Optimal. Leaf size=26 \[ -3 x^{2/3}+x+6 \sqrt [3]{x}-6 \log \left (\sqrt [3]{x}+1\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {376, 77} \[ -3 x^{2/3}+x+6 \sqrt [3]{x}-6 \log \left (\sqrt [3]{x}+1\right ) \]
Antiderivative was successfully verified.
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Rule 77
Rule 376
Rubi steps
\begin {align*} \int \frac {-1+\sqrt [3]{x}}{1+\sqrt [3]{x}} \, dx &=3 \operatorname {Subst}\left (\int \frac {(-1+x) x^2}{1+x} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (2-2 x+x^2-\frac {2}{1+x}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=6 \sqrt [3]{x}-3 x^{2/3}+x-6 \log \left (1+\sqrt [3]{x}\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.00 \[ -3 x^{2/3}+x+6 \sqrt [3]{x}-6 \log \left (\sqrt [3]{x}+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 20, normalized size = 0.77 \[ x - 3 \, x^{\frac {2}{3}} + 6 \, x^{\frac {1}{3}} - 6 \, \log \left (x^{\frac {1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 20, normalized size = 0.77 \[ x - 3 \, x^{\frac {2}{3}} + 6 \, x^{\frac {1}{3}} - 6 \, \log \left (x^{\frac {1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.81 \[ x -6 \ln \left (x^{\frac {1}{3}}+1\right )-3 x^{\frac {2}{3}}+6 x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 20, normalized size = 0.77 \[ x - 3 \, x^{\frac {2}{3}} + 6 \, x^{\frac {1}{3}} - 6 \, \log \left (x^{\frac {1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.77 \[ x-6\,\ln \left (x^{1/3}+1\right )+6\,x^{1/3}-3\,x^{2/3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 24, normalized size = 0.92 \[ - 3 x^{\frac {2}{3}} + 6 \sqrt [3]{x} + x - 6 \log {\left (\sqrt [3]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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