Optimal. Leaf size=16 \[ 5+e-x \log (4) \log \left (e^x x^2\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(39\) vs. \(2(16)=32\).
time = 0.01, 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 = {2628}
\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 2628
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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Maple [A]
time = 0.12, size = 13, normalized size = 0.81
method | result | size |
default | \(-2 \ln \left ({\mathrm e}^{x} x^{2}\right ) \ln \left (2\right ) x\) | \(13\) |
norman | \(-2 \ln \left ({\mathrm e}^{x} x^{2}\right ) \ln \left (2\right ) x\) | \(13\) |
risch | \(-2 x \ln \left ({\mathrm e}^{x}\right ) \ln \left (2\right )-4 x \ln \left (2\right ) \ln \left (x \right )+i \ln \left (2\right ) \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 i \ln \left (2\right ) \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+i \ln \left (2\right ) \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}-i \ln \left (2\right ) \pi x \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )^{2}+i \ln \left (2\right ) \pi x \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x}\right )+i \ln \left (2\right ) \pi x \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )^{3}-i \ln \left (2\right ) \pi x \mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{x}\right )\) | \(171\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 12, normalized size = 0.75 \begin {gather*} -2 \, x \log \left (2\right ) \log \left (x^{2} e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 12, normalized size = 0.75 \begin {gather*} -2 \, x \log \left (2\right ) \log \left (x^{2} e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 15, normalized size = 0.94 \begin {gather*} - 2 x \log {\left (2 \right )} \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 = 0.38, size = 32, normalized size = 2.00 \begin {gather*} {\left (x^{2} - 2 \, x \log \left (x^{2} e^{x}\right ) + 4 \, x\right )} \log \left (2\right ) - {\left (x^{2} + 4 \, x\right )} \log \left (2\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 \left (2\right )\,\left (x+\ln \left (x^2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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