d*x + c)^2*a*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) + 1/4*(d*x + c)*b*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/4*b*(sqrt(-(d*x + c)^2 + 1) + 1)*e^(-3)/((d*x + c)*d) - 1/8*a*(sqrt(-(d*x + c)^2 + 1) + 1)^2*e^(-3)/((d*x + c)^2*d)","B",0
185,1,376,0,2.338326," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^4,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)}^{3} b \arcsin\left(d x + c\right) e^{\left(-4\right)}}{24 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3}} - \frac{{\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{\left(-4\right)}}{8 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} \arcsin\left(d x + c\right) e^{\left(-4\right)}}{8 \, {\left(d x + c\right)} d} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3} \arcsin\left(d x + c\right) e^{\left(-4\right)}}{24 \, {\left(d x + c\right)}^{3} d} - \frac{b e^{\left(-4\right)} \log\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}{6 \, d} + \frac{b e^{\left(-4\right)} \log\left({\left| d x + c \right|}\right)}{6 \, d} - \frac{{\left(d x + c\right)}^{3} a e^{\left(-4\right)}}{24 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3}} + \frac{{\left(d x + c\right)}^{2} b e^{\left(-4\right)}}{24 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} - \frac{{\left(d x + c\right)} a e^{\left(-4\right)}}{8 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} e^{\left(-4\right)}}{8 \, {\left(d x + c\right)} d} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} e^{\left(-4\right)}}{24 \, {\left(d x + c\right)}^{2} d} - \frac{a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3} e^{\left(-4\right)}}{24 \, {\left(d x + c\right)}^{3} d}"," ",0,"-1/24*(d*x + c)^3*b*arcsin(d*x + c)*e^(-4)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^3) - 1/8*(d*x + c)*b*arcsin(d*x + c)*e^(-4)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/8*b*(sqrt(-(d*x + c)^2 + 1) + 1)*arcsin(d*x + c)*e^(-4)/((d*x + c)*d) - 1/24*b*(sqrt(-(d*x + c)^2 + 1) + 1)^3*arcsin(d*x + c)*e^(-4)/((d*x + c)^3*d) - 1/6*b*e^(-4)*log(sqrt(-(d*x + c)^2 + 1) + 1)/d + 1/6*b*e^(-4)*log(abs(d*x + c))/d - 1/24*(d*x + c)^3*a*e^(-4)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^3) + 1/24*(d*x + c)^2*b*e^(-4)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) - 1/8*(d*x + c)*a*e^(-4)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/8*a*(sqrt(-(d*x + c)^2 + 1) + 1)*e^(-4)/((d*x + c)*d) - 1/24*b*(sqrt(-(d*x + c)^2 + 1) + 1)^2*e^(-4)/((d*x + c)^2*d) - 1/24*a*(sqrt(-(d*x + c)^2 + 1) + 1)^3*e^(-4)/((d*x + c)^3*d)","B",0
186,1,432,0,0.314920," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^5,x, algorithm=""giac"")","-\frac{1}{192} \, d {\left(\frac{18 \, b \arcsin\left(d x + c\right) e^{\left(-7\right)}}{d^{2}} + \frac{3 \, {\left(d x + c\right)}^{4} b \arcsin\left(d x + c\right) e^{\left(-7\right)}}{d^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{4}} + \frac{12 \, {\left(d x + c\right)}^{2} b \arcsin\left(d x + c\right) e^{\left(-7\right)}}{d^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} + \frac{12 \, b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} \arcsin\left(d x + c\right) e^{\left(-7\right)}}{{\left(d x + c\right)}^{2} d^{2}} + \frac{3 \, b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{4} \arcsin\left(d x + c\right) e^{\left(-7\right)}}{{\left(d x + c\right)}^{4} d^{2}} + \frac{18 \, a e^{\left(-7\right)}}{d^{2}} + \frac{3 \, {\left(d x + c\right)}^{4} a e^{\left(-7\right)}}{d^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{4}} - \frac{2 \, {\left(d x + c\right)}^{3} b e^{\left(-7\right)}}{d^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3}} + \frac{12 \, {\left(d x + c\right)}^{2} a e^{\left(-7\right)}}{d^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} - \frac{18 \, {\left(d x + c\right)} b e^{\left(-7\right)}}{d^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} + \frac{18 \, b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} e^{\left(-7\right)}}{{\left(d x + c\right)} d^{2}} + \frac{12 \, a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} e^{\left(-7\right)}}{{\left(d x + c\right)}^{2} d^{2}} + \frac{2 \, b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3} e^{\left(-7\right)}}{{\left(d x + c\right)}^{3} d^{2}} + \frac{3 \, a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{4} e^{\left(-7\right)}}{{\left(d x + c\right)}^{4} d^{2}}\right)} e^{2}"," ",0,"-1/192*d*(18*b*arcsin(d*x + c)*e^(-7)/d^2 + 3*(d*x + c)^4*b*arcsin(d*x + c)*e^(-7)/(d^2*(sqrt(-(d*x + c)^2 + 1) + 1)^4) + 12*(d*x + c)^2*b*arcsin(d*x + c)*e^(-7)/(d^2*(sqrt(-(d*x + c)^2 + 1) + 1)^2) + 12*b*(sqrt(-(d*x + c)^2 + 1) + 1)^2*arcsin(d*x + c)*e^(-7)/((d*x + c)^2*d^2) + 3*b*(sqrt(-(d*x + c)^2 + 1) + 1)^4*arcsin(d*x + c)*e^(-7)/((d*x + c)^4*d^2) + 18*a*e^(-7)/d^2 + 3*(d*x + c)^4*a*e^(-7)/(d^2*(sqrt(-(d*x + c)^2 + 1) + 1)^4) - 2*(d*x + c)^3*b*e^(-7)/(d^2*(sqrt(-(d*x + c)^2 + 1) + 1)^3) + 12*(d*x + c)^2*a*e^(-7)/(d^2*(sqrt(-(d*x + c)^2 + 1) + 1)^2) - 18*(d*x + c)*b*e^(-7)/(d^2*(sqrt(-(d*x + c)^2 + 1) + 1)) + 18*b*(sqrt(-(d*x + c)^2 + 1) + 1)*e^(-7)/((d*x + c)*d^2) + 12*a*(sqrt(-(d*x + c)^2 + 1) + 1)^2*e^(-7)/((d*x + c)^2*d^2) + 2*b*(sqrt(-(d*x + c)^2 + 1) + 1)^3*e^(-7)/((d*x + c)^3*d^2) + 3*a*(sqrt(-(d*x + c)^2 + 1) + 1)^4*e^(-7)/((d*x + c)^4*d^2))*e^2","B",0
187,1,580,0,1.521552," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^6,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)}^{5} b \arcsin\left(d x + c\right) e^{\left(-6\right)}}{160 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{5}} - \frac{{\left(d x + c\right)}^{3} b \arcsin\left(d x + c\right) e^{\left(-6\right)}}{32 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3}} - \frac{{\left(d x + c\right)} b \arcsin\left(d x + c\right) e^{\left(-6\right)}}{16 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} \arcsin\left(d x + c\right) e^{\left(-6\right)}}{16 \, {\left(d x + c\right)} d} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3} \arcsin\left(d x + c\right) e^{\left(-6\right)}}{32 \, {\left(d x + c\right)}^{3} d} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{5} \arcsin\left(d x + c\right) e^{\left(-6\right)}}{160 \, {\left(d x + c\right)}^{5} d} - \frac{3 \, b e^{\left(-6\right)} \log\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}{40 \, d} + \frac{3 \, b e^{\left(-6\right)} \log\left({\left| d x + c \right|}\right)}{40 \, d} - \frac{{\left(d x + c\right)}^{5} a e^{\left(-6\right)}}{160 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{5}} + \frac{{\left(d x + c\right)}^{4} b e^{\left(-6\right)}}{320 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{4}} - \frac{{\left(d x + c\right)}^{3} a e^{\left(-6\right)}}{32 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3}} + \frac{{\left(d x + c\right)}^{2} b e^{\left(-6\right)}}{40 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} - \frac{{\left(d x + c\right)} a e^{\left(-6\right)}}{16 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} e^{\left(-6\right)}}{16 \, {\left(d x + c\right)} d} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} e^{\left(-6\right)}}{40 \, {\left(d x + c\right)}^{2} d} - \frac{a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{3} e^{\left(-6\right)}}{32 \, {\left(d x + c\right)}^{3} d} - \frac{b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{4} e^{\left(-6\right)}}{320 \, {\left(d x + c\right)}^{4} d} - \frac{a {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{5} e^{\left(-6\right)}}{160 \, {\left(d x + c\right)}^{5} d}"," ",0,"-1/160*(d*x + c)^5*b*arcsin(d*x + c)*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^5) - 1/32*(d*x + c)^3*b*arcsin(d*x + c)*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^3) - 1/16*(d*x + c)*b*arcsin(d*x + c)*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/16*b*(sqrt(-(d*x + c)^2 + 1) + 1)*arcsin(d*x + c)*e^(-6)/((d*x + c)*d) - 1/32*b*(sqrt(-(d*x + c)^2 + 1) + 1)^3*arcsin(d*x + c)*e^(-6)/((d*x + c)^3*d) - 1/160*b*(sqrt(-(d*x + c)^2 + 1) + 1)^5*arcsin(d*x + c)*e^(-6)/((d*x + c)^5*d) - 3/40*b*e^(-6)*log(sqrt(-(d*x + c)^2 + 1) + 1)/d + 3/40*b*e^(-6)*log(abs(d*x + c))/d - 1/160*(d*x + c)^5*a*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^5) + 1/320*(d*x + c)^4*b*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^4) - 1/32*(d*x + c)^3*a*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^3) + 1/40*(d*x + c)^2*b*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) - 1/16*(d*x + c)*a*e^(-6)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/16*a*(sqrt(-(d*x + c)^2 + 1) + 1)*e^(-6)/((d*x + c)*d) - 1/40*b*(sqrt(-(d*x + c)^2 + 1) + 1)^2*e^(-6)/((d*x + c)^2*d) - 1/32*a*(sqrt(-(d*x + c)^2 + 1) + 1)^3*e^(-6)/((d*x + c)^3*d) - 1/320*b*(sqrt(-(d*x + c)^2 + 1) + 1)^4*e^(-6)/((d*x + c)^4*d) - 1/160*a*(sqrt(-(d*x + c)^2 + 1) + 1)^5*e^(-6)/((d*x + c)^5*d)","B",0
188,1,427,0,0.481645," ","integrate((d*e*x+c*e)^4*(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{5} a^{2} e^{4}}{5 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} a b \arcsin\left(d x + c\right) e^{4}}{5 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} \arcsin\left(d x + c\right) e^{4}}{25 \, d} - \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b^{2} e^{4}}{125 \, d} + \frac{4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b \arcsin\left(d x + c\right) e^{4}}{5 \, d} + \frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} a b e^{4}}{25 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{2} \arcsin\left(d x + c\right) e^{4}}{15 \, d} - \frac{76 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{2} e^{4}}{1125 \, d} + \frac{2 \, {\left(d x + c\right)} a b \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b e^{4}}{15 \, d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{298 \, {\left(d x + c\right)} b^{2} e^{4}}{1125 \, d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b e^{4}}{5 \, d}"," ",0,"1/5*(d*x + c)^5*a^2*e^4/d + 1/5*((d*x + c)^2 - 1)^2*(d*x + c)*b^2*arcsin(d*x + c)^2*e^4/d + 2/5*((d*x + c)^2 - 1)^2*(d*x + c)*a*b*arcsin(d*x + c)*e^4/d + 2/5*((d*x + c)^2 - 1)*(d*x + c)*b^2*arcsin(d*x + c)^2*e^4/d + 2/25*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b^2*arcsin(d*x + c)*e^4/d - 2/125*((d*x + c)^2 - 1)^2*(d*x + c)*b^2*e^4/d + 4/5*((d*x + c)^2 - 1)*(d*x + c)*a*b*arcsin(d*x + c)*e^4/d + 1/5*(d*x + c)*b^2*arcsin(d*x + c)^2*e^4/d + 2/25*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*a*b*e^4/d - 4/15*(-(d*x + c)^2 + 1)^(3/2)*b^2*arcsin(d*x + c)*e^4/d - 76/1125*((d*x + c)^2 - 1)*(d*x + c)*b^2*e^4/d + 2/5*(d*x + c)*a*b*arcsin(d*x + c)*e^4/d - 4/15*(-(d*x + c)^2 + 1)^(3/2)*a*b*e^4/d + 2/5*sqrt(-(d*x + c)^2 + 1)*b^2*arcsin(d*x + c)*e^4/d - 298/1125*(d*x + c)*b^2*e^4/d + 2/5*sqrt(-(d*x + c)^2 + 1)*a*b*e^4/d","B",0
189,1,328,0,0.281465," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{4} a^{2} e^{3}}{4 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{4 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{3}}{8 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b \arcsin\left(d x + c\right) e^{3}}{2 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{2 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a b e^{3}}{8 \, d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{3}}{16 \, d} - \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{2} e^{3}}{32 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a b \arcsin\left(d x + c\right) e^{3}}{d} + \frac{5 \, b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{32 \, d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b e^{3}}{16 \, d} - \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{2} e^{3}}{32 \, d} + \frac{5 \, a b \arcsin\left(d x + c\right) e^{3}}{16 \, d} - \frac{17 \, b^{2} e^{3}}{256 \, d}"," ",0,"1/4*(d*x + c)^4*a^2*e^3/d + 1/4*((d*x + c)^2 - 1)^2*b^2*arcsin(d*x + c)^2*e^3/d - 1/8*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^2*arcsin(d*x + c)*e^3/d + 1/2*((d*x + c)^2 - 1)^2*a*b*arcsin(d*x + c)*e^3/d + 1/2*((d*x + c)^2 - 1)*b^2*arcsin(d*x + c)^2*e^3/d - 1/8*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a*b*e^3/d + 5/16*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^2*arcsin(d*x + c)*e^3/d - 1/32*((d*x + c)^2 - 1)^2*b^2*e^3/d + ((d*x + c)^2 - 1)*a*b*arcsin(d*x + c)*e^3/d + 5/32*b^2*arcsin(d*x + c)^2*e^3/d + 5/16*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b*e^3/d - 5/32*((d*x + c)^2 - 1)*b^2*e^3/d + 5/16*a*b*arcsin(d*x + c)*e^3/d - 17/256*b^2*e^3/d","B",0
190,1,263,0,0.263898," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)^{2} e^{2}}{3 \, d} + \frac{{\left(d x + c\right)}^{3} a^{2} e^{2}}{3 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b \arcsin\left(d x + c\right) e^{2}}{3 \, d} + \frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)^{2} e^{2}}{3 \, d} - \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{2} \arcsin\left(d x + c\right) e^{2}}{9 \, d} - \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{2} e^{2}}{27 \, d} + \frac{2 \, {\left(d x + c\right)} a b \arcsin\left(d x + c\right) e^{2}}{3 \, d} - \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b e^{2}}{9 \, d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} \arcsin\left(d x + c\right) e^{2}}{3 \, d} - \frac{14 \, {\left(d x + c\right)} b^{2} e^{2}}{27 \, d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b e^{2}}{3 \, d}"," ",0,"1/3*((d*x + c)^2 - 1)*(d*x + c)*b^2*arcsin(d*x + c)^2*e^2/d + 1/3*(d*x + c)^3*a^2*e^2/d + 2/3*((d*x + c)^2 - 1)*(d*x + c)*a*b*arcsin(d*x + c)*e^2/d + 1/3*(d*x + c)*b^2*arcsin(d*x + c)^2*e^2/d - 2/9*(-(d*x + c)^2 + 1)^(3/2)*b^2*arcsin(d*x + c)*e^2/d - 2/27*((d*x + c)^2 - 1)*(d*x + c)*b^2*e^2/d + 2/3*(d*x + c)*a*b*arcsin(d*x + c)*e^2/d - 2/9*(-(d*x + c)^2 + 1)^(3/2)*a*b*e^2/d + 2/3*sqrt(-(d*x + c)^2 + 1)*b^2*arcsin(d*x + c)*e^2/d - 14/27*(d*x + c)*b^2*e^2/d + 2/3*sqrt(-(d*x + c)^2 + 1)*a*b*e^2/d","B",0
191,1,193,0,1.528910," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{2} \arcsin\left(d x + c\right)^{2} e}{2 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e}{2 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a b \arcsin\left(d x + c\right) e}{d} + \frac{b^{2} \arcsin\left(d x + c\right)^{2} e}{4 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b e}{2 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} e}{2 \, d} - \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{2} e}{4 \, d} + \frac{a b \arcsin\left(d x + c\right) e}{2 \, d} - \frac{b^{2} e}{8 \, d}"," ",0,"1/2*((d*x + c)^2 - 1)*b^2*arcsin(d*x + c)^2*e/d + 1/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^2*arcsin(d*x + c)*e/d + ((d*x + c)^2 - 1)*a*b*arcsin(d*x + c)*e/d + 1/4*b^2*arcsin(d*x + c)^2*e/d + 1/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b*e/d + 1/2*((d*x + c)^2 - 1)*a^2*e/d - 1/4*((d*x + c)^2 - 1)*b^2*e/d + 1/2*a*b*arcsin(d*x + c)*e/d - 1/8*b^2*e/d","B",0
192,1,111,0,0.191579," ","integrate((a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)^{2}}{d} + \frac{2 \, {\left(d x + c\right)} a b \arcsin\left(d x + c\right)}{d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} \arcsin\left(d x + c\right)}{d} + \frac{{\left(d x + c\right)} a^{2}}{d} - \frac{2 \, {\left(d x + c\right)} b^{2}}{d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b}{d}"," ",0,"(d*x + c)*b^2*arcsin(d*x + c)^2/d + 2*(d*x + c)*a*b*arcsin(d*x + c)/d + 2*sqrt(-(d*x + c)^2 + 1)*b^2*arcsin(d*x + c)/d + (d*x + c)*a^2/d - 2*(d*x + c)*b^2/d + 2*sqrt(-(d*x + c)^2 + 1)*a*b/d","A",0
193,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(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=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{{\left(d e x + c e\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(d*e*x + c*e)^2, x)","F",0
195,1,493,0,0.340676," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^3,x, algorithm=""giac"")","-\frac{b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-3\right)}}{4 \, d} - \frac{{\left(d x + c\right)}^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-3\right)}}{8 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} - \frac{b^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-3\right)}}{8 \, {\left(d x + c\right)}^{2} d} - \frac{a b \arcsin\left(d x + c\right) e^{\left(-3\right)}}{2 \, d} - \frac{{\left(d x + c\right)}^{2} a b \arcsin\left(d x + c\right) e^{\left(-3\right)}}{4 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} + \frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{\left(-3\right)}}{2 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{b^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} \arcsin\left(d x + c\right) e^{\left(-3\right)}}{2 \, {\left(d x + c\right)} d} - \frac{a b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} \arcsin\left(d x + c\right) e^{\left(-3\right)}}{4 \, {\left(d x + c\right)}^{2} d} + \frac{2 \, b^{2} e^{\left(-3\right)} \log\left(2\right)}{d} - \frac{b^{2} e^{\left(-3\right)} \log\left(2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} + 2\right)}{d} + \frac{b^{2} e^{\left(-3\right)} \log\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}{d} + \frac{b^{2} e^{\left(-3\right)} \log\left({\left| d x + c \right|}\right)}{d} - \frac{a^{2} e^{\left(-3\right)}}{4 \, d} - \frac{{\left(d x + c\right)}^{2} a^{2} e^{\left(-3\right)}}{8 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2}} + \frac{{\left(d x + c\right)} a b e^{\left(-3\right)}}{2 \, d {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}} - \frac{a b {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)} e^{\left(-3\right)}}{2 \, {\left(d x + c\right)} d} - \frac{a^{2} {\left(\sqrt{-{\left(d x + c\right)}^{2} + 1} + 1\right)}^{2} e^{\left(-3\right)}}{8 \, {\left(d x + c\right)}^{2} d}"," ",0,"-1/4*b^2*arcsin(d*x + c)^2*e^(-3)/d - 1/8*(d*x + c)^2*b^2*arcsin(d*x + c)^2*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) - 1/8*b^2*(sqrt(-(d*x + c)^2 + 1) + 1)^2*arcsin(d*x + c)^2*e^(-3)/((d*x + c)^2*d) - 1/2*a*b*arcsin(d*x + c)*e^(-3)/d - 1/4*(d*x + c)^2*a*b*arcsin(d*x + c)*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) + 1/2*(d*x + c)*b^2*arcsin(d*x + c)*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/2*b^2*(sqrt(-(d*x + c)^2 + 1) + 1)*arcsin(d*x + c)*e^(-3)/((d*x + c)*d) - 1/4*a*b*(sqrt(-(d*x + c)^2 + 1) + 1)^2*arcsin(d*x + c)*e^(-3)/((d*x + c)^2*d) + 2*b^2*e^(-3)*log(2)/d - b^2*e^(-3)*log(2*sqrt(-(d*x + c)^2 + 1) + 2)/d + b^2*e^(-3)*log(sqrt(-(d*x + c)^2 + 1) + 1)/d + b^2*e^(-3)*log(abs(d*x + c))/d - 1/4*a^2*e^(-3)/d - 1/8*(d*x + c)^2*a^2*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)^2) + 1/2*(d*x + c)*a*b*e^(-3)/(d*(sqrt(-(d*x + c)^2 + 1) + 1)) - 1/2*a*b*(sqrt(-(d*x + c)^2 + 1) + 1)*e^(-3)/((d*x + c)*d) - 1/8*a^2*(sqrt(-(d*x + c)^2 + 1) + 1)^2*e^(-3)/((d*x + c)^2*d)","B",0
196,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{{\left(d e x + c e\right)}^{4}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(d*e*x + c*e)^4, x)","F",0
197,1,804,0,1.284823," ","integrate((d*e*x+c*e)^4*(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{3} e^{4}}{5 \, d} + \frac{{\left(d x + c\right)}^{5} a^{3} e^{4}}{5 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{3} e^{4}}{5 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2} e^{4}}{25 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} a^{2} b \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{6 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{4}}{125 \, d} + \frac{6 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} + \frac{{\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{3} e^{4}}{5 \, d} + \frac{6 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right) e^{4}}{25 \, d} - \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} - \frac{6 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} a b^{2} e^{4}}{125 \, d} + \frac{6 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a^{2} b \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{76 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{4}}{375 \, d} + \frac{3 \, {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b e^{4}}{25 \, d} - \frac{6 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} e^{4}}{625 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b^{2} \arcsin\left(d x + c\right) e^{4}}{5 \, d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2} e^{4}}{5 \, d} - \frac{76 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{2} e^{4}}{375 \, d} + \frac{3 \, {\left(d x + c\right)} a^{2} b \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{298 \, {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{4}}{375 \, d} - \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a^{2} b e^{4}}{5 \, d} + \frac{76 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} e^{4}}{1125 \, d} + \frac{6 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right) e^{4}}{5 \, d} - \frac{298 \, {\left(d x + c\right)} a b^{2} e^{4}}{375 \, d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b e^{4}}{5 \, d} - \frac{298 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} e^{4}}{375 \, d}"," ",0,"1/5*((d*x + c)^2 - 1)^2*(d*x + c)*b^3*arcsin(d*x + c)^3*e^4/d + 1/5*(d*x + c)^5*a^3*e^4/d + 3/5*((d*x + c)^2 - 1)^2*(d*x + c)*a*b^2*arcsin(d*x + c)^2*e^4/d + 2/5*((d*x + c)^2 - 1)*(d*x + c)*b^3*arcsin(d*x + c)^3*e^4/d + 3/25*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2*e^4/d + 3/5*((d*x + c)^2 - 1)^2*(d*x + c)*a^2*b*arcsin(d*x + c)*e^4/d - 6/125*((d*x + c)^2 - 1)^2*(d*x + c)*b^3*arcsin(d*x + c)*e^4/d + 6/5*((d*x + c)^2 - 1)*(d*x + c)*a*b^2*arcsin(d*x + c)^2*e^4/d + 1/5*(d*x + c)*b^3*arcsin(d*x + c)^3*e^4/d + 6/25*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)*e^4/d - 2/5*(-(d*x + c)^2 + 1)^(3/2)*b^3*arcsin(d*x + c)^2*e^4/d - 6/125*((d*x + c)^2 - 1)^2*(d*x + c)*a*b^2*e^4/d + 6/5*((d*x + c)^2 - 1)*(d*x + c)*a^2*b*arcsin(d*x + c)*e^4/d - 76/375*((d*x + c)^2 - 1)*(d*x + c)*b^3*arcsin(d*x + c)*e^4/d + 3/5*(d*x + c)*a*b^2*arcsin(d*x + c)^2*e^4/d + 3/25*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*a^2*b*e^4/d - 6/625*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b^3*e^4/d - 4/5*(-(d*x + c)^2 + 1)^(3/2)*a*b^2*arcsin(d*x + c)*e^4/d + 3/5*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2*e^4/d - 76/375*((d*x + c)^2 - 1)*(d*x + c)*a*b^2*e^4/d + 3/5*(d*x + c)*a^2*b*arcsin(d*x + c)*e^4/d - 298/375*(d*x + c)*b^3*arcsin(d*x + c)*e^4/d - 2/5*(-(d*x + c)^2 + 1)^(3/2)*a^2*b*e^4/d + 76/1125*(-(d*x + c)^2 + 1)^(3/2)*b^3*e^4/d + 6/5*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)*e^4/d - 298/375*(d*x + c)*a*b^2*e^4/d + 3/5*sqrt(-(d*x + c)^2 + 1)*a^2*b*e^4/d - 298/375*sqrt(-(d*x + c)^2 + 1)*b^3*e^4/d","B",0
198,1,617,0,0.725713," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{3} \arcsin\left(d x + c\right)^{3} e^{3}}{4 \, d} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{2} e^{3}}{16 \, d} + \frac{{\left(d x + c\right)}^{4} a^{3} e^{3}}{4 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{4 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{3} \arcsin\left(d x + c\right)^{3} e^{3}}{2 \, d} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right) e^{3}}{8 \, d} + \frac{15 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{2} e^{3}}{32 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a^{2} b \arcsin\left(d x + c\right) e^{3}}{4 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{3} \arcsin\left(d x + c\right) e^{3}}{32 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{2 \, d} + \frac{5 \, b^{3} \arcsin\left(d x + c\right)^{3} e^{3}}{32 \, d} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a^{2} b e^{3}}{16 \, d} + \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{3} e^{3}}{128 \, d} + \frac{15 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right) e^{3}}{16 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b^{2} e^{3}}{32 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} b \arcsin\left(d x + c\right) e^{3}}{2 \, d} - \frac{15 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{3} \arcsin\left(d x + c\right) e^{3}}{32 \, d} + \frac{15 \, a b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{32 \, d} + \frac{15 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{2} b e^{3}}{32 \, d} - \frac{51 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} e^{3}}{256 \, d} - \frac{15 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{2} e^{3}}{32 \, d} + \frac{15 \, a^{2} b \arcsin\left(d x + c\right) e^{3}}{32 \, d} - \frac{51 \, b^{3} \arcsin\left(d x + c\right) e^{3}}{256 \, d} - \frac{51 \, a b^{2} e^{3}}{256 \, d}"," ",0,"1/4*((d*x + c)^2 - 1)^2*b^3*arcsin(d*x + c)^3*e^3/d - 3/16*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^3*arcsin(d*x + c)^2*e^3/d + 1/4*(d*x + c)^4*a^3*e^3/d + 3/4*((d*x + c)^2 - 1)^2*a*b^2*arcsin(d*x + c)^2*e^3/d + 1/2*((d*x + c)^2 - 1)*b^3*arcsin(d*x + c)^3*e^3/d - 3/8*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a*b^2*arcsin(d*x + c)*e^3/d + 15/32*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*arcsin(d*x + c)^2*e^3/d + 3/4*((d*x + c)^2 - 1)^2*a^2*b*arcsin(d*x + c)*e^3/d - 3/32*((d*x + c)^2 - 1)^2*b^3*arcsin(d*x + c)*e^3/d + 3/2*((d*x + c)^2 - 1)*a*b^2*arcsin(d*x + c)^2*e^3/d + 5/32*b^3*arcsin(d*x + c)^3*e^3/d - 3/16*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a^2*b*e^3/d + 3/128*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^3*e^3/d + 15/16*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^2*arcsin(d*x + c)*e^3/d - 3/32*((d*x + c)^2 - 1)^2*a*b^2*e^3/d + 3/2*((d*x + c)^2 - 1)*a^2*b*arcsin(d*x + c)*e^3/d - 15/32*((d*x + c)^2 - 1)*b^3*arcsin(d*x + c)*e^3/d + 15/32*a*b^2*arcsin(d*x + c)^2*e^3/d + 15/32*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^2*b*e^3/d - 51/256*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*e^3/d - 15/32*((d*x + c)^2 - 1)*a*b^2*e^3/d + 15/32*a^2*b*arcsin(d*x + c)*e^3/d - 51/256*b^3*arcsin(d*x + c)*e^3/d - 51/256*a*b^2*e^3/d","B",0
199,1,485,0,0.321941," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{3} e^{2}}{3 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e^{2}}{d} + \frac{{\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{3} e^{2}}{3 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} \arcsin\left(d x + c\right)^{2} e^{2}}{3 \, d} + \frac{{\left(d x + c\right)}^{3} a^{3} e^{2}}{3 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a^{2} b \arcsin\left(d x + c\right) e^{2}}{d} - \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{2}}{9 \, d} + \frac{{\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e^{2}}{d} - \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b^{2} \arcsin\left(d x + c\right) e^{2}}{3 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2} e^{2}}{d} - \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{2} e^{2}}{9 \, d} + \frac{{\left(d x + c\right)} a^{2} b \arcsin\left(d x + c\right) e^{2}}{d} - \frac{14 \, {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{2}}{9 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a^{2} b e^{2}}{3 \, d} + \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} e^{2}}{27 \, d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right) e^{2}}{d} - \frac{14 \, {\left(d x + c\right)} a b^{2} e^{2}}{9 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b e^{2}}{d} - \frac{14 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} e^{2}}{9 \, d}"," ",0,"1/3*((d*x + c)^2 - 1)*(d*x + c)*b^3*arcsin(d*x + c)^3*e^2/d + ((d*x + c)^2 - 1)*(d*x + c)*a*b^2*arcsin(d*x + c)^2*e^2/d + 1/3*(d*x + c)*b^3*arcsin(d*x + c)^3*e^2/d - 1/3*(-(d*x + c)^2 + 1)^(3/2)*b^3*arcsin(d*x + c)^2*e^2/d + 1/3*(d*x + c)^3*a^3*e^2/d + ((d*x + c)^2 - 1)*(d*x + c)*a^2*b*arcsin(d*x + c)*e^2/d - 2/9*((d*x + c)^2 - 1)*(d*x + c)*b^3*arcsin(d*x + c)*e^2/d + (d*x + c)*a*b^2*arcsin(d*x + c)^2*e^2/d - 2/3*(-(d*x + c)^2 + 1)^(3/2)*a*b^2*arcsin(d*x + c)*e^2/d + sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2*e^2/d - 2/9*((d*x + c)^2 - 1)*(d*x + c)*a*b^2*e^2/d + (d*x + c)*a^2*b*arcsin(d*x + c)*e^2/d - 14/9*(d*x + c)*b^3*arcsin(d*x + c)*e^2/d - 1/3*(-(d*x + c)^2 + 1)^(3/2)*a^2*b*e^2/d + 2/27*(-(d*x + c)^2 + 1)^(3/2)*b^3*e^2/d + 2*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)*e^2/d - 14/9*(d*x + c)*a*b^2*e^2/d + sqrt(-(d*x + c)^2 + 1)*a^2*b*e^2/d - 14/9*sqrt(-(d*x + c)^2 + 1)*b^3*e^2/d","B",0
200,1,355,0,0.344194," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{3} \arcsin\left(d x + c\right)^{3} e}{2 \, d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{2} e}{4 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{2} \arcsin\left(d x + c\right)^{2} e}{2 \, d} + \frac{b^{3} \arcsin\left(d x + c\right)^{3} e}{4 \, d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right) e}{2 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} b \arcsin\left(d x + c\right) e}{2 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{3} \arcsin\left(d x + c\right) e}{4 \, d} + \frac{3 \, a b^{2} \arcsin\left(d x + c\right)^{2} e}{4 \, d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{2} b e}{4 \, d} - \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} e}{8 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a^{3} e}{2 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{2} e}{4 \, d} + \frac{3 \, a^{2} b \arcsin\left(d x + c\right) e}{4 \, d} - \frac{3 \, b^{3} \arcsin\left(d x + c\right) e}{8 \, d} - \frac{3 \, a b^{2} e}{8 \, d}"," ",0,"1/2*((d*x + c)^2 - 1)*b^3*arcsin(d*x + c)^3*e/d + 3/4*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*arcsin(d*x + c)^2*e/d + 3/2*((d*x + c)^2 - 1)*a*b^2*arcsin(d*x + c)^2*e/d + 1/4*b^3*arcsin(d*x + c)^3*e/d + 3/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^2*arcsin(d*x + c)*e/d + 3/2*((d*x + c)^2 - 1)*a^2*b*arcsin(d*x + c)*e/d - 3/4*((d*x + c)^2 - 1)*b^3*arcsin(d*x + c)*e/d + 3/4*a*b^2*arcsin(d*x + c)^2*e/d + 3/4*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^2*b*e/d - 3/8*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*e/d + 1/2*((d*x + c)^2 - 1)*a^3*e/d - 3/4*((d*x + c)^2 - 1)*a*b^2*e/d + 3/4*a^2*b*arcsin(d*x + c)*e/d - 3/8*b^3*arcsin(d*x + c)*e/d - 3/8*a*b^2*e/d","B",0
201,1,208,0,0.211529," ","integrate((a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{3}}{d} + \frac{3 \, {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right)^{2}}{d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2}}{d} + \frac{3 \, {\left(d x + c\right)} a^{2} b \arcsin\left(d x + c\right)}{d} - \frac{6 \, {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)}{d} + \frac{6 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right)}{d} + \frac{{\left(d x + c\right)} a^{3}}{d} - \frac{6 \, {\left(d x + c\right)} a b^{2}}{d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b}{d} - \frac{6 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3}}{d}"," ",0,"(d*x + c)*b^3*arcsin(d*x + c)^3/d + 3*(d*x + c)*a*b^2*arcsin(d*x + c)^2/d + 3*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2/d + 3*(d*x + c)*a^2*b*arcsin(d*x + c)/d - 6*(d*x + c)*b^3*arcsin(d*x + c)/d + 6*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)/d + (d*x + c)*a^3/d - 6*(d*x + c)*a*b^2/d + 3*sqrt(-(d*x + c)^2 + 1)*a^2*b/d - 6*sqrt(-(d*x + c)^2 + 1)*b^3/d","B",0
