Optimal. Leaf size=13 \[ x \left (2-\frac {4}{5} x^2 \log (5)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12}
\begin {gather*} 2 x-\frac {4}{5} x^3 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (10-12 x^2 \log (5)\right ) \, dx\\ &=2 x-\frac {4}{5} x^3 \log (5)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} 2 x-\frac {4}{5} x^3 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 12, normalized size = 0.92
method | result | size |
default | \(-\frac {4 x^{3} \ln \left (5\right )}{5}+2 x\) | \(12\) |
norman | \(-\frac {4 x^{3} \ln \left (5\right )}{5}+2 x\) | \(12\) |
risch | \(-\frac {4 x^{3} \ln \left (5\right )}{5}+2 x\) | \(12\) |
gosper | \(-\frac {2 x \left (2 x^{2} \ln \left (5\right )-5\right )}{5}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{5} \, x^{3} \log \left (5\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{5} \, x^{3} \log \left (5\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.92 \begin {gather*} - \frac {4 x^{3} \log {\left (5 \right )}}{5} + 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{5} \, x^{3} \log \left (5\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 11, normalized size = 0.85 \begin {gather*} 2\,x-\frac {4\,x^3\,\ln \left (5\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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