Optimal. Leaf size=32 \[ -\frac{3 x^{2/3}}{2}+x+3 \sqrt [3]{x}-3 \log \left (\frac{1}{\sqrt [3]{x}}+1\right )-\log (x) \]
[Out]
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Rubi [A] time = 0.0275681, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ -\frac{3 x^{2/3}}{2}+x+3 \sqrt [3]{x}-3 \log \left (\frac{1}{\sqrt [3]{x}}+1\right )-\log (x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^(-1/3))^(-1),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 3 \sqrt [3]{x} + x - 3 \log{\left (\sqrt [3]{x} + 1 \right )} - 3 \int ^{\sqrt [3]{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+1/x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.00853203, size = 28, normalized size = 0.88 \[ -\frac{3 x^{2/3}}{2}+x+3 \sqrt [3]{x}-3 \log \left (\sqrt [3]{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^(-1/3))^(-1),x]
[Out]
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Maple [A] time = 0.004, size = 21, normalized size = 0.7 \[ x-{\frac{3}{2}{x}^{{\frac{2}{3}}}}+3\,\sqrt [3]{x}-3\,\ln \left ( \sqrt [3]{x}+1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+1/x^(1/3)),x)
[Out]
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Maxima [A] time = 1.34434, size = 38, normalized size = 1.19 \[ -\frac{1}{2} \, x{\left (\frac{3}{x^{\frac{1}{3}}} - \frac{6}{x^{\frac{2}{3}}} - 2\right )} - \log \left (x\right ) - 3 \, \log \left (\frac{1}{x^{\frac{1}{3}}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1/x^(1/3) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20167, size = 27, normalized size = 0.84 \[ x - \frac{3}{2} \, x^{\frac{2}{3}} + 3 \, x^{\frac{1}{3}} - 3 \, \log \left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1/x^(1/3) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.145261, size = 26, normalized size = 0.81 \[ - \frac{3 x^{\frac{2}{3}}}{2} + 3 \sqrt [3]{x} + x - 3 \log{\left (\sqrt [3]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+1/x**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.208532, size = 27, normalized size = 0.84 \[ x - \frac{3}{2} \, x^{\frac{2}{3}} + 3 \, x^{\frac{1}{3}} - 3 \,{\rm ln}\left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1/x^(1/3) + 1),x, algorithm="giac")
[Out]