202,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/(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=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{{\left(d e x + c e\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/(d*e*x + c*e)^2, x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^3,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{{\left(d e x + c e\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/(d*e*x + c*e)^3, x)","F",0
205,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{{\left(d e x + c e\right)}^{4}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/(d*e*x + c*e)^4, x)","F",0
206,1,979,0,0.381866," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{4} \arcsin\left(d x + c\right)^{4} e^{3}}{4 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{3} e^{3}}{4 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b^{3} \arcsin\left(d x + c\right)^{3} e^{3}}{d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{4} \arcsin\left(d x + c\right)^{4} e^{3}}{2 \, d} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{2} e^{3}}{4 \, d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{3} e^{3}}{8 \, d} + \frac{{\left(d x + c\right)}^{4} a^{4} e^{3}}{4 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{2 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{4} \arcsin\left(d x + c\right)^{2} e^{3}}{16 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{3} \arcsin\left(d x + c\right)^{3} e^{3}}{d} + \frac{5 \, b^{4} \arcsin\left(d x + c\right)^{4} e^{3}}{32 \, d} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right) e^{3}}{4 \, d} + \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right) e^{3}}{32 \, d} + \frac{15 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{2} e^{3}}{8 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a^{3} b \arcsin\left(d x + c\right) e^{3}}{d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b^{3} \arcsin\left(d x + c\right) e^{3}}{8 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{d} - \frac{15 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{4} \arcsin\left(d x + c\right)^{2} e^{3}}{16 \, d} + \frac{5 \, a b^{3} \arcsin\left(d x + c\right)^{3} e^{3}}{8 \, d} - \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a^{3} b e^{3}}{4 \, d} + \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a b^{3} e^{3}}{32 \, d} + \frac{15 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right) e^{3}}{8 \, d} - \frac{51 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right) e^{3}}{64 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a^{2} b^{2} e^{3}}{16 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{4} e^{3}}{128 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{3} b \arcsin\left(d x + c\right) e^{3}}{d} - \frac{15 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{3} \arcsin\left(d x + c\right) e^{3}}{8 \, d} + \frac{15 \, a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{3}}{16 \, d} - \frac{51 \, b^{4} \arcsin\left(d x + c\right)^{2} e^{3}}{128 \, d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{3} b e^{3}}{8 \, d} - \frac{51 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{3} e^{3}}{64 \, d} - \frac{15 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} b^{2} e^{3}}{16 \, d} + \frac{51 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{4} e^{3}}{128 \, d} + \frac{5 \, a^{3} b \arcsin\left(d x + c\right) e^{3}}{8 \, d} - \frac{51 \, a b^{3} \arcsin\left(d x + c\right) e^{3}}{64 \, d} - \frac{51 \, a^{2} b^{2} e^{3}}{128 \, d} + \frac{195 \, b^{4} e^{3}}{1024 \, d}"," ",0,"1/4*((d*x + c)^2 - 1)^2*b^4*arcsin(d*x + c)^4*e^3/d - 1/4*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^4*arcsin(d*x + c)^3*e^3/d + ((d*x + c)^2 - 1)^2*a*b^3*arcsin(d*x + c)^3*e^3/d + 1/2*((d*x + c)^2 - 1)*b^4*arcsin(d*x + c)^4*e^3/d - 3/4*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a*b^3*arcsin(d*x + c)^2*e^3/d + 5/8*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^4*arcsin(d*x + c)^3*e^3/d + 1/4*(d*x + c)^4*a^4*e^3/d + 3/2*((d*x + c)^2 - 1)^2*a^2*b^2*arcsin(d*x + c)^2*e^3/d - 3/16*((d*x + c)^2 - 1)^2*b^4*arcsin(d*x + c)^2*e^3/d + 2*((d*x + c)^2 - 1)*a*b^3*arcsin(d*x + c)^3*e^3/d + 5/32*b^4*arcsin(d*x + c)^4*e^3/d - 3/4*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a^2*b^2*arcsin(d*x + c)*e^3/d + 3/32*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^4*arcsin(d*x + c)*e^3/d + 15/8*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^3*arcsin(d*x + c)^2*e^3/d + ((d*x + c)^2 - 1)^2*a^3*b*arcsin(d*x + c)*e^3/d - 3/8*((d*x + c)^2 - 1)^2*a*b^3*arcsin(d*x + c)*e^3/d + 3*((d*x + c)^2 - 1)*a^2*b^2*arcsin(d*x + c)^2*e^3/d - 15/16*((d*x + c)^2 - 1)*b^4*arcsin(d*x + c)^2*e^3/d + 5/8*a*b^3*arcsin(d*x + c)^3*e^3/d - 1/4*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a^3*b*e^3/d + 3/32*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a*b^3*e^3/d + 15/8*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^2*b^2*arcsin(d*x + c)*e^3/d - 51/64*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^4*arcsin(d*x + c)*e^3/d - 3/16*((d*x + c)^2 - 1)^2*a^2*b^2*e^3/d + 3/128*((d*x + c)^2 - 1)^2*b^4*e^3/d + 2*((d*x + c)^2 - 1)*a^3*b*arcsin(d*x + c)*e^3/d - 15/8*((d*x + c)^2 - 1)*a*b^3*arcsin(d*x + c)*e^3/d + 15/16*a^2*b^2*arcsin(d*x + c)^2*e^3/d - 51/128*b^4*arcsin(d*x + c)^2*e^3/d + 5/8*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^3*b*e^3/d - 51/64*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^3*e^3/d - 15/16*((d*x + c)^2 - 1)*a^2*b^2*e^3/d + 51/128*((d*x + c)^2 - 1)*b^4*e^3/d + 5/8*a^3*b*arcsin(d*x + c)*e^3/d - 51/64*a*b^3*arcsin(d*x + c)*e^3/d - 51/128*a^2*b^2*e^3/d + 195/1024*b^4*e^3/d","B",0
207,1,780,0,0.879421," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{4} e^{2}}{3 \, d} + \frac{4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{3} e^{2}}{3 \, d} + \frac{{\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{4} e^{2}}{3 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{4} \arcsin\left(d x + c\right)^{3} e^{2}}{9 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{2}}{d} - \frac{4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{2} e^{2}}{9 \, d} + \frac{4 \, {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{3} e^{2}}{3 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b^{3} \arcsin\left(d x + c\right)^{2} e^{2}}{3 \, d} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{4} \arcsin\left(d x + c\right)^{3} e^{2}}{3 \, d} + \frac{{\left(d x + c\right)}^{3} a^{4} e^{2}}{3 \, d} + \frac{4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a^{3} b \arcsin\left(d x + c\right) e^{2}}{3 \, d} - \frac{8 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right) e^{2}}{9 \, d} + \frac{2 \, {\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e^{2}}{d} - \frac{28 \, {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{2} e^{2}}{9 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a^{2} b^{2} \arcsin\left(d x + c\right) e^{2}}{3 \, d} + \frac{8 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{4} \arcsin\left(d x + c\right) e^{2}}{27 \, d} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{3} \arcsin\left(d x + c\right)^{2} e^{2}}{d} - \frac{4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a^{2} b^{2} e^{2}}{9 \, d} + \frac{8 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{4} e^{2}}{81 \, d} + \frac{4 \, {\left(d x + c\right)} a^{3} b \arcsin\left(d x + c\right) e^{2}}{3 \, d} - \frac{56 \, {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right) e^{2}}{9 \, d} - \frac{4 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a^{3} b e^{2}}{9 \, d} + \frac{8 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b^{3} e^{2}}{27 \, d} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b^{2} \arcsin\left(d x + c\right) e^{2}}{d} - \frac{56 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{4} \arcsin\left(d x + c\right) e^{2}}{9 \, d} - \frac{28 \, {\left(d x + c\right)} a^{2} b^{2} e^{2}}{9 \, d} + \frac{488 \, {\left(d x + c\right)} b^{4} e^{2}}{81 \, d} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{3} b e^{2}}{3 \, d} - \frac{56 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{3} e^{2}}{9 \, d}"," ",0,"1/3*((d*x + c)^2 - 1)*(d*x + c)*b^4*arcsin(d*x + c)^4*e^2/d + 4/3*((d*x + c)^2 - 1)*(d*x + c)*a*b^3*arcsin(d*x + c)^3*e^2/d + 1/3*(d*x + c)*b^4*arcsin(d*x + c)^4*e^2/d - 4/9*(-(d*x + c)^2 + 1)^(3/2)*b^4*arcsin(d*x + c)^3*e^2/d + 2*((d*x + c)^2 - 1)*(d*x + c)*a^2*b^2*arcsin(d*x + c)^2*e^2/d - 4/9*((d*x + c)^2 - 1)*(d*x + c)*b^4*arcsin(d*x + c)^2*e^2/d + 4/3*(d*x + c)*a*b^3*arcsin(d*x + c)^3*e^2/d - 4/3*(-(d*x + c)^2 + 1)^(3/2)*a*b^3*arcsin(d*x + c)^2*e^2/d + 4/3*sqrt(-(d*x + c)^2 + 1)*b^4*arcsin(d*x + c)^3*e^2/d + 1/3*(d*x + c)^3*a^4*e^2/d + 4/3*((d*x + c)^2 - 1)*(d*x + c)*a^3*b*arcsin(d*x + c)*e^2/d - 8/9*((d*x + c)^2 - 1)*(d*x + c)*a*b^3*arcsin(d*x + c)*e^2/d + 2*(d*x + c)*a^2*b^2*arcsin(d*x + c)^2*e^2/d - 28/9*(d*x + c)*b^4*arcsin(d*x + c)^2*e^2/d - 4/3*(-(d*x + c)^2 + 1)^(3/2)*a^2*b^2*arcsin(d*x + c)*e^2/d + 8/27*(-(d*x + c)^2 + 1)^(3/2)*b^4*arcsin(d*x + c)*e^2/d + 4*sqrt(-(d*x + c)^2 + 1)*a*b^3*arcsin(d*x + c)^2*e^2/d - 4/9*((d*x + c)^2 - 1)*(d*x + c)*a^2*b^2*e^2/d + 8/81*((d*x + c)^2 - 1)*(d*x + c)*b^4*e^2/d + 4/3*(d*x + c)*a^3*b*arcsin(d*x + c)*e^2/d - 56/9*(d*x + c)*a*b^3*arcsin(d*x + c)*e^2/d - 4/9*(-(d*x + c)^2 + 1)^(3/2)*a^3*b*e^2/d + 8/27*(-(d*x + c)^2 + 1)^(3/2)*a*b^3*e^2/d + 4*sqrt(-(d*x + c)^2 + 1)*a^2*b^2*arcsin(d*x + c)*e^2/d - 56/9*sqrt(-(d*x + c)^2 + 1)*b^4*arcsin(d*x + c)*e^2/d - 28/9*(d*x + c)*a^2*b^2*e^2/d + 488/81*(d*x + c)*b^4*e^2/d + 4/3*sqrt(-(d*x + c)^2 + 1)*a^3*b*e^2/d - 56/9*sqrt(-(d*x + c)^2 + 1)*a*b^3*e^2/d","B",0
208,1,556,0,0.352906," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{4} \arcsin\left(d x + c\right)^{4} e}{2 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{3} e}{d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{3} \arcsin\left(d x + c\right)^{3} e}{d} + \frac{b^{4} \arcsin\left(d x + c\right)^{4} e}{4 \, d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{2} e}{d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e}{d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{4} \arcsin\left(d x + c\right)^{2} e}{2 \, d} + \frac{a b^{3} \arcsin\left(d x + c\right)^{3} e}{d} + \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right) e}{d} - \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right) e}{2 \, d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{3} b \arcsin\left(d x + c\right) e}{d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{3} \arcsin\left(d x + c\right) e}{d} + \frac{3 \, a^{2} b^{2} \arcsin\left(d x + c\right)^{2} e}{2 \, d} - \frac{3 \, b^{4} \arcsin\left(d x + c\right)^{2} e}{4 \, d} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{3} b e}{d} - \frac{3 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{3} e}{2 \, d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a^{4} e}{2 \, d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a^{2} b^{2} e}{2 \, d} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{4} e}{4 \, d} + \frac{a^{3} b \arcsin\left(d x + c\right) e}{d} - \frac{3 \, a b^{3} \arcsin\left(d x + c\right) e}{2 \, d} - \frac{3 \, a^{2} b^{2} e}{4 \, d} + \frac{3 \, b^{4} e}{8 \, d}"," ",0,"1/2*((d*x + c)^2 - 1)*b^4*arcsin(d*x + c)^4*e/d + sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^4*arcsin(d*x + c)^3*e/d + 2*((d*x + c)^2 - 1)*a*b^3*arcsin(d*x + c)^3*e/d + 1/4*b^4*arcsin(d*x + c)^4*e/d + 3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^3*arcsin(d*x + c)^2*e/d + 3*((d*x + c)^2 - 1)*a^2*b^2*arcsin(d*x + c)^2*e/d - 3/2*((d*x + c)^2 - 1)*b^4*arcsin(d*x + c)^2*e/d + a*b^3*arcsin(d*x + c)^3*e/d + 3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^2*b^2*arcsin(d*x + c)*e/d - 3/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^4*arcsin(d*x + c)*e/d + 2*((d*x + c)^2 - 1)*a^3*b*arcsin(d*x + c)*e/d - 3*((d*x + c)^2 - 1)*a*b^3*arcsin(d*x + c)*e/d + 3/2*a^2*b^2*arcsin(d*x + c)^2*e/d - 3/4*b^4*arcsin(d*x + c)^2*e/d + sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^3*b*e/d - 3/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^3*e/d + 1/2*((d*x + c)^2 - 1)*a^4*e/d - 3/2*((d*x + c)^2 - 1)*a^2*b^2*e/d + 3/4*((d*x + c)^2 - 1)*b^4*e/d + a^3*b*arcsin(d*x + c)*e/d - 3/2*a*b^3*arcsin(d*x + c)*e/d - 3/4*a^2*b^2*e/d + 3/8*b^4*e/d","B",0
209,1,329,0,0.245242," ","integrate((a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{4}}{d} + \frac{4 \, {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{3}}{d} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{4} \arcsin\left(d x + c\right)^{3}}{d} + \frac{6 \, {\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right)^{2}}{d} - \frac{12 \, {\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{2}}{d} + \frac{12 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{3} \arcsin\left(d x + c\right)^{2}}{d} + \frac{4 \, {\left(d x + c\right)} a^{3} b \arcsin\left(d x + c\right)}{d} - \frac{24 \, {\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)}{d} + \frac{12 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b^{2} \arcsin\left(d x + c\right)}{d} - \frac{24 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{4} \arcsin\left(d x + c\right)}{d} + \frac{{\left(d x + c\right)} a^{4}}{d} - \frac{12 \, {\left(d x + c\right)} a^{2} b^{2}}{d} + \frac{24 \, {\left(d x + c\right)} b^{4}}{d} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{3} b}{d} - \frac{24 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{3}}{d}"," ",0,"(d*x + c)*b^4*arcsin(d*x + c)^4/d + 4*(d*x + c)*a*b^3*arcsin(d*x + c)^3/d + 4*sqrt(-(d*x + c)^2 + 1)*b^4*arcsin(d*x + c)^3/d + 6*(d*x + c)*a^2*b^2*arcsin(d*x + c)^2/d - 12*(d*x + c)*b^4*arcsin(d*x + c)^2/d + 12*sqrt(-(d*x + c)^2 + 1)*a*b^3*arcsin(d*x + c)^2/d + 4*(d*x + c)*a^3*b*arcsin(d*x + c)/d - 24*(d*x + c)*a*b^3*arcsin(d*x + c)/d + 12*sqrt(-(d*x + c)^2 + 1)*a^2*b^2*arcsin(d*x + c)/d - 24*sqrt(-(d*x + c)^2 + 1)*b^4*arcsin(d*x + c)/d + (d*x + c)*a^4/d - 12*(d*x + c)*a^2*b^2/d + 24*(d*x + c)*b^4/d + 4*sqrt(-(d*x + c)^2 + 1)*a^3*b/d - 24*sqrt(-(d*x + c)^2 + 1)*a*b^3/d","B",0
210,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{d e x + c e}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/(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=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{{\left(d e x + c e\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/(d*e*x + c*e)^2, x)","F",0
212,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^3,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{{\left(d e x + c e\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/(d*e*x + c*e)^3, x)","F",0
213,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^4,x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{{\left(d e x + c e\right)}^{4}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/(d*e*x + c*e)^4, x)","F",0
214,1,482,0,0.290123," ","integrate((a+b*arcsin(d*x+c))^5,x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b^{5} \arcsin\left(d x + c\right)^{5}}{d} + \frac{5 \, {\left(d x + c\right)} a b^{4} \arcsin\left(d x + c\right)^{4}}{d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{5} \arcsin\left(d x + c\right)^{4}}{d} + \frac{10 \, {\left(d x + c\right)} a^{2} b^{3} \arcsin\left(d x + c\right)^{3}}{d} - \frac{20 \, {\left(d x + c\right)} b^{5} \arcsin\left(d x + c\right)^{3}}{d} + \frac{20 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{4} \arcsin\left(d x + c\right)^{3}}{d} + \frac{10 \, {\left(d x + c\right)} a^{3} b^{2} \arcsin\left(d x + c\right)^{2}}{d} - \frac{60 \, {\left(d x + c\right)} a b^{4} \arcsin\left(d x + c\right)^{2}}{d} + \frac{30 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b^{3} \arcsin\left(d x + c\right)^{2}}{d} - \frac{60 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{5} \arcsin\left(d x + c\right)^{2}}{d} + \frac{5 \, {\left(d x + c\right)} a^{4} b \arcsin\left(d x + c\right)}{d} - \frac{60 \, {\left(d x + c\right)} a^{2} b^{3} \arcsin\left(d x + c\right)}{d} + \frac{120 \, {\left(d x + c\right)} b^{5} \arcsin\left(d x + c\right)}{d} + \frac{20 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{3} b^{2} \arcsin\left(d x + c\right)}{d} - \frac{120 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{4} \arcsin\left(d x + c\right)}{d} + \frac{{\left(d x + c\right)} a^{5}}{d} - \frac{20 \, {\left(d x + c\right)} a^{3} b^{2}}{d} + \frac{120 \, {\left(d x + c\right)} a b^{4}}{d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{4} b}{d} - \frac{60 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b^{3}}{d} + \frac{120 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{5}}{d}"," ",0,"(d*x + c)*b^5*arcsin(d*x + c)^5/d + 5*(d*x + c)*a*b^4*arcsin(d*x + c)^4/d + 5*sqrt(-(d*x + c)^2 + 1)*b^5*arcsin(d*x + c)^4/d + 10*(d*x + c)*a^2*b^3*arcsin(d*x + c)^3/d - 20*(d*x + c)*b^5*arcsin(d*x + c)^3/d + 20*sqrt(-(d*x + c)^2 + 1)*a*b^4*arcsin(d*x + c)^3/d + 10*(d*x + c)*a^3*b^2*arcsin(d*x + c)^2/d - 60*(d*x + c)*a*b^4*arcsin(d*x + c)^2/d + 30*sqrt(-(d*x + c)^2 + 1)*a^2*b^3*arcsin(d*x + c)^2/d - 60*sqrt(-(d*x + c)^2 + 1)*b^5*arcsin(d*x + c)^2/d + 5*(d*x + c)*a^4*b*arcsin(d*x + c)/d - 60*(d*x + c)*a^2*b^3*arcsin(d*x + c)/d + 120*(d*x + c)*b^5*arcsin(d*x + c)/d + 20*sqrt(-(d*x + c)^2 + 1)*a^3*b^2*arcsin(d*x + c)/d - 120*sqrt(-(d*x + c)^2 + 1)*a*b^4*arcsin(d*x + c)/d + (d*x + c)*a^5/d - 20*(d*x + c)*a^3*b^2/d + 120*(d*x + c)*a*b^4/d + 5*sqrt(-(d*x + c)^2 + 1)*a^4*b/d - 60*sqrt(-(d*x + c)^2 + 1)*a^2*b^3/d + 120*sqrt(-(d*x + c)^2 + 1)*b^5/d","B",0
215,1,407,0,0.217322," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{\cos\left(\frac{a}{b}\right)^{5} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{b d} + \frac{\cos\left(\frac{a}{b}\right)^{4} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{b d} - \frac{5 \, \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{4 \, b d} - \frac{3 \, \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{4 \, b d} - \frac{3 \, \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{4 \, b d} - \frac{3 \, \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, b d} + \frac{5 \, \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{16 \, b d} + \frac{9 \, \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{16 \, b d} + \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4}}{8 \, b d} + \frac{e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{16 \, b d} + \frac{3 \, e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{16 \, b d} + \frac{e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, b d}"," ",0,"cos(a/b)^5*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b*d) + cos(a/b)^4*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b*d) - 5/4*cos(a/b)^3*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b*d) - 3/4*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b*d) - 3/4*cos(a/b)^2*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b*d) - 3/4*cos(a/b)^2*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b*d) + 5/16*cos(a/b)*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b*d) + 9/16*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b*d) + 1/8*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^4/(b*d) + 1/16*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b*d) + 3/16*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b*d) + 1/8*e^4*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b*d)","B",0
216,1,269,0,0.256889," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{\cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b d} - \frac{\cos\left(\frac{a}{b}\right)^{4} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b d} - \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{2 \, b d} - \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{2 \, b d} + \frac{\cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b d} + \frac{\cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{2 \, b d} - \frac{e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{8 \, b d} - \frac{e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{4 \, b d}"," ",0,"cos(a/b)^3*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b*d) - cos(a/b)^4*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b*d) - 1/2*cos(a/b)*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b*d) - 1/2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3*sin(a/b)/(b*d) + cos(a/b)^2*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b*d) + 1/2*cos(a/b)^2*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b*d) - 1/8*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b*d) - 1/4*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b*d)","A",0
217,1,197,0,0.251522," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","-\frac{\cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{b d} - \frac{\cos\left(\frac{a}{b}\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{b d} + \frac{3 \, \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{4 \, b d} + \frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2}}{4 \, b d} + \frac{e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, b d} + \frac{e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{4 \, b d}"," ",0,"-cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b*d) - cos(a/b)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b*d) + 3/4*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b*d) + 1/4*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^2/(b*d) + 1/4*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b*d) + 1/4*e^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b*d)","A",0
218,1,98,0,0.203246," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","-\frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e \sin\left(\frac{a}{b}\right)}{b d} + \frac{\cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b d} - \frac{e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{2 \, b d}"," ",0,"-cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e*sin(a/b)/(b*d) + cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b*d) - 1/2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b*d)","A",0
219,1,53,0,0.189991," ","integrate(1/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{b d} + \frac{\sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{b d}"," ",0,"cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b*d) + sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b*d)","A",0
220,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\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
221,1,1374,0,0.466539," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{5 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{5} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{5 \, a \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{5 \, a \cos\left(\frac{a}{b}\right)^{5} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{15 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{9 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{25 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{9 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{15 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{9 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{25 \, a \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{9 \, a \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{5 \, b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{9 \, b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{25 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{27 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b e^{4}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{5 \, a \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{9 \, a \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{a \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{25 \, a \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{27 \, a \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{a \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b e^{4}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b e^{4}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d}"," ",0,"5*b*arcsin(d*x + c)*cos(a/b)^4*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 5*b*arcsin(d*x + c)*cos(a/b)^5*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 5*a*cos(a/b)^4*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 5*a*cos(a/b)^5*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 15/4*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 9/4*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 25/4*b*arcsin(d*x + c)*cos(a/b)^3*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 9/4*b*arcsin(d*x + c)*cos(a/b)^3*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 15/4*a*cos(a/b)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 9/4*a*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 25/4*a*cos(a/b)^3*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 9/4*a*cos(a/b)^3*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 5/16*b*arcsin(d*x + c)*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 9/16*b*arcsin(d*x + c)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 1/8*b*arcsin(d*x + c)*cos_integral(a/b + arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 25/16*b*arcsin(d*x + c)*cos(a/b)*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 27/16*b*arcsin(d*x + c)*cos(a/b)*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/8*b*arcsin(d*x + c)*cos(a/b)*e^4*sin_integral(a/b + arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - ((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b*e^4/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 5/16*a*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 9/16*a*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 1/8*a*cos_integral(a/b + arcsin(d*x + c))*e^4*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 25/16*a*cos(a/b)*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 27/16*a*cos(a/b)*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/8*a*cos(a/b)*e^4*sin_integral(a/b + arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 2*(-(d*x + c)^2 + 1)^(3/2)*b*e^4/(b^3*d*arcsin(d*x + c) + a*b^2*d) - sqrt(-(d*x + c)^2 + 1)*b*e^4/(b^3*d*arcsin(d*x + c) + a*b^2*d)","B",0
222,1,910,0,0.422797," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{4 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{4 \, a \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{4 \, a \cos\left(\frac{a}{b}\right)^{3} e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{4 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{2 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{4 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{2 \, a \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{a \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{2 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{2 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b e^{3}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{a \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{2 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{a \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{2 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}}"," ",0,"-4*b*arcsin(d*x + c)*cos(a/b)^4*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 4*b*arcsin(d*x + c)*cos(a/b)^3*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 4*a*cos(a/b)^4*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 4*a*cos(a/b)^3*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 4*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) + b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 2*b*arcsin(d*x + c)*cos(a/b)*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + b*arcsin(d*x + c)*cos(a/b)*e^3*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 4*a*cos(a/b)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) + a*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 2*a*cos(a/b)*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + a*cos(a/b)*e^3*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + (-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/2*b*arcsin(d*x + c)*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/2*b*arcsin(d*x + c)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/2*a*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/2*a*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^3*d*arcsin(d*x + c) + a*b^2*d)","B",0
223,1,684,0,0.391065," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{3 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{3 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{3 \, a \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{3 \, b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{9 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{3 \, a \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{a \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{9 \, a \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} - \frac{a \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{3} d \arcsin\left(d x + c\right) + a b^{2} d\right)}} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b e^{2}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b e^{2}}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d}"," ",0,"-3*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 3*b*arcsin(d*x + c)*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 3*a*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 3*a*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 3/4*b*arcsin(d*x + c)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 1/4*b*arcsin(d*x + c)*cos_integral(a/b + arcsin(d*x + c))*e^2*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 9/4*b*arcsin(d*x + c)*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/4*b*arcsin(d*x + c)*cos(a/b)*e^2*sin_integral(a/b + arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 3/4*a*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 1/4*a*cos_integral(a/b + arcsin(d*x + c))*e^2*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 9/4*a*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - 1/4*a*cos(a/b)*e^2*sin_integral(a/b + arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + (-(d*x + c)^2 + 1)^(3/2)*b*e^2/(b^3*d*arcsin(d*x + c) + a*b^2*d) - sqrt(-(d*x + c)^2 + 1)*b*e^2/(b^3*d*arcsin(d*x + c) + a*b^2*d)","B",0
224,1,348,0,0.398823," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{2 \, b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{2 \, a \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{2 \, a \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b e}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{a \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d}"," ",0,"2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 2*b*arcsin(d*x + c)*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 2*a*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^3*d*arcsin(d*x + c) + a*b^2*d) + 2*a*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - b*arcsin(d*x + c)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^3*d*arcsin(d*x + c) + a*b^2*d) - sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b*e/(b^3*d*arcsin(d*x + c) + a*b^2*d) - a*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^3*d*arcsin(d*x + c) + a*b^2*d)","B",0
