Optimal. Leaf size=14 \[ \frac{1}{3} \sinh ^{-1}\left (\frac{x^3}{\sqrt{2}}\right ) \]
[Out]
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Rubi [A] time = 0.0188563, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{3} \sinh ^{-1}\left (\frac{x^3}{\sqrt{2}}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^2/Sqrt[2 + x^6],x]
[Out]
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Rubi in Sympy [A] time = 2.5975, size = 12, normalized size = 0.86 \[ \frac{\operatorname{asinh}{\left (\frac{\sqrt{2} x^{3}}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(x**6+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00754584, size = 14, normalized size = 1. \[ \frac{1}{3} \sinh ^{-1}\left (\frac{x^3}{\sqrt{2}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/Sqrt[2 + x^6],x]
[Out]
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Maple [A] time = 0.024, size = 12, normalized size = 0.9 \[{\frac{1}{3}{\it Arcsinh} \left ({\frac{{x}^{3}\sqrt{2}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(x^6+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.42528, size = 45, normalized size = 3.21 \[ \frac{1}{6} \, \log \left (\frac{\sqrt{x^{6} + 2}}{x^{3}} + 1\right ) - \frac{1}{6} \, \log \left (\frac{\sqrt{x^{6} + 2}}{x^{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(x^6 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215762, size = 22, normalized size = 1.57 \[ -\frac{1}{3} \, \log \left (-x^{3} + \sqrt{x^{6} + 2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(x^6 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.30877, size = 12, normalized size = 0.86 \[ \frac{\operatorname{asinh}{\left (\frac{\sqrt{2} x^{3}}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(x**6+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.224504, size = 22, normalized size = 1.57 \[ -\frac{1}{3} \,{\rm ln}\left (-x^{3} + \sqrt{x^{6} + 2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(x^6 + 2),x, algorithm="giac")
[Out]