Optimal. Leaf size=25 \[ \frac {(5-e)^2}{3 x-\log (x)+2 x \log (4 x)} \]
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Rubi [A] time = 0.21, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 91, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {(5-e)^2}{\log (x)-x (2 \log (4 x)+3)} \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 {(5-e)^2 (1-5 x-2 x \log (4 x))}{x (\log (x)-x (3+2 \log (4 x)))^2} \, dx\\ &=(5-e)^2 \int \frac {1-5 x-2 x \log (4 x)}{x (\log (x)-x (3+2 \log (4 x)))^2} \, dx\\ &=-\frac {(5-e)^2}{\log (x)-x (3+2 \log (4 x))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 0.92 \begin {gather*} -\frac {(-5+e)^2}{\log (x)-x (3+2 \log (4 x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 28, normalized size = 1.12 \begin {gather*} \frac {e^{2} - 10 \, e + 25}{4 \, x \log \relax (2) + {\left (2 \, x - 1\right )} \log \relax (x) + 3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.81, size = 29, normalized size = 1.16 \begin {gather*} \frac {e^{2} - 10 \, e + 25}{4 \, x \log \relax (2) + 2 \, x \log \relax (x) + 3 \, x - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.14, size = 87, normalized size = 3.48
method | result | size |
risch | \(\frac {i {\mathrm e}^{2}}{4 i x \ln \relax (2)+2 i x \ln \relax (x )+3 i x -i \ln \relax (x )}-\frac {10 i {\mathrm e}}{4 i x \ln \relax (2)+2 i x \ln \relax (x )+3 i x -i \ln \relax (x )}+\frac {25 i}{4 i x \ln \relax (2)+2 i x \ln \relax (x )+3 i x -i \ln \relax (x )}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 28, normalized size = 1.12 \begin {gather*} \frac {e^{2} - 10 \, e + 25}{x {\left (4 \, \log \relax (2) + 3\right )} + {\left (2 \, x - 1\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.25, size = 24, normalized size = 0.96 \begin {gather*} -\frac {{\left (\mathrm {e}-5\right )}^2}{\ln \relax (x)-x\,\left (2\,\ln \left (4\,x\right )+3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 27, normalized size = 1.08 \begin {gather*} \frac {- 10 e + e^{2} + 25}{4 x \log {\relax (2 )} + 3 x + \left (2 x - 1\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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