Optimal. Leaf size=19 \[ \log (4)+\frac {25 \log (\log (x))}{4 (2+x)^2 \log (25)} \]
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Rubi [F] time = 0.34, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {50+25 x-50 x \log (x) \log (\log (x))}{\left (32 x+48 x^2+24 x^3+4 x^4\right ) \log (25) \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {50+25 x-50 x \log (x) \log (\log (x))}{\left (32 x+48 x^2+24 x^3+4 x^4\right ) \log (x)} \, dx}{\log (25)}\\ &=\frac {\int \frac {25 (2+x-2 x \log (x) \log (\log (x)))}{4 x (2+x)^3 \log (x)} \, dx}{\log (25)}\\ &=\frac {25 \int \frac {2+x-2 x \log (x) \log (\log (x))}{x (2+x)^3 \log (x)} \, dx}{4 \log (25)}\\ &=\frac {25 \int \left (\frac {1}{x (2+x)^2 \log (x)}-\frac {2 \log (\log (x))}{(2+x)^3}\right ) \, dx}{4 \log (25)}\\ &=\frac {25 \int \frac {1}{x (2+x)^2 \log (x)} \, dx}{4 \log (25)}-\frac {25 \int \frac {\log (\log (x))}{(2+x)^3} \, dx}{2 \log (25)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 16, normalized size = 0.84 \begin {gather*} \frac {25 \log (\log (x))}{4 (2+x)^2 \log (25)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 19, normalized size = 1.00 \begin {gather*} \frac {25 \, \log \left (\log \relax (x)\right )}{8 \, {\left (x^{2} + 4 \, x + 4\right )} \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 19, normalized size = 1.00 \begin {gather*} \frac {25 \, \log \left (\log \relax (x)\right )}{8 \, {\left (x^{2} + 4 \, x + 4\right )} \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 1.05
method | result | size |
risch | \(\frac {25 \ln \left (\ln \relax (x )\right )}{8 \ln \relax (5) \left (x^{2}+4 x +4\right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 19, normalized size = 1.00 \begin {gather*} \frac {25 \, \log \left (\log \relax (x)\right )}{8 \, {\left (x^{2} + 4 \, x + 4\right )} \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.67, size = 14, normalized size = 0.74 \begin {gather*} \frac {25\,\ln \left (\ln \relax (x)\right )}{8\,\ln \relax (5)\,{\left (x+2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.36, size = 26, normalized size = 1.37 \begin {gather*} \frac {25 \log {\left (\log {\relax (x )} \right )}}{8 x^{2} \log {\relax (5 )} + 32 x \log {\relax (5 )} + 32 \log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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