Optimal. Leaf size=44 \[ \frac{1}{10} \left (x^3-3 \sqrt{1-x^2} x^2-3 \sqrt{1-x^2}+3 x\right ) e^{\sin ^{-1}(x)} \]
[Out]
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Rubi [A] time = 1.13222, antiderivative size = 62, normalized size of antiderivative = 1.41, number of steps used = 5, number of rules used = 5, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.263 \[ \frac{1}{10} x^3 e^{\sin ^{-1}(x)}-\frac{3}{10} \sqrt{1-x^2} x^2 e^{\sin ^{-1}(x)}-\frac{3}{10} \sqrt{1-x^2} e^{\sin ^{-1}(x)}+\frac{3}{10} x e^{\sin ^{-1}(x)} \]
Antiderivative was successfully verified.
[In] Int[(E^ArcSin[x]*x^3)/Sqrt[1 - x^2],x]
[Out]
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Rubi in Sympy [A] time = 14.9857, size = 56, normalized size = 1.27 \[ \frac{x^{3} e^{\operatorname{asin}{\left (x \right )}}}{10} - \frac{3 x^{2} \sqrt{- x^{2} + 1} e^{\operatorname{asin}{\left (x \right )}}}{10} + \frac{3 x e^{\operatorname{asin}{\left (x \right )}}}{10} - \frac{3 \sqrt{- x^{2} + 1} e^{\operatorname{asin}{\left (x \right )}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(asin(x))*x**3/(-x**2+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.194815, size = 38, normalized size = 0.86 \[ -\frac{1}{40} e^{\sin ^{-1}(x)} \left (15 \left (\sqrt{1-x^2}-x\right )+\sin \left (3 \sin ^{-1}(x)\right )-3 \cos \left (3 \sin ^{-1}(x)\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(E^ArcSin[x]*x^3)/Sqrt[1 - x^2],x]
[Out]
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Maple [F] time = 0.055, size = 0, normalized size = 0. \[ \int{{{\rm e}^{\arcsin \left ( x \right ) }}{x}^{3}{\frac{1}{\sqrt{-{x}^{2}+1}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(arcsin(x))*x^3/(-x^2+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3} e^{\arcsin \left (x\right )}}{\sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^arcsin(x)/sqrt(-x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248903, size = 38, normalized size = 0.86 \[ \frac{1}{10} \,{\left (x^{3} - 3 \,{\left (x^{2} + 1\right )} \sqrt{-x^{2} + 1} + 3 \, x\right )} e^{\arcsin \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^arcsin(x)/sqrt(-x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.26085, size = 56, normalized size = 1.27 \[ \frac{x^{3} e^{\operatorname{asin}{\left (x \right )}}}{10} - \frac{3 x^{2} \sqrt{- x^{2} + 1} e^{\operatorname{asin}{\left (x \right )}}}{10} + \frac{3 x e^{\operatorname{asin}{\left (x \right )}}}{10} - \frac{3 \sqrt{- x^{2} + 1} e^{\operatorname{asin}{\left (x \right )}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(asin(x))*x**3/(-x**2+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215279, size = 62, normalized size = 1.41 \[ \frac{1}{10} \,{\left (x^{2} - 1\right )} x e^{\arcsin \left (x\right )} + \frac{3}{10} \,{\left (-x^{2} + 1\right )}^{\frac{3}{2}} e^{\arcsin \left (x\right )} + \frac{2}{5} \, x e^{\arcsin \left (x\right )} - \frac{3}{5} \, \sqrt{-x^{2} + 1} e^{\arcsin \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*e^arcsin(x)/sqrt(-x^2 + 1),x, algorithm="giac")
[Out]