Optimal. Leaf size=15 \[ x \left (5-\frac {3}{8} x^2 \log \left (x^2\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2304} \begin {gather*} 5 x-\frac {3}{8} x^3 \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \left (40-6 x^2-9 x^2 \log \left (x^2\right )\right ) \, dx\\ &=5 x-\frac {x^3}{4}-\frac {9}{8} \int x^2 \log \left (x^2\right ) \, dx\\ &=5 x-\frac {3}{8} x^3 \log \left (x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} 5 x-\frac {3}{8} x^3 \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3}{8} \, x^{3} \log \left (x^{2}\right ) + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3}{8} \, x^{3} \log \left (x^{2}\right ) + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.93
method | result | size |
default | \(5 x -\frac {3 x^{3} \ln \left (x^{2}\right )}{8}\) | \(14\) |
norman | \(5 x -\frac {3 x^{3} \ln \left (x^{2}\right )}{8}\) | \(14\) |
risch | \(5 x -\frac {3 x^{3} \ln \left (x^{2}\right )}{8}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3}{8} \, x^{3} \log \left (x^{2}\right ) + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.39, size = 13, normalized size = 0.87 \begin {gather*} 5\,x-\frac {3\,x^3\,\ln \left (x^2\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.93 \begin {gather*} - \frac {3 x^{3} \log {\left (x^{2} \right )}}{8} + 5 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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