Optimal. Leaf size=25 \[ 1+\log \left (-e^4+e^{\frac {x}{\log \left (e^x-5 x^2\right )}}\right ) \]
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Rubi [A]
time = 1.07, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps
used = 2, number of rules used = 2, integrand size = 119, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6873, 6816}
\begin {gather*} \log \left (e^4-e^{\frac {x}{\log \left (e^x-5 x^2\right )}}\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^{\frac {x}{\log \left (e^x-5 x^2\right )}} \left (e^x x-10 x^2-\left (e^x-5 x^2\right ) \log \left (e^x-5 x^2\right )\right )}{\left (e^4-e^{\frac {x}{\log \left (e^x-5 x^2\right )}}\right ) \left (e^x-5 x^2\right ) \log ^2\left (e^x-5 x^2\right )} \, dx\\ &=\log \left (e^4-e^{\frac {x}{\log \left (e^x-5 x^2\right )}}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 23, normalized size = 0.92 \begin {gather*} \log \left (-e^4+e^{\frac {x}{\log \left (e^x-5 x^2\right )}}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 21, normalized size = 0.84
method | result | size |
risch | \(\ln \left (-{\mathrm e}^{4}+{\mathrm e}^{\frac {x}{\ln \left ({\mathrm e}^{x}-5 x^{2}\right )}}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 20, normalized size = 0.80 \begin {gather*} \log \left (-e^{4} + e^{\left (\frac {x}{\log \left (-5 \, x^{2} + e^{x}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 30, normalized size = 1.20 \begin {gather*} \log \left (-e^{4} + e^{\left (\frac {x}{\log \left (-{\left (5 \, x^{2} e^{4} - e^{\left (x + 4\right )}\right )} e^{\left (-4\right )}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 0.80 \begin {gather*} \log \left (e^{4} - e^{\left (\frac {x}{\log \left (-5 \, x^{2} + e^{x}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.01, size = 20, normalized size = 0.80 \begin {gather*} \ln \left ({\mathrm {e}}^{\frac {x}{\ln \left ({\mathrm {e}}^x-5\,x^2\right )}}-{\mathrm {e}}^4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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