Optimal. Leaf size=16 \[ x \left (-3-2 x+3 x^2+x \log (x)\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.25, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2341}
\begin {gather*} 3 x^3-2 x^2+x^2 \log (x)-3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x-\frac {3 x^2}{2}+3 x^3+2 \int x \log (x) \, dx\\ &=-3 x-2 x^2+3 x^3+x^2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.25 \begin {gather*} -3 x-2 x^2+3 x^3+x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 21, normalized size = 1.31
method | result | size |
default | \(-3 x -2 x^{2}+3 x^{3}+x^{2} \ln \left (x \right )\) | \(21\) |
norman | \(-3 x -2 x^{2}+3 x^{3}+x^{2} \ln \left (x \right )\) | \(21\) |
risch | \(-3 x -2 x^{2}+3 x^{3}+x^{2} \ln \left (x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 20, normalized size = 1.25 \begin {gather*} 3 \, x^{3} + x^{2} \log \left (x\right ) - 2 \, x^{2} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 20, normalized size = 1.25 \begin {gather*} 3 \, x^{3} + x^{2} \log \left (x\right ) - 2 \, x^{2} - 3 \, x \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 = 1.19 \begin {gather*} 3 x^{3} + x^{2} \log {\left (x \right )} - 2 x^{2} - 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 1.25 \begin {gather*} 3 \, x^{3} + x^{2} \log \left (x\right ) - 2 \, x^{2} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.16, size = 18, normalized size = 1.12 \begin {gather*} -x\,\left (2\,x-x\,\ln \left (x\right )-3\,x^2+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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