Optimal. Leaf size=31 \[ 4+x^2+\frac {x \left (2+\frac {2 (3+x)}{5-x}\right )^2 \log (x)}{\log \left (x^2\right )} \]
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Rubi [F] time = 0.81, 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 {(2560-512 x) \log (x)+(-1280+256 x+(-1280-256 x) \log (x)) \log \left (x^2\right )+\left (-250 x+150 x^2-30 x^3+2 x^4\right ) \log ^2\left (x^2\right )}{\left (-125+75 x-15 x^2+x^3\right ) \log ^2\left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 (-5+x) \log \left (x^2\right ) \left (128+(-5+x)^2 x \log \left (x^2\right )\right )+256 \log (x) \left (2 (-5+x)+(5+x) \log \left (x^2\right )\right )}{(5-x)^3 \log ^2\left (x^2\right )} \, dx\\ &=\int \left (2 x-\frac {512 \log (x)}{(-5+x)^2 \log ^2\left (x^2\right )}-\frac {256 (5-x+5 \log (x)+x \log (x))}{(-5+x)^3 \log \left (x^2\right )}\right ) \, dx\\ &=x^2-256 \int \frac {5-x+5 \log (x)+x \log (x)}{(-5+x)^3 \log \left (x^2\right )} \, dx-512 \int \frac {\log (x)}{(-5+x)^2 \log ^2\left (x^2\right )} \, dx\\ &=x^2-256 \int \left (\frac {5}{(-5+x)^3 \log \left (x^2\right )}-\frac {x}{(-5+x)^3 \log \left (x^2\right )}+\frac {5 \log (x)}{(-5+x)^3 \log \left (x^2\right )}+\frac {x \log (x)}{(-5+x)^3 \log \left (x^2\right )}\right ) \, dx-512 \int \frac {\log (x)}{(-5+x)^2 \log ^2\left (x^2\right )} \, dx\\ &=x^2+256 \int \frac {x}{(-5+x)^3 \log \left (x^2\right )} \, dx-256 \int \frac {x \log (x)}{(-5+x)^3 \log \left (x^2\right )} \, dx-512 \int \frac {\log (x)}{(-5+x)^2 \log ^2\left (x^2\right )} \, dx-1280 \int \frac {1}{(-5+x)^3 \log \left (x^2\right )} \, dx-1280 \int \frac {\log (x)}{(-5+x)^3 \log \left (x^2\right )} \, dx\\ &=x^2-256 \int \left (\frac {5 \log (x)}{(-5+x)^3 \log \left (x^2\right )}+\frac {\log (x)}{(-5+x)^2 \log \left (x^2\right )}\right ) \, dx+256 \int \frac {x}{(-5+x)^3 \log \left (x^2\right )} \, dx-512 \int \frac {\log (x)}{(-5+x)^2 \log ^2\left (x^2\right )} \, dx-1280 \int \frac {1}{(-5+x)^3 \log \left (x^2\right )} \, dx-1280 \int \frac {\log (x)}{(-5+x)^3 \log \left (x^2\right )} \, dx\\ &=x^2+256 \int \frac {x}{(-5+x)^3 \log \left (x^2\right )} \, dx-256 \int \frac {\log (x)}{(-5+x)^2 \log \left (x^2\right )} \, dx-512 \int \frac {\log (x)}{(-5+x)^2 \log ^2\left (x^2\right )} \, dx-1280 \int \frac {1}{(-5+x)^3 \log \left (x^2\right )} \, dx-2 \left (1280 \int \frac {\log (x)}{(-5+x)^3 \log \left (x^2\right )} \, dx\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 29, normalized size = 0.94 \begin {gather*} \frac {x \left (256 \log (x)+(-5+x)^2 x \log \left (x^2\right )\right )}{(-5+x)^2 \log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 28, normalized size = 0.90 \begin {gather*} \frac {x^{4} - 10 \, x^{3} + 25 \, x^{2} + 128 \, x}{x^{2} - 10 \, x + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 17, normalized size = 0.55 \begin {gather*} x^{2} + \frac {128 \, x}{x^{2} - 10 \, x + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.11, size = 131, normalized size = 4.23
method | result | size |
risch | \(\frac {x \left (x^{3}-10 x^{2}+25 x +128\right )}{x^{2}-10 x +25}-\frac {128 x \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (\mathrm {csgn}\left (i x \right )^{2}-2 \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )+\mathrm {csgn}\left (i x^{2}\right )^{2}\right )}{\left (x^{2}-10 x +25\right ) \left (4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}\right )}\) | \(131\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 28, normalized size = 0.90 \begin {gather*} \frac {x^{4} - 10 \, x^{3} + 25 \, x^{2} + 128 \, x}{x^{2} - 10 \, x + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.90, size = 42, normalized size = 1.35 \begin {gather*} \frac {x\,\left (256\,\ln \relax (x)+25\,x\,\ln \left (x^2\right )-10\,x^2\,\ln \left (x^2\right )+x^3\,\ln \left (x^2\right )\right )}{\ln \left (x^2\right )\,{\left (x-5\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 14, normalized size = 0.45 \begin {gather*} x^{2} + \frac {128 x}{x^{2} - 10 x + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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