Optimal. Leaf size=16 \[ 9 \left (3+x+\frac {9}{25} x (-5+x \log (x))\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2304} \begin {gather*} \frac {81}{25} x^2 \log (x)-\frac {36 x}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int (-180+81 x+162 x \log (x)) \, dx\\ &=-\frac {36 x}{5}+\frac {81 x^2}{50}+\frac {162}{25} \int x \log (x) \, dx\\ &=-\frac {36 x}{5}+\frac {81}{25} x^2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} -\frac {36 x}{5}+\frac {81}{25} x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 11, normalized size = 0.69 \begin {gather*} \frac {81}{25} \, x^{2} \log \relax (x) - \frac {36}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 11, normalized size = 0.69 \begin {gather*} \frac {81}{25} \, x^{2} \log \relax (x) - \frac {36}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 0.75
method | result | size |
default | \(-\frac {36 x}{5}+\frac {81 x^{2} \ln \relax (x )}{25}\) | \(12\) |
norman | \(-\frac {36 x}{5}+\frac {81 x^{2} \ln \relax (x )}{25}\) | \(12\) |
risch | \(-\frac {36 x}{5}+\frac {81 x^{2} \ln \relax (x )}{25}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 11, normalized size = 0.69 \begin {gather*} \frac {81}{25} \, x^{2} \log \relax (x) - \frac {36}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.00, size = 10, normalized size = 0.62 \begin {gather*} \frac {9\,x\,\left (9\,x\,\ln \relax (x)-20\right )}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.88 \begin {gather*} \frac {81 x^{2} \log {\relax (x )}}{25} - \frac {36 x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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