225,1,215,0,0.374962," ","integrate(1/(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\frac{b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} + \frac{a \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) \sin\left(\frac{a}{b}\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{a \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b}{b^{3} d \arcsin\left(d x + c\right) + a b^{2} d}"," ",0,"b*arcsin(d*x + c)*cos_integral(a/b + arcsin(d*x + c))*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - b*arcsin(d*x + c)*cos(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) + a*cos_integral(a/b + arcsin(d*x + c))*sin(a/b)/(b^3*d*arcsin(d*x + c) + a*b^2*d) - a*cos(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^3*d*arcsin(d*x + c) + a*b^2*d) - sqrt(-(d*x + c)^2 + 1)*b/(b^3*d*arcsin(d*x + c) + a*b^2*d)","B",0
226,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^2), x)","F",0
227,1,3135,0,0.717624," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","-\frac{25 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{5} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{4} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{5} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{25 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{4} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{125 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, a^{2} \cos\left(\frac{a}{b}\right)^{5} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{27 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{75 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, a^{2} \cos\left(\frac{a}{b}\right)^{4} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{27 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{125 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{27 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{75 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{27 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{125 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{125 \, a^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{81 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{27 \, a^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4}}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, b^{2} \arcsin\left(d x + c\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{75 \, a^{2} \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{27 \, b^{2} \arcsin\left(d x + c\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{27 \, a^{2} \cos\left(\frac{a}{b}\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{b^{2} \arcsin\left(d x + c\right)^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} a b e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{4}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{125 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{81 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, a b \arcsin\left(d x + c\right) e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{27 \, a b \arcsin\left(d x + c\right) e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a b \arcsin\left(d x + c\right) e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b e^{4}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{125 \, a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4}}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{81 \, a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4}}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4}}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{25 \, a^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{27 \, a^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} e^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{2} e^{4}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{{\left(d x + c\right)} a b e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} e^{4}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}}"," ",0,"-25/2*b^2*arcsin(d*x + c)^2*cos(a/b)^5*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25/2*b^2*arcsin(d*x + c)^2*cos(a/b)^4*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25*a*b*arcsin(d*x + c)*cos(a/b)^5*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25*a*b*arcsin(d*x + c)*cos(a/b)^4*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 125/8*b^2*arcsin(d*x + c)^2*cos(a/b)^3*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25/2*a^2*cos(a/b)^5*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 27/8*b^2*arcsin(d*x + c)^2*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 75/8*b^2*arcsin(d*x + c)^2*cos(a/b)^2*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25/2*a^2*cos(a/b)^4*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 27/8*b^2*arcsin(d*x + c)^2*cos(a/b)^2*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 125/4*a*b*arcsin(d*x + c)*cos(a/b)^3*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 27/4*a*b*arcsin(d*x + c)*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 75/4*a*b*arcsin(d*x + c)*cos(a/b)^2*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 27/4*a*b*arcsin(d*x + c)*cos(a/b)^2*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 5/2*((d*x + c)^2 - 1)^2*(d*x + c)*b^2*arcsin(d*x + c)*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 125/32*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 125/8*a^2*cos(a/b)^3*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 81/32*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 27/8*a^2*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/16*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25/32*b^2*arcsin(d*x + c)^2*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 75/8*a^2*cos(a/b)^2*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 27/32*b^2*arcsin(d*x + c)^2*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 27/8*a^2*cos(a/b)^2*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/16*b^2*arcsin(d*x + c)^2*e^4*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 5/2*((d*x + c)^2 - 1)^2*(d*x + c)*a*b*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 3*((d*x + c)^2 - 1)*(d*x + c)*b^2*arcsin(d*x + c)*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 125/16*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 81/16*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/8*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25/16*a*b*arcsin(d*x + c)*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 27/16*a*b*arcsin(d*x + c)*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/8*a*b*arcsin(d*x + c)*e^4*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b^2*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 3*((d*x + c)^2 - 1)*(d*x + c)*a*b*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(d*x + c)*b^2*arcsin(d*x + c)*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 125/32*a^2*cos(a/b)*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 81/32*a^2*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/16*a^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 25/32*a^2*e^4*sin(a/b)*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 27/32*a^2*e^4*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/16*a^2*e^4*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + (-(d*x + c)^2 + 1)^(3/2)*b^2*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(d*x + c)*a*b*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*sqrt(-(d*x + c)^2 + 1)*b^2*e^4/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d)","B",0
228,1,2169,0,0.825715," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","-\frac{8 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{8 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{4} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{16 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{16 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{4} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{4 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{8 \, a^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{8 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{8 \, a^{2} \cos\left(\frac{a}{b}\right)^{4} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{8 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{2 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{16 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{2 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{2} \arcsin\left(d x + c\right) e^{3}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{4 \, a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3} \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{b^{2} \arcsin\left(d x + c\right)^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{8 \, a^{2} \cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{b^{2} \arcsin\left(d x + c\right)^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} \cos\left(\frac{a}{b}\right)^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{2} e^{3}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b e^{3}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{2} \arcsin\left(d x + c\right) e^{3}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{2 \, a b \arcsin\left(d x + c\right) e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{a b \arcsin\left(d x + c\right) e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{2} e^{3}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b e^{3}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{b^{2} \arcsin\left(d x + c\right) e^{3}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{a^{2} e^{3} \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{a^{2} e^{3} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{a b e^{3}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}}"," ",0,"-8*b^2*arcsin(d*x + c)^2*cos(a/b)^3*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 8*b^2*arcsin(d*x + c)^2*cos(a/b)^4*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 16*a*b*arcsin(d*x + c)*cos(a/b)^3*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 16*a*b*arcsin(d*x + c)*cos(a/b)^4*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 4*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 8*a^2*cos(a/b)^3*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 8*b^2*arcsin(d*x + c)^2*cos(a/b)^2*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 8*a^2*cos(a/b)^4*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - b^2*arcsin(d*x + c)^2*cos(a/b)^2*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 8*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 2*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 16*a*b*arcsin(d*x + c)*cos(a/b)^2*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 2*a*b*arcsin(d*x + c)*cos(a/b)^2*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 2*((d*x + c)^2 - 1)^2*b^2*arcsin(d*x + c)*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 4*a^2*cos(a/b)*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + a^2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + b^2*arcsin(d*x + c)^2*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 8*a^2*cos(a/b)^2*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*b^2*arcsin(d*x + c)^2*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - a^2*cos(a/b)^2*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^2*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 2*((d*x + c)^2 - 1)^2*a*b*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 5/2*((d*x + c)^2 - 1)*b^2*arcsin(d*x + c)*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 2*a*b*arcsin(d*x + c)*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + a*b*arcsin(d*x + c)*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^2*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 5/2*((d*x + c)^2 - 1)*a*b*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*b^2*arcsin(d*x + c)*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + a^2*e^3*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*a^2*e^3*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*a*b*e^3/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d)","B",0
229,1,1617,0,0.780886," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{9 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{9 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{9 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{9 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{27 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{9 \, a^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{9 \, b^{2} \arcsin\left(d x + c\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{9 \, a^{2} \cos\left(\frac{a}{b}\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{b^{2} \arcsin\left(d x + c\right)^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{27 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2}}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{9 \, a b \arcsin\left(d x + c\right) e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a b \arcsin\left(d x + c\right) e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{3 \, {\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right) e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{27 \, a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2}}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{9 \, a^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} e^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{2} e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{{\left(d x + c\right)} a b e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2} e^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}}"," ",0,"9/2*b^2*arcsin(d*x + c)^2*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 9/2*b^2*arcsin(d*x + c)^2*cos(a/b)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 9*a*b*arcsin(d*x + c)*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 9*a*b*arcsin(d*x + c)*cos(a/b)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 27/8*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 9/2*a^2*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/8*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 9/8*b^2*arcsin(d*x + c)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 9/2*a^2*cos(a/b)^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/8*b^2*arcsin(d*x + c)^2*e^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 3/2*((d*x + c)^2 - 1)*(d*x + c)*b^2*arcsin(d*x + c)*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 27/4*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/4*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 9/4*a*b*arcsin(d*x + c)*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/4*a*b*arcsin(d*x + c)*e^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 3/2*((d*x + c)^2 - 1)*(d*x + c)*a*b*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(d*x + c)*b^2*arcsin(d*x + c)*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 27/8*a^2*cos(a/b)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/8*a^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 9/8*a^2*e^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/8*a^2*e^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(-(d*x + c)^2 + 1)^(3/2)*b^2*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(d*x + c)*a*b*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*sqrt(-(d*x + c)^2 + 1)*b^2*e^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d)","B",0
230,1,902,0,1.584631," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{2 \, b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{4 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{4 \, a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{2 \, a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e \sin\left(\frac{a}{b}\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{b^{2} \arcsin\left(d x + c\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{2 \, a^{2} \cos\left(\frac{a}{b}\right)^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{2} \arcsin\left(d x + c\right) e}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{2 \, a b \arcsin\left(d x + c\right) e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{2} e}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a b e}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{b^{2} \arcsin\left(d x + c\right) e}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{a^{2} e \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{a b e}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}}"," ",0,"2*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 2*b^2*arcsin(d*x + c)^2*cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 4*a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 4*a*b*arcsin(d*x + c)*cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 2*a^2*cos(a/b)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e*sin(a/b)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + b^2*arcsin(d*x + c)^2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 2*a^2*cos(a/b)^2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + ((d*x + c)^2 - 1)*b^2*arcsin(d*x + c)*e/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 2*a*b*arcsin(d*x + c)*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^2*e/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + ((d*x + c)^2 - 1)*a*b*e/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*b^2*arcsin(d*x + c)*e/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + a^2*e*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*a*b*e/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d)","B",0
231,1,547,0,0.219874," ","integrate(1/(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","-\frac{b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{b^{2} \arcsin\left(d x + c\right)^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} - \frac{a b \arcsin\left(d x + c\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d} + \frac{{\left(d x + c\right)} b^{2} \arcsin\left(d x + c\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{a^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} + \frac{{\left(d x + c\right)} a b}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{2}}{2 \, {\left(b^{5} d \arcsin\left(d x + c\right)^{2} + 2 \, a b^{4} d \arcsin\left(d x + c\right) + a^{2} b^{3} d\right)}}"," ",0,"-1/2*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*b^2*arcsin(d*x + c)^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - a*b*arcsin(d*x + c)*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - a*b*arcsin(d*x + c)*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(d*x + c)*b^2*arcsin(d*x + c)/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*a^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*a^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) + 1/2*(d*x + c)*a*b/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d) - 1/2*sqrt(-(d*x + c)^2 + 1)*b^2/(b^5*d*arcsin(d*x + c)^2 + 2*a*b^4*d*arcsin(d*x + c) + a^2*b^3*d)","B",0
232,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^3), x)","F",0
233,1,5804,0,1.251799," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","-\frac{125 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{125 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{5} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{125 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{125 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{5} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{125 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{125 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{27 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{625 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{125 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{5} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{375 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{125 \, a^{3} \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{81 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{625 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{125 \, a^{3} \cos\left(\frac{a}{b}\right)^{5} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{81 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{125 \, b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{96 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{375 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{81 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{48 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{625 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{96 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{625 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{81 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{81 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{48 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{25 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2} e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{125 \, a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{125 \, a^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{81 \, a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{27 \, a^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{16 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{625 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{625 \, a^{3} \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{243 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, a^{3} \cos\left(\frac{a}{b}\right)^{3} e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{25 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right) e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{19 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} \arcsin\left(d x + c\right)^{2} e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} {\left(d x + c\right)} a b^{2} e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{4}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{125 \, a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{81 \, a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{16 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{625 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{243 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{16 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{25 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{{\left({\left(d x + c\right)}^{2} - 1\right)}^{2} \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{38 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b^{2} \arcsin\left(d x + c\right) e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{13 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2} e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{2} e^{4}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{{\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{125 \, a^{3} \operatorname{Ci}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{96 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, a^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a^{3} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{4} \sin\left(\frac{a}{b}\right)}{48 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{625 \, a^{3} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{5 \, a}{b} + 5 \, \arcsin\left(d x + c\right)\right)}{96 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{81 \, a^{3} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{32 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{3} \cos\left(\frac{a}{b}\right) e^{4} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{48 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{19 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a^{2} b e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{2 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{13 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right) e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(d x + c\right)} a b^{2} e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{13 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b e^{4}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} e^{4}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}}"," ",0,"-125/6*b^3*arcsin(d*x + c)^3*cos(a/b)^4*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 125/6*b^3*arcsin(d*x + c)^3*cos(a/b)^5*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/2*a*b^2*arcsin(d*x + c)^2*cos(a/b)^4*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 125/2*a*b^2*arcsin(d*x + c)^2*cos(a/b)^5*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 125/8*b^3*arcsin(d*x + c)^3*cos(a/b)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/2*a^2*b*arcsin(d*x + c)*cos(a/b)^4*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 27/8*b^3*arcsin(d*x + c)^3*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 625/24*b^3*arcsin(d*x + c)^3*cos(a/b)^3*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 125/2*a^2*b*arcsin(d*x + c)*cos(a/b)^5*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/8*b^3*arcsin(d*x + c)^3*cos(a/b)^3*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 375/8*a*b^2*arcsin(d*x + c)^2*cos(a/b)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/6*a^3*cos(a/b)^4*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 81/8*a*b^2*arcsin(d*x + c)^2*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 625/8*a*b^2*arcsin(d*x + c)^2*cos(a/b)^3*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 125/6*a^3*cos(a/b)^5*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 81/8*a*b^2*arcsin(d*x + c)^2*cos(a/b)^3*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/96*b^3*arcsin(d*x + c)^3*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 375/8*a^2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/32*b^3*arcsin(d*x + c)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 81/8*a^2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/48*b^3*arcsin(d*x + c)^3*cos_integral(a/b + arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 625/96*b^3*arcsin(d*x + c)^3*cos(a/b)*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 625/8*a^2*b*arcsin(d*x + c)*cos(a/b)^3*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 81/32*b^3*arcsin(d*x + c)^3*cos(a/b)*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 81/8*a^2*b*arcsin(d*x + c)*cos(a/b)^3*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/48*b^3*arcsin(d*x + c)^3*cos(a/b)*e^4*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 25/6*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 5/6*((d*x + c)^2 - 1)^2*(d*x + c)*b^3*arcsin(d*x + c)*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/32*a*b^2*arcsin(d*x + c)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 125/8*a^3*cos(a/b)^2*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 81/32*a*b^2*arcsin(d*x + c)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 27/8*a^3*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/16*a*b^2*arcsin(d*x + c)^2*cos_integral(a/b + arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 625/32*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 625/24*a^3*cos(a/b)^3*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 243/32*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/8*a^3*cos(a/b)^3*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/16*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^4*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 25/3*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 19/3*(-(d*x + c)^2 + 1)^(3/2)*b^3*arcsin(d*x + c)^2*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 5/6*((d*x + c)^2 - 1)^2*(d*x + c)*a*b^2*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + ((d*x + c)^2 - 1)*(d*x + c)*b^3*arcsin(d*x + c)*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/32*a^2*b*arcsin(d*x + c)*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 81/32*a^2*b*arcsin(d*x + c)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/16*a^2*b*arcsin(d*x + c)*cos_integral(a/b + arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 625/32*a^2*b*arcsin(d*x + c)*cos(a/b)*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 243/32*a^2*b*arcsin(d*x + c)*cos(a/b)*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/16*a^2*b*arcsin(d*x + c)*cos(a/b)*e^4*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 25/6*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*a^2*b*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/3*((d*x + c)^2 - 1)^2*sqrt(-(d*x + c)^2 + 1)*b^3*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 38/3*(-(d*x + c)^2 + 1)^(3/2)*a*b^2*arcsin(d*x + c)*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 13/6*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + ((d*x + c)^2 - 1)*(d*x + c)*a*b^2*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*(d*x + c)*b^3*arcsin(d*x + c)*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 125/96*a^3*cos_integral(5*a/b + 5*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/32*a^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/48*a^3*cos_integral(a/b + arcsin(d*x + c))*e^4*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 625/96*a^3*cos(a/b)*e^4*sin_integral(5*a/b + 5*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 81/32*a^3*cos(a/b)*e^4*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/48*a^3*cos(a/b)*e^4*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 19/3*(-(d*x + c)^2 + 1)^(3/2)*a^2*b*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*(-(d*x + c)^2 + 1)^(3/2)*b^3*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 13/3*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*(d*x + c)*a*b^2*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 13/6*sqrt(-(d*x + c)^2 + 1)*a^2*b*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/3*sqrt(-(d*x + c)^2 + 1)*b^3*e^4/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d)","B",0
