Optimal. Leaf size=16 \[ \frac {1}{9} (-1+4 x (-1+2 x)) \log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.44, number of steps
used = 7, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 14, 2350}
\begin {gather*} \frac {8}{9} x^2 \log (x)-\frac {4}{9} x \log (x)-\frac {\log (x)}{9} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2350
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {-1-4 x+8 x^2+\left (-4 x+16 x^2\right ) \log (x)}{x} \, dx\\ &=\frac {1}{9} \int \left (\frac {-1-4 x+8 x^2}{x}+4 (-1+4 x) \log (x)\right ) \, dx\\ &=\frac {1}{9} \int \frac {-1-4 x+8 x^2}{x} \, dx+\frac {4}{9} \int (-1+4 x) \log (x) \, dx\\ &=-\frac {4}{9} \left (x-2 x^2\right ) \log (x)+\frac {1}{9} \int \left (-4-\frac {1}{x}+8 x\right ) \, dx-\frac {4}{9} \int (-1+2 x) \, dx\\ &=-\frac {\log (x)}{9}-\frac {4}{9} \left (x-2 x^2\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 23, normalized size = 1.44 \begin {gather*} -\frac {\log (x)}{9}-\frac {4}{9} x \log (x)+\frac {8}{9} x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 18, normalized size = 1.12
method | result | size |
default | \(\frac {8 x^{2} \ln \left (x \right )}{9}-\frac {4 x \ln \left (x \right )}{9}-\frac {\ln \left (x \right )}{9}\) | \(18\) |
norman | \(\frac {8 x^{2} \ln \left (x \right )}{9}-\frac {4 x \ln \left (x \right )}{9}-\frac {\ln \left (x \right )}{9}\) | \(18\) |
risch | \(\frac {\left (8 x^{2}-4 x \right ) \ln \left (x \right )}{9}-\frac {\ln \left (x \right )}{9}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 1.06 \begin {gather*} \frac {8}{9} \, x^{2} \log \left (x\right ) - \frac {4}{9} \, x \log \left (x\right ) - \frac {1}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 14, normalized size = 0.88 \begin {gather*} \frac {1}{9} \, {\left (8 \, x^{2} - 4 \, x - 1\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 19, normalized size = 1.19 \begin {gather*} \left (\frac {8 x^{2}}{9} - \frac {4 x}{9}\right ) \log {\left (x \right )} - \frac {\log {\left (x \right )}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 18, normalized size = 1.12 \begin {gather*} \frac {4}{9} \, {\left (2 \, x^{2} - x\right )} \log \left (x\right ) - \frac {1}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.25, size = 14, normalized size = 0.88 \begin {gather*} -\frac {\ln \left (x\right )\,\left (-8\,x^2+4\,x+1\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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