Optimal. Leaf size=39 \[ \frac{3 x^{4/3}}{4}+\frac{3 x^{2/3}}{2}-x-3 \sqrt [3]{x}+3 \log \left (\sqrt [3]{x}+1\right ) \]
[Out]
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Rubi [A] time = 0.0427283, antiderivative size = 39, 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 \[ \frac{3 x^{4/3}}{4}+\frac{3 x^{2/3}}{2}-x-3 \sqrt [3]{x}+3 \log \left (\sqrt [3]{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^(2/3)/(1 + x^(1/3)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{3 x^{\frac{4}{3}}}{4} - 3 \sqrt [3]{x} - x + 3 \log{\left (\sqrt [3]{x} + 1 \right )} + 3 \int ^{\sqrt [3]{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(2/3)/(1+x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.0106657, size = 39, normalized size = 1. \[ \frac{3 x^{4/3}}{4}+\frac{3 x^{2/3}}{2}-x-3 \sqrt [3]{x}+3 \log \left (\sqrt [3]{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^(2/3)/(1 + x^(1/3)),x]
[Out]
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Maple [A] time = 0.003, size = 28, normalized size = 0.7 \[ -3\,\sqrt [3]{x}+{\frac{3}{2}{x}^{{\frac{2}{3}}}}-x+{\frac{3}{4}{x}^{{\frac{4}{3}}}}+3\,\ln \left ( 1+\sqrt [3]{x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(2/3)/(1+x^(1/3)),x)
[Out]
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Maxima [A] time = 1.43089, size = 57, normalized size = 1.46 \[ \frac{3}{4} \,{\left (x^{\frac{1}{3}} + 1\right )}^{4} - 4 \,{\left (x^{\frac{1}{3}} + 1\right )}^{3} + 9 \,{\left (x^{\frac{1}{3}} + 1\right )}^{2} - 12 \, x^{\frac{1}{3}} + 3 \, \log \left (x^{\frac{1}{3}} + 1\right ) - 12 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(2/3)/(x^(1/3) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221714, size = 34, normalized size = 0.87 \[ \frac{3}{4} \,{\left (x - 4\right )} x^{\frac{1}{3}} - x + \frac{3}{2} \, x^{\frac{2}{3}} + 3 \, \log \left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(2/3)/(x^(1/3) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.597698, size = 34, normalized size = 0.87 \[ \frac{3 x^{\frac{4}{3}}}{4} + \frac{3 x^{\frac{2}{3}}}{2} - 3 \sqrt [3]{x} - x + 3 \log{\left (\sqrt [3]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(2/3)/(1+x**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.223957, size = 36, normalized size = 0.92 \[ \frac{3}{4} \, x^{\frac{4}{3}} - x + \frac{3}{2} \, x^{\frac{2}{3}} - 3 \, x^{\frac{1}{3}} + 3 \,{\rm ln}\left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(2/3)/(x^(1/3) + 1),x, algorithm="giac")
[Out]