Optimal. Leaf size=26 \[ \frac {4}{\frac {25}{9}+2 x^2+x \log \left (\frac {3}{(-5+x)^4 x^2}\right )} \]
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Rubi [A]
time = 0.17, antiderivative size = 27, normalized size of antiderivative = 1.04, number of steps
used = 3, number of rules used = 3, integrand size = 165, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6820, 12,
6818} \begin {gather*} \frac {36}{18 x^2+9 x \log \left (\frac {3}{(5-x)^4 x^2}\right )+25} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {324 \left (10-26 x+4 x^2+(-5+x) \log \left (\frac {3}{(-5+x)^4 x^2}\right )\right )}{(5-x) \left (25+18 x^2+9 x \log \left (\frac {3}{(-5+x)^4 x^2}\right )\right )^2} \, dx\\ &=324 \int \frac {10-26 x+4 x^2+(-5+x) \log \left (\frac {3}{(-5+x)^4 x^2}\right )}{(5-x) \left (25+18 x^2+9 x \log \left (\frac {3}{(-5+x)^4 x^2}\right )\right )^2} \, dx\\ &=\frac {36}{25+18 x^2+9 x \log \left (\frac {3}{(5-x)^4 x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 25, normalized size = 0.96 \begin {gather*} \frac {36}{25+18 x^2+9 x \log \left (\frac {3}{(-5+x)^4 x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.30, size = 44, normalized size = 1.69
method | result | size |
norman | \(\frac {36}{18 x^{2}+9 \ln \left (\frac {3}{x^{6}-20 x^{5}+150 x^{4}-500 x^{3}+625 x^{2}}\right ) x +25}\) | \(44\) |
risch | \(\frac {36}{18 x^{2}+9 \ln \left (\frac {3}{x^{6}-20 x^{5}+150 x^{4}-500 x^{3}+625 x^{2}}\right ) x +25}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 28, normalized size = 1.08 \begin {gather*} \frac {36}{18 \, x^{2} + 9 \, x \log \left (3\right ) - 36 \, x \log \left (x - 5\right ) - 18 \, x \log \left (x\right ) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 43, normalized size = 1.65 \begin {gather*} \frac {36}{18 \, x^{2} + 9 \, x \log \left (\frac {3}{x^{6} - 20 \, x^{5} + 150 \, x^{4} - 500 \, x^{3} + 625 \, x^{2}}\right ) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 37, normalized size = 1.42 \begin {gather*} \frac {36}{18 x^{2} + 9 x \log {\left (\frac {3}{x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2}} \right )} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.49, size = 43, normalized size = 1.65 \begin {gather*} \frac {36}{18 \, x^{2} + 9 \, x \log \left (\frac {3}{x^{6} - 20 \, x^{5} + 150 \, x^{4} - 500 \, x^{3} + 625 \, x^{2}}\right ) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.02, size = 43, normalized size = 1.65 \begin {gather*} \frac {36}{9\,x\,\ln \left (\frac {3}{x^6-20\,x^5+150\,x^4-500\,x^3+625\,x^2}\right )+18\,x^2+25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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