Optimal. Leaf size=15 \[ \frac {1}{x \left (e^x-5 x \log (x)\right )} \]
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Rubi [A]
time = 0.18, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {6820, 6819}
\begin {gather*} \frac {1}{x \left (e^x-5 x \log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6819
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 x-e^x (1+x)+10 x \log (x)}{x^2 \left (e^x-5 x \log (x)\right )^2} \, dx\\ &=\frac {1}{x \left (e^x-5 x \log (x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 15, normalized size = 1.00 \begin {gather*} \frac {1}{e^x x-5 x^2 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 18, normalized size = 1.20
method | result | size |
risch | \(-\frac {1}{x \left (5 x \ln \left (x \right )-{\mathrm e}^{x}\right )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 17, normalized size = 1.13 \begin {gather*} -\frac {1}{5 \, x^{2} \log \left (x\right ) - x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 17, normalized size = 1.13 \begin {gather*} -\frac {1}{5 \, x^{2} \log \left (x\right ) - x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.93 \begin {gather*} \frac {1}{- 5 x^{2} \log {\left (x \right )} + x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 1.13 \begin {gather*} -\frac {1}{5 \, x^{2} \log \left (x\right ) - x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.07, size = 17, normalized size = 1.13 \begin {gather*} -\frac {1}{5\,x^2\,\ln \left (x\right )-x\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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