Optimal. Leaf size=24 \[ \log \left (\frac {1}{\left (-1-x+2 \left (4+\frac {1}{3} (2-x) x^2\right )\right )^2}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps
used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {1601}
\begin {gather*} -2 \log \left (-2 x^3+4 x^2-3 x+21\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-2 \log \left (21-3 x+4 x^2-2 x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 0.75 \begin {gather*} -2 \log \left (21-3 x+4 x^2-2 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 19, normalized size = 0.79
method | result | size |
default | \(-2 \ln \left (2 x^{3}-4 x^{2}+3 x -21\right )\) | \(19\) |
norman | \(-2 \ln \left (2 x^{3}-4 x^{2}+3 x -21\right )\) | \(19\) |
risch | \(-2 \ln \left (2 x^{3}-4 x^{2}+3 x -21\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 18, normalized size = 0.75 \begin {gather*} -2 \, \log \left (2 \, x^{3} - 4 \, x^{2} + 3 \, x - 21\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 18, normalized size = 0.75 \begin {gather*} -2 \, \log \left (2 \, x^{3} - 4 \, x^{2} + 3 \, x - 21\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 0.79 \begin {gather*} - 2 \log {\left (2 x^{3} - 4 x^{2} + 3 x - 21 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.37, size = 19, normalized size = 0.79 \begin {gather*} -2 \, \log \left ({\left | 2 \, x^{3} - 4 \, x^{2} + 3 \, x - 21 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 16, normalized size = 0.67 \begin {gather*} -2\,\ln \left (x^3-2\,x^2+\frac {3\,x}{2}-\frac {21}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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