Optimal. Leaf size=18 \[ -\frac {3 \left (x^3+x^2\right )^{2/3}}{2 x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2014} \begin {gather*} -\frac {3 \left (x^3+x^2\right )^{2/3}}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt [3]{x^2+x^3}} \, dx &=-\frac {3 \left (x^2+x^3\right )^{2/3}}{2 x^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} -\frac {3 (x+1)}{2 \sqrt [3]{x^2 (x+1)}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.12, size = 18, normalized size = 1.00 \begin {gather*} -\frac {3 \left (x^2+x^3\right )^{2/3}}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 14, normalized size = 0.78 \begin {gather*} -\frac {3 \, {\left (x^{3} + x^{2}\right )}^{\frac {2}{3}}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 9, normalized size = 0.50 \begin {gather*} -\frac {3}{2} \, {\left (\frac {1}{x} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 11, normalized size = 0.61
method | result | size |
meijerg | \(-\frac {3 \left (1+x \right )^{\frac {2}{3}}}{2 x^{\frac {2}{3}}}\) | \(11\) |
gosper | \(-\frac {3 \left (1+x \right )}{2 \left (x^{3}+x^{2}\right )^{\frac {1}{3}}}\) | \(15\) |
trager | \(-\frac {3 \left (x^{3}+x^{2}\right )^{\frac {2}{3}}}{2 x^{2}}\) | \(15\) |
risch | \(-\frac {3 \left (1+x \right )}{2 \left (x^{2} \left (1+x \right )\right )^{\frac {1}{3}}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{{\left (x^{3} + x^{2}\right )}^{\frac {1}{3}} x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 14, normalized size = 0.78 \begin {gather*} -\frac {3\,{\left (x^3+x^2\right )}^{2/3}}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \sqrt [3]{x^{2} \left (x + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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