Optimal. Leaf size=14 \[ \frac {2 \log (x)}{\left (-5+e^4\right ) x} \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps
used = 3, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {6, 12, 2340}
\begin {gather*} -\frac {2 \log (x)}{\left (5-e^4\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 2340
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2-2 \log (x)}{\left (-5+e^4\right ) x^2} \, dx\\ &=\frac {\int \frac {2-2 \log (x)}{x^2} \, dx}{-5+e^4}\\ &=-\frac {2 \log (x)}{\left (5-e^4\right ) x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {2 \log (x)}{\left (-5+e^4\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(33\) vs.
\(2(13)=26\).
time = 1.81, size = 34, normalized size = 2.43
method | result | size |
norman | \(\frac {2 \ln \left (x \right )}{\left ({\mathrm e}^{4}-5\right ) x}\) | \(14\) |
risch | \(\frac {2 \ln \left (x \right )}{\left ({\mathrm e}^{4}-5\right ) x}\) | \(14\) |
default | \(-\frac {2 \left (-\frac {\ln \left (x \right )}{x}-\frac {1}{x}\right )}{{\mathrm e}^{4}-5}-\frac {2}{\left ({\mathrm e}^{4}-5\right ) x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 27 vs.
\(2 (13) = 26\).
time = 0.28, size = 27, normalized size = 1.93 \begin {gather*} \frac {2 \, {\left (\log \left (x\right ) + 1\right )}}{x {\left (e^{4} - 5\right )}} - \frac {2}{x {\left (e^{4} - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 14, normalized size = 1.00 \begin {gather*} \frac {2 \, \log \left (x\right )}{x e^{4} - 5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \log {\left (x \right )}}{- 5 x + x e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 14, normalized size = 1.00 \begin {gather*} \frac {2 \, \log \left (x\right )}{x e^{4} - 5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.33, size = 13, normalized size = 0.93 \begin {gather*} \frac {2\,\ln \left (x\right )}{x\,\left ({\mathrm {e}}^4-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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