Integrand size = 165, antiderivative size = 26 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {4}{\frac {25}{9}+2 x^2+x \log \left (\frac {3}{(-5+x)^4 x^2}\right )} \]
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Time = 0.17 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.04, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6820, 12, 6818} \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{18 x^2+9 x \log \left (\frac {3}{(5-x)^4 x^2}\right )+25} \]
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Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \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{align*}
Time = 0.05 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{25+18 x^2+9 x \log \left (\frac {3}{(-5+x)^4 x^2}\right )} \]
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Time = 1.05 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58
method | result | size |
parallelrisch | \(\frac {36}{9 \ln \left (\frac {3}{x^{2} \left (x^{4}-20 x^{3}+150 x^{2}-500 x +625\right )}\right ) x +18 x^{2}+25}\) | \(41\) |
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 | \(\frac {36}{18 x^{2}+9 \ln \left (\frac {3}{x^{6}-20 x^{5}+150 x^{4}-500 x^{3}+625 x^{2}}\right ) x +25}\) | \(44\) |
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Time = 0.38 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.65 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{18 \, x^{2} + 9 \, x \log \left (\frac {3}{x^{6} - 20 \, x^{5} + 150 \, x^{4} - 500 \, x^{3} + 625 \, x^{2}}\right ) + 25} \]
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Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{18 x^{2} + 9 x \log {\left (\frac {3}{x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2}} \right )} + 25} \]
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Time = 0.35 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{18 \, x^{2} + 9 \, x \log \left (3\right ) - 36 \, x \log \left (x - 5\right ) - 18 \, x \log \left (x\right ) + 25} \]
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Time = 0.40 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.65 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{18 \, x^{2} + 9 \, x \log \left (\frac {3}{x^{6} - 20 \, x^{5} + 150 \, x^{4} - 500 \, x^{3} + 625 \, x^{2}}\right ) + 25} \]
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Time = 13.74 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.65 \[ \int \frac {-3240+8424 x-1296 x^2+(1620-324 x) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )}{-3125+625 x-4500 x^2+900 x^3-1620 x^4+324 x^5+\left (-2250 x+450 x^2-1620 x^3+324 x^4\right ) \log \left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )+\left (-405 x^2+81 x^3\right ) \log ^2\left (\frac {3}{625 x^2-500 x^3+150 x^4-20 x^5+x^6}\right )} \, dx=\frac {36}{9\,x\,\ln \left (\frac {3}{x^6-20\,x^5+150\,x^4-500\,x^3+625\,x^2}\right )+18\,x^2+25} \]
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