Optimal. Leaf size=18 \[ \frac {1}{36} e^4 x^2 \log \left (\frac {x^2}{5}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 2304} \begin {gather*} \frac {1}{36} e^4 x^2 \log \left (\frac {x^2}{5}\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}{18} \int \left (e^4 x+e^4 x \log \left (\frac {x^2}{5}\right )\right ) \, dx\\ &=\frac {e^4 x^2}{36}+\frac {1}{18} e^4 \int x \log \left (\frac {x^2}{5}\right ) \, dx\\ &=\frac {1}{36} e^4 x^2 \log \left (\frac {x^2}{5}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} \frac {1}{36} e^4 x^2 \log \left (\frac {x^2}{5}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 13, normalized size = 0.72 \begin {gather*} \frac {1}{36} \, x^{2} e^{4} \log \left (\frac {1}{5} \, x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 28, normalized size = 1.56 \begin {gather*} \frac {1}{36} \, x^{2} e^{4} + \frac {1}{36} \, {\left (x^{2} \log \left (\frac {1}{5} \, x^{2}\right ) - x^{2}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.78
method | result | size |
default | \(\frac {x^{2} \ln \left (\frac {x^{2}}{5}\right ) {\mathrm e}^{4}}{36}\) | \(14\) |
norman | \(\frac {x^{2} \ln \left (\frac {x^{2}}{5}\right ) {\mathrm e}^{4}}{36}\) | \(14\) |
risch | \(\frac {x^{2} \ln \left (\frac {x^{2}}{5}\right ) {\mathrm e}^{4}}{36}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.34, size = 28, normalized size = 1.56 \begin {gather*} \frac {1}{36} \, x^{2} e^{4} + \frac {1}{36} \, {\left (x^{2} \log \left (\frac {1}{5} \, x^{2}\right ) - x^{2}\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.67, size = 16, normalized size = 0.89 \begin {gather*} \frac {x^2\,{\mathrm {e}}^4\,\left (\ln \left (x^2\right )-\ln \relax (5)\right )}{36} \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 = 0.78 \begin {gather*} \frac {x^{2} e^{4} \log {\left (\frac {x^{2}}{5} \right )}}{36} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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