234,1,3994,0,1.482064," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\frac{32 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{32 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{3} e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{32 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{32 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{32 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{32 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{2 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{16 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{32 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{2 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{32 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{32 \, a^{3} \cos\left(\frac{a}{b}\right)^{4} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{2 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{16 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{32 \, a^{3} \cos\left(\frac{a}{b}\right)^{3} e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{2 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{8 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{2} e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{4 \, b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{32 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{2 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{16 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{2 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{16 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{2} e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} b^{3} \arcsin\left(d x + c\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{4 \, a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{32 \, a^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{2 \, a^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{16 \, a^{3} \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{2 \, a^{3} \cos\left(\frac{a}{b}\right) e^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{8 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} a^{2} b e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(d x + c\right)} b^{3} e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{10 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{2 \, {\left({\left(d x + c\right)}^{2} - 1\right)}^{2} a b^{2} e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)} b^{3} \arcsin\left(d x + c\right) e^{3}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{4 \, a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{5 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{2} b e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{5 \, {\left({\left(d x + c\right)}^{2} - 1\right)} a b^{2} e^{3}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{b^{3} \arcsin\left(d x + c\right) e^{3}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{4 \, a^{3} \operatorname{Ci}\left(\frac{4 \, a}{b} + 4 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{3} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a b^{2} e^{3}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}}"," ",0,"32/3*b^3*arcsin(d*x + c)^3*cos(a/b)^4*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32/3*b^3*arcsin(d*x + c)^3*cos(a/b)^3*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32*a*b^2*arcsin(d*x + c)^2*cos(a/b)^4*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32*a*b^2*arcsin(d*x + c)^2*cos(a/b)^3*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 32/3*b^3*arcsin(d*x + c)^3*cos(a/b)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32*a^2*b*arcsin(d*x + c)*cos(a/b)^4*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2/3*b^3*arcsin(d*x + c)^3*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 16/3*b^3*arcsin(d*x + c)^3*cos(a/b)*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32*a^2*b*arcsin(d*x + c)*cos(a/b)^3*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2/3*b^3*arcsin(d*x + c)^3*cos(a/b)*e^3*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 32*a*b^2*arcsin(d*x + c)^2*cos(a/b)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32/3*a^3*cos(a/b)^4*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2*a*b^2*arcsin(d*x + c)^2*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 16*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 32/3*a^3*cos(a/b)^3*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^3*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 8/3*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^3*arcsin(d*x + c)^2*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 4/3*b^3*arcsin(d*x + c)^3*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 32*a^2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*b^3*arcsin(d*x + c)^3*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2*a^2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 16*a^2*b*arcsin(d*x + c)*cos(a/b)*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2*a^2*b*arcsin(d*x + c)*cos(a/b)*e^3*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 16/3*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a*b^2*arcsin(d*x + c)*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 5/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*arcsin(d*x + c)^2*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*((d*x + c)^2 - 1)^2*b^3*arcsin(d*x + c)*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 4*a*b^2*arcsin(d*x + c)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 32/3*a^3*cos(a/b)^2*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + a*b^2*arcsin(d*x + c)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2/3*a^3*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 16/3*a^3*cos(a/b)*e^3*sin(a/b)*sin_integral(4*a/b + 4*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 2/3*a^3*cos(a/b)*e^3*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 8/3*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*a^2*b*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*(-(d*x + c)^2 + 1)^(3/2)*(d*x + c)*b^3*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 10/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^2*arcsin(d*x + c)*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*((d*x + c)^2 - 1)^2*a*b^2*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 5/6*((d*x + c)^2 - 1)*b^3*arcsin(d*x + c)*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 4*a^2*b*arcsin(d*x + c)*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + a^2*b*arcsin(d*x + c)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 5/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^2*b*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 5/6*((d*x + c)^2 - 1)*a*b^2*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*b^3*arcsin(d*x + c)*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 4/3*a^3*cos_integral(4*a/b + 4*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*a^3*cos_integral(2*a/b + 2*arcsin(d*x + c))*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*a*b^2*e^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d)","B",0
235,1,3073,0,1.193793," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\frac{9 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{9 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{27 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{9 \, b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{27 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{24 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{27 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{9 \, a^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{81 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{9 \, a^{3} \cos\left(\frac{a}{b}\right)^{3} e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} \arcsin\left(d x + c\right)^{2} e^{2}}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{2}}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{27 \, a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{81 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a b^{2} \arcsin\left(d x + c\right) e^{2}}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{7 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2} e^{2}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} {\left(d x + c\right)} a b^{2} e^{2}}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right) e^{2}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{9 \, a^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a^{3} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) e^{2} \sin\left(\frac{a}{b}\right)}{24 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{27 \, a^{3} \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(d x + c\right)\right)}{8 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{3} \cos\left(\frac{a}{b}\right) e^{2} \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{3 \, {\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} a^{2} b e^{2}}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(-{\left(d x + c\right)}^{2} + 1\right)}^{\frac{3}{2}} b^{3} e^{2}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{7 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right) e^{2}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(d x + c\right)} a b^{2} e^{2}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{7 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b e^{2}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} e^{2}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}}"," ",0,"9/2*b^3*arcsin(d*x + c)^3*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 9/2*b^3*arcsin(d*x + c)^3*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 27/2*a*b^2*arcsin(d*x + c)^2*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/2*a*b^2*arcsin(d*x + c)^2*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 9/8*b^3*arcsin(d*x + c)^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 27/2*a^2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/24*b^3*arcsin(d*x + c)^3*cos_integral(a/b + arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 27/8*b^3*arcsin(d*x + c)^3*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/2*a^2*b*arcsin(d*x + c)*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/24*b^3*arcsin(d*x + c)^3*cos(a/b)*e^2*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/8*a*b^2*arcsin(d*x + c)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 9/2*a^3*cos(a/b)^2*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/8*a*b^2*arcsin(d*x + c)^2*cos_integral(a/b + arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 81/8*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 9/2*a^3*cos(a/b)^3*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/8*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e^2*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 3/2*(-(d*x + c)^2 + 1)^(3/2)*b^3*arcsin(d*x + c)^2*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/2*((d*x + c)^2 - 1)*(d*x + c)*b^3*arcsin(d*x + c)*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 27/8*a^2*b*arcsin(d*x + c)*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/8*a^2*b*arcsin(d*x + c)*cos_integral(a/b + arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 81/8*a^2*b*arcsin(d*x + c)*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/8*a^2*b*arcsin(d*x + c)*cos(a/b)*e^2*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 3*(-(d*x + c)^2 + 1)^(3/2)*a*b^2*arcsin(d*x + c)*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 7/6*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/2*((d*x + c)^2 - 1)*(d*x + c)*a*b^2*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*(d*x + c)*b^3*arcsin(d*x + c)*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 9/8*a^3*cos_integral(3*a/b + 3*arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/24*a^3*cos_integral(a/b + arcsin(d*x + c))*e^2*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 27/8*a^3*cos(a/b)*e^2*sin_integral(3*a/b + 3*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/24*a^3*cos(a/b)*e^2*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 3/2*(-(d*x + c)^2 + 1)^(3/2)*a^2*b*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*(-(d*x + c)^2 + 1)^(3/2)*b^3*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 7/3*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*(d*x + c)*a*b^2*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 7/6*sqrt(-(d*x + c)^2 + 1)*a^2*b*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/3*sqrt(-(d*x + c)^2 + 1)*b^3*e^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d)","B",0
236,1,1685,0,1.113174," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","-\frac{4 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{4 \, b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{4 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{4 \, a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{2 \, b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{4 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{4 \, a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)^{2} e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{2 \, a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} - \frac{4 \, a^{3} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{4 \, a^{3} \cos\left(\frac{a}{b}\right) e \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{4 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a b^{2} \arcsin\left(d x + c\right) e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} b^{3} \arcsin\left(d x + c\right) e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{2 \, a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d} + \frac{2 \, \sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} a^{2} b e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} {\left(d x + c\right)} b^{3} e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left({\left(d x + c\right)}^{2} - 1\right)} a b^{2} e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{b^{3} \arcsin\left(d x + c\right) e}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{2 \, a^{3} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(d x + c\right)\right) e}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a b^{2} e}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}}"," ",0,"-4/3*b^3*arcsin(d*x + c)^3*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4/3*b^3*arcsin(d*x + c)^3*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4*a*b^2*arcsin(d*x + c)^2*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4*a*b^2*arcsin(d*x + c)^2*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*b^3*arcsin(d*x + c)^3*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4*a^2*b*arcsin(d*x + c)*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4*a^2*b*arcsin(d*x + c)*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*arcsin(d*x + c)^2*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2*a*b^2*arcsin(d*x + c)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4/3*a^3*cos(a/b)^2*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 4/3*a^3*cos(a/b)*e*sin(a/b)*sin_integral(2*a/b + 2*arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 4/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a*b^2*arcsin(d*x + c)*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*((d*x + c)^2 - 1)*b^3*arcsin(d*x + c)*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2*a^2*b*arcsin(d*x + c)*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*a^2*b*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/3*sqrt(-(d*x + c)^2 + 1)*(d*x + c)*b^3*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*((d*x + c)^2 - 1)*a*b^2*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*b^3*arcsin(d*x + c)*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 2/3*a^3*cos_integral(2*a/b + 2*arcsin(d*x + c))*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*a*b^2*e/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d)","B",0
237,1,1112,0,0.253662," ","integrate(1/(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","-\frac{b^{3} \arcsin\left(d x + c\right)^{3} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) \sin\left(\frac{a}{b}\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a^{2} b \arcsin\left(d x + c\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) \sin\left(\frac{a}{b}\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{2} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{2 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3} \arcsin\left(d x + c\right)^{2}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(d x + c\right)} b^{3} \arcsin\left(d x + c\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{a^{3} \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right) \sin\left(\frac{a}{b}\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{a^{3} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{2} \arcsin\left(d x + c\right)}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{{\left(d x + c\right)} a b^{2}}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b}{6 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{3}}{3 \, {\left(b^{7} d \arcsin\left(d x + c\right)^{3} + 3 \, a b^{6} d \arcsin\left(d x + c\right)^{2} + 3 \, a^{2} b^{5} d \arcsin\left(d x + c\right) + a^{3} b^{4} d\right)}}"," ",0,"-1/6*b^3*arcsin(d*x + c)^3*cos_integral(a/b + arcsin(d*x + c))*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*b^3*arcsin(d*x + c)^3*cos(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/2*a*b^2*arcsin(d*x + c)^2*cos_integral(a/b + arcsin(d*x + c))*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/2*a*b^2*arcsin(d*x + c)^2*cos(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/2*a^2*b*arcsin(d*x + c)*cos_integral(a/b + arcsin(d*x + c))*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/2*a^2*b*arcsin(d*x + c)*cos(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*sqrt(-(d*x + c)^2 + 1)*b^3*arcsin(d*x + c)^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*(d*x + c)*b^3*arcsin(d*x + c)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/6*a^3*cos_integral(a/b + arcsin(d*x + c))*sin(a/b)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*a^3*cos(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/3*sqrt(-(d*x + c)^2 + 1)*a*b^2*arcsin(d*x + c)/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*(d*x + c)*a*b^2/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) + 1/6*sqrt(-(d*x + c)^2 + 1)*a^2*b/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d) - 1/3*sqrt(-(d*x + c)^2 + 1)*b^3/(b^7*d*arcsin(d*x + c)^3 + 3*a*b^6*d*arcsin(d*x + c)^2 + 3*a^2*b^5*d*arcsin(d*x + c) + a^3*b^4*d)","B",0
238,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{1}{{\left(d e x + c e\right)} {\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(1/((d*e*x + c*e)*(b*arcsin(d*x + c) + a)^4), x)","F",0
239,1,1915,0,0.326010," ","integrate(1/(a+b*arcsin(d*x+c))^5,x, algorithm=""giac"")","\frac{b^{4} \arcsin\left(d x + c\right)^{4} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{b^{4} \arcsin\left(d x + c\right)^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a b^{3} \arcsin\left(d x + c\right)^{3} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a b^{3} \arcsin\left(d x + c\right)^{3} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} - \frac{{\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)^{3}}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a^{2} b^{2} \arcsin\left(d x + c\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a^{2} b^{2} \arcsin\left(d x + c\right)^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{4 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} - \frac{{\left(d x + c\right)} a b^{3} \arcsin\left(d x + c\right)^{2}}{8 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a^{3} b \arcsin\left(d x + c\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a^{3} b \arcsin\left(d x + c\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{6 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{4} \arcsin\left(d x + c\right)^{2}}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} - \frac{{\left(d x + c\right)} a^{2} b^{2} \arcsin\left(d x + c\right)}{8 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{{\left(d x + c\right)} b^{4} \arcsin\left(d x + c\right)}{12 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a^{4} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{a^{4} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(d x + c\right)\right)}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} a b^{3} \arcsin\left(d x + c\right)}{12 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} - \frac{{\left(d x + c\right)} a^{3} b}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{{\left(d x + c\right)} a b^{3}}{12 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} + \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} a^{2} b^{2}}{24 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}} - \frac{\sqrt{-{\left(d x + c\right)}^{2} + 1} b^{4}}{4 \, {\left(b^{9} d \arcsin\left(d x + c\right)^{4} + 4 \, a b^{8} d \arcsin\left(d x + c\right)^{3} + 6 \, a^{2} b^{7} d \arcsin\left(d x + c\right)^{2} + 4 \, a^{3} b^{6} d \arcsin\left(d x + c\right) + a^{4} b^{5} d\right)}}"," ",0,"1/24*b^4*arcsin(d*x + c)^4*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/24*b^4*arcsin(d*x + c)^4*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/6*a*b^3*arcsin(d*x + c)^3*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/6*a*b^3*arcsin(d*x + c)^3*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) - 1/24*(d*x + c)*b^4*arcsin(d*x + c)^3/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/4*a^2*b^2*arcsin(d*x + c)^2*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/4*a^2*b^2*arcsin(d*x + c)^2*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) - 1/8*(d*x + c)*a*b^3*arcsin(d*x + c)^2/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/6*a^3*b*arcsin(d*x + c)*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/6*a^3*b*arcsin(d*x + c)*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/24*sqrt(-(d*x + c)^2 + 1)*b^4*arcsin(d*x + c)^2/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) - 1/8*(d*x + c)*a^2*b^2*arcsin(d*x + c)/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/12*(d*x + c)*b^4*arcsin(d*x + c)/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/24*a^4*cos(a/b)*cos_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/24*a^4*sin(a/b)*sin_integral(a/b + arcsin(d*x + c))/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/12*sqrt(-(d*x + c)^2 + 1)*a*b^3*arcsin(d*x + c)/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) - 1/24*(d*x + c)*a^3*b/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/12*(d*x + c)*a*b^3/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) + 1/24*sqrt(-(d*x + c)^2 + 1)*a^2*b^2/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d) - 1/4*sqrt(-(d*x + c)^2 + 1)*b^4/(b^9*d*arcsin(d*x + c)^4 + 4*a*b^8*d*arcsin(d*x + c)^3 + 6*a^2*b^7*d*arcsin(d*x + c)^2 + 4*a^3*b^6*d*arcsin(d*x + c) + a^4*b^5*d)","B",0
240,1,1111,0,2.190587," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} a b i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{2} i}{{\left| b \right|}} + \sqrt{2} b\right)} d} + \frac{\sqrt{\pi} a \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{\sqrt{\pi} a \sqrt{b} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} + \frac{\sqrt{\pi} a i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{3}{2}} i}{{\left| b \right|}} + \sqrt{2} \sqrt{b}\right)} d} - \frac{\sqrt{\pi} a i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{b}\right)} d} - \frac{\sqrt{\pi} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{2} \sqrt{b}\right)} d} + \frac{\sqrt{\pi} b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{\sqrt{2} b^{2} i}{{\left| b \right|}} + \sqrt{2} b\right)} d} - \frac{\sqrt{\pi} b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{32 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} - \frac{\sqrt{\pi} a i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, \sqrt{b} d {\left(\frac{b i}{{\left| b \right|}} + 1\right)}} + \frac{\sqrt{\pi} b^{\frac{3}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{32 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d}"," ",0,"-1/16*sqrt(pi)*a*b*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) - 1/16*sqrt(pi)*a*sqrt(b)*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^2*i/abs(b) + sqrt(2)*b)*d) + 1/8*sqrt(pi)*a*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) + 1/8*sqrt(pi)*a*sqrt(b)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^2*i/abs(b) - b)*d) + 1/16*sqrt(pi)*a*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(3/2)*i/abs(b) + sqrt(2)*sqrt(b))*d) - 1/8*sqrt(pi)*a*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(3/2)*i/abs(b) - sqrt(b))*d) - 1/128*sqrt(pi)*b^2*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) + 1/16*sqrt(pi)*a*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(3/2)*i/abs(b) - sqrt(2)*sqrt(b))*d) + 1/128*sqrt(pi)*b^(3/2)*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^2*i/abs(b) + sqrt(2)*b)*d) - 1/32*sqrt(pi)*b^(3/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) - 1/8*sqrt(pi)*a*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/(sqrt(b)*d*(b*i/abs(b) + 1)) + 1/32*sqrt(pi)*b^(3/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^2*i/abs(b) - b)*d) + 1/64*sqrt(b*arcsin(d*x + c) + a)*e^(4*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*e^(2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*e^(-2*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*e^(-4*i*arcsin(d*x + c) + 3)/d","B",0
241,1,1191,0,2.394379," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{24 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{24 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} - \frac{\sqrt{\pi} a \sqrt{b} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{\sqrt{\pi} a \sqrt{b} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} + \frac{\sqrt{\pi} a \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{3}{2}} i}{{\left| b \right|}} + \sqrt{6} \sqrt{b}\right)} d} - \frac{\sqrt{\pi} a \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{6} \sqrt{b}\right)} d}"," ",0,"1/16*sqrt(2)*sqrt(pi)*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 1/16*sqrt(2)*sqrt(pi)*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/24*sqrt(pi)*b^(3/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 1/8*sqrt(2)*sqrt(pi)*a*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 1/8*sqrt(2)*sqrt(pi)*a*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/24*sqrt(pi)*b^(3/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) - 1/4*sqrt(pi)*a*sqrt(b)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 1/4*sqrt(pi)*a*sqrt(b)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*i*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*i*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*i*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*i*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/4*sqrt(pi)*a*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(3/2)*i/abs(b) + sqrt(6)*sqrt(b))*d) - 1/4*sqrt(pi)*a*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*a*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*a*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(3/2)*i/abs(b) - sqrt(6)*sqrt(b))*d)","B",0
242,1,517,0,1.853717," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} a \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{\sqrt{\pi} a \sqrt{b} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{\sqrt{\pi} a i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{b}\right)} d} - \frac{\sqrt{\pi} b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} - \frac{\sqrt{\pi} a i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, \sqrt{b} d {\left(\frac{b i}{{\left| b \right|}} + 1\right)}} + \frac{\sqrt{\pi} b^{\frac{3}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d}"," ",0,"1/4*sqrt(pi)*a*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 1/4*sqrt(pi)*a*sqrt(b)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 1/4*sqrt(pi)*a*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(3/2)*i/abs(b) - sqrt(b))*d) - 1/16*sqrt(pi)*b^(3/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) - 1/4*sqrt(pi)*a*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/(sqrt(b)*d*(b*i/abs(b) + 1)) + 1/16*sqrt(pi)*b^(3/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 1/8*sqrt(b*arcsin(d*x + c) + a)*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*e^(-2*i*arcsin(d*x + c) + 1)/d","B",0
243,1,579,0,0.995039," ","integrate((a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{\pi} a \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d}"," ",0,"1/4*sqrt(2)*sqrt(pi)*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 1/4*sqrt(2)*sqrt(pi)*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*i*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*i*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + sqrt(pi)*a*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d)","B",0
244,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(1/2)/(d*e*x+c*e),x, algorithm=""giac"")","\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
245,1,2282,0,2.472070," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{5}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{5}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{\sqrt{2} b^{3} i}{{\left| b \right|}} + \sqrt{2} b^{2}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{3} i}{{\left| b \right|}} - \sqrt{2} b^{2}\right)} d} + \frac{\sqrt{\pi} a^{2} b i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{5}{2}}\right)} d} + \frac{\sqrt{\pi} a^{2} b i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{1024 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{3} i}{{\left| b \right|}} + \sqrt{2} b^{2}\right)} d} - \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{1024 \, {\left(\frac{\sqrt{2} b^{2} i}{{\left| b \right|}} + \sqrt{2} b\right)} d} - \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} - \frac{\sqrt{\pi} a^{2} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{512 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{512 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d}"," ",0,"1/16*sqrt(pi)*a^2*b^2*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) + sqrt(2)*b^(5/2))*d) - 1/8*sqrt(pi)*a^2*b^2*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) - sqrt(2)*b^(5/2))*d) - 1/8*sqrt(pi)*a^2*b^(3/2)*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^3*i/abs(b) + sqrt(2)*b^2)*d) + 1/8*sqrt(pi)*a^2*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^3*i/abs(b) + b^2)*d) + 1/8*sqrt(pi)*a^2*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^3*i/abs(b) - b^2)*d) + 1/16*sqrt(pi)*a^2*b^(3/2)*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^3*i/abs(b) - sqrt(2)*b^2)*d) + 1/16*sqrt(pi)*a^2*b*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) + sqrt(2)*b^(3/2))*d) - 1/8*sqrt(pi)*a^2*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 1/64*sqrt(pi)*a*b^3*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) - sqrt(2)*b^(5/2))*d) + 1/16*sqrt(pi)*a^2*b*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) - 3/1024*sqrt(pi)*b^3*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) + 1/64*sqrt(pi)*a*b^(5/2)*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^3*i/abs(b) + sqrt(2)*b^2)*d) - 3/1024*sqrt(pi)*b^(5/2)*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^2*i/abs(b) + sqrt(2)*b)*d) - 1/16*sqrt(pi)*a*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^3*i/abs(b) + b^2)*d) - 1/8*sqrt(pi)*a^2*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) + 3/128*sqrt(pi)*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) + 1/16*sqrt(pi)*a*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^3*i/abs(b) - b^2)*d) + 3/128*sqrt(pi)*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^2*i/abs(b) - b)*d) - 1/64*sqrt(pi)*a*b^2*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) + sqrt(2)*b^(3/2))*d) + 1/16*sqrt(pi)*a*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 1/16*sqrt(pi)*a*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(5/2)*i/abs(b) - b^(3/2))*d) + 1/64*sqrt(pi)*a*b^2*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) + 3/512*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(4*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(4*i*arcsin(d*x + c) + 3)/d - 3/64*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 3)/d + 3/64*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(-2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 3)/d - 3/512*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(-4*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(-4*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*a*e^(4*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*a*e^(2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*a*e^(-2*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*a*e^(-4*i*arcsin(d*x + c) + 3)/d","B",0
