Optimal. Leaf size=16 \[ 5+e-x \log (4) \log \left (e^x x^2\right ) \]
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Rubi [B] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 2.44, number of steps used = 3, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2548} \begin {gather*} \frac {1}{2} x^2 \log (4)-x \log (4) \log \left (e^x x^2\right )+2 x \log (4)-\frac {1}{2} (x+2)^2 \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 2548
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{2} (2+x)^2 \log (4)-\log (4) \int \log \left (e^x x^2\right ) \, dx\\ &=-\frac {1}{2} (2+x)^2 \log (4)-x \log (4) \log \left (e^x x^2\right )+\log (4) \int (2+x) \, dx\\ &=2 x \log (4)+\frac {1}{2} x^2 \log (4)-\frac {1}{2} (2+x)^2 \log (4)-x \log (4) \log \left (e^x x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.81 \begin {gather*} -x \log (4) \log \left (e^x x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 12, normalized size = 0.75 \begin {gather*} -2 \, x \log \relax (2) \log \left (x^{2} e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 32, normalized size = 2.00 \begin {gather*} {\left (x^{2} - 2 \, x \log \left (x^{2} e^{x}\right ) + 4 \, x\right )} \log \relax (2) - {\left (x^{2} + 4 \, x\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 13, normalized size = 0.81
method | result | size |
default | \(-2 \ln \left ({\mathrm e}^{x} x^{2}\right ) \ln \relax (2) x\) | \(13\) |
norman | \(-2 \ln \left ({\mathrm e}^{x} x^{2}\right ) \ln \relax (2) x\) | \(13\) |
risch | \(-2 \ln \relax (2) x \ln \left ({\mathrm e}^{x}\right )-4 x \ln \relax (2) \ln \relax (x )+i \ln \relax (2) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) x -2 i \ln \relax (2) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} x +i \ln \relax (2) \pi \mathrm {csgn}\left (i x^{2}\right )^{3} x +i \ln \relax (2) \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right ) x -i \ln \relax (2) \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )^{2} x -i \ln \relax (2) \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )^{2} x +i \ln \relax (2) \pi \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )^{3} x\) | \(171\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 12, normalized size = 0.75 \begin {gather*} -2 \, x \log \relax (2) \log \left (x^{2} e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.95, size = 11, normalized size = 0.69 \begin {gather*} -2\,x\,\ln \relax (2)\,\left (x+\ln \left (x^2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 15, normalized size = 0.94 \begin {gather*} - 2 x \log {\relax (2 )} \log {\left (x^{2} e^{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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