Optimal. Leaf size=38 \[ -\frac{1}{8} \sin ^{-1}\left (x^2\right )+\frac{1}{8} \sqrt{1-x^4} x^2+\frac{1}{4} x^4 \sin ^{-1}\left (x^2\right ) \]
[Out]
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Rubi [A] time = 0.0545805, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.625 \[ -\frac{1}{8} \sin ^{-1}\left (x^2\right )+\frac{1}{8} \sqrt{1-x^4} x^2+\frac{1}{4} x^4 \sin ^{-1}\left (x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[x^3*ArcSin[x^2],x]
[Out]
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Rubi in Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*asin(x**2),x)
[Out]
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Mathematica [A] time = 0.0167284, size = 32, normalized size = 0.84 \[ \frac{1}{8} \left (\sqrt{1-x^4} x^2+\left (2 x^4-1\right ) \sin ^{-1}\left (x^2\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3*ArcSin[x^2],x]
[Out]
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Maple [A] time = 0.004, size = 31, normalized size = 0.8 \[ -{\frac{\arcsin \left ({x}^{2} \right ) }{8}}+{\frac{{x}^{4}\arcsin \left ({x}^{2} \right ) }{4}}+{\frac{{x}^{2}}{8}\sqrt{-{x}^{4}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*arcsin(x^2),x)
[Out]
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Maxima [A] time = 1.60733, size = 72, normalized size = 1.89 \[ \frac{1}{4} \, x^{4} \arcsin \left (x^{2}\right ) - \frac{\sqrt{-x^{4} + 1}}{8 \, x^{2}{\left (\frac{x^{4} - 1}{x^{4}} - 1\right )}} + \frac{1}{8} \, \arctan \left (\frac{\sqrt{-x^{4} + 1}}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*arcsin(x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226749, size = 38, normalized size = 1. \[ \frac{1}{8} \, \sqrt{-x^{4} + 1} x^{2} + \frac{1}{8} \,{\left (2 \, x^{4} - 1\right )} \arcsin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*arcsin(x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.896623, size = 29, normalized size = 0.76 \[ \frac{x^{4} \operatorname{asin}{\left (x^{2} \right )}}{4} + \frac{x^{2} \sqrt{- x^{4} + 1}}{8} - \frac{\operatorname{asin}{\left (x^{2} \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*asin(x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.204829, size = 43, normalized size = 1.13 \[ \frac{1}{8} \, \sqrt{-x^{4} + 1} x^{2} + \frac{1}{4} \,{\left (x^{4} - 1\right )} \arcsin \left (x^{2}\right ) + \frac{1}{8} \, \arcsin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3*arcsin(x^2),x, algorithm="giac")
[Out]