246,1,2237,0,3.034397," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{12 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{12 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{\sqrt{\pi} a b^{2} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{12 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a b^{2} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{12 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{32 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{32 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} + \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{48 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{\sqrt{\pi} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{48 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{48 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{48 \, d}"," ",0,"1/8*sqrt(2)*sqrt(pi)*a*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) + 1/8*sqrt(2)*sqrt(pi)*a*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/12*sqrt(pi)*a*b^(5/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) + 1/8*sqrt(2)*sqrt(pi)*a^2*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/8*sqrt(2)*sqrt(pi)*a*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 1/8*sqrt(2)*sqrt(pi)*a^2*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/8*sqrt(2)*sqrt(pi)*a*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/12*sqrt(pi)*a*b^(5/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 1/12*sqrt(pi)*a*b^2*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) + 1/12*sqrt(pi)*a*b^2*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^2*b^(3/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) + 3/32*sqrt(2)*sqrt(pi)*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 3/32*sqrt(2)*sqrt(pi)*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*a^2*b^(3/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/4*sqrt(pi)*a^2*b*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^2*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*a^2*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*a^2*b*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/48*sqrt(pi)*b^(5/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 1/48*sqrt(pi)*b^(5/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(-3*i*arcsin(d*x + c) + 2)/d - 1/48*sqrt(b*arcsin(d*x + c) + a)*b*e^(3*i*arcsin(d*x + c) + 2)/d + 3/16*sqrt(b*arcsin(d*x + c) + a)*b*e^(i*arcsin(d*x + c) + 2)/d + 3/16*sqrt(b*arcsin(d*x + c) + a)*b*e^(-i*arcsin(d*x + c) + 2)/d - 1/48*sqrt(b*arcsin(d*x + c) + a)*b*e^(-3*i*arcsin(d*x + c) + 2)/d","B",0
247,1,984,0,1.329576," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} - \frac{\sqrt{\pi} a^{2} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} - \frac{\sqrt{\pi} a^{2} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{3 \, \sqrt{\pi} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} + \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b i e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d}"," ",0,"1/4*sqrt(pi)*a^2*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) + 1/4*sqrt(pi)*a^2*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) - 1/4*sqrt(pi)*a^2*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 1/8*sqrt(pi)*a*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) - 1/4*sqrt(pi)*a^2*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 3/64*sqrt(pi)*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 1/8*sqrt(pi)*a*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) + 3/64*sqrt(pi)*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) + 1/8*sqrt(pi)*a*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 1/8*sqrt(pi)*a*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 3/32*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 1)/d + 3/32*sqrt(b*arcsin(d*x + c) + a)*b*i*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*e^(-2*i*arcsin(d*x + c) + 1)/d","B",0
248,1,1091,0,1.542875," ","integrate((a+b*arcsin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{2} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} b e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/2*sqrt(2)*sqrt(pi)*a*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a^2*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a^2*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 3/8*sqrt(2)*sqrt(pi)*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 3/8*sqrt(2)*sqrt(pi)*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a^2*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + sqrt(pi)*a^2*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*a*i*e^(-i*arcsin(d*x + c))/d + 3/4*sqrt(b*arcsin(d*x + c) + a)*b*e^(i*arcsin(d*x + c))/d + 3/4*sqrt(b*arcsin(d*x + c) + a)*b*e^(-i*arcsin(d*x + c))/d","B",0
249,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(3/2)/(d*e*x+c*e),x, algorithm=""giac"")","\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
250,1,3439,0,3.571823," ","integrate((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{9}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{7}{2}}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{5}{2}}\right)} d} - \frac{\sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{5}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{3} i}{{\left| b \right|}} + \sqrt{2} b^{2}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{\sqrt{2} b^{3} i}{{\left| b \right|}} - \sqrt{2} b^{2}\right)} d} + \frac{3 \, \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{5}{2}}\right)} d} + \frac{\sqrt{\pi} a^{3} b i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{1024 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{3}{2}}\right)} d} - \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{3} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{\frac{7}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{5}{2}}\right)} d} + \frac{\sqrt{\pi} a^{3} b i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{\sqrt{2} b^{3} i}{{\left| b \right|}} + \sqrt{2} b^{2}\right)} d} - \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{1024 \, {\left(\frac{\sqrt{2} b^{2} i}{{\left| b \right|}} + \sqrt{2} b\right)} d} - \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} - \frac{\sqrt{\pi} a^{3} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{128 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{512 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{512 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{3}{2}}\right)} d} - \frac{15 \, \sqrt{\pi} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{8192 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} + \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{64 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{15 \, \sqrt{\pi} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{8192 \, {\left(\frac{\sqrt{2} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{2} b^{\frac{3}{2}}\right)} d} + \frac{15 \, \sqrt{\pi} b^{\frac{7}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{512 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} - \frac{15 \, \sqrt{\pi} b^{\frac{7}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{512 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{512 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{32 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{8 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{8 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{512 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{32 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(4 \, i \arcsin\left(d x + c\right) + 3\right)}}{4096 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 3\right)}}{256 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{16 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 3\right)}}{256 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{64 \, d} - \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(-4 \, i \arcsin\left(d x + c\right) + 3\right)}}{4096 \, d}"," ",0,"-1/16*sqrt(pi)*a^3*b^3*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(9/2)*i/abs(b) - sqrt(2)*b^(7/2))*d) + 1/8*sqrt(pi)*a^3*b^2*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) + sqrt(2)*b^(5/2))*d) - 1/8*sqrt(pi)*a^3*b^2*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) - sqrt(2)*b^(5/2))*d) - 3/16*sqrt(pi)*a^3*b^(3/2)*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^3*i/abs(b) + sqrt(2)*b^2)*d) + 1/8*sqrt(pi)*a^3*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^3*i/abs(b) + b^2)*d) + 1/8*sqrt(pi)*a^3*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^3*i/abs(b) - b^2)*d) + 1/8*sqrt(pi)*a^3*b^(3/2)*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^3*i/abs(b) - sqrt(2)*b^2)*d) + 3/128*sqrt(pi)*a^2*b^3*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) + sqrt(2)*b^(5/2))*d) + 1/16*sqrt(pi)*a^3*b*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) + sqrt(2)*b^(3/2))*d) + 9/1024*sqrt(pi)*a*b^3*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) + sqrt(2)*b^(3/2))*d) - 9/128*sqrt(pi)*a*b^3*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 1/8*sqrt(pi)*a^3*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 9/128*sqrt(pi)*a*b^3*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 3/64*sqrt(pi)*a^2*b^3*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(7/2)*i/abs(b) - sqrt(2)*b^(5/2))*d) + 1/16*sqrt(pi)*a^3*b*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) + 3/128*sqrt(pi)*a^2*b^(5/2)*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^3*i/abs(b) + sqrt(2)*b^2)*d) - 9/1024*sqrt(pi)*a*b^(5/2)*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^2*i/abs(b) + sqrt(2)*b)*d) - 3/16*sqrt(pi)*a^2*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^3*i/abs(b) + b^2)*d) - 1/8*sqrt(pi)*a^3*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) + 9/128*sqrt(pi)*a*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) + 3/16*sqrt(pi)*a^2*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^3*i/abs(b) - b^2)*d) + 9/128*sqrt(pi)*a*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^2*i/abs(b) - b)*d) + 5/512*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(4*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(4*i*arcsin(d*x + c) + 3)/d - 5/64*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(2*i*arcsin(d*x + c) + 3)/d + 5/64*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(-2*i*arcsin(d*x + c) + 3)/d - 5/512*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(-4*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(-4*i*arcsin(d*x + c) + 3)/d - 3/64*sqrt(pi)*a^2*b^2*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) + sqrt(2)*b^(3/2))*d) - 15/8192*sqrt(pi)*b^4*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) + sqrt(2)*b^(3/2))*d) + 3/16*sqrt(pi)*a^2*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 3/16*sqrt(pi)*a^2*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(5/2)*i/abs(b) - b^(3/2))*d) + 3/64*sqrt(pi)*a^2*b^2*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) + 15/8192*sqrt(pi)*b^4*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(5/2)*i/abs(b) - sqrt(2)*b^(3/2))*d) + 15/512*sqrt(pi)*b^(7/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/((b^2*i/abs(b) + b)*d) - 15/512*sqrt(pi)*b^(7/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^2*i/abs(b) - b)*d) + 5/512*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(4*i*arcsin(d*x + c) + 3)/d + 1/32*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(4*i*arcsin(d*x + c) + 3)/d - 5/64*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(2*i*arcsin(d*x + c) + 3)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 3)/d + 5/64*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(-2*i*arcsin(d*x + c) + 3)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 3)/d - 5/512*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(-4*i*arcsin(d*x + c) + 3)/d + 1/32*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(-4*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(4*i*arcsin(d*x + c) + 3)/d - 15/4096*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(4*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(2*i*arcsin(d*x + c) + 3)/d + 15/256*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(2*i*arcsin(d*x + c) + 3)/d - 1/16*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(-2*i*arcsin(d*x + c) + 3)/d + 15/256*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(-2*i*arcsin(d*x + c) + 3)/d + 1/64*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(-4*i*arcsin(d*x + c) + 3)/d - 15/4096*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(-4*i*arcsin(d*x + c) + 3)/d","B",0
251,1,3080,0,5.978795," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{64 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{64 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} + \frac{\sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} + \frac{5 \, \sqrt{\pi} b^{\frac{7}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{288 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{5 \, \sqrt{\pi} b^{\frac{7}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{288 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{12 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{4 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{4 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{12 \, d} + \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a b^{3} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{16 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a b^{3} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{16 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{16 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{\sqrt{\pi} a b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{16 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{288 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{32 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{32 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{288 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d}"," ",0,"1/8*sqrt(2)*sqrt(pi)*a^3*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 3/8*sqrt(2)*sqrt(pi)*a^2*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/8*sqrt(2)*sqrt(pi)*a^3*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 3/8*sqrt(2)*sqrt(pi)*a^2*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*a^2*b^(5/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) - 3/8*sqrt(2)*sqrt(pi)*a^2*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 15/64*sqrt(2)*sqrt(pi)*b^4*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 3/8*sqrt(2)*sqrt(pi)*a^2*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 15/64*sqrt(2)*sqrt(pi)*b^4*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*a^2*b^(5/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/4*sqrt(pi)*a^2*b^2*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) + 1/4*sqrt(pi)*a^2*b^2*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^3*b^(3/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) + 5/288*sqrt(pi)*b^(7/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 1/4*sqrt(pi)*a^3*b^(3/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 5/288*sqrt(pi)*b^(7/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) + 1/12*sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(3*i*arcsin(d*x + c) + 2)/d - 1/4*sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c) + 2)/d + 1/4*sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c) + 2)/d - 1/12*sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/4*sqrt(pi)*a^3*b*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) + 1/16*sqrt(pi)*a*b^3*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^3*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*a^3*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*a^3*b*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/16*sqrt(pi)*a*b^3*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/16*sqrt(pi)*a*b^(5/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 1/16*sqrt(pi)*a*b^(5/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(3*i*arcsin(d*x + c) + 2)/d - 5/288*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(3*i*arcsin(d*x + c) + 2)/d - 5/144*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(i*arcsin(d*x + c) + 2)/d + 15/32*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(i*arcsin(d*x + c) + 2)/d + 5/16*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(-i*arcsin(d*x + c) + 2)/d - 15/32*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(-i*arcsin(d*x + c) + 2)/d + 5/16*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(-3*i*arcsin(d*x + c) + 2)/d + 5/288*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(-3*i*arcsin(d*x + c) + 2)/d - 5/144*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(-3*i*arcsin(d*x + c) + 2)/d - 5/144*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(3*i*arcsin(d*x + c) + 2)/d + 5/16*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(i*arcsin(d*x + c) + 2)/d + 5/16*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(-i*arcsin(d*x + c) + 2)/d - 5/144*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(-3*i*arcsin(d*x + c) + 2)/d","B",0
252,1,1534,0,2.322972," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} - \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{3} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{9 \, \sqrt{\pi} a b^{3} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} - \frac{\sqrt{\pi} a^{3} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{3 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{9 \, \sqrt{\pi} a b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} a^{2} b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{8 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} + \frac{15 \, \sqrt{\pi} b^{\frac{7}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{256 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} - \frac{15 \, \sqrt{\pi} b^{\frac{7}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{256 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{4 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b i e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{4 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{128 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{128 \, d}"," ",0,"1/4*sqrt(pi)*a^3*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) + 1/4*sqrt(pi)*a^3*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) - 9/64*sqrt(pi)*a*b^3*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 1/4*sqrt(pi)*a^3*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 9/64*sqrt(pi)*a*b^3*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 3/8*sqrt(pi)*a^2*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) - 1/4*sqrt(pi)*a^3*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 9/64*sqrt(pi)*a*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 3/8*sqrt(pi)*a^2*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) + 9/64*sqrt(pi)*a*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 5/32*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(2*i*arcsin(d*x + c) + 1)/d + 5/32*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)^2*e^(-2*i*arcsin(d*x + c) + 1)/d + 3/8*sqrt(pi)*a^2*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 3/8*sqrt(pi)*a^2*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) + 15/256*sqrt(pi)*b^(7/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) - 15/256*sqrt(pi)*b^(7/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 5/32*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(2*i*arcsin(d*x + c) + 1)/d - 1/4*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 1)/d + 5/32*sqrt(b*arcsin(d*x + c) + a)*a*b*i*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/4*sqrt(b*arcsin(d*x + c) + a)*a*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(2*i*arcsin(d*x + c) + 1)/d + 15/128*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*e^(-2*i*arcsin(d*x + c) + 1)/d + 15/128*sqrt(b*arcsin(d*x + c) + a)*b^2*e^(-2*i*arcsin(d*x + c) + 1)/d","B",0
253,1,1317,0,3.171709," ","integrate((a+b*arcsin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{2} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{15 \, \sqrt{2} \sqrt{\pi} b^{4} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{d} - \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{3} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{15 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{2} \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{5 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/2*sqrt(2)*sqrt(pi)*a^3*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 3/2*sqrt(2)*sqrt(pi)*a^2*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a^3*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 3/2*sqrt(2)*sqrt(pi)*a^2*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 3/2*sqrt(2)*sqrt(pi)*a^2*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 15/16*sqrt(2)*sqrt(pi)*b^4*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 3/2*sqrt(2)*sqrt(pi)*a^2*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 15/16*sqrt(2)*sqrt(pi)*b^4*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*b^2*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d - sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + sqrt(b*arcsin(d*x + c) + a)*a*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a^3*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + sqrt(pi)*a^3*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(i*arcsin(d*x + c))/d + 15/8*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*a^2*i*e^(-i*arcsin(d*x + c))/d - 15/8*sqrt(b*arcsin(d*x + c) + a)*b^2*i*e^(-i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*b^2*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(i*arcsin(d*x + c))/d + 5/4*sqrt(b*arcsin(d*x + c) + a)*a*b*e^(-i*arcsin(d*x + c))/d","B",0
254,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(5/2)/(d*e*x+c*e),x, algorithm=""giac"")","\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
255,1,5404,0,8.636775," ","integrate((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{\pi} a^{4} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{5} i}{\sqrt{{\left| b \right|}}} + b^{4} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{4} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{8 \, {\left(\frac{b^{5} i}{\sqrt{{\left| b \right|}}} - b^{4} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{4} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{2 \, {\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} + \frac{\sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{24 \, {\left(\frac{\sqrt{6} b^{\frac{7}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{5}{2}}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{24 \, {\left(\frac{\sqrt{6} b^{\frac{7}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{5}{2}}\right)} d} - \frac{13 \, \sqrt{\pi} a^{3} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{24 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{16 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{16 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{13 \, \sqrt{\pi} a^{3} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{24 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{2 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{5 \, \sqrt{\pi} a b^{4} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{72 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{2 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{5 \, \sqrt{\pi} a b^{4} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{72 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{4} b^{\frac{3}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{\frac{7}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{8 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} + \sqrt{6} b^{2}\right)} d} + \frac{5 \, \sqrt{\pi} a b^{\frac{7}{2}} i \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{72 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} - \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{105 \, \sqrt{2} \sqrt{\pi} b^{5} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{128 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{16 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{105 \, \sqrt{2} \sqrt{\pi} b^{5} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{128 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{4} b^{\frac{3}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{7}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{8 \, {\left(\frac{\sqrt{6} b^{3} i}{{\left| b \right|}} - \sqrt{6} b^{2}\right)} d} + \frac{5 \, \sqrt{\pi} a b^{\frac{7}{2}} i \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{72 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{864 \, d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{32 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{32 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{864 \, d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} + \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} + \frac{\sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} + \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{5}{2}} i}{{\left| b \right|}} - \sqrt{6} b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{8 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{35 \, \sqrt{\pi} b^{\frac{9}{2}} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{1728 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} + \sqrt{6} b\right)} d} + \frac{\sqrt{\pi} a^{2} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{8 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} - \frac{35 \, \sqrt{\pi} b^{\frac{9}{2}} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{1728 \, {\left(\frac{\sqrt{6} b^{2} i}{{\left| b \right|}} - \sqrt{6} b\right)} d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{864 \, d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{72 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{32 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{32 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{8 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{24 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{864 \, d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{72 \, d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(3 \, i \arcsin\left(d x + c\right) + 2\right)}}{1728 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(i \arcsin\left(d x + c\right) + 2\right)}}{64 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{16 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(-i \arcsin\left(d x + c\right) + 2\right)}}{64 \, d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{144 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(-3 \, i \arcsin\left(d x + c\right) + 2\right)}}{1728 \, d}"," ",0,"-1/8*sqrt(2)*sqrt(pi)*a^4*b^4*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^5*i/sqrt(abs(b)) + b^4*sqrt(abs(b)))*d) - 1/4*sqrt(2)*sqrt(pi)*a^3*b^4*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 1/8*sqrt(2)*sqrt(pi)*a^4*b^4*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^5*i/sqrt(abs(b)) - b^4*sqrt(abs(b)))*d) - 1/4*sqrt(2)*sqrt(pi)*a^3*b^4*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a^4*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + sqrt(2)*sqrt(pi)*a^3*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 1/2*sqrt(2)*sqrt(pi)*a^4*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + sqrt(2)*sqrt(pi)*a^3*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/24*sqrt(pi)*a^3*b^3*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(7/2)*i/abs(b) + sqrt(6)*b^(5/2))*d) + 1/24*sqrt(pi)*a^3*b^3*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(7/2)*i/abs(b) - sqrt(6)*b^(5/2))*d) - 13/24*sqrt(pi)*a^3*b^(5/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) - 1/4*sqrt(2)*sqrt(pi)*a^4*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) + 9/16*sqrt(2)*sqrt(pi)*a^2*b^4*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 3/4*sqrt(2)*sqrt(pi)*a^3*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 1/4*sqrt(2)*sqrt(pi)*a^4*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 9/16*sqrt(2)*sqrt(pi)*a^2*b^4*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 3/4*sqrt(2)*sqrt(pi)*a^3*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 13/24*sqrt(pi)*a^3*b^(5/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 1/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(3*i*arcsin(d*x + c) + 2)/d - 3/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c) + 2)/d + 3/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/2*sqrt(pi)*a^3*b^2*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) - 5/72*sqrt(pi)*a*b^4*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) + 1/2*sqrt(pi)*a^3*b^2*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 5/72*sqrt(pi)*a*b^4*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^4*b^(3/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) - 1/8*sqrt(pi)*a^2*b^(7/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) + sqrt(6)*b^2)*d) + 5/72*sqrt(pi)*a*b^(7/2)*i*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) - 9/16*sqrt(2)*sqrt(pi)*a^2*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 105/128*sqrt(2)*sqrt(pi)*b^5*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 9/16*sqrt(2)*sqrt(pi)*a^2*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 105/128*sqrt(2)*sqrt(pi)*b^5*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*a^4*b^(3/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 1/8*sqrt(pi)*a^2*b^(7/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^3*i/abs(b) - sqrt(6)*b^2)*d) + 5/72*sqrt(pi)*a*b^(7/2)*i*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) + 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(3*i*arcsin(d*x + c) + 2)/d - 35/864*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(3*i*arcsin(d*x + c) + 2)/d - 7/144*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(3*i*arcsin(d*x + c) + 2)/d - 3/8*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c) + 2)/d + 35/32*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c) + 2)/d + 7/16*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c) + 2)/d + 3/8*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c) + 2)/d - 35/32*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c) + 2)/d + 7/16*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(-3*i*arcsin(d*x + c) + 2)/d + 35/864*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(-3*i*arcsin(d*x + c) + 2)/d - 7/144*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(-3*i*arcsin(d*x + c) + 2)/d + 1/4*sqrt(pi)*a^4*b*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) + 1/4*sqrt(pi)*a^2*b^3*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) + sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^4*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*a^4*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*a^4*b*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/4*sqrt(pi)*a^2*b^3*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(5/2)*i/abs(b) - sqrt(6)*b^(3/2))*d) - 1/8*sqrt(pi)*a^2*b^(5/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 35/1728*sqrt(pi)*b^(9/2)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) + sqrt(6)*b)*d) + 1/8*sqrt(pi)*a^2*b^(5/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) - 35/1728*sqrt(pi)*b^(9/2)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^2*i/abs(b) - sqrt(6)*b)*d) + 1/24*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(3*i*arcsin(d*x + c) + 2)/d - 35/864*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(3*i*arcsin(d*x + c) + 2)/d - 7/72*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(3*i*arcsin(d*x + c) + 2)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(i*arcsin(d*x + c) + 2)/d + 35/32*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(i*arcsin(d*x + c) + 2)/d + 7/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(i*arcsin(d*x + c) + 2)/d + 1/8*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(-i*arcsin(d*x + c) + 2)/d - 35/32*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(-i*arcsin(d*x + c) + 2)/d + 7/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(-i*arcsin(d*x + c) + 2)/d - 1/24*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(-3*i*arcsin(d*x + c) + 2)/d + 35/864*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(-3*i*arcsin(d*x + c) + 2)/d - 7/72*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(-3*i*arcsin(d*x + c) + 2)/d - 7/144*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(3*i*arcsin(d*x + c) + 2)/d + 35/1728*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(3*i*arcsin(d*x + c) + 2)/d + 7/16*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(i*arcsin(d*x + c) + 2)/d - 105/64*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(i*arcsin(d*x + c) + 2)/d + 7/16*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(-i*arcsin(d*x + c) + 2)/d - 105/64*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(-i*arcsin(d*x + c) + 2)/d - 7/144*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(-3*i*arcsin(d*x + c) + 2)/d + 35/1728*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(-3*i*arcsin(d*x + c) + 2)/d","B",0
