Optimal. Leaf size=17 \[ \log \left (-2+x+\frac {1}{2} \left (-2+\frac {x^3}{192}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.65, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {1587} \begin {gather*} \log \left (-x^3-384 x+1152\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (1152-384 x-x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 0.53 \begin {gather*} \log \left (-1152+384 x+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 9, normalized size = 0.53 \begin {gather*} \log \left (x^{3} + 384 \, x - 1152\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 10, normalized size = 0.59 \begin {gather*} \log \left ({\left | x^{3} + 384 \, x - 1152 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 0.59
method | result | size |
derivativedivides | \(\ln \left (x^{3}+384 x -1152\right )\) | \(10\) |
default | \(\ln \left (x^{3}+384 x -1152\right )\) | \(10\) |
norman | \(\ln \left (x^{3}+384 x -1152\right )\) | \(10\) |
risch | \(\ln \left (x^{3}+384 x -1152\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 9, normalized size = 0.53 \begin {gather*} \log \left (x^{3} + 384 \, x - 1152\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 9, normalized size = 0.53 \begin {gather*} \ln \left (x^3+384\,x-1152\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.47 \begin {gather*} \log {\left (x^{3} + 384 x - 1152 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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