Optimal. Leaf size=19 \[ e^{2+5 (5-x) \log ^2(2 x)} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(19)=38\).
time = 0.11, antiderivative size = 64, normalized size of antiderivative = 3.37, number of steps
used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {2326}
\begin {gather*} \frac {e^{5 (5-x) \log ^2(2 x)+2} \left (2 (5-x) \log (2 x)-x \log ^2(2 x)\right )}{\frac {2 (5-x) \log (2 x)}{x}-\log ^2(2 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{2+5 (5-x) \log ^2(2 x)} \left (2 (5-x) \log (2 x)-x \log ^2(2 x)\right )}{\frac {2 (5-x) \log (2 x)}{x}-\log ^2(2 x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 17, normalized size = 0.89 \begin {gather*} e^{2-5 (-5+x) \log ^2(2 x)} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 18, normalized size = 0.95
method | result | size |
norman | \({\mathrm e}^{\left (-5 x +25\right ) \ln \left (2 x \right )^{2}+2} x\) | \(18\) |
risch | \({\mathrm e}^{-5 x \ln \left (2 x \right )^{2}+25 \ln \left (2 x \right )^{2}+2} x\) | \(23\) |
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. 44 vs.
\(2 (16) = 32\).
time = 0.71, size = 44, normalized size = 2.32 \begin {gather*} x e^{\left (-5 \, x \log \left (2\right )^{2} - 10 \, x \log \left (2\right ) \log \left (x\right ) - 5 \, x \log \left (x\right )^{2} + 25 \, \log \left (2\right )^{2} + 50 \, \log \left (2\right ) \log \left (x\right ) + 25 \, \log \left (x\right )^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 0.84 \begin {gather*} x e^{\left (-5 \, {\left (x - 5\right )} \log \left (2 \, x\right )^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 15, normalized size = 0.79 \begin {gather*} x e^{\left (25 - 5 x\right ) \log {\left (2 x \right )}^{2} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 22, normalized size = 1.16 \begin {gather*} x e^{\left (-5 \, x \log \left (2 \, x\right )^{2} + 25 \, \log \left (2 \, x\right )^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.37, size = 46, normalized size = 2.42 \begin {gather*} x^{50\,\ln \left (2\right )-10\,x\,\ln \left (2\right )+1}\,{\mathrm {e}}^{-5\,x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{25\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^2\,{\mathrm {e}}^{-5\,x\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{25\,{\ln \left (2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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