256,1,2496,0,5.558296," ","integrate((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} a^{4} b^{\frac{3}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} + \frac{9 \, \sqrt{\pi} a^{2} b^{\frac{7}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{32 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} + \frac{\sqrt{\pi} a^{4} b^{\frac{3}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{9 \, \sqrt{\pi} a^{2} b^{\frac{7}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{32 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{3} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{3} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{\sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{\frac{7}{2}} i}{{\left| b \right|}} + b^{\frac{5}{2}}\right)} d} - \frac{9 \, \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{\sqrt{\pi} a^{3} b^{3} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{\frac{7}{2}} i}{{\left| b \right|}} - b^{\frac{5}{2}}\right)} d} - \frac{\sqrt{\pi} a^{4} b i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{9 \, \sqrt{\pi} a^{2} b^{3} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} - \frac{13 \, \sqrt{\pi} a^{3} b^{\frac{5}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} + b^{2}\right)} d} - \frac{\sqrt{\pi} a^{4} \sqrt{b} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{9 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{32 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} - \frac{105 \, \sqrt{\pi} b^{\frac{9}{2}} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{1024 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} + \frac{13 \, \sqrt{\pi} a^{3} b^{\frac{5}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{16 \, {\left(\frac{b^{3} i}{{\left| b \right|}} - b^{2}\right)} d} + \frac{9 \, \sqrt{\pi} a^{2} b^{\frac{5}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{32 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{105 \, \sqrt{\pi} b^{\frac{9}{2}} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{1024 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{16 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{16 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right)^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{3 \, \sqrt{\pi} a^{3} b^{2} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{15 \, \sqrt{\pi} a b^{4} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} + b^{\frac{3}{2}}\right)} d} - \frac{3 \, \sqrt{\pi} a^{3} b^{2} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} + \frac{15 \, \sqrt{\pi} a b^{4} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{\frac{5}{2}} i}{{\left| b \right|}} - b^{\frac{3}{2}}\right)} d} + \frac{15 \, \sqrt{\pi} a b^{\frac{7}{2}} \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} + b\right)} d} - \frac{15 \, \sqrt{\pi} a b^{\frac{7}{2}} \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{64 \, {\left(\frac{b^{2} i}{{\left| b \right|}} - b\right)} d} - \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} + \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{512 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right) e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{128 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{32 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{512 \, d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right) e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{128 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} e^{\left(2 \, i \arcsin\left(d x + c\right) + 1\right)}}{128 \, d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{8 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} e^{\left(-2 \, i \arcsin\left(d x + c\right) + 1\right)}}{128 \, d}"," ",0,"1/4*sqrt(pi)*a^4*b^(3/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) + 9/32*sqrt(pi)*a^2*b^(7/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) + 1/4*sqrt(pi)*a^4*b^(3/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) + 9/32*sqrt(pi)*a^2*b^(7/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) - 7/32*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^2*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^3*e^(2*i*arcsin(d*x + c) + 1)/d + 7/32*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^2*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^3*e^(-2*i*arcsin(d*x + c) + 1)/d + 1/16*sqrt(pi)*a^3*b^3*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(7/2)*i/abs(b) + b^(5/2))*d) - 9/16*sqrt(pi)*a^2*b^3*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 1/16*sqrt(pi)*a^3*b^3*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(7/2)*i/abs(b) - b^(5/2))*d) - 1/4*sqrt(pi)*a^4*b*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 9/16*sqrt(pi)*a^2*b^3*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) - 13/16*sqrt(pi)*a^3*b^(5/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^3*i/abs(b) + b^2)*d) - 1/4*sqrt(pi)*a^4*sqrt(b)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 9/32*sqrt(pi)*a^2*b^(5/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) - 105/1024*sqrt(pi)*b^(9/2)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) + 13/16*sqrt(pi)*a^3*b^(5/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^3*i/abs(b) - b^2)*d) + 9/32*sqrt(pi)*a^2*b^(5/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 105/1024*sqrt(pi)*b^(9/2)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 7/16*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 1)/d - 3/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)^2*e^(2*i*arcsin(d*x + c) + 1)/d + 7/16*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 1)/d - 3/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)^2*e^(-2*i*arcsin(d*x + c) + 1)/d + 3/4*sqrt(pi)*a^3*b^2*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 15/64*sqrt(pi)*a*b^4*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^(5/2)*i/abs(b) + b^(3/2))*d) - 3/4*sqrt(pi)*a^3*b^2*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) + 15/64*sqrt(pi)*a*b^4*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(5/2)*i/abs(b) - b^(3/2))*d) + 15/64*sqrt(pi)*a*b^(7/2)*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/((b^2*i/abs(b) + b)*d) - 15/64*sqrt(pi)*a*b^(7/2)*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^2*i/abs(b) - b)*d) - 7/32*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*e^(2*i*arcsin(d*x + c) + 1)/d + 105/512*sqrt(b*arcsin(d*x + c) + a)*b^3*i*e^(2*i*arcsin(d*x + c) + 1)/d - 3/8*sqrt(b*arcsin(d*x + c) + a)*a^2*b*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 1)/d + 35/128*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)*e^(2*i*arcsin(d*x + c) + 1)/d + 7/32*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*e^(-2*i*arcsin(d*x + c) + 1)/d - 105/512*sqrt(b*arcsin(d*x + c) + a)*b^3*i*e^(-2*i*arcsin(d*x + c) + 1)/d - 3/8*sqrt(b*arcsin(d*x + c) + a)*a^2*b*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 1)/d + 35/128*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)*e^(-2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^3*e^(2*i*arcsin(d*x + c) + 1)/d + 35/128*sqrt(b*arcsin(d*x + c) + a)*a*b^2*e^(2*i*arcsin(d*x + c) + 1)/d - 1/8*sqrt(b*arcsin(d*x + c) + a)*a^3*e^(-2*i*arcsin(d*x + c) + 1)/d + 35/128*sqrt(b*arcsin(d*x + c) + a)*a*b^2*e^(-2*i*arcsin(d*x + c) + 1)/d","B",0
257,1,2541,0,5.065763," ","integrate((a+b*arcsin(d*x+c))^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{\pi} a^{4} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{5} i}{\sqrt{{\left| b \right|}}} + b^{4} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{4} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{2 \, {\left(\frac{b^{5} i}{\sqrt{{\left| b \right|}}} - b^{4} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{2} \sqrt{\pi} a^{3} b^{4} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{2 \, \sqrt{2} \sqrt{\pi} a^{4} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} + b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{4 \, \sqrt{2} \sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{2 \, \sqrt{2} \sqrt{\pi} a^{4} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{4} i}{\sqrt{{\left| b \right|}}} - b^{3} \sqrt{{\left| b \right|}}\right)} d} + \frac{4 \, \sqrt{2} \sqrt{\pi} a^{3} b^{3} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right)^{3} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{2} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{4} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} + b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{2} \sqrt{\pi} a^{4} b^{2} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{4} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{3} i}{\sqrt{{\left| b \right|}}} - b^{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{2} \sqrt{\pi} a^{3} b^{2} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} - \frac{105 \, \sqrt{2} \sqrt{\pi} b^{5} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{32 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} + b \sqrt{{\left| b \right|}}\right)} d} + \frac{9 \, \sqrt{2} \sqrt{\pi} a^{2} b^{3} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{4 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} + \frac{105 \, \sqrt{2} \sqrt{\pi} b^{5} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{32 \, {\left(\frac{b^{2} i}{\sqrt{{\left| b \right|}}} - b \sqrt{{\left| b \right|}}\right)} d} - \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} + \frac{3 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} i \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} \arcsin\left(d x + c\right)^{2} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d} - \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} + \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} a^{4} b \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b^{2} i}{\sqrt{{\left| b \right|}}} - \sqrt{2} b \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{\sqrt{b \arcsin\left(d x + c\right) + a} a^{3} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} - \frac{35 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} i e^{\left(-i \arcsin\left(d x + c\right)\right)}}{8 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a b^{2} \arcsin\left(d x + c\right) e^{\left(-i \arcsin\left(d x + c\right)\right)}}{2 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(i \arcsin\left(d x + c\right)\right)}}{4 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(i \arcsin\left(d x + c\right)\right)}}{16 \, d} + \frac{7 \, \sqrt{b \arcsin\left(d x + c\right) + a} a^{2} b e^{\left(-i \arcsin\left(d x + c\right)\right)}}{4 \, d} - \frac{105 \, \sqrt{b \arcsin\left(d x + c\right) + a} b^{3} e^{\left(-i \arcsin\left(d x + c\right)\right)}}{16 \, d}"," ",0,"-1/2*sqrt(2)*sqrt(pi)*a^4*b^4*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^5*i/sqrt(abs(b)) + b^4*sqrt(abs(b)))*d) - sqrt(2)*sqrt(pi)*a^3*b^4*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 1/2*sqrt(2)*sqrt(pi)*a^4*b^4*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^5*i/sqrt(abs(b)) - b^4*sqrt(abs(b)))*d) - sqrt(2)*sqrt(pi)*a^3*b^4*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 2*sqrt(2)*sqrt(pi)*a^4*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^4*i/sqrt(abs(b)) + b^3*sqrt(abs(b)))*d) + 4*sqrt(2)*sqrt(pi)*a^3*b^3*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 2*sqrt(2)*sqrt(pi)*a^4*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^4*i/sqrt(abs(b)) - b^3*sqrt(abs(b)))*d) + 4*sqrt(2)*sqrt(pi)*a^3*b^3*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)^3*e^(-i*arcsin(d*x + c))/d - sqrt(2)*sqrt(pi)*a^4*b^2*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) + 9/4*sqrt(2)*sqrt(pi)*a^2*b^4*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^3*i/sqrt(abs(b)) + b^2*sqrt(abs(b)))*d) - 3*sqrt(2)*sqrt(pi)*a^3*b^2*i*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + sqrt(2)*sqrt(pi)*a^4*b^2*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 9/4*sqrt(2)*sqrt(pi)*a^2*b^4*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^3*i/sqrt(abs(b)) - b^2*sqrt(abs(b)))*d) - 3*sqrt(2)*sqrt(pi)*a^3*b^2*i*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 3/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d + 3/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d - 9/4*sqrt(2)*sqrt(pi)*a^2*b^3*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) - 105/32*sqrt(2)*sqrt(pi)*b^5*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((b^2*i/sqrt(abs(b)) + b*sqrt(abs(b)))*d) + 9/4*sqrt(2)*sqrt(pi)*a^2*b^3*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) + 105/32*sqrt(2)*sqrt(pi)*b^5*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((b^2*i/sqrt(abs(b)) - b*sqrt(abs(b)))*d) - 3/2*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 35/8*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(i*arcsin(d*x + c))/d + 3/2*sqrt(b*arcsin(d*x + c) + a)*a^2*b*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d - 35/8*sqrt(b*arcsin(d*x + c) + a)*b^3*i*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*b^3*arcsin(d*x + c)^2*e^(-i*arcsin(d*x + c))/d - sqrt(pi)*a^4*b*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) + sqrt(2)*b*sqrt(abs(b)))*d) + sqrt(pi)*a^4*b*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b^2*i/sqrt(abs(b)) - sqrt(2)*b*sqrt(abs(b)))*d) - 1/2*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(i*arcsin(d*x + c))/d + 35/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(i*arcsin(d*x + c))/d + 7/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(i*arcsin(d*x + c))/d + 1/2*sqrt(b*arcsin(d*x + c) + a)*a^3*i*e^(-i*arcsin(d*x + c))/d - 35/8*sqrt(b*arcsin(d*x + c) + a)*a*b^2*i*e^(-i*arcsin(d*x + c))/d + 7/2*sqrt(b*arcsin(d*x + c) + a)*a*b^2*arcsin(d*x + c)*e^(-i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(i*arcsin(d*x + c))/d - 105/16*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(i*arcsin(d*x + c))/d + 7/4*sqrt(b*arcsin(d*x + c) + a)*a^2*b*e^(-i*arcsin(d*x + c))/d - 105/16*sqrt(b*arcsin(d*x + c) + a)*b^3*e^(-i*arcsin(d*x + c))/d","B",0
258,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^(7/2)/(d*e*x+c*e),x, algorithm=""giac"")","\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
259,1,514,0,3.161828," ","integrate((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{10} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{10} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{5 \, a i}{b} + 4\right)}}{16 \, {\left(\frac{\sqrt{10} b^{\frac{3}{2}} i}{{\left| b \right|}} + \sqrt{10} \sqrt{b}\right)} d} + \frac{\sqrt{6} \sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 4\right)}}{32 \, \sqrt{b} d {\left(\frac{b i}{{\left| b \right|}} + 1\right)}} - \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 4\right)}}{8 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 4\right)}}{8 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{6} \sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 4\right)}}{32 \, \sqrt{b} d {\left(\frac{b i}{{\left| b \right|}} - 1\right)}} + \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{10} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{10} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{5 \, a i}{b} + 4\right)}}{16 \, {\left(\frac{\sqrt{10} b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{10} \sqrt{b}\right)} d}"," ",0,"-1/16*sqrt(pi)*erf(-1/2*sqrt(10)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(10)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(5*a*i/b + 4)/((sqrt(10)*b^(3/2)*i/abs(b) + sqrt(10)*sqrt(b))*d) + 1/32*sqrt(6)*sqrt(pi)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 4)/(sqrt(b)*d*(b*i/abs(b) + 1)) - 1/8*sqrt(pi)*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 4)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + 1/8*sqrt(pi)*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 4)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d) - 1/32*sqrt(6)*sqrt(pi)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 4)/(sqrt(b)*d*(b*i/abs(b) - 1)) + 1/16*sqrt(pi)*erf(1/2*sqrt(10)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(10)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-5*a*i/b + 4)/((sqrt(10)*b^(3/2)*i/abs(b) - sqrt(10)*sqrt(b))*d)","A",0
260,1,327,0,3.399513," ","integrate((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} i \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{3}{2}} i}{{\left| b \right|}} + \sqrt{2} \sqrt{b}\right)} d} - \frac{\sqrt{\pi} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 3\right)}}{8 \, {\left(\frac{b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{b}\right)} d} + \frac{\sqrt{\pi} i \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{4 \, a i}{b} + 3\right)}}{16 \, {\left(\frac{\sqrt{2} b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{2} \sqrt{b}\right)} d} - \frac{\sqrt{\pi} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 3\right)}}{8 \, \sqrt{b} d {\left(\frac{b i}{{\left| b \right|}} + 1\right)}}"," ",0,"1/16*sqrt(pi)*i*erf(-sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(4*a*i/b + 3)/((sqrt(2)*b^(3/2)*i/abs(b) + sqrt(2)*sqrt(b))*d) - 1/8*sqrt(pi)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 3)/((b^(3/2)*i/abs(b) - sqrt(b))*d) + 1/16*sqrt(pi)*i*erf(sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(2)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-4*a*i/b + 3)/((sqrt(2)*b^(3/2)*i/abs(b) - sqrt(2)*sqrt(b))*d) - 1/8*sqrt(pi)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 3)/(sqrt(b)*d*(b*i/abs(b) + 1))","A",0
261,1,350,0,2.620183," ","integrate((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{3}{2}} i}{{\left| b \right|}} + \sqrt{6} \sqrt{b}\right)} d} - \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} - \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{2 \, {\left| b \right|}} - \frac{\sqrt{6} \sqrt{b \arcsin\left(d x + c\right) + a}}{2 \, \sqrt{b}}\right) e^{\left(-\frac{3 \, a i}{b} + 2\right)}}{4 \, {\left(\frac{\sqrt{6} b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{6} \sqrt{b}\right)} d}"," ",0,"1/4*sqrt(pi)*erf(-1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(3*a*i/b + 2)/((sqrt(6)*b^(3/2)*i/abs(b) + sqrt(6)*sqrt(b))*d) - 1/4*sqrt(pi)*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b + 2)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + 1/4*sqrt(pi)*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b + 2)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d) - 1/4*sqrt(pi)*erf(1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - 1/2*sqrt(6)*sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-3*a*i/b + 2)/((sqrt(6)*b^(3/2)*i/abs(b) - sqrt(6)*sqrt(b))*d)","A",0
262,1,151,0,2.549247," ","integrate((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} i \operatorname{erf}\left(\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(-\frac{2 \, a i}{b} + 1\right)}}{4 \, {\left(\frac{b^{\frac{3}{2}} i}{{\left| b \right|}} - \sqrt{b}\right)} d} - \frac{\sqrt{\pi} i \operatorname{erf}\left(-\frac{\sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{b} i}{{\left| b \right|}} - \frac{\sqrt{b \arcsin\left(d x + c\right) + a}}{\sqrt{b}}\right) e^{\left(\frac{2 \, a i}{b} + 1\right)}}{4 \, \sqrt{b} d {\left(\frac{b i}{{\left| b \right|}} + 1\right)}}"," ",0,"-1/4*sqrt(pi)*i*erf(sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(-2*a*i/b + 1)/((b^(3/2)*i/abs(b) - sqrt(b))*d) - 1/4*sqrt(pi)*i*erf(-sqrt(b*arcsin(d*x + c) + a)*sqrt(b)*i/abs(b) - sqrt(b*arcsin(d*x + c) + a)/sqrt(b))*e^(2*a*i/b + 1)/(sqrt(b)*d*(b*i/abs(b) + 1))","A",0
263,1,170,0,2.125264," ","integrate(1/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} + \sqrt{2} \sqrt{{\left| b \right|}}\right)} d} + \frac{\sqrt{\pi} \operatorname{erf}\left(\frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} i}{2 \, \sqrt{{\left| b \right|}}} - \frac{\sqrt{2} \sqrt{b \arcsin\left(d x + c\right) + a} \sqrt{{\left| b \right|}}}{2 \, b}\right) e^{\left(-\frac{a i}{b}\right)}}{{\left(\frac{\sqrt{2} b i}{\sqrt{{\left| b \right|}}} - \sqrt{2} \sqrt{{\left| b \right|}}\right)} d}"," ",0,"-sqrt(pi)*erf(-1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) + sqrt(2)*sqrt(abs(b)))*d) + sqrt(pi)*erf(1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*i/sqrt(abs(b)) - 1/2*sqrt(2)*sqrt(b*arcsin(d*x + c) + a)*sqrt(abs(b))/b)*e^(-a*i/b)/((sqrt(2)*b*i/sqrt(abs(b)) - sqrt(2)*sqrt(abs(b)))*d)","A",0
264,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int {\left(d e x + c e\right)}^{\frac{7}{2}} {\left(b \arcsin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(7/2)*(b*arcsin(d*x + c) + a), x)","F",0
282,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\int {\left(d e x + c e\right)}^{\frac{5}{2}} {\left(b \arcsin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(5/2)*(b*arcsin(d*x + c) + a), x)","F",0
283,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\int {\left(d e x + c e\right)}^{\frac{3}{2}} {\left(b \arcsin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(3/2)*(b*arcsin(d*x + c) + a), x)","F",0
284,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\int \sqrt{d e x + c e} {\left(b \arcsin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(d*e*x + c*e)*(b*arcsin(d*x + c) + a), x)","F",0
285,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(1/2),x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{\sqrt{d e x + c e}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/sqrt(d*e*x + c*e), x)","F",0
286,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(3/2),x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{{\left(d e x + c e\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/(d*e*x + c*e)^(3/2), x)","F",0
287,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(5/2),x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{{\left(d e x + c e\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/(d*e*x + c*e)^(5/2), x)","F",0
288,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(7/2),x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{{\left(d e x + c e\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/(d*e*x + c*e)^(7/2), x)","F",0
289,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(9/2),x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{{\left(d e x + c e\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/(d*e*x + c*e)^(9/2), x)","F",0
290,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(11/2),x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x + c\right) + a}{{\left(d e x + c e\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)/(d*e*x + c*e)^(11/2), x)","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=""giac"")","\int {\left(d e x + c e\right)}^{\frac{7}{2}} {\left(b \arcsin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(7/2)*(b*arcsin(d*x + c) + a)^2, x)","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=""giac"")","\int {\left(d e x + c e\right)}^{\frac{5}{2}} {\left(b \arcsin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(5/2)*(b*arcsin(d*x + c) + a)^2, x)","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=""giac"")","\int {\left(d e x + c e\right)}^{\frac{3}{2}} {\left(b \arcsin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(3/2)*(b*arcsin(d*x + c) + a)^2, x)","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=""giac"")","\int \sqrt{d e x + c e} {\left(b \arcsin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(d*e*x + c*e)*(b*arcsin(d*x + c) + a)^2, x)","F",0
295,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{\sqrt{d e x + c e}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/sqrt(d*e*x + c*e), x)","F",0
296,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{{\left(d e x + c e\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(d*e*x + c*e)^(3/2), x)","F",0
297,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{{\left(d e x + c e\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(d*e*x + c*e)^(5/2), x)","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=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{{\left(d e x + c e\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(d*e*x + c*e)^(7/2), x)","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=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{2}}{{\left(d e x + c e\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2/(d*e*x + c*e)^(9/2), x)","F",0
300,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\int \sqrt{d e x + c e} {\left(b \arcsin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(d*e*x + c*e)*(b*arcsin(d*x + c) + a)^3, x)","F",0
301,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{\sqrt{d e x + c e}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/sqrt(d*e*x + c*e), x)","F",0
302,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{{\left(d e x + c e\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/(d*e*x + c*e)^(3/2), x)","F",0
303,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{3}}{{\left(d e x + c e\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3/(d*e*x + c*e)^(5/2), x)","F",0
304,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\int \sqrt{d e x + c e} {\left(b \arcsin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(d*e*x + c*e)*(b*arcsin(d*x + c) + a)^4, x)","F",0
305,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{\sqrt{d e x + c e}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/sqrt(d*e*x + c*e), x)","F",0
306,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{{\left(d e x + c e\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/(d*e*x + c*e)^(3/2), x)","F",0
307,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \arcsin\left(d x + c\right) + a\right)}^{4}}{{\left(d e x + c e\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4/(d*e*x + c*e)^(5/2), x)","F",0
308,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^4,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{4} {\left(d e x + c e\right)}^{m}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^4*(d*e*x + c*e)^m, x)","F",0
309,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{3} {\left(d e x + c e\right)}^{m}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^3*(d*e*x + c*e)^m, x)","F",0
310,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)}^{2} {\left(d e x + c e\right)}^{m}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)^2*(d*e*x + c*e)^m, x)","F",0
311,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m*(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x + c\right) + a\right)} {\left(d e x + c e\right)}^{m}\,{d x}"," ",0,"integrate((b*arcsin(d*x + c) + a)*(d*e*x + c*e)^m, x)","F",0
312,0,0,0,0.000000," ","integrate((d*e*x+c*e)^m/(a+b*arcsin(d*x+c)),x, algorithm=""giac"")","\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
313,1,162,0,2.240026," ","integrate(arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{3}}{2 \, b} + \frac{\arcsin\left(b x + a\right)^{4}}{8 \, b} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \arcsin\left(b x + a\right)^{2}}{4 \, b} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{4 \, b} - \frac{3 \, \arcsin\left(b x + a\right)^{2}}{8 \, b} + \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}{8 \, b} + \frac{3}{16 \, b}"," ",0,"1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)^3/b + 1/8*arcsin(b*x + a)^4/b - 3/4*(b^2*x^2 + 2*a*b*x + a^2 - 1)*arcsin(b*x + a)^2/b - 3/4*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)/b - 3/8*arcsin(b*x + a)^2/b + 3/8*(b^2*x^2 + 2*a*b*x + a^2 - 1)/b + 3/16/b","A",0
