Optimal. Leaf size=13 \[ \frac {25}{-4+x+\log \left (e^x+x\right )} \]
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Rubi [A]
time = 0.22, antiderivative size = 17, normalized size of antiderivative = 1.31, number of steps
used = 3, number of rules used = 3, integrand size = 76, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {6820, 12, 6818}
\begin {gather*} -\frac {25}{-x-\log \left (x+e^x\right )+4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 \left (-1-2 e^x-x\right )}{\left (e^x+x\right ) \left (4-x-\log \left (e^x+x\right )\right )^2} \, dx\\ &=25 \int \frac {-1-2 e^x-x}{\left (e^x+x\right ) \left (4-x-\log \left (e^x+x\right )\right )^2} \, dx\\ &=-\frac {25}{4-x-\log \left (e^x+x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 13, normalized size = 1.00 \begin {gather*} \frac {25}{-4+x+\log \left (e^x+x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 13, normalized size = 1.00
method | result | size |
risch | \(\frac {25}{\ln \left ({\mathrm e}^{x}+x \right )-4+x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 12, normalized size = 0.92 \begin {gather*} \frac {25}{x + \log \left (x + e^{x}\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 12, normalized size = 0.92 \begin {gather*} \frac {25}{x + \log \left (x + e^{x}\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 10, normalized size = 0.77 \begin {gather*} \frac {25}{x + \log {\left (x + e^{x} \right )} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [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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Mupad [B]
time = 9.86, size = 12, normalized size = 0.92 \begin {gather*} \frac {25}{x+\ln \left (x+{\mathrm {e}}^x\right )-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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