Optimal. Leaf size=15 \[ \frac {1}{5} \left (3-3 x^2 \log (5)+\log (x)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.07, number of steps
used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14}
\begin {gather*} \frac {\log (x)}{5}-\frac {3}{5} x^2 \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {1-6 x^2 \log (5)}{x} \, dx\\ &=\frac {1}{5} \int \left (\frac {1}{x}-6 x \log (5)\right ) \, dx\\ &=-\frac {3}{5} x^2 \log (5)+\frac {\log (x)}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.07 \begin {gather*} -\frac {3}{5} x^2 \log (5)+\frac {\log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 13, normalized size = 0.87
method | result | size |
default | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
norman | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
risch | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.93 \begin {gather*} -\frac {3}{5} \, x^{2} \log \left (5\right ) + \frac {1}{10} \, \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 12, normalized size = 0.80 \begin {gather*} -\frac {3}{5} \, x^{2} \log \left (5\right ) + \frac {1}{5} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.93 \begin {gather*} - \frac {3 x^{2} \log {\left (5 \right )}}{5} + \frac {\log {\left (x \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 0.93 \begin {gather*} -\frac {3}{5} \, x^{2} \log \left (5\right ) + \frac {1}{10} \, \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.61, size = 12, normalized size = 0.80 \begin {gather*} \frac {\ln \left (x\right )}{5}-\frac {3\,x^2\,\ln \left (5\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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