314,1,125,0,0.404083," ","integrate(arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{2 \, b} + \frac{\arcsin\left(b x + a\right)^{3}}{6 \, b} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \arcsin\left(b x + a\right)}{2 \, b} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)}}{4 \, b} - \frac{\arcsin\left(b x + a\right)}{4 \, b}"," ",0,"1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)^2/b + 1/6*arcsin(b*x + a)^3/b - 1/2*(b^2*x^2 + 2*a*b*x + a^2 - 1)*arcsin(b*x + a)/b - 1/4*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)/b - 1/4*arcsin(b*x + a)/b","A",0
315,1,79,0,0.369556," ","integrate(arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{2 \, b} + \frac{\arcsin\left(b x + a\right)^{2}}{4 \, b} - \frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{4 \, b} - \frac{1}{8 \, b}"," ",0,"1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)/b + 1/4*arcsin(b*x + a)^2/b - 1/4*(b^2*x^2 + 2*a*b*x + a^2 - 1)/b - 1/8/b","A",0
316,1,27,0,1.250958," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a),x, algorithm=""giac"")","\frac{\operatorname{Ci}\left(2 \, \arcsin\left(b x + a\right)\right)}{2 \, b} + \frac{\log\left(\arcsin\left(b x + a\right)\right)}{2 \, b}"," ",0,"1/2*cos_integral(2*arcsin(b*x + a))/b + 1/2*log(arcsin(b*x + a))/b","A",0
317,1,44,0,0.450608," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{b} + \frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b \arcsin\left(b x + a\right)}"," ",0,"-sin_integral(2*arcsin(b*x + a))/b + (b^2*x^2 + 2*a*b*x + a^2 - 1)/(b*arcsin(b*x + a))","A",0
318,1,84,0,0.433995," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^3,x, algorithm=""giac"")","-\frac{\operatorname{Ci}\left(2 \, \arcsin\left(b x + a\right)\right)}{b} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)}}{b \arcsin\left(b x + a\right)} + \frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{2 \, b \arcsin\left(b x + a\right)^{2}}"," ",0,"-cos_integral(2*arcsin(b*x + a))/b + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)/(b*arcsin(b*x + a)) + 1/2*(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b*arcsin(b*x + a)^2)","A",0
319,1,128,0,0.519061," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^4,x, algorithm=""giac"")","\frac{2 \, \operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{3 \, b} - \frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}{3 \, b \arcsin\left(b x + a\right)} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)}}{3 \, b \arcsin\left(b x + a\right)^{2}} - \frac{1}{3 \, b \arcsin\left(b x + a\right)} + \frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{3 \, b \arcsin\left(b x + a\right)^{3}}"," ",0,"2/3*sin_integral(2*arcsin(b*x + a))/b - 2/3*(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b*arcsin(b*x + a)) + 1/3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)/(b*arcsin(b*x + a)^2) - 1/3/(b*arcsin(b*x + a)) + 1/3*(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b*arcsin(b*x + a)^3)","A",0
320,1,296,0,2.290515," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{3}}{4 \, b} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{3}}{8 \, b} + \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2} \arcsin\left(b x + a\right)^{2}}{16 \, b} + \frac{3 \, \arcsin\left(b x + a\right)^{4}}{32 \, b} - \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{32 \, b} - \frac{9 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \arcsin\left(b x + a\right)^{2}}{16 \, b} - \frac{45 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{64 \, b} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2}}{128 \, b} - \frac{45 \, \arcsin\left(b x + a\right)^{2}}{128 \, b} + \frac{45 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}{128 \, b} + \frac{189}{1024 \, b}"," ",0,"1/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)*arcsin(b*x + a)^3/b + 3/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)^3/b + 3/16*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2*arcsin(b*x + a)^2/b + 3/32*arcsin(b*x + a)^4/b - 3/32*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)*arcsin(b*x + a)/b - 9/16*(b^2*x^2 + 2*a*b*x + a^2 - 1)*arcsin(b*x + a)^2/b - 45/64*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)/b - 3/128*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2/b - 45/128*arcsin(b*x + a)^2/b + 45/128*(b^2*x^2 + 2*a*b*x + a^2 - 1)/b + 189/1024/b","A",0
321,1,227,0,0.476752," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{4 \, b} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)^{2}}{8 \, b} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2} \arcsin\left(b x + a\right)}{8 \, b} + \frac{\arcsin\left(b x + a\right)^{3}}{8 \, b} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)}}{32 \, b} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \arcsin\left(b x + a\right)}{8 \, b} - \frac{15 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)}}{64 \, b} - \frac{15 \, \arcsin\left(b x + a\right)}{64 \, b}"," ",0,"1/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)*arcsin(b*x + a)^2/b + 3/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)^2/b + 1/8*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2*arcsin(b*x + a)/b + 1/8*arcsin(b*x + a)^3/b - 1/32*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)/b - 3/8*(b^2*x^2 + 2*a*b*x + a^2 - 1)*arcsin(b*x + a)/b - 15/64*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)/b - 15/64*arcsin(b*x + a)/b","A",0
322,1,141,0,1.439973," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a),x, algorithm=""giac"")","\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{4 \, b} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(b x + a\right)} \arcsin\left(b x + a\right)}{8 \, b} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2}}{16 \, b} + \frac{3 \, \arcsin\left(b x + a\right)^{2}}{16 \, b} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}{16 \, b} - \frac{15}{128 \, b}"," ",0,"1/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)*arcsin(b*x + a)/b + 3/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(b*x + a)*arcsin(b*x + a)/b + 1/16*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2/b + 3/16*arcsin(b*x + a)^2/b - 3/16*(b^2*x^2 + 2*a*b*x + a^2 - 1)/b - 15/128/b","A",0
323,1,41,0,0.401413," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a),x, algorithm=""giac"")","\frac{\operatorname{Ci}\left(4 \, \arcsin\left(b x + a\right)\right)}{8 \, b} + \frac{\operatorname{Ci}\left(2 \, \arcsin\left(b x + a\right)\right)}{2 \, b} + \frac{3 \, \log\left(\arcsin\left(b x + a\right)\right)}{8 \, b}"," ",0,"1/8*cos_integral(4*arcsin(b*x + a))/b + 1/2*cos_integral(2*arcsin(b*x + a))/b + 3/8*log(arcsin(b*x + a))/b","A",0
324,1,61,0,2.520360," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2}}{b \arcsin\left(b x + a\right)} - \frac{\operatorname{Si}\left(4 \, \arcsin\left(b x + a\right)\right)}{2 \, b} - \frac{\operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{b}"," ",0,"-(b^2*x^2 + 2*a*b*x + a^2 - 1)^2/(b*arcsin(b*x + a)) - 1/2*sin_integral(4*arcsin(b*x + a))/b - sin_integral(2*arcsin(b*x + a))/b","A",0
325,1,101,0,1.960941," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)}}{b \arcsin\left(b x + a\right)} - \frac{\operatorname{Ci}\left(4 \, \arcsin\left(b x + a\right)\right)}{b} - \frac{\operatorname{Ci}\left(2 \, \arcsin\left(b x + a\right)\right)}{b} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2}}{2 \, b \arcsin\left(b x + a\right)^{2}}"," ",0,"2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)/(b*arcsin(b*x + a)) - cos_integral(4*arcsin(b*x + a))/b - cos_integral(2*arcsin(b*x + a))/b - 1/2*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2/(b*arcsin(b*x + a)^2)","A",0
326,1,163,0,2.973048," ","integrate((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^4,x, algorithm=""giac"")","\frac{8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2}}{3 \, b \arcsin\left(b x + a\right)} + \frac{4 \, \operatorname{Si}\left(4 \, \arcsin\left(b x + a\right)\right)}{3 \, b} + \frac{2 \, \operatorname{Si}\left(2 \, \arcsin\left(b x + a\right)\right)}{3 \, b} + \frac{2 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)}}{3 \, b \arcsin\left(b x + a\right)^{2}} + \frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}}{b \arcsin\left(b x + a\right)} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)}^{2}}{3 \, b \arcsin\left(b x + a\right)^{3}}"," ",0,"8/3*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2/(b*arcsin(b*x + a)) + 4/3*sin_integral(4*arcsin(b*x + a))/b + 2/3*sin_integral(2*arcsin(b*x + a))/b + 2/3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*(b*x + a)/(b*arcsin(b*x + a)^2) + 2*(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b*arcsin(b*x + a)) - 1/3*(b^2*x^2 + 2*a*b*x + a^2 - 1)^2/(b*arcsin(b*x + a)^3)","A",0
327,1,19,0,3.947155," ","integrate(arcsin(b*x+a)^n/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\arcsin\left(b x + a\right)^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"arcsin(b*x + a)^(n + 1)/(b*(n + 1))","A",0
328,1,13,0,1.322807," ","integrate(arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\arcsin\left(b x + a\right)^{3}}{3 \, b}"," ",0,"1/3*arcsin(b*x + a)^3/b","A",0
329,1,13,0,0.350564," ","integrate(arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\arcsin\left(b x + a\right)^{2}}{2 \, b}"," ",0,"1/2*arcsin(b*x + a)^2/b","A",0
330,1,12,0,0.323522," ","integrate(1/arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| \arcsin\left(b x + a\right) \right|}\right)}{b}"," ",0,"log(abs(arcsin(b*x + a)))/b","A",0
331,1,13,0,0.323037," ","integrate(1/arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{b \arcsin\left(b x + a\right)}"," ",0,"-1/(b*arcsin(b*x + a))","A",0
332,1,13,0,0.530308," ","integrate(1/arcsin(b*x+a)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2 \, b \arcsin\left(b x + a\right)^{2}}"," ",0,"-1/2/(b*arcsin(b*x + a)^2)","A",0
333,0,0,0,0.000000," ","integrate(arcsin(b*x+a)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)^{3}}{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)^3/(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2), x)","F",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=""giac"")","\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
335,1,83,0,1.169849," ","integrate(arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(x + \frac{a}{b}\right)} \arcsin\left(b x + a\right)}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} + \frac{\log\left({\left| b x + a + 1 \right|}\right)}{2 \, b} + \frac{\log\left({\left| b x + a - 1 \right|}\right)}{2 \, b}"," ",0,"-sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(x + a/b)*arcsin(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 - 1) + 1/2*log(abs(b*x + a + 1))/b + 1/2*log(abs(b*x + a - 1))/b","A",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=""giac"")","\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=""giac"")","\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)^{2}}\,{d x}"," ",0,"integrate(1/((-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*arcsin(b*x + a)^2), x)","F",0
338,0,0,0,0.000000," ","integrate(arcsin(b*x+a)/(c-c*(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)}{\sqrt{-{\left(b x + a\right)}^{2} c + c}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)/sqrt(-(b*x + a)^2*c + c), x)","F",0
339,0,0,0,0.000000," ","integrate(arcsin(b*x+a)/((-a^2+1)*c-2*a*b*c*x-c*x^2*b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\arcsin\left(b x + a\right)}{\sqrt{-b^{2} c x^{2} - 2 \, a b c x - {\left(a^{2} - 1\right)} c}}\,{d x}"," ",0,"integrate(arcsin(b*x + a)/sqrt(-b^2*c*x^2 - 2*a*b*c*x - (a^2 - 1)*c), x)","F",0
340,1,140,0,0.376390," ","integrate(x^9*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\frac{15 \, a c x^{10} + {\left(\frac{15 \, {\left(c^{2} x^{4} - 1\right)}^{2} x^{2} \arcsin\left(c x^{2}\right)}{c^{3}} + \frac{30 \, {\left(c^{2} x^{4} - 1\right)} x^{2} \arcsin\left(c x^{2}\right)}{c^{3}} + \frac{15 \, x^{2} \arcsin\left(c x^{2}\right)}{c^{3}} + \frac{3 \, {\left(c^{2} x^{4} - 1\right)}^{2} \sqrt{-c^{2} x^{4} + 1}}{c^{4}} - \frac{10 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{4} + 1}}{c^{4}}\right)} b}{150 \, c}"," ",0,"1/150*(15*a*c*x^10 + (15*(c^2*x^4 - 1)^2*x^2*arcsin(c*x^2)/c^3 + 30*(c^2*x^4 - 1)*x^2*arcsin(c*x^2)/c^3 + 15*x^2*arcsin(c*x^2)/c^3 + 3*(c^2*x^4 - 1)^2*sqrt(-c^2*x^4 + 1)/c^4 - 10*(-c^2*x^4 + 1)^(3/2)/c^4 + 15*sqrt(-c^2*x^4 + 1)/c^4)*b)/c","A",0
341,1,110,0,0.202496," ","integrate(x^7*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\frac{8 \, a c x^{8} - {\left(\frac{2 \, {\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}} x^{2}}{c^{2}} - \frac{5 \, \sqrt{-c^{2} x^{4} + 1} x^{2}}{c^{2}} - \frac{8 \, {\left(c^{2} x^{4} - 1\right)}^{2} \arcsin\left(c x^{2}\right)}{c^{3}} - \frac{16 \, {\left(c^{2} x^{4} - 1\right)} \arcsin\left(c x^{2}\right)}{c^{3}} - \frac{5 \, \arcsin\left(c x^{2}\right)}{c^{3}}\right)} b}{64 \, c}"," ",0,"1/64*(8*a*c*x^8 - (2*(-c^2*x^4 + 1)^(3/2)*x^2/c^2 - 5*sqrt(-c^2*x^4 + 1)*x^2/c^2 - 8*(c^2*x^4 - 1)^2*arcsin(c*x^2)/c^3 - 16*(c^2*x^4 - 1)*arcsin(c*x^2)/c^3 - 5*arcsin(c*x^2)/c^3)*b)/c","A",0
342,1,87,0,0.934269," ","integrate(x^5*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\frac{3 \, a c x^{6} + {\left(\frac{3 \, {\left(c^{2} x^{4} - 1\right)} x^{2} \arcsin\left(c x^{2}\right)}{c} + \frac{3 \, x^{2} \arcsin\left(c x^{2}\right)}{c} - \frac{{\left(-c^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{4} + 1}}{c^{2}}\right)} b}{18 \, c}"," ",0,"1/18*(3*a*c*x^6 + (3*(c^2*x^4 - 1)*x^2*arcsin(c*x^2)/c + 3*x^2*arcsin(c*x^2)/c - (-c^2*x^4 + 1)^(3/2)/c^2 + 3*sqrt(-c^2*x^4 + 1)/c^2)*b)/c","A",0
343,1,59,0,0.141248," ","integrate(x^3*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\frac{2 \, a c x^{4} + \frac{{\left(\sqrt{-c^{2} x^{4} + 1} c x^{2} + 2 \, {\left(c^{2} x^{4} - 1\right)} \arcsin\left(c x^{2}\right) + \arcsin\left(c x^{2}\right)\right)} b}{c}}{8 \, c}"," ",0,"1/8*(2*a*c*x^4 + (sqrt(-c^2*x^4 + 1)*c*x^2 + 2*(c^2*x^4 - 1)*arcsin(c*x^2) + arcsin(c*x^2))*b/c)/c","A",0
344,1,38,0,0.230247," ","integrate(x*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\frac{a c x^{2} + {\left(c x^{2} \arcsin\left(c x^{2}\right) + \sqrt{-c^{2} x^{4} + 1}\right)} b}{2 \, c}"," ",0,"1/2*(a*c*x^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=""giac"")","\int \frac{b \arcsin\left(c x^{2}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)/x, x)","F",0
346,1,354,0,0.352322," ","integrate((a+b*arcsin(c*x^2))/x^3,x, algorithm=""giac"")","-\frac{\frac{\sqrt{-c^{2} x^{4} + 1} b c^{3} x^{2} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{b c^{3} x^{2} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{\sqrt{-c^{2} x^{4} + 1} a c^{3} x^{2}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{a c^{3} x^{2}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} - \frac{2 \, \sqrt{-c^{2} x^{4} + 1} b c^{2} \log\left(x^{2} {\left| c \right|}\right)}{\sqrt{-c^{2} x^{4} + 1} + 1} + \frac{2 \, \sqrt{-c^{2} x^{4} + 1} b c^{2} \log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}{\sqrt{-c^{2} x^{4} + 1} + 1} - \frac{2 \, b c^{2} \log\left(x^{2} {\left| c \right|}\right)}{\sqrt{-c^{2} x^{4} + 1} + 1} + \frac{2 \, b c^{2} \log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}{\sqrt{-c^{2} x^{4} + 1} + 1} + \frac{\sqrt{-c^{2} x^{4} + 1} b c \arcsin\left(c x^{2}\right)}{x^{2}} + \frac{b c \arcsin\left(c x^{2}\right)}{x^{2}} + \frac{\sqrt{-c^{2} x^{4} + 1} a c}{x^{2}} + \frac{a c}{x^{2}}}{4 \, c}"," ",0,"-1/4*(sqrt(-c^2*x^4 + 1)*b*c^3*x^2*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^2 + b*c^3*x^2*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^2 + sqrt(-c^2*x^4 + 1)*a*c^3*x^2/(sqrt(-c^2*x^4 + 1) + 1)^2 + a*c^3*x^2/(sqrt(-c^2*x^4 + 1) + 1)^2 - 2*sqrt(-c^2*x^4 + 1)*b*c^2*log(x^2*abs(c))/(sqrt(-c^2*x^4 + 1) + 1) + 2*sqrt(-c^2*x^4 + 1)*b*c^2*log(sqrt(-c^2*x^4 + 1) + 1)/(sqrt(-c^2*x^4 + 1) + 1) - 2*b*c^2*log(x^2*abs(c))/(sqrt(-c^2*x^4 + 1) + 1) + 2*b*c^2*log(sqrt(-c^2*x^4 + 1) + 1)/(sqrt(-c^2*x^4 + 1) + 1) + sqrt(-c^2*x^4 + 1)*b*c*arcsin(c*x^2)/x^2 + b*c*arcsin(c*x^2)/x^2 + sqrt(-c^2*x^4 + 1)*a*c/x^2 + a*c/x^2)/c","B",0
347,1,176,0,0.240267," ","integrate((a+b*arcsin(c*x^2))/x^5,x, algorithm=""giac"")","-\frac{\frac{b c^{5} x^{4} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{a c^{5} x^{4}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} - \frac{2 \, b c^{4} x^{2}}{\sqrt{-c^{2} x^{4} + 1} + 1} + 2 \, b c^{3} \arcsin\left(c x^{2}\right) + 2 \, a c^{3} + \frac{2 \, b c^{2} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}}{x^{2}} + \frac{b c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2} \arcsin\left(c x^{2}\right)}{x^{4}} + \frac{a c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}}{x^{4}}}{16 \, c}"," ",0,"-1/16*(b*c^5*x^4*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^2 + a*c^5*x^4/(sqrt(-c^2*x^4 + 1) + 1)^2 - 2*b*c^4*x^2/(sqrt(-c^2*x^4 + 1) + 1) + 2*b*c^3*arcsin(c*x^2) + 2*a*c^3 + 2*b*c^2*(sqrt(-c^2*x^4 + 1) + 1)/x^2 + b*c*(sqrt(-c^2*x^4 + 1) + 1)^2*arcsin(c*x^2)/x^4 + a*c*(sqrt(-c^2*x^4 + 1) + 1)^2/x^4)/c","B",0
348,1,301,0,0.602529," ","integrate((a+b*arcsin(c*x^2))/x^7,x, algorithm=""giac"")","-\frac{\frac{b c^{7} x^{6} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}} + \frac{a c^{7} x^{6}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}} - \frac{b c^{6} x^{4}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{3 \, b c^{5} x^{2} \arcsin\left(c x^{2}\right)}{\sqrt{-c^{2} x^{4} + 1} + 1} + \frac{3 \, a c^{5} x^{2}}{\sqrt{-c^{2} x^{4} + 1} + 1} - 4 \, b c^{4} \log\left(x^{2} {\left| c \right|}\right) + 4 \, b c^{4} \log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right) + \frac{3 \, b c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)} \arcsin\left(c x^{2}\right)}{x^{2}} + \frac{3 \, a c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}}{x^{2}} + \frac{b c^{2} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}}{x^{4}} + \frac{b c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3} \arcsin\left(c x^{2}\right)}{x^{6}} + \frac{a c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}}{x^{6}}}{48 \, c}"," ",0,"-1/48*(b*c^7*x^6*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^3 + a*c^7*x^6/(sqrt(-c^2*x^4 + 1) + 1)^3 - b*c^6*x^4/(sqrt(-c^2*x^4 + 1) + 1)^2 + 3*b*c^5*x^2*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1) + 3*a*c^5*x^2/(sqrt(-c^2*x^4 + 1) + 1) - 4*b*c^4*log(x^2*abs(c)) + 4*b*c^4*log(sqrt(-c^2*x^4 + 1) + 1) + 3*b*c^3*(sqrt(-c^2*x^4 + 1) + 1)*arcsin(c*x^2)/x^2 + 3*a*c^3*(sqrt(-c^2*x^4 + 1) + 1)/x^2 + b*c^2*(sqrt(-c^2*x^4 + 1) + 1)^2/x^4 + b*c*(sqrt(-c^2*x^4 + 1) + 1)^3*arcsin(c*x^2)/x^6 + a*c*(sqrt(-c^2*x^4 + 1) + 1)^3/x^6)/c","B",0
349,1,342,0,1.066181," ","integrate((a+b*arcsin(c*x^2))/x^9,x, algorithm=""giac"")","-\frac{\frac{3 \, b c^{9} x^{8} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}} + \frac{3 \, a c^{9} x^{8}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}} - \frac{2 \, b c^{8} x^{6}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}} + \frac{12 \, b c^{7} x^{4} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{12 \, a c^{7} x^{4}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} - \frac{18 \, b c^{6} x^{2}}{\sqrt{-c^{2} x^{4} + 1} + 1} + 18 \, b c^{5} \arcsin\left(c x^{2}\right) + 18 \, a c^{5} + \frac{18 \, b c^{4} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}}{x^{2}} + \frac{12 \, b c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2} \arcsin\left(c x^{2}\right)}{x^{4}} + \frac{12 \, a c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}}{x^{4}} + \frac{2 \, b c^{2} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}}{x^{6}} + \frac{3 \, b c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4} \arcsin\left(c x^{2}\right)}{x^{8}} + \frac{3 \, a c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}}{x^{8}}}{384 \, c}"," ",0,"-1/384*(3*b*c^9*x^8*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^4 + 3*a*c^9*x^8/(sqrt(-c^2*x^4 + 1) + 1)^4 - 2*b*c^8*x^6/(sqrt(-c^2*x^4 + 1) + 1)^3 + 12*b*c^7*x^4*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^2 + 12*a*c^7*x^4/(sqrt(-c^2*x^4 + 1) + 1)^2 - 18*b*c^6*x^2/(sqrt(-c^2*x^4 + 1) + 1) + 18*b*c^5*arcsin(c*x^2) + 18*a*c^5 + 18*b*c^4*(sqrt(-c^2*x^4 + 1) + 1)/x^2 + 12*b*c^3*(sqrt(-c^2*x^4 + 1) + 1)^2*arcsin(c*x^2)/x^4 + 12*a*c^3*(sqrt(-c^2*x^4 + 1) + 1)^2/x^4 + 2*b*c^2*(sqrt(-c^2*x^4 + 1) + 1)^3/x^6 + 3*b*c*(sqrt(-c^2*x^4 + 1) + 1)^4*arcsin(c*x^2)/x^8 + 3*a*c*(sqrt(-c^2*x^4 + 1) + 1)^4/x^8)/c","B",0
350,1,467,0,1.548963," ","integrate((a+b*arcsin(c*x^2))/x^11,x, algorithm=""giac"")","-\frac{\frac{2 \, b c^{11} x^{10} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{5}} + \frac{2 \, a c^{11} x^{10}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{5}} - \frac{b c^{10} x^{8}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}} + \frac{10 \, b c^{9} x^{6} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}} + \frac{10 \, a c^{9} x^{6}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}} - \frac{8 \, b c^{8} x^{4}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{20 \, b c^{7} x^{2} \arcsin\left(c x^{2}\right)}{\sqrt{-c^{2} x^{4} + 1} + 1} + \frac{20 \, a c^{7} x^{2}}{\sqrt{-c^{2} x^{4} + 1} + 1} - 24 \, b c^{6} \log\left(x^{2} {\left| c \right|}\right) + 24 \, b c^{6} \log\left(\sqrt{-c^{2} x^{4} + 1} + 1\right) + \frac{20 \, b c^{5} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)} \arcsin\left(c x^{2}\right)}{x^{2}} + \frac{20 \, a c^{5} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}}{x^{2}} + \frac{8 \, b c^{4} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}}{x^{4}} + \frac{10 \, b c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3} \arcsin\left(c x^{2}\right)}{x^{6}} + \frac{10 \, a c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}}{x^{6}} + \frac{b c^{2} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}}{x^{8}} + \frac{2 \, b c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{5} \arcsin\left(c x^{2}\right)}{x^{10}} + \frac{2 \, a c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{5}}{x^{10}}}{640 \, c}"," ",0,"-1/640*(2*b*c^11*x^10*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^5 + 2*a*c^11*x^10/(sqrt(-c^2*x^4 + 1) + 1)^5 - b*c^10*x^8/(sqrt(-c^2*x^4 + 1) + 1)^4 + 10*b*c^9*x^6*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^3 + 10*a*c^9*x^6/(sqrt(-c^2*x^4 + 1) + 1)^3 - 8*b*c^8*x^4/(sqrt(-c^2*x^4 + 1) + 1)^2 + 20*b*c^7*x^2*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1) + 20*a*c^7*x^2/(sqrt(-c^2*x^4 + 1) + 1) - 24*b*c^6*log(x^2*abs(c)) + 24*b*c^6*log(sqrt(-c^2*x^4 + 1) + 1) + 20*b*c^5*(sqrt(-c^2*x^4 + 1) + 1)*arcsin(c*x^2)/x^2 + 20*a*c^5*(sqrt(-c^2*x^4 + 1) + 1)/x^2 + 8*b*c^4*(sqrt(-c^2*x^4 + 1) + 1)^2/x^4 + 10*b*c^3*(sqrt(-c^2*x^4 + 1) + 1)^3*arcsin(c*x^2)/x^6 + 10*a*c^3*(sqrt(-c^2*x^4 + 1) + 1)^3/x^6 + b*c^2*(sqrt(-c^2*x^4 + 1) + 1)^4/x^8 + 2*b*c*(sqrt(-c^2*x^4 + 1) + 1)^5*arcsin(c*x^2)/x^10 + 2*a*c*(sqrt(-c^2*x^4 + 1) + 1)^5/x^10)/c","B",0
351,1,504,0,0.259243," ","integrate((a+b*arcsin(c*x^2))/x^13,x, algorithm=""giac"")","-\frac{\frac{15 \, b c^{13} x^{12} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{6}} + \frac{15 \, a c^{13} x^{12}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{6}} - \frac{6 \, b c^{12} x^{10}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{5}} + \frac{90 \, b c^{11} x^{8} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}} + \frac{90 \, a c^{11} x^{8}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}} - \frac{50 \, b c^{10} x^{6}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}} + \frac{225 \, b c^{9} x^{4} \arcsin\left(c x^{2}\right)}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} + \frac{225 \, a c^{9} x^{4}}{{\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}} - \frac{300 \, b c^{8} x^{2}}{\sqrt{-c^{2} x^{4} + 1} + 1} + 300 \, b c^{7} \arcsin\left(c x^{2}\right) + 300 \, a c^{7} + \frac{300 \, b c^{6} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}}{x^{2}} + \frac{225 \, b c^{5} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2} \arcsin\left(c x^{2}\right)}{x^{4}} + \frac{225 \, a c^{5} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{2}}{x^{4}} + \frac{50 \, b c^{4} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{3}}{x^{6}} + \frac{90 \, b c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4} \arcsin\left(c x^{2}\right)}{x^{8}} + \frac{90 \, a c^{3} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{4}}{x^{8}} + \frac{6 \, b c^{2} {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{5}}{x^{10}} + \frac{15 \, b c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{6} \arcsin\left(c x^{2}\right)}{x^{12}} + \frac{15 \, a c {\left(\sqrt{-c^{2} x^{4} + 1} + 1\right)}^{6}}{x^{12}}}{11520 \, c}"," ",0,"-1/11520*(15*b*c^13*x^12*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^6 + 15*a*c^13*x^12/(sqrt(-c^2*x^4 + 1) + 1)^6 - 6*b*c^12*x^10/(sqrt(-c^2*x^4 + 1) + 1)^5 + 90*b*c^11*x^8*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^4 + 90*a*c^11*x^8/(sqrt(-c^2*x^4 + 1) + 1)^4 - 50*b*c^10*x^6/(sqrt(-c^2*x^4 + 1) + 1)^3 + 225*b*c^9*x^4*arcsin(c*x^2)/(sqrt(-c^2*x^4 + 1) + 1)^2 + 225*a*c^9*x^4/(sqrt(-c^2*x^4 + 1) + 1)^2 - 300*b*c^8*x^2/(sqrt(-c^2*x^4 + 1) + 1) + 300*b*c^7*arcsin(c*x^2) + 300*a*c^7 + 300*b*c^6*(sqrt(-c^2*x^4 + 1) + 1)/x^2 + 225*b*c^5*(sqrt(-c^2*x^4 + 1) + 1)^2*arcsin(c*x^2)/x^4 + 225*a*c^5*(sqrt(-c^2*x^4 + 1) + 1)^2/x^4 + 50*b*c^4*(sqrt(-c^2*x^4 + 1) + 1)^3/x^6 + 90*b*c^3*(sqrt(-c^2*x^4 + 1) + 1)^4*arcsin(c*x^2)/x^8 + 90*a*c^3*(sqrt(-c^2*x^4 + 1) + 1)^4/x^8 + 6*b*c^2*(sqrt(-c^2*x^4 + 1) + 1)^5/x^10 + 15*b*c*(sqrt(-c^2*x^4 + 1) + 1)^6*arcsin(c*x^2)/x^12 + 15*a*c*(sqrt(-c^2*x^4 + 1) + 1)^6/x^12)/c","B",0
352,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x^{2}\right) + a\right)} x^{6}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)*x^6, x)","F",0
353,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x^{2}\right) + a\right)} x^{4}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)*x^4, x)","F",0
354,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x^2)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x^{2}\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)*x^2, x)","F",0
355,0,0,0,0.000000," ","integrate(a+b*arcsin(c*x^2),x, algorithm=""giac"")","\int b \arcsin\left(c x^{2}\right) + a\,{d x}"," ",0,"integrate(b*arcsin(c*x^2) + a, x)","F",0
356,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^2,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{2}\right) + a}{x^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)/x^2, x)","F",0
357,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^4,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{2}\right) + a}{x^{4}}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)/x^4, x)","F",0
358,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^6,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{2}\right) + a}{x^{6}}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)/x^6, x)","F",0
359,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^2))/x^8,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{2}\right) + a}{x^{8}}\,{d x}"," ",0,"integrate((b*arcsin(c*x^2) + a)/x^8, x)","F",0
360,0,0,0,0.000000," ","integrate(arcsin(a*x^5)/x,x, algorithm=""giac"")","\int \frac{\arcsin\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arcsin(a*x^5)/x, x)","F",0
361,1,77,0,0.163344," ","integrate(x^2*arcsin(x^(1/2)),x, algorithm=""giac"")","\frac{1}{3} \, {\left(x - 1\right)}^{3} \arcsin\left(\sqrt{x}\right) + \frac{1}{18} \, {\left(x - 1\right)}^{2} \sqrt{x} \sqrt{-x + 1} + {\left(x - 1\right)}^{2} \arcsin\left(\sqrt{x}\right) - \frac{13}{72} \, \sqrt{x} {\left(-x + 1\right)}^{\frac{3}{2}} + {\left(x - 1\right)} \arcsin\left(\sqrt{x}\right) + \frac{11}{48} \, \sqrt{x} \sqrt{-x + 1} + \frac{11}{48} \, \arcsin\left(\sqrt{x}\right)"," ",0,"1/3*(x - 1)^3*arcsin(sqrt(x)) + 1/18*(x - 1)^2*sqrt(x)*sqrt(-x + 1) + (x - 1)^2*arcsin(sqrt(x)) - 13/72*sqrt(x)*(-x + 1)^(3/2) + (x - 1)*arcsin(sqrt(x)) + 11/48*sqrt(x)*sqrt(-x + 1) + 11/48*arcsin(sqrt(x))","A",0
362,1,50,0,0.169128," ","integrate(x*arcsin(x^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x - 1\right)}^{2} \arcsin\left(\sqrt{x}\right) - \frac{1}{8} \, \sqrt{x} {\left(-x + 1\right)}^{\frac{3}{2}} + {\left(x - 1\right)} \arcsin\left(\sqrt{x}\right) + \frac{5}{16} \, \sqrt{x} \sqrt{-x + 1} + \frac{5}{16} \, \arcsin\left(\sqrt{x}\right)"," ",0,"1/2*(x - 1)^2*arcsin(sqrt(x)) - 1/8*sqrt(x)*(-x + 1)^(3/2) + (x - 1)*arcsin(sqrt(x)) + 5/16*sqrt(x)*sqrt(-x + 1) + 5/16*arcsin(sqrt(x))","A",0
363,1,27,0,0.168975," ","integrate(arcsin(x^(1/2)),x, algorithm=""giac"")","{\left(x - 1\right)} \arcsin\left(\sqrt{x}\right) + \frac{1}{2} \, \sqrt{x} \sqrt{-x + 1} + \frac{1}{2} \, \arcsin\left(\sqrt{x}\right)"," ",0,"(x - 1)*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=""giac"")","\int \frac{\arcsin\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arcsin(sqrt(x))/x, x)","F",0
365,1,40,0,0.419882," ","integrate(arcsin(x^(1/2))/x^2,x, algorithm=""giac"")","-\frac{\sqrt{-x + 1} - 1}{2 \, \sqrt{x}} - \frac{\arcsin\left(\sqrt{x}\right)}{x} + \frac{\sqrt{x}}{2 \, {\left(\sqrt{-x + 1} - 1\right)}}"," ",0,"-1/2*(sqrt(-x + 1) - 1)/sqrt(x) - arcsin(sqrt(x))/x + 1/2*sqrt(x)/(sqrt(-x + 1) - 1)","A",0
366,1,74,0,0.247077," ","integrate(arcsin(x^(1/2))/x^3,x, algorithm=""giac"")","-\frac{{\left(\sqrt{-x + 1} - 1\right)}^{3}}{48 \, x^{\frac{3}{2}}} - \frac{3 \, {\left(\sqrt{-x + 1} - 1\right)}}{16 \, \sqrt{x}} + \frac{x^{\frac{3}{2}} {\left(\frac{9 \, {\left(\sqrt{-x + 1} - 1\right)}^{2}}{x} + 1\right)}}{48 \, {\left(\sqrt{-x + 1} - 1\right)}^{3}} - \frac{\arcsin\left(\sqrt{x}\right)}{2 \, x^{2}}"," ",0,"-1/48*(sqrt(-x + 1) - 1)^3/x^(3/2) - 3/16*(sqrt(-x + 1) - 1)/sqrt(x) + 1/48*x^(3/2)*(9*(sqrt(-x + 1) - 1)^2/x + 1)/(sqrt(-x + 1) - 1)^3 - 1/2*arcsin(sqrt(x))/x^2","B",0
367,1,106,0,0.280484," ","integrate(arcsin(x^(1/2))/x^4,x, algorithm=""giac"")","-\frac{{\left(\sqrt{-x + 1} - 1\right)}^{5}}{480 \, x^{\frac{5}{2}}} - \frac{5 \, {\left(\sqrt{-x + 1} - 1\right)}^{3}}{288 \, x^{\frac{3}{2}}} - \frac{5 \, {\left(\sqrt{-x + 1} - 1\right)}}{48 \, \sqrt{x}} + \frac{{\left(\frac{150 \, {\left(\sqrt{-x + 1} - 1\right)}^{4}}{x^{2}} + \frac{25 \, {\left(\sqrt{-x + 1} - 1\right)}^{2}}{x} + 3\right)} x^{\frac{5}{2}}}{1440 \, {\left(\sqrt{-x + 1} - 1\right)}^{5}} - \frac{\arcsin\left(\sqrt{x}\right)}{3 \, x^{3}}"," ",0,"-1/480*(sqrt(-x + 1) - 1)^5/x^(5/2) - 5/288*(sqrt(-x + 1) - 1)^3/x^(3/2) - 5/48*(sqrt(-x + 1) - 1)/sqrt(x) + 1/1440*(150*(sqrt(-x + 1) - 1)^4/x^2 + 25*(sqrt(-x + 1) - 1)^2/x + 3)*x^(5/2)/(sqrt(-x + 1) - 1)^5 - 1/3*arcsin(sqrt(x))/x^3","B",0
