Optimal. Leaf size=15 \[ 8+x+\log ^2(15)+x \log \left (2 x^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps
used = 2, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2332}
\begin {gather*} x \log \left (2 x^2\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 x+\int \log \left (2 x^2\right ) \, dx\\ &=x+x \log \left (2 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.67 \begin {gather*} x+x \log \left (2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 13, normalized size = 0.87
method | result | size |
norman | \(x +x \ln \left (2 x^{2}\right )\) | \(11\) |
risch | \(x +x \ln \left (2 x^{2}\right )\) | \(11\) |
default | \(x +x \ln \left (2\right )+x \ln \left (x^{2}\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 10, normalized size = 0.67 \begin {gather*} x \log \left (2 \, x^{2}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 10, normalized size = 0.67 \begin {gather*} x \log \left (2 \, x^{2}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.53 \begin {gather*} x \log {\left (2 x^{2} \right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 10, normalized size = 0.67 \begin {gather*} x \log \left (2 \, x^{2}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.04, size = 10, normalized size = 0.67 \begin {gather*} x\,\left (\ln \left (2\,x^2\right )+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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