Optimal. Leaf size=19 \[ \frac {\log (x)}{\left (3+e^{4+4 e^7}\right ) x} \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6, 12, 2303} \begin {gather*} \frac {\log (x)}{\left (3+e^{4+4 e^7}\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 2303
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e-e \log (x)}{\left (3 e+e^{5+4 e^7}\right ) x^2} \, dx\\ &=\frac {\int \frac {e-e \log (x)}{x^2} \, dx}{3 e+e^{5+4 e^7}}\\ &=\frac {\log (x)}{\left (3+e^{4+4 e^7}\right ) x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {\log (x)}{\left (3+e^{4+4 e^7}\right ) x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.88, size = 22, normalized size = 1.16 \begin {gather*} \frac {e \log \relax (x)}{3 \, x e + x e^{\left (4 \, e^{7} + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 22, normalized size = 1.16 \begin {gather*} \frac {e \log \relax (x)}{3 \, x e + x e^{\left (4 \, e^{7} + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 18, normalized size = 0.95
method | result | size |
risch | \(\frac {\ln \relax (x )}{x \left ({\mathrm e}^{4+4 \,{\mathrm e}^{7}}+3\right )}\) | \(18\) |
norman | \(\frac {{\mathrm e} \ln \relax (x )}{\left ({\mathrm e}^{5} {\mathrm e}^{4 \,{\mathrm e}^{7}}+3 \,{\mathrm e}\right ) x}\) | \(24\) |
default | \(-\frac {{\mathrm e} \left (-\frac {\ln \relax (x )}{x}-\frac {1}{x}\right )}{{\mathrm e}^{5} {\mathrm e}^{4 \,{\mathrm e}^{7}}+3 \,{\mathrm e}}-\frac {{\mathrm e}}{\left ({\mathrm e}^{5} {\mathrm e}^{4 \,{\mathrm e}^{7}}+3 \,{\mathrm e}\right ) x}\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 36, normalized size = 1.89 \begin {gather*} \frac {\log \relax (x) + 1}{x {\left (e^{\left (4 \, e^{7} + 4\right )} + 3\right )}} - \frac {1}{x {\left (e^{\left (4 \, e^{7} + 4\right )} + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.33, size = 22, normalized size = 1.16 \begin {gather*} \frac {\mathrm {e}\,\ln \relax (x)}{x\,\left (3\,\mathrm {e}+{\mathrm {e}}^{4\,{\mathrm {e}}^7+5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 17, normalized size = 0.89 \begin {gather*} \frac {\log {\relax (x )}}{3 x + x e^{4} e^{4 e^{7}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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