Optimal. Leaf size=28 \[ \frac {e^{-x \left (-\frac {4}{e^2}+\log \left (x^2\right )\right )} \log \left (\frac {25}{2}\right )}{\log (5-x)} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(104\) vs. \(2(28)=56\).
time = 0.49, antiderivative size = 104, normalized size of antiderivative = 3.71, number of steps
used = 1, number of rules used = 1, integrand size = 94, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {2326}
\begin {gather*} \frac {e^{\frac {4 x}{e^2}} \left (x^2\right )^{-x} \left (2 \left (-e^2 (5-x)-2 x+10\right ) \log \left (\frac {25}{2}\right ) \log (5-x)-e^2 (5-x) \log \left (\frac {25}{2}\right ) \log (5-x) \log \left (x^2\right )\right )}{(5-x) \log ^2(5-x) \left (2 \left (2-e^2\right )-e^2 \log \left (x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{\frac {4 x}{e^2}} \left (x^2\right )^{-x} \left (2 \left (10-e^2 (5-x)-2 x\right ) \log \left (\frac {25}{2}\right ) \log (5-x)-e^2 (5-x) \log \left (\frac {25}{2}\right ) \log (5-x) \log \left (x^2\right )\right )}{(5-x) \log ^2(5-x) \left (2 \left (2-e^2\right )-e^2 \log \left (x^2\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.21, size = 28, normalized size = 1.00 \begin {gather*} \frac {e^{\frac {4 x}{e^2}} \left (x^2\right )^{-x} \log \left (\frac {25}{2}\right )}{\log (5-x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 3.89, size = 88, normalized size = 3.14
method | result | size |
risch | \(\frac {\left (2 \ln \left (5\right )-\ln \left (2\right )\right ) {\mathrm e}^{-\frac {x \left (-i {\mathrm e}^{2} \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i {\mathrm e}^{2} \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )-i {\mathrm e}^{2} \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+4 \,{\mathrm e}^{2} \ln \left (x \right )-8\right ) {\mathrm e}^{-2}}{2}}}{\ln \left (5-x \right )}\) | \(88\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.63, size = 30, normalized size = 1.07 \begin {gather*} \frac {{\left (2 \, \log \left (5\right ) - \log \left (2\right )\right )} e^{\left (4 \, x e^{\left (-2\right )} - 2 \, x \log \left (x\right )\right )}}{\log \left (-x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 34, normalized size = 1.21 \begin {gather*} \frac {e^{\left (-{\left (x e^{2} \log \left (x^{2}\right ) - 4 \, x + 2 \, e^{2}\right )} e^{\left (-2\right )} + 2\right )} \log \left (\frac {25}{2}\right )}{\log \left (-x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.24, size = 31, normalized size = 1.11 \begin {gather*} \frac {\left (- \log {\left (2 \right )} + 2 \log {\left (5 \right )}\right ) e^{- \frac {x e^{2} \log {\left (x^{2} \right )} - 4 x}{e^{2}}}}{\log {\left (5 - x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{-2}\,{\mathrm {e}}^{{\mathrm {e}}^{-2}\,\left (4\,x-x\,\ln \left (x^2\right )\,{\mathrm {e}}^2\right )}\,\left ({\mathrm {e}}^2\,\ln \left (\frac {25}{2}\right )+\ln \left (\frac {25}{2}\right )\,\ln \left (5-x\right )\,\left ({\mathrm {e}}^2\,\left (2\,x-10\right )-4\,x+20\right )+\ln \left (x^2\right )\,{\mathrm {e}}^2\,\ln \left (\frac {25}{2}\right )\,\ln \left (5-x\right )\,\left (x-5\right )\right )}{{\ln \left (5-x\right )}^2\,\left (x-5\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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