Optimal. Leaf size=20 \[ e^{\frac {4 \log ^2(4)}{5}} x^2 \log \left (\frac {x}{e^4}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2341}
\begin {gather*} x^2 e^{\frac {4 \log ^2(4)}{5}} \log \left (\frac {x}{e^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} e^{\frac {4 \log ^2(4)}{5}} x^2+\left (2 e^{\frac {4 \log ^2(4)}{5}}\right ) \int x \log \left (\frac {x}{e^4}\right ) \, dx\\ &=e^{\frac {4 \log ^2(4)}{5}} x^2 \log \left (\frac {x}{e^4}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 1.15 \begin {gather*} e^{\frac {4 \log ^2(4)}{5}} \left (-4 x^2+x^2 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 19, normalized size = 0.95
method | result | size |
risch | \({\mathrm e}^{\frac {16 \ln \left (2\right )^{2}}{5}} x^{2} \ln \left (x \,{\mathrm e}^{-4}\right )\) | \(17\) |
derivativedivides | \({\mathrm e}^{\frac {16 \ln \left (2\right )^{2}}{5}} x^{2} \ln \left (x \,{\mathrm e}^{-4}\right )\) | \(19\) |
default | \({\mathrm e}^{\frac {16 \ln \left (2\right )^{2}}{5}} x^{2} \ln \left (x \,{\mathrm e}^{-4}\right )\) | \(19\) |
norman | \({\mathrm e}^{\frac {16 \ln \left (2\right )^{2}}{5}} x^{2} \ln \left (x \,{\mathrm e}^{-4}\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 38 vs.
\(2 (16) = 32\).
time = 0.26, size = 38, normalized size = 1.90 \begin {gather*} \frac {1}{2} \, x^{2} e^{\left (\frac {16}{5} \, \log \left (2\right )^{2}\right )} + \frac {1}{2} \, {\left (2 \, x^{2} \log \left (x e^{\left (-4\right )}\right ) - x^{2}\right )} e^{\left (\frac {16}{5} \, \log \left (2\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 16, normalized size = 0.80 \begin {gather*} x^{2} e^{\left (\frac {16}{5} \, \log \left (2\right )^{2}\right )} \log \left (x e^{\left (-4\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 19, normalized size = 0.95 \begin {gather*} x^{2} e^{\frac {16 \log {\left (2 \right )}^{2}}{5}} \log {\left (\frac {x}{e^{4}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 38 vs.
\(2 (16) = 32\).
time = 0.36, size = 38, normalized size = 1.90 \begin {gather*} \frac {1}{2} \, x^{2} e^{\left (\frac {16}{5} \, \log \left (2\right )^{2}\right )} + \frac {1}{2} \, {\left (2 \, x^{2} \log \left (x e^{\left (-4\right )}\right ) - x^{2}\right )} e^{\left (\frac {16}{5} \, \log \left (2\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.81, size = 15, normalized size = 0.75 \begin {gather*} x^2\,{\mathrm {e}}^{\frac {16\,{\ln \left (2\right )}^2}{5}}\,\left (\ln \left (x\right )-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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