Integrand size = 32, antiderivative size = 24 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=-\left (\left (-4+\frac {10}{x}\right ) x\right )+\frac {x}{-\frac {2401}{625}+x}-\log (x) \]
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Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {1608, 27, 1634} \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=4 x-\frac {2401}{2401-625 x}-\log (x) \]
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Rule 27
Rule 1608
Rule 1634
Rubi steps \begin{align*} \text {integral}& = \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{x \left (5764801-3001250 x+390625 x^2\right )} \, dx \\ & = \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{x (-2401+625 x)^2} \, dx \\ & = \int \left (4-\frac {1}{x}-\frac {1500625}{(-2401+625 x)^2}\right ) \, dx \\ & = -\frac {2401}{2401-625 x}+4 x-\log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=4 x+\frac {2401}{-2401+625 x}-\log (x) \]
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Time = 0.06 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67
method | result | size |
risch | \(4 x +\frac {2401}{625 \left (x -\frac {2401}{625}\right )}-\ln \left (x \right )\) | \(16\) |
default | \(4 x -\ln \left (x \right )+\frac {2401}{625 x -2401}\) | \(18\) |
norman | \(\frac {2500 x^{2}-\frac {21558579}{625}}{625 x -2401}-\ln \left (x \right )\) | \(21\) |
parallelrisch | \(-\frac {390625 x \ln \left (x \right )-1562500 x^{2}+21558579-1500625 \ln \left (x \right )}{625 \left (625 x -2401\right )}\) | \(26\) |
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Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=\frac {2500 \, x^{2} - {\left (625 \, x - 2401\right )} \log \left (x\right ) - 9604 \, x + 2401}{625 \, x - 2401} \]
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Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.50 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=4 x - \log {\left (x \right )} + \frac {2401}{625 x - 2401} \]
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Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=4 \, x + \frac {2401}{625 \, x - 2401} - \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=4 \, x + \frac {2401}{625 \, x - 2401} - \log \left ({\left | x \right |}\right ) \]
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Time = 8.99 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {-5764801+24559829 x-12395625 x^2+1562500 x^3}{5764801 x-3001250 x^2+390625 x^3} \, dx=4\,x-\ln \left (x\right )+\frac {2401}{625\,\left (x-\frac {2401}{625}\right )} \]
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