Optimal. Leaf size=27 \[ \frac {1}{(\log (x)-1)^2}+\frac {1}{1-\log (x)}-\frac {2}{3 (1-\log (x))^3} \]
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Rubi [A] time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {698} \[ \frac {1}{(\log (x)-1)^2}+\frac {1}{1-\log (x)}-\frac {2}{3 (1-\log (x))^3} \]
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin {align*} \int \frac {1-4 \log (x)+\log ^2(x)}{x (-1+\log (x))^4} \, dx &=\operatorname {Subst}\left (\int \frac {1-4 x+x^2}{(-1+x)^4} \, dx,x,\log (x)\right )\\ &=\operatorname {Subst}\left (\int \left (-\frac {2}{(-1+x)^4}-\frac {2}{(-1+x)^3}+\frac {1}{(-1+x)^2}\right ) \, dx,x,\log (x)\right )\\ &=-\frac {2}{3 (1-\log (x))^3}+\frac {1}{1-\log (x)}+\frac {1}{(-1+\log (x))^2}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 22, normalized size = 0.81 \[ \frac {-3 \log ^2(x)+9 \log (x)-4}{3 (\log (x)-1)^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 2.13, size = 32, normalized size = 1.19 \[ -\frac {3 \, \log \relax (x)^{2} - 9 \, \log \relax (x) + 4}{3 \, {\left (\log \relax (x)^{3} - 3 \, \log \relax (x)^{2} + 3 \, \log \relax (x) - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 20, normalized size = 0.74 \[ -\frac {3 \, \log \relax (x)^{2} - 9 \, \log \relax (x) + 4}{3 \, {\left (\log \relax (x) - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 24, normalized size = 0.89 \[ -\frac {1}{\ln \relax (x )-1}+\frac {1}{\left (\ln \relax (x )-1\right )^{2}}+\frac {2}{3 \left (\ln \relax (x )-1\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 32, normalized size = 1.19 \[ -\frac {3 \, \log \relax (x)^{2} - 9 \, \log \relax (x) + 4}{3 \, {\left (\log \relax (x)^{3} - 3 \, \log \relax (x)^{2} + 3 \, \log \relax (x) - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.42, size = 18, normalized size = 0.67 \[ -\frac {{\ln \relax (x)}^2-3\,\ln \relax (x)+\frac {4}{3}}{{\left (\ln \relax (x)-1\right )}^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 32, normalized size = 1.19 \[ \frac {- 3 \log {\relax (x )}^{2} + 9 \log {\relax (x )} - 4}{3 \log {\relax (x )}^{3} - 9 \log {\relax (x )}^{2} + 9 \log {\relax (x )} - 3} \]
Verification of antiderivative is not currently implemented for this CAS.
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