Optimal. Leaf size=14 \[ \frac {1}{e+\frac {e^x}{4}+x+\log (x)} \]
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Rubi [A] time = 0.31, antiderivative size = 18, normalized size of antiderivative = 1.29, number of steps used = 3, number of rules used = 3, integrand size = 89, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6688, 12, 6686} \begin {gather*} \frac {4}{4 x+e^x+4 \log (x)+4 e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (-4-\left (4+e^x\right ) x\right )}{x \left (4 e+e^x+4 x+4 \log (x)\right )^2} \, dx\\ &=4 \int \frac {-4-\left (4+e^x\right ) x}{x \left (4 e+e^x+4 x+4 \log (x)\right )^2} \, dx\\ &=\frac {4}{4 e+e^x+4 x+4 \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 18, normalized size = 1.29 \begin {gather*} \frac {4}{4 e+e^x+4 x+4 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 21, normalized size = 1.50 \begin {gather*} \frac {1}{x e^{\left (x - 2 \, \log \relax (2) - \log \relax (x)\right )} + x + e + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 18, normalized size = 1.29 \begin {gather*} \frac {4}{4 \, x + 4 \, e + e^{x} + 4 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 13, normalized size = 0.93
method | result | size |
risch | \(\frac {1}{\frac {{\mathrm e}^{x}}{4}+{\mathrm e}+x +\ln \relax (x )}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 18, normalized size = 1.29 \begin {gather*} \frac {4}{4 \, x + 4 \, e + e^{x} + 4 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.05, size = 18, normalized size = 1.29 \begin {gather*} \frac {4}{4\,x+4\,\mathrm {e}+{\mathrm {e}}^x+4\,\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 17, normalized size = 1.21 \begin {gather*} \frac {4}{4 x + e^{x} + 4 \log {\relax (x )} + 4 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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