Integrand size = 107, antiderivative size = 24 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=x+\frac {x}{-5+x-24 x^2+\frac {\log (x)}{5-2 x}} \]
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\[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=\int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{\left (25-15 x+122 x^2-48 x^3-\log (x)\right )^2} \, dx \\ & = \int \left (1+\frac {-5-73 x+1250 x^2-1208 x^3+288 x^4}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2}+\frac {5-4 x}{-25+15 x-122 x^2+48 x^3+\log (x)}\right ) \, dx \\ & = x+\int \frac {-5-73 x+1250 x^2-1208 x^3+288 x^4}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2} \, dx+\int \frac {5-4 x}{-25+15 x-122 x^2+48 x^3+\log (x)} \, dx \\ & = x+\int \left (-\frac {5}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2}-\frac {73 x}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2}+\frac {1250 x^2}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2}-\frac {1208 x^3}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2}+\frac {288 x^4}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2}\right ) \, dx+\int \left (\frac {5}{-25+15 x-122 x^2+48 x^3+\log (x)}-\frac {4 x}{-25+15 x-122 x^2+48 x^3+\log (x)}\right ) \, dx \\ & = x-4 \int \frac {x}{-25+15 x-122 x^2+48 x^3+\log (x)} \, dx-5 \int \frac {1}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2} \, dx+5 \int \frac {1}{-25+15 x-122 x^2+48 x^3+\log (x)} \, dx-73 \int \frac {x}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2} \, dx+288 \int \frac {x^4}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2} \, dx-1208 \int \frac {x^3}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2} \, dx+1250 \int \frac {x^2}{\left (-25+15 x-122 x^2+48 x^3+\log (x)\right )^2} \, dx \\ \end{align*}
Time = 0.22 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=x-\frac {x (-5+2 x)}{-25+15 x-122 x^2+48 x^3+\log (x)} \]
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Time = 0.37 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.25
method | result | size |
risch | \(x -\frac {x \left (-5+2 x \right )}{48 x^{3}-122 x^{2}+\ln \left (x \right )+15 x -25}\) | \(30\) |
default | \(\frac {-122 x^{3}-20 x +13 x^{2}+x \ln \left (x \right )+48 x^{4}}{48 x^{3}-122 x^{2}+\ln \left (x \right )+15 x -25}\) | \(44\) |
norman | \(\frac {x \ln \left (x \right )-\frac {3565 x^{2}}{12}+\frac {61 \ln \left (x \right )}{24}+\frac {145 x}{8}+48 x^{4}-\frac {1525}{24}}{48 x^{3}-122 x^{2}+\ln \left (x \right )+15 x -25}\) | \(44\) |
parallelrisch | \(\frac {-122 x^{3}-20 x +13 x^{2}+x \ln \left (x \right )+48 x^{4}}{48 x^{3}-122 x^{2}+\ln \left (x \right )+15 x -25}\) | \(44\) |
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Time = 0.25 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {48 \, x^{4} - 122 \, x^{3} + 13 \, x^{2} + x \log \left (x\right ) - 20 \, x}{48 \, x^{3} - 122 \, x^{2} + 15 \, x + \log \left (x\right ) - 25} \]
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Time = 0.07 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=x + \frac {- 2 x^{2} + 5 x}{48 x^{3} - 122 x^{2} + 15 x + \log {\left (x \right )} - 25} \]
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Time = 0.22 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {48 \, x^{4} - 122 \, x^{3} + 13 \, x^{2} + x \log \left (x\right ) - 20 \, x}{48 \, x^{3} - 122 \, x^{2} + 15 \, x + \log \left (x\right ) - 25} \]
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Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=x - \frac {2 \, x^{2} - 5 \, x}{48 \, x^{3} - 122 \, x^{2} + 15 \, x + \log \left (x\right ) - 25} \]
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Time = 9.46 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {495-648 x+6905 x^2-6540 x^3+16420 x^4-11712 x^5+2304 x^6+\left (-45+26 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)}{625-750 x+6325 x^2-6060 x^3+16324 x^4-11712 x^5+2304 x^6+\left (-50+30 x-244 x^2+96 x^3\right ) \log (x)+\log ^2(x)} \, dx=x+\frac {5\,x-2\,x^2}{15\,x+\ln \left (x\right )-122\,x^2+48\,x^3-25} \]
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