Optimal. Leaf size=25 \[ 5-\frac {9}{4 \left (-x+\frac {2 x}{3 \left (5+\log ^2(5)\right )}\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {6, 12, 30} \begin {gather*} \frac {27 \left (5+\log ^2(5)\right )}{4 x \left (13+3 \log ^2(5)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-135-27 \log ^2(5)}{x^2 \left (52+12 \log ^2(5)\right )} \, dx\\ &=-\frac {\left (27 \left (5+\log ^2(5)\right )\right ) \int \frac {1}{x^2} \, dx}{4 \left (13+3 \log ^2(5)\right )}\\ &=\frac {27 \left (5+\log ^2(5)\right )}{4 x \left (13+3 \log ^2(5)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 23, normalized size = 0.92 \begin {gather*} \frac {27 \left (5+\log ^2(5)\right )}{4 x \left (13+3 \log ^2(5)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 21, normalized size = 0.84 \begin {gather*} \frac {27 \, {\left (\log \relax (5)^{2} + 5\right )}}{4 \, {\left (3 \, x \log \relax (5)^{2} + 13 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 21, normalized size = 0.84 \begin {gather*} \frac {27 \, {\left (\log \relax (5)^{2} + 5\right )}}{4 \, {\left (3 \, \log \relax (5)^{2} + 13\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 22, normalized size = 0.88
method | result | size |
gosper | \(\frac {\frac {27 \ln \relax (5)^{2}}{4}+\frac {135}{4}}{x \left (3 \ln \relax (5)^{2}+13\right )}\) | \(22\) |
norman | \(\frac {\frac {27 \ln \relax (5)^{2}}{4}+\frac {135}{4}}{x \left (3 \ln \relax (5)^{2}+13\right )}\) | \(22\) |
default | \(-\frac {-\frac {27 \ln \relax (5)^{2}}{4}-\frac {135}{4}}{\left (3 \ln \relax (5)^{2}+13\right ) x}\) | \(24\) |
risch | \(\frac {27 \ln \relax (5)^{2}}{4 x \left (3 \ln \relax (5)^{2}+13\right )}+\frac {135}{4 \left (3 \ln \relax (5)^{2}+13\right ) x}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 21, normalized size = 0.84 \begin {gather*} \frac {27 \, {\left (\log \relax (5)^{2} + 5\right )}}{4 \, {\left (3 \, \log \relax (5)^{2} + 13\right )} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 21, normalized size = 0.84 \begin {gather*} \frac {27\,\left ({\ln \relax (5)}^2+5\right )}{4\,x\,\left (3\,{\ln \relax (5)}^2+13\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 20, normalized size = 0.80 \begin {gather*} - \frac {-135 - 27 \log {\relax (5 )}^{2}}{x \left (12 \log {\relax (5 )}^{2} + 52\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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