Optimal. Leaf size=20 \[ \frac {1}{128} e^{2 e^2-x} x^2 \log (x) \]
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Rubi [A]
time = 0.20, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 9, number of rules used = 7, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.184, Rules used = {12, 6820, 6874,
2207, 2225, 2227, 2634} \begin {gather*} \frac {1}{128} e^{2 e^2-x} x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rule 2227
Rule 2634
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{128} \int e^{-x} \left (e^{2 e^2} x+e^{2 e^2} \left (2 x-x^2\right ) \log (x)\right ) \, dx\\ &=\frac {1}{128} \int e^{2 e^2-x} x (1-(-2+x) \log (x)) \, dx\\ &=\frac {1}{128} \int \left (e^{2 e^2-x} x-e^{2 e^2-x} (-2+x) x \log (x)\right ) \, dx\\ &=\frac {1}{128} \int e^{2 e^2-x} x \, dx-\frac {1}{128} \int e^{2 e^2-x} (-2+x) x \log (x) \, dx\\ &=-\frac {1}{128} e^{2 e^2-x} x+\frac {1}{128} e^{2 e^2-x} x^2 \log (x)+\frac {1}{128} \int e^{2 e^2-x} \, dx-\frac {1}{128} \int e^{2 e^2-x} x \, dx\\ &=-\frac {1}{128} e^{2 e^2-x}+\frac {1}{128} e^{2 e^2-x} x^2 \log (x)-\frac {1}{128} \int e^{2 e^2-x} \, dx\\ &=\frac {1}{128} e^{2 e^2-x} x^2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 20, normalized size = 1.00 \begin {gather*} \frac {1}{128} e^{2 e^2-x} x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 17, normalized size = 0.85
method | result | size |
norman | \(\frac {{\mathrm e}^{2 \,{\mathrm e}^{2}} {\mathrm e}^{-x} x^{2} \ln \left (x \right )}{128}\) | \(17\) |
risch | \(\frac {x^{2} \ln \left (x \right ) {\mathrm e}^{2 \,{\mathrm e}^{2}-x}}{128}\) | \(17\) |
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. 50 vs.
\(2 (16) = 32\).
time = 0.35, size = 50, normalized size = 2.50 \begin {gather*} \frac {1}{128} \, {\left (x^{2} e^{\left (2 \, e^{2}\right )} \log \left (x\right ) + x e^{\left (2 \, e^{2}\right )} + e^{\left (2 \, e^{2}\right )}\right )} e^{\left (-x\right )} - \frac {1}{128} \, {\left (x e^{\left (2 \, e^{2}\right )} + e^{\left (2 \, e^{2}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{128} \, x^{2} e^{\left (-x + 2 \, e^{2}\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 17, normalized size = 0.85 \begin {gather*} \frac {x^{2} e^{- x} e^{2 e^{2}} \log {\left (x \right )}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{128} \, x^{2} e^{\left (-x + 2 \, e^{2}\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.14, size = 16, normalized size = 0.80 \begin {gather*} \frac {x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-x}\,\ln \left (x\right )}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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