Optimal. Leaf size=28 \[ 2 \left (-3+\frac {1}{2 e}\right )+\log (x)-\log ^4\left (1+x-\frac {5}{\log (x)}\right ) \]
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Rubi [A]
time = 0.51, antiderivative size = 17, normalized size of antiderivative = 0.61, number of steps
used = 4, number of rules used = 3, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.052, Rules used = {6873, 6874,
6818} \begin {gather*} \log (x)-\log ^4\left (x-\frac {5}{\log (x)}+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \log (x)-(1+x) \log ^2(x)-\left (-20-4 x \log ^2(x)\right ) \log ^3\left (\frac {-5+(1+x) \log (x)}{\log (x)}\right )}{x \log (x) (5-\log (x)-x \log (x))} \, dx\\ &=\int \left (\frac {1}{x}-\frac {4 \left (5+x \log ^2(x)\right ) \log ^3\left (1+x-\frac {5}{\log (x)}\right )}{x \log (x) (-5+\log (x)+x \log (x))}\right ) \, dx\\ &=\log (x)-4 \int \frac {\left (5+x \log ^2(x)\right ) \log ^3\left (1+x-\frac {5}{\log (x)}\right )}{x \log (x) (-5+\log (x)+x \log (x))} \, dx\\ &=\log (x)-\log ^4\left (1+x-\frac {5}{\log (x)}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 17, normalized size = 0.61 \begin {gather*} \log (x)-\log ^4\left (1+x-\frac {5}{\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.13, size = 0, normalized size = 0.00 \[\int \frac {\left (-4 x \ln \left (x \right )^{2}-20\right ) \ln \left (\frac {\ln \left (x \right ) \left (x +1\right )-5}{\ln \left (x \right )}\right )^{3}+\left (x +1\right ) \ln \left (x \right )^{2}-5 \ln \left (x \right )}{\left (x^{2}+x \right ) \ln \left (x \right )^{2}-5 x \ln \left (x \right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 21, normalized size = 0.75 \begin {gather*} -\log \left (\frac {{\left (x + 1\right )} \log \left (x\right ) - 5}{\log \left (x\right )}\right )^{4} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 17, normalized size = 0.61 \begin {gather*} \log {\left (x \right )} - \log {\left (\frac {\left (x + 1\right ) \log {\left (x \right )} - 5}{\log {\left (x \right )}} \right )}^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (20) = 40\).
time = 0.55, size = 72, normalized size = 2.57 \begin {gather*} -4 \, {\left (\log \left (x \log \left (x\right ) + \log \left (x\right ) - 5\right ) - \log \left (\log \left (x\right )\right )\right )} \log \left (x \log \left (x\right ) + \log \left (x\right ) - 5\right )^{3} - 6 \, \log \left (x \log \left (x\right ) + \log \left (x\right ) - 5\right )^{2} \log \left (\log \left (x\right )\right )^{2} + 4 \, \log \left (x \log \left (x\right ) + \log \left (x\right ) - 5\right ) \log \left (\log \left (x\right )\right )^{3} - \log \left (\log \left (x\right )\right )^{4} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.52, size = 21, normalized size = 0.75 \begin {gather*} \ln \left (x\right )-{\ln \left (\frac {\ln \left (x\right )\,\left (x+1\right )-5}{\ln \left (x\right )}\right )}^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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