368,1,138,0,0.234161," ","integrate(arcsin(x^(1/2))/x^5,x, algorithm=""giac"")","-\frac{{\left(\sqrt{-x + 1} - 1\right)}^{7}}{3584 \, x^{\frac{7}{2}}} - \frac{7 \, {\left(\sqrt{-x + 1} - 1\right)}^{5}}{2560 \, x^{\frac{5}{2}}} - \frac{7 \, {\left(\sqrt{-x + 1} - 1\right)}^{3}}{512 \, x^{\frac{3}{2}}} - \frac{35 \, {\left(\sqrt{-x + 1} - 1\right)}}{512 \, \sqrt{x}} + \frac{{\left(\frac{1225 \, {\left(\sqrt{-x + 1} - 1\right)}^{6}}{x^{3}} + \frac{245 \, {\left(\sqrt{-x + 1} - 1\right)}^{4}}{x^{2}} + \frac{49 \, {\left(\sqrt{-x + 1} - 1\right)}^{2}}{x} + 5\right)} x^{\frac{7}{2}}}{17920 \, {\left(\sqrt{-x + 1} - 1\right)}^{7}} - \frac{\arcsin\left(\sqrt{x}\right)}{4 \, x^{4}}"," ",0,"-1/3584*(sqrt(-x + 1) - 1)^7/x^(7/2) - 7/2560*(sqrt(-x + 1) - 1)^5/x^(5/2) - 7/512*(sqrt(-x + 1) - 1)^3/x^(3/2) - 35/512*(sqrt(-x + 1) - 1)/sqrt(x) + 1/17920*(1225*(sqrt(-x + 1) - 1)^6/x^3 + 245*(sqrt(-x + 1) - 1)^4/x^2 + 49*(sqrt(-x + 1) - 1)^2/x + 5)*x^(7/2)/(sqrt(-x + 1) - 1)^7 - 1/4*arcsin(sqrt(x))/x^4","B",0
369,1,464,0,2.309052," ","integrate(x^4*(a+b*arcsin(c/x)),x, algorithm=""giac"")","\frac{2 \, b c x^{5} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{c}{x}\right) + 2 \, a c x^{5} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{5} + b c^{2} x^{4} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{4} + 10 \, b c^{3} x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{c}{x}\right) + 10 \, a c^{3} x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3} + 8 \, b c^{4} x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2} + 20 \, b c^{5} x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)} \arcsin\left(\frac{c}{x}\right) + 20 \, a c^{5} x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)} + 24 \, b c^{6} \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right) - 24 \, b c^{6} \log\left(\frac{{\left| c \right|}}{{\left| x \right|}}\right) + \frac{20 \, b c^{7} \arcsin\left(\frac{c}{x}\right)}{x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}} + \frac{20 \, a c^{7}}{x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}} - \frac{8 \, b c^{8}}{x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2}} + \frac{10 \, b c^{9} \arcsin\left(\frac{c}{x}\right)}{x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3}} + \frac{10 \, a c^{9}}{x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3}} - \frac{b c^{10}}{x^{4} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{4}} + \frac{2 \, b c^{11} \arcsin\left(\frac{c}{x}\right)}{x^{5} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{5}} + \frac{2 \, a c^{11}}{x^{5} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{5}}}{320 \, c}"," ",0,"1/320*(2*b*c*x^5*(sqrt(-c^2/x^2 + 1) + 1)^5*arcsin(c/x) + 2*a*c*x^5*(sqrt(-c^2/x^2 + 1) + 1)^5 + b*c^2*x^4*(sqrt(-c^2/x^2 + 1) + 1)^4 + 10*b*c^3*x^3*(sqrt(-c^2/x^2 + 1) + 1)^3*arcsin(c/x) + 10*a*c^3*x^3*(sqrt(-c^2/x^2 + 1) + 1)^3 + 8*b*c^4*x^2*(sqrt(-c^2/x^2 + 1) + 1)^2 + 20*b*c^5*x*(sqrt(-c^2/x^2 + 1) + 1)*arcsin(c/x) + 20*a*c^5*x*(sqrt(-c^2/x^2 + 1) + 1) + 24*b*c^6*log(sqrt(-c^2/x^2 + 1) + 1) - 24*b*c^6*log(abs(c)/abs(x)) + 20*b*c^7*arcsin(c/x)/(x*(sqrt(-c^2/x^2 + 1) + 1)) + 20*a*c^7/(x*(sqrt(-c^2/x^2 + 1) + 1)) - 8*b*c^8/(x^2*(sqrt(-c^2/x^2 + 1) + 1)^2) + 10*b*c^9*arcsin(c/x)/(x^3*(sqrt(-c^2/x^2 + 1) + 1)^3) + 10*a*c^9/(x^3*(sqrt(-c^2/x^2 + 1) + 1)^3) - b*c^10/(x^4*(sqrt(-c^2/x^2 + 1) + 1)^4) + 2*b*c^11*arcsin(c/x)/(x^5*(sqrt(-c^2/x^2 + 1) + 1)^5) + 2*a*c^11/(x^5*(sqrt(-c^2/x^2 + 1) + 1)^5))/c","B",0
370,1,340,0,0.311359," ","integrate(x^3*(a+b*arcsin(c/x)),x, algorithm=""giac"")","\frac{3 \, b c x^{4} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{c}{x}\right) + 3 \, a c x^{4} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{4} + 2 \, b c^{2} x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3} + 12 \, b c^{3} x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{c}{x}\right) + 12 \, a c^{3} x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2} + 18 \, b c^{4} x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)} + 18 \, b c^{5} \arcsin\left(\frac{c}{x}\right) + 18 \, a c^{5} - \frac{18 \, b c^{6}}{x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}} + \frac{12 \, b c^{7} \arcsin\left(\frac{c}{x}\right)}{x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, a c^{7}}{x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2}} - \frac{2 \, b c^{8}}{x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3}} + \frac{3 \, b c^{9} \arcsin\left(\frac{c}{x}\right)}{x^{4} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{4}} + \frac{3 \, a c^{9}}{x^{4} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{4}}}{192 \, c}"," ",0,"1/192*(3*b*c*x^4*(sqrt(-c^2/x^2 + 1) + 1)^4*arcsin(c/x) + 3*a*c*x^4*(sqrt(-c^2/x^2 + 1) + 1)^4 + 2*b*c^2*x^3*(sqrt(-c^2/x^2 + 1) + 1)^3 + 12*b*c^3*x^2*(sqrt(-c^2/x^2 + 1) + 1)^2*arcsin(c/x) + 12*a*c^3*x^2*(sqrt(-c^2/x^2 + 1) + 1)^2 + 18*b*c^4*x*(sqrt(-c^2/x^2 + 1) + 1) + 18*b*c^5*arcsin(c/x) + 18*a*c^5 - 18*b*c^6/(x*(sqrt(-c^2/x^2 + 1) + 1)) + 12*b*c^7*arcsin(c/x)/(x^2*(sqrt(-c^2/x^2 + 1) + 1)^2) + 12*a*c^7/(x^2*(sqrt(-c^2/x^2 + 1) + 1)^2) - 2*b*c^8/(x^3*(sqrt(-c^2/x^2 + 1) + 1)^3) + 3*b*c^9*arcsin(c/x)/(x^4*(sqrt(-c^2/x^2 + 1) + 1)^4) + 3*a*c^9/(x^4*(sqrt(-c^2/x^2 + 1) + 1)^4))/c","B",0
371,1,298,0,0.688937," ","integrate(x^2*(a+b*arcsin(c/x)),x, algorithm=""giac"")","\frac{b c x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{c}{x}\right) + a c x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3} + b c^{2} x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2} + 3 \, b c^{3} x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)} \arcsin\left(\frac{c}{x}\right) + 3 \, a c^{3} x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)} + 4 \, b c^{4} \log\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right) - 4 \, b c^{4} \log\left(\frac{{\left| c \right|}}{{\left| x \right|}}\right) + \frac{3 \, b c^{5} \arcsin\left(\frac{c}{x}\right)}{x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}} + \frac{3 \, a c^{5}}{x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}} - \frac{b c^{6}}{x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2}} + \frac{b c^{7} \arcsin\left(\frac{c}{x}\right)}{x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3}} + \frac{a c^{7}}{x^{3} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{3}}}{24 \, c}"," ",0,"1/24*(b*c*x^3*(sqrt(-c^2/x^2 + 1) + 1)^3*arcsin(c/x) + a*c*x^3*(sqrt(-c^2/x^2 + 1) + 1)^3 + b*c^2*x^2*(sqrt(-c^2/x^2 + 1) + 1)^2 + 3*b*c^3*x*(sqrt(-c^2/x^2 + 1) + 1)*arcsin(c/x) + 3*a*c^3*x*(sqrt(-c^2/x^2 + 1) + 1) + 4*b*c^4*log(sqrt(-c^2/x^2 + 1) + 1) - 4*b*c^4*log(abs(c)/abs(x)) + 3*b*c^5*arcsin(c/x)/(x*(sqrt(-c^2/x^2 + 1) + 1)) + 3*a*c^5/(x*(sqrt(-c^2/x^2 + 1) + 1)) - b*c^6/(x^2*(sqrt(-c^2/x^2 + 1) + 1)^2) + b*c^7*arcsin(c/x)/(x^3*(sqrt(-c^2/x^2 + 1) + 1)^3) + a*c^7/(x^3*(sqrt(-c^2/x^2 + 1) + 1)^3))/c","B",0
372,1,174,0,0.213699," ","integrate(x*(a+b*arcsin(c/x)),x, algorithm=""giac"")","\frac{b c x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{c}{x}\right) + a c x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2} + 2 \, b c^{2} x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)} + 2 \, b c^{3} \arcsin\left(\frac{c}{x}\right) + 2 \, a c^{3} - \frac{2 \, b c^{4}}{x {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}} + \frac{b c^{5} \arcsin\left(\frac{c}{x}\right)}{x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2}} + \frac{a c^{5}}{x^{2} {\left(\sqrt{-\frac{c^{2}}{x^{2}} + 1} + 1\right)}^{2}}}{8 \, c}"," ",0,"1/8*(b*c*x^2*(sqrt(-c^2/x^2 + 1) + 1)^2*arcsin(c/x) + a*c*x^2*(sqrt(-c^2/x^2 + 1) + 1)^2 + 2*b*c^2*x*(sqrt(-c^2/x^2 + 1) + 1) + 2*b*c^3*arcsin(c/x) + 2*a*c^3 - 2*b*c^4/(x*(sqrt(-c^2/x^2 + 1) + 1)) + b*c^5*arcsin(c/x)/(x^2*(sqrt(-c^2/x^2 + 1) + 1)^2) + a*c^5/(x^2*(sqrt(-c^2/x^2 + 1) + 1)^2))/c","B",0
373,1,60,0,0.711692," ","integrate(a+b*arcsin(c/x),x, algorithm=""giac"")","a x + \frac{{\left(c^{2} {\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 \, c x \arcsin\left(\frac{c}{x}\right)\right)} b}{2 \, c}"," ",0,"a*x + 1/2*(c^2*(log(sqrt(-c^2/x^2 + 1) + 1) - log(-sqrt(-c^2/x^2 + 1) + 1)) + 2*c*x*arcsin(c/x))*b/c","B",0
374,-2,0,0,0.000000," ","integrate((a+b*arcsin(c/x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
375,1,38,0,0.257084," ","integrate((a+b*arcsin(c/x))/x^2,x, algorithm=""giac"")","-\frac{\frac{b c \arcsin\left(\frac{c}{x}\right)}{x} + b \sqrt{-\frac{c^{2}}{x^{2}} + 1} + \frac{a c}{x}}{c}"," ",0,"-(b*c*arcsin(c/x)/x + b*sqrt(-c^2/x^2 + 1) + a*c/x)/c","A",0
376,1,70,0,0.204719," ","integrate((a+b*arcsin(c/x))/x^3,x, algorithm=""giac"")","-\frac{\frac{2 \, b {\left(\frac{c^{2}}{x^{2}} - 1\right)} \arcsin\left(\frac{c}{x}\right)}{c} + \frac{2 \, a {\left(\frac{c^{2}}{x^{2}} - 1\right)}}{c} + \frac{b \arcsin\left(\frac{c}{x}\right)}{c} + \frac{b \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{x}}{4 \, c}"," ",0,"-1/4*(2*b*(c^2/x^2 - 1)*arcsin(c/x)/c + 2*a*(c^2/x^2 - 1)/c + b*arcsin(c/x)/c + b*sqrt(-c^2/x^2 + 1)/x)/c","A",0
377,1,88,0,0.262097," ","integrate((a+b*arcsin(c/x))/x^4,x, algorithm=""giac"")","-\frac{\frac{3 \, b {\left(\frac{c^{2}}{x^{2}} - 1\right)} \arcsin\left(\frac{c}{x}\right)}{c x} - \frac{b {\left(-\frac{c^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}}}{c^{2}} + \frac{3 \, b \arcsin\left(\frac{c}{x}\right)}{c x} + \frac{3 \, b \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c^{2}} + \frac{3 \, a c}{x^{3}}}{9 \, c}"," ",0,"-1/9*(3*b*(c^2/x^2 - 1)*arcsin(c/x)/(c*x) - b*(-c^2/x^2 + 1)^(3/2)/c^2 + 3*b*arcsin(c/x)/(c*x) + 3*b*sqrt(-c^2/x^2 + 1)/c^2 + 3*a*c/x^3)/c","A",0
378,1,111,0,0.243411," ","integrate((a+b*arcsin(c/x))/x^5,x, algorithm=""giac"")","-\frac{\frac{8 \, b {\left(\frac{c^{2}}{x^{2}} - 1\right)}^{2} \arcsin\left(\frac{c}{x}\right)}{c^{3}} + \frac{16 \, b {\left(\frac{c^{2}}{x^{2}} - 1\right)} \arcsin\left(\frac{c}{x}\right)}{c^{3}} - \frac{2 \, b {\left(-\frac{c^{2}}{x^{2}} + 1\right)}^{\frac{3}{2}}}{c^{2} x} + \frac{5 \, b \arcsin\left(\frac{c}{x}\right)}{c^{3}} + \frac{5 \, b \sqrt{-\frac{c^{2}}{x^{2}} + 1}}{c^{2} x} + \frac{8 \, a c}{x^{4}}}{32 \, c}"," ",0,"-1/32*(8*b*(c^2/x^2 - 1)^2*arcsin(c/x)/c^3 + 16*b*(c^2/x^2 - 1)*arcsin(c/x)/c^3 - 2*b*(-c^2/x^2 + 1)^(3/2)/(c^2*x) + 5*b*arcsin(c/x)/c^3 + 5*b*sqrt(-c^2/x^2 + 1)/(c^2*x) + 8*a*c/x^4)/c","A",0
379,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x^n)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x^{n}\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((b*arcsin(c*x^n) + a)*x^m, x)","F",0
380,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x^n)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x^{n}\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate((b*arcsin(c*x^n) + a)*x^2, x)","F",0
381,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x^n)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(c x^{n}\right) + a\right)} x\,{d x}"," ",0,"integrate((b*arcsin(c*x^n) + a)*x, x)","F",0
382,0,0,0,0.000000," ","integrate(a+b*arcsin(c*x^n),x, algorithm=""giac"")","\int b \arcsin\left(c x^{n}\right) + a\,{d x}"," ",0,"integrate(b*arcsin(c*x^n) + a, x)","F",0
383,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^n))/x,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{n}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arcsin(c*x^n) + a)/x, x)","F",0
384,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^n))/x^2,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{n}\right) + a}{x^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x^n) + a)/x^2, x)","F",0
385,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x^n))/x^3,x, algorithm=""giac"")","\int \frac{b \arcsin\left(c x^{n}\right) + a}{x^{3}}\,{d x}"," ",0,"integrate((b*arcsin(c*x^n) + a)/x^3, x)","F",0
386,1,220,0,0.699903," ","integrate(x^5*(a+b*arcsin(d*x^2+c)),x, algorithm=""giac"")","\frac{6 \, a d x^{6} + {\left(\frac{18 \, {\left(d x^{2} + c\right)} c^{2} \arcsin\left(d x^{2} + c\right)}{d^{2}} + \frac{6 \, {\left(d x^{2} + c\right)} {\left({\left(d x^{2} + c\right)}^{2} - 1\right)} \arcsin\left(d x^{2} + c\right)}{d^{2}} - \frac{18 \, {\left({\left(d x^{2} + c\right)}^{2} - 1\right)} c \arcsin\left(d x^{2} + c\right)}{d^{2}} - \frac{9 \, {\left(d x^{2} + c\right)} \sqrt{-{\left(d x^{2} + c\right)}^{2} + 1} c}{d^{2}} + \frac{18 \, \sqrt{-{\left(d x^{2} + c\right)}^{2} + 1} c^{2}}{d^{2}} + \frac{6 \, {\left(d x^{2} + c\right)} \arcsin\left(d x^{2} + c\right)}{d^{2}} - \frac{9 \, c \arcsin\left(d x^{2} + c\right)}{d^{2}} - \frac{2 \, {\left(-{\left(d x^{2} + c\right)}^{2} + 1\right)}^{\frac{3}{2}}}{d^{2}} + \frac{6 \, \sqrt{-{\left(d x^{2} + c\right)}^{2} + 1}}{d^{2}}\right)} b}{36 \, d}"," ",0,"1/36*(6*a*d*x^6 + (18*(d*x^2 + c)*c^2*arcsin(d*x^2 + c)/d^2 + 6*(d*x^2 + c)*((d*x^2 + c)^2 - 1)*arcsin(d*x^2 + c)/d^2 - 18*((d*x^2 + c)^2 - 1)*c*arcsin(d*x^2 + c)/d^2 - 9*(d*x^2 + c)*sqrt(-(d*x^2 + c)^2 + 1)*c/d^2 + 18*sqrt(-(d*x^2 + c)^2 + 1)*c^2/d^2 + 6*(d*x^2 + c)*arcsin(d*x^2 + c)/d^2 - 9*c*arcsin(d*x^2 + c)/d^2 - 2*(-(d*x^2 + c)^2 + 1)^(3/2)/d^2 + 6*sqrt(-(d*x^2 + c)^2 + 1)/d^2)*b)/d","A",0
387,1,130,0,0.927460," ","integrate(x^3*(a+b*arcsin(d*x^2+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left({\left(d x^{2} + c\right)}^{2} - 2 \, {\left(d x^{2} + c\right)} c\right)} a}{d} - \frac{{\left(4 \, {\left(d x^{2} + c\right)} c \arcsin\left(d x^{2} + c\right) - 2 \, {\left({\left(d x^{2} + c\right)}^{2} - 1\right)} \arcsin\left(d x^{2} + c\right) - {\left(d x^{2} + c\right)} \sqrt{-{\left(d x^{2} + c\right)}^{2} + 1} + 4 \, \sqrt{-{\left(d x^{2} + c\right)}^{2} + 1} c - \arcsin\left(d x^{2} + c\right)\right)} b}{d}}{8 \, d}"," ",0,"1/8*(2*((d*x^2 + c)^2 - 2*(d*x^2 + c)*c)*a/d - (4*(d*x^2 + c)*c*arcsin(d*x^2 + c) - 2*((d*x^2 + c)^2 - 1)*arcsin(d*x^2 + c) - (d*x^2 + c)*sqrt(-(d*x^2 + c)^2 + 1) + 4*sqrt(-(d*x^2 + c)^2 + 1)*c - arcsin(d*x^2 + c))*b/d)/d","A",0
388,1,49,0,2.458608," ","integrate(x*(a+b*arcsin(d*x^2+c)),x, algorithm=""giac"")","\frac{{\left(d x^{2} + c\right)} a + {\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*((d*x^2 + c)*a + ((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=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x, x)","F",0
390,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^3,x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x^{3}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x^3, x)","F",0
391,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^5,x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x^{5}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x^5, x)","F",0
392,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^7,x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x^{7}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x^7, x)","F",0
393,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(d*x^2+c)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} + c\right) + a\right)} x^{4}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)*x^4, x)","F",0
394,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(d*x^2+c)),x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} + c\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)*x^2, x)","F",0
395,0,0,0,0.000000," ","integrate(a+b*arcsin(d*x^2+c),x, algorithm=""giac"")","\int b \arcsin\left(d x^{2} + c\right) + a\,{d x}"," ",0,"integrate(b*arcsin(d*x^2 + c) + a, x)","F",0
396,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^2,x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x^{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x^2, x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^4,x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x^{4}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x^4, x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+c))/x^6,x, algorithm=""giac"")","\int \frac{b \arcsin\left(d x^{2} + c\right) + a}{x^{6}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + c) + a)/x^6, x)","F",0
399,1,37,0,3.460374," ","integrate(x^3*arcsin(b*x^4+a),x, algorithm=""giac"")","\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
400,1,39,0,0.239560," ","integrate(x^(-1+n)*arcsin(a+b*x^n),x, algorithm=""giac"")","\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
401,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^4,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} + 1\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + 1) + a)^4, x)","F",0
402,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^3,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} + 1\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + 1) + a)^3, x)","F",0
403,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^2,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} + 1\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + 1) + a)^2, x)","F",0
404,1,55,0,0.254042," ","integrate(a+b*arcsin(d*x^2+1),x, algorithm=""giac"")","{\left(x \arcsin\left(d x^{2} + 1\right) - \frac{2 \, \sqrt{2} \sqrt{-d} \mathrm{sgn}\left(x\right)}{d} + \frac{2 \, \sqrt{-d^{2} x^{2} - 2 \, d}}{d \mathrm{sgn}\left(x\right)}\right)} b + a x"," ",0,"(x*arcsin(d*x^2 + 1) - 2*sqrt(2)*sqrt(-d)*sgn(x)/d + 2*sqrt(-d^2*x^2 - 2*d)/(d*sgn(x)))*b + a*x","A",0
405,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1)),x, algorithm=""giac"")","\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
406,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} + 1\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + 1) + a)^(-2), x)","F",0
407,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} + 1\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 + 1) + a)^(-3), x)","F",0
408,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^4,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^4, x)","F",0
409,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^3,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^3, x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^2,x, algorithm=""giac"")","\int {\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^2, x)","F",0
411,1,50,0,0.273452," ","integrate(a+b*arcsin(d*x^2-1),x, algorithm=""giac"")","{\left(x \arcsin\left(d x^{2} - 1\right) - \frac{2 \, \sqrt{2} \mathrm{sgn}\left(x\right)}{\sqrt{d}} + \frac{2 \, \sqrt{-d^{2} x^{2} + 2 \, d}}{d \mathrm{sgn}\left(x\right)}\right)} b + a x"," ",0,"(x*arcsin(d*x^2 - 1) - 2*sqrt(2)*sgn(x)/sqrt(d) + 2*sqrt(-d^2*x^2 + 2*d)/(d*sgn(x)))*b + a*x","A",0
412,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1)),x, algorithm=""giac"")","\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=""giac"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(-2), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2-1))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \arcsin\left(d x^{2} - 1\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsin(d*x^2 - 1) + a)^(-3), x)","F",0
415,0,0,0,0.000000," ","integrate(arcsin(x^2+1)^2,x, algorithm=""giac"")","\int \arcsin\left(x^{2} + 1\right)^{2}\,{d x}"," ",0,"integrate(arcsin(x^2 + 1)^2, x)","F",0
416,1,58,0,1.758831," ","integrate(arcsin(x^2-1)^2,x, algorithm=""giac"")","x \arcsin\left(x^{2} - 1\right)^{2} + 2 \, {\left(\sqrt{2} \pi - 4 \, \sqrt{2}\right)} \mathrm{sgn}\left(x\right) + \frac{4 \, {\left(\sqrt{-x^{2} + 2} \arcsin\left(x^{2} - 1\right) + 2 \, \sqrt{2} - 2 \, {\left| x \right|}\right)}}{\mathrm{sgn}\left(x\right)}"," ",0,"x*arcsin(x^2 - 1)^2 + 2*(sqrt(2)*pi - 4*sqrt(2))*sgn(x) + 4*(sqrt(-x^2 + 2)*arcsin(x^2 - 1) + 2*sqrt(2) - 2*abs(x))/sgn(x)","A",0
417,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^(5/2),x, algorithm=""giac"")","\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
418,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^(3/2),x, algorithm=""giac"")","\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
419,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2+1))^(1/2),x, algorithm=""giac"")","\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
420,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(1/2),x, algorithm=""giac"")","\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
421,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(3/2),x, algorithm=""giac"")","\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
422,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(5/2),x, algorithm=""giac"")","\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
423,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(d*x^2+1))^(7/2),x, algorithm=""giac"")","\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
424,0,0,0,0.000000," ","integrate((a+b*arcsin(d*x^2-1))^(5/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int -\frac{{\left(b \arcsin\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{3}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*arcsin(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^3/(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=""giac"")","\int -\frac{{\left(b \arcsin\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{2}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*arcsin(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^2/(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=""giac"")","\int -\frac{b \arcsin\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*arcsin(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)/(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=""giac"")","\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=""giac"")","\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)}^{2}}\,{d x}"," ",0,"integrate(-1/((c^2*x^2 - 1)*(b*arcsin(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^2), x)","F",0
437,1,17,0,1.987861," ","integrate(exp(x)*arcsin(exp(x)),x, algorithm=""giac"")","\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=""giac"")","\int \arcsin\left(c e^{\left(b x + a\right)}\right)\,{d x}"," ",0,"integrate(arcsin(c*e^(b*x + a)), x)","F",0
439,1,97,0,0.174804," ","integrate(exp(arcsin(a*x))*x^3,x, algorithm=""giac"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x e^{\left(\arcsin\left(a x\right)\right)}}{17 \, a^{3}} + \frac{11 \, \sqrt{-a^{2} x^{2} + 1} x e^{\left(\arcsin\left(a x\right)\right)}}{85 \, a^{3}} + \frac{4 \, {\left(a^{2} x^{2} - 1\right)}^{2} e^{\left(\arcsin\left(a x\right)\right)}}{17 \, a^{4}} + \frac{37 \, {\left(a^{2} x^{2} - 1\right)} e^{\left(\arcsin\left(a x\right)\right)}}{85 \, a^{4}} + \frac{11 \, e^{\left(\arcsin\left(a x\right)\right)}}{85 \, a^{4}}"," ",0,"-1/17*(-a^2*x^2 + 1)^(3/2)*x*e^(arcsin(a*x))/a^3 + 11/85*sqrt(-a^2*x^2 + 1)*x*e^(arcsin(a*x))/a^3 + 4/17*(a^2*x^2 - 1)^2*e^(arcsin(a*x))/a^4 + 37/85*(a^2*x^2 - 1)*e^(arcsin(a*x))/a^4 + 11/85*e^(arcsin(a*x))/a^4","A",0
440,1,76,0,2.793931," ","integrate(exp(arcsin(a*x))*x^2,x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} x^{2} - 1\right)} x e^{\left(\arcsin\left(a x\right)\right)}}{10 \, a^{2}} + \frac{x e^{\left(\arcsin\left(a x\right)\right)}}{5 \, a^{2}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} e^{\left(\arcsin\left(a x\right)\right)}}{10 \, a^{3}} + \frac{\sqrt{-a^{2} x^{2} + 1} e^{\left(\arcsin\left(a x\right)\right)}}{5 \, a^{3}}"," ",0,"3/10*(a^2*x^2 - 1)*x*e^(arcsin(a*x))/a^2 + 1/5*x*e^(arcsin(a*x))/a^2 - 1/10*(-a^2*x^2 + 1)^(3/2)*e^(arcsin(a*x))/a^3 + 1/5*sqrt(-a^2*x^2 + 1)*e^(arcsin(a*x))/a^3","A",0
441,1,53,0,1.968958," ","integrate(exp(arcsin(a*x))*x,x, algorithm=""giac"")","\frac{\sqrt{-a^{2} x^{2} + 1} x e^{\left(\arcsin\left(a x\right)\right)}}{5 \, a} + \frac{2 \, {\left(a^{2} x^{2} - 1\right)} e^{\left(\arcsin\left(a x\right)\right)}}{5 \, a^{2}} + \frac{e^{\left(\arcsin\left(a x\right)\right)}}{5 \, a^{2}}"," ",0,"1/5*sqrt(-a^2*x^2 + 1)*x*e^(arcsin(a*x))/a + 2/5*(a^2*x^2 - 1)*e^(arcsin(a*x))/a^2 + 1/5*e^(arcsin(a*x))/a^2","A",0
442,1,31,0,0.179413," ","integrate(exp(arcsin(a*x)),x, algorithm=""giac"")","\frac{1}{2} \, x e^{\left(\arcsin\left(a x\right)\right)} + \frac{\sqrt{-a^{2} x^{2} + 1} e^{\left(\arcsin\left(a x\right)\right)}}{2 \, a}"," ",0,"1/2*x*e^(arcsin(a*x)) + 1/2*sqrt(-a^2*x^2 + 1)*e^(arcsin(a*x))/a","A",0
443,0,0,0,0.000000," ","integrate(exp(arcsin(a*x))/x,x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
451,1,334,0,3.852219," ","integrate(exp(arcsin(b*x+a))*x^3,x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a^{3} e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b^{4}} + \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a^{2} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{4}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a^{3} e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b^{4}} - \frac{9 \, {\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} a e^{\left(\arcsin\left(b x + a\right)\right)}}{10 \, b^{4}} + \frac{6 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a^{2} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{4}} - \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} {\left(b x + a\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{17 \, b^{4}} + \frac{3 \, {\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} a e^{\left(\arcsin\left(b x + a\right)\right)}}{10 \, b^{4}} + \frac{4 \, {\left({\left(b x + a\right)}^{2} - 1\right)}^{2} e^{\left(\arcsin\left(b x + a\right)\right)}}{17 \, b^{4}} - \frac{3 \, {\left(b x + a\right)} a e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{4}} + \frac{3 \, a^{2} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{4}} + \frac{11 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{85 \, b^{4}} - \frac{3 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} a e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{4}} + \frac{37 \, {\left({\left(b x + a\right)}^{2} - 1\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{85 \, b^{4}} + \frac{11 \, e^{\left(\arcsin\left(b x + a\right)\right)}}{85 \, b^{4}}"," ",0,"-1/2*(b*x + a)*a^3*e^(arcsin(b*x + a))/b^4 + 3/5*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a^2*e^(arcsin(b*x + a))/b^4 - 1/2*sqrt(-(b*x + a)^2 + 1)*a^3*e^(arcsin(b*x + a))/b^4 - 9/10*((b*x + a)^2 - 1)*(b*x + a)*a*e^(arcsin(b*x + a))/b^4 + 6/5*((b*x + a)^2 - 1)*a^2*e^(arcsin(b*x + a))/b^4 - 1/17*(-(b*x + a)^2 + 1)^(3/2)*(b*x + a)*e^(arcsin(b*x + a))/b^4 + 3/10*(-(b*x + a)^2 + 1)^(3/2)*a*e^(arcsin(b*x + a))/b^4 + 4/17*((b*x + a)^2 - 1)^2*e^(arcsin(b*x + a))/b^4 - 3/5*(b*x + a)*a*e^(arcsin(b*x + a))/b^4 + 3/5*a^2*e^(arcsin(b*x + a))/b^4 + 11/85*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*e^(arcsin(b*x + a))/b^4 - 3/5*sqrt(-(b*x + a)^2 + 1)*a*e^(arcsin(b*x + a))/b^4 + 37/85*((b*x + a)^2 - 1)*e^(arcsin(b*x + a))/b^4 + 11/85*e^(arcsin(b*x + a))/b^4","A",0
452,1,208,0,1.053791," ","integrate(exp(arcsin(b*x+a))*x^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)} a^{2} e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b^{3}} - \frac{2 \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} a e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{3}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a^{2} e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b^{3}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} - 1\right)} {\left(b x + a\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{10 \, b^{3}} - \frac{4 \, {\left({\left(b x + a\right)}^{2} - 1\right)} a e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{3}} - \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}} e^{\left(\arcsin\left(b x + a\right)\right)}}{10 \, b^{3}} + \frac{{\left(b x + a\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{3}} - \frac{2 \, a e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{3}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{3}}"," ",0,"1/2*(b*x + a)*a^2*e^(arcsin(b*x + a))/b^3 - 2/5*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*a*e^(arcsin(b*x + a))/b^3 + 1/2*sqrt(-(b*x + a)^2 + 1)*a^2*e^(arcsin(b*x + a))/b^3 + 3/10*((b*x + a)^2 - 1)*(b*x + a)*e^(arcsin(b*x + a))/b^3 - 4/5*((b*x + a)^2 - 1)*a*e^(arcsin(b*x + a))/b^3 - 1/10*(-(b*x + a)^2 + 1)^(3/2)*e^(arcsin(b*x + a))/b^3 + 1/5*(b*x + a)*e^(arcsin(b*x + a))/b^3 - 2/5*a*e^(arcsin(b*x + a))/b^3 + 1/5*sqrt(-(b*x + a)^2 + 1)*e^(arcsin(b*x + a))/b^3","A",0
453,1,108,0,3.860833," ","integrate(exp(arcsin(b*x+a))*x,x, algorithm=""giac"")","-\frac{{\left(b x + a\right)} a e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b^{2}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(b x + a\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{2}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} a e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b^{2}} + \frac{2 \, {\left({\left(b x + a\right)}^{2} - 1\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{2}} + \frac{e^{\left(\arcsin\left(b x + a\right)\right)}}{5 \, b^{2}}"," ",0,"-1/2*(b*x + a)*a*e^(arcsin(b*x + a))/b^2 + 1/5*sqrt(-(b*x + a)^2 + 1)*(b*x + a)*e^(arcsin(b*x + a))/b^2 - 1/2*sqrt(-(b*x + a)^2 + 1)*a*e^(arcsin(b*x + a))/b^2 + 2/5*((b*x + a)^2 - 1)*e^(arcsin(b*x + a))/b^2 + 1/5*e^(arcsin(b*x + a))/b^2","A",0
454,1,43,0,5.989163," ","integrate(exp(arcsin(b*x+a)),x, algorithm=""giac"")","\frac{{\left(b x + a\right)} e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} e^{\left(\arcsin\left(b x + a\right)\right)}}{2 \, b}"," ",0,"1/2*(b*x + a)*e^(arcsin(b*x + a))/b + 1/2*sqrt(-(b*x + a)^2 + 1)*e^(arcsin(b*x + a))/b","A",0
455,0,0,0,0.000000," ","integrate(exp(arcsin(b*x+a))/x,x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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,-2,0,0,0.000000," ","integrate(exp(arcsin(a*x))*(-a^2*x^2+1)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
464,-2,0,0,0.000000," ","integrate(exp(arcsin(a*x))*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
465,-2,0,0,0.000000," ","integrate(exp(arcsin(a*x))*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
466,1,9,0,0.182491," ","integrate(exp(arcsin(a*x))/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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
469,1,95,0,1.989920," ","integrate(arcsin(c/(b*x+a)),x, algorithm=""giac"")","\frac{b {\left(\frac{c^{2} {\left(\log\left(\sqrt{-\frac{c^{2}}{{\left(b x + a\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{c^{2}}{{\left(b x + a\right)}^{2}} + 1} + 1\right)\right)}}{b^{2}} + \frac{2 \, {\left(b x + a\right)} c \arcsin\left(-\frac{c}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{b^{2}}\right)}}{2 \, c}"," ",0,"1/2*b*(c^2*(log(sqrt(-c^2/(b*x + a)^2 + 1) + 1) - log(-sqrt(-c^2/(b*x + a)^2 + 1) + 1))/b^2 + 2*(b*x + a)*c*arcsin(-c/((b*x + a)*(a/(b*x + a) - 1) - a))/b^2)/c","B",0
470,0,0,0,0.000000," ","integrate(x/arcsin(sin(x)),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
471,-1,0,0,0.000000," ","integrate(arcsin((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,0,0,0,0.000000," ","integrate(1/arcsin((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + 1} \arcsin\left(\sqrt{b x^{2} + 1}\right)}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + 1)*arcsin(sqrt(b*x^2 + 1))), x)","F",0
473,1,14,0,1.875385," ","integrate(x/(-x^2+1)+1/arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| x^{2} - 1 \right|}\right) + \log\left({\left| \arcsin\left(x\right) \right|}\right)"," ",0,"-1/2*log(abs(x^2 - 1)) + log(abs(arcsin(x)))","A",0
474,1,20,0,1.327922," ","integrate((x*arcsin(x)+(-x^2+1)^(1/2))/(arcsin(x)-x^2*arcsin(x)),x, algorithm=""giac"")","-\log\left(2\right) - \frac{1}{2} \, \log\left({\left| -x^{2} + 1 \right|}\right) + \log\left({\left| \arcsin\left(x\right) \right|}\right)"," ",0,"-log(2) - 1/2*log(abs(-x^2 + 1)) + log(abs(arcsin(x)))","A",0
