Optimal. Leaf size=28 \[ \frac{x^4}{4}-\frac{x^2}{\sqrt{2}}+\log \left (x^2+\sqrt{2}\right ) \]
[Out]
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Rubi [A] time = 0.0455685, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{x^4}{4}-\frac{x^2}{\sqrt{2}}+\log \left (x^2+\sqrt{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^5/(Sqrt[2] + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\log{\left (x^{2} + \sqrt{2} \right )}}{4} - \frac{\int ^{x^{2}} \sqrt{2}\, dx}{2} + \frac{\int ^{x^{2}} x\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(x**2+2**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0143151, size = 31, normalized size = 1.11 \[ \frac{1}{4} \left (x^4-2 \sqrt{2} x^2+4 \log \left (x^2+\sqrt{2}\right )-6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(Sqrt[2] + x^2),x]
[Out]
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Maple [A] time = 0.01, size = 23, normalized size = 0.8 \[{\frac{{x}^{4}}{4}}+\ln \left ({x}^{2}+\sqrt{2} \right ) -{\frac{{x}^{2}\sqrt{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(x^2+2^(1/2)),x)
[Out]
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Maxima [A] time = 1.48534, size = 30, normalized size = 1.07 \[ \frac{1}{4} \, x^{4} - \frac{1}{2} \, \sqrt{2} x^{2} + \log \left (x^{2} + \sqrt{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^2 + sqrt(2)),x, algorithm="maxima")
[Out]
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^2 + sqrt(2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.143149, size = 24, normalized size = 0.86 \[ \frac{x^{4}}{4} - \frac{\sqrt{2} x^{2}}{2} + \log{\left (x^{2} + \sqrt{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(x**2+2**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.205903, size = 30, normalized size = 1.07 \[ \frac{1}{4} \, x^{4} - \frac{1}{2} \, \sqrt{2} x^{2} +{\rm ln}\left (x^{2} + \sqrt{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^2 + sqrt(2)),x, algorithm="giac")
[Out]