Optimal. Leaf size=26 \[ \log \left (e^{-\frac {x^2}{-e^5+\log \left (20 x^2\right )}}-x\right ) \]
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Rubi [A]
time = 0.56, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps
used = 2, number of rules used = 2, integrand size = 146, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6873, 6816}
\begin {gather*} \log \left (e^{\frac {x^2}{e^5-\log \left (20 x^2\right )}}-x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{10}+2 e^5 \log \left (20 x^2\right )-\log ^2\left (20 x^2\right )+e^{-\frac {x^2}{-e^5+\log \left (20 x^2\right )}} \left (2 x+2 e^5 x-2 x \log \left (20 x^2\right )\right )}{\left (e^{\frac {x^2}{e^5-\log \left (20 x^2\right )}}-x\right ) \left (e^5-\log \left (20 x^2\right )\right )^2} \, dx\\ &=\log \left (e^{\frac {x^2}{e^5-\log \left (20 x^2\right )}}-x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.20, size = 46, normalized size = 1.77 \begin {gather*} -\frac {x^2}{-e^5+\log \left (20 x^2\right )}+\log \left (1-e^{\frac {x^2}{-e^5+\log \left (20 x^2\right )}} x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.53, size = 25, normalized size = 0.96
method | result | size |
default | \(\ln \left (x -{\mathrm e}^{-\frac {x^{2}}{\ln \left (20 x^{2}\right )-{\mathrm e}^{5}}}\right )\) | \(25\) |
norman | \(\ln \left (x -{\mathrm e}^{-\frac {x^{2}}{\ln \left (20 x^{2}\right )-{\mathrm e}^{5}}}\right )\) | \(25\) |
risch | \(\frac {x^{2}}{-\ln \left (20 x^{2}\right )+{\mathrm e}^{5}}+\frac {x^{2}}{\ln \left (20 x^{2}\right )-{\mathrm e}^{5}}+\ln \left ({\mathrm e}^{\frac {x^{2}}{-\ln \left (20 x^{2}\right )+{\mathrm e}^{5}}}-x \right )\) | \(59\) |
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. 56 vs.
\(2 (23) = 46\).
time = 0.58, size = 56, normalized size = 2.15 \begin {gather*} \frac {x^{2}}{e^{5} - \log \left (5\right ) - 2 \, \log \left (2\right ) - 2 \, \log \left (x\right )} + \log \left (x\right ) + \log \left (\frac {x e^{\left (-\frac {x^{2}}{e^{5} - \log \left (5\right ) - 2 \, \log \left (2\right ) - 2 \, \log \left (x\right )}\right )} - 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 23, normalized size = 0.88 \begin {gather*} \log \left (-x + e^{\left (\frac {x^{2}}{e^{5} - \log \left (20 \, x^{2}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.33, size = 19, normalized size = 0.73 \begin {gather*} \log {\left (- x + e^{- \frac {x^{2}}{\log {\left (20 x^{2} \right )} - e^{5}}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.96, size = 23, normalized size = 0.88 \begin {gather*} \log \left (x - e^{\left (\frac {x^{2}}{e^{5} - \log \left (20 \, x^{2}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.55, size = 23, normalized size = 0.88 \begin {gather*} \ln \left ({\mathrm {e}}^{\frac {x^2}{{\mathrm {e}}^5-\ln \left (20\,x^2\right )}}-x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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