Integrand size = 49, antiderivative size = 17 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x \log \left (-x+9216 (1-x)^2 x\right ) \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 10, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.122, Rules used = {6860, 907, 2603, 1671, 646, 31} \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x \log \left (x \left (9216 x^2-18432 x+9215\right )\right ) \]
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Rule 31
Rule 646
Rule 907
Rule 1671
Rule 2603
Rule 6860
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {9215-36864 x+27648 x^2}{(-97+96 x) (-95+96 x)}+\log \left (x \left (9215-18432 x+9216 x^2\right )\right )\right ) \, dx \\ & = \int \frac {9215-36864 x+27648 x^2}{(-97+96 x) (-95+96 x)} \, dx+\int \log \left (x \left (9215-18432 x+9216 x^2\right )\right ) \, dx \\ & = x \log \left (x \left (9215-18432 x+9216 x^2\right )\right )-\int \frac {9215-36864 x+27648 x^2}{9215-18432 x+9216 x^2} \, dx+\int \left (3+\frac {97}{-97+96 x}+\frac {95}{-95+96 x}\right ) \, dx \\ & = 3 x+\frac {95}{96} \log (95-96 x)+\frac {97}{96} \log (97-96 x)+x \log \left (x \left (9215-18432 x+9216 x^2\right )\right )-\int \left (3-\frac {2 (9215-9216 x)}{9215-18432 x+9216 x^2}\right ) \, dx \\ & = \frac {95}{96} \log (95-96 x)+\frac {97}{96} \log (97-96 x)+x \log \left (x \left (9215-18432 x+9216 x^2\right )\right )+2 \int \frac {9215-9216 x}{9215-18432 x+9216 x^2} \, dx \\ & = \frac {95}{96} \log (95-96 x)+\frac {97}{96} \log (97-96 x)+x \log \left (x \left (9215-18432 x+9216 x^2\right )\right )-9120 \int \frac {1}{-9120+9216 x} \, dx-9312 \int \frac {1}{-9312+9216 x} \, dx \\ & = x \log \left (x \left (9215-18432 x+9216 x^2\right )\right ) \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x \log \left (x \left (9215-18432 x+9216 x^2\right )\right ) \]
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Time = 0.37 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06
method | result | size |
default | \(\ln \left (9216 x^{3}-18432 x^{2}+9215 x \right ) x\) | \(18\) |
norman | \(\ln \left (9216 x^{3}-18432 x^{2}+9215 x \right ) x\) | \(18\) |
risch | \(\ln \left (9216 x^{3}-18432 x^{2}+9215 x \right ) x\) | \(18\) |
parallelrisch | \(\ln \left (9216 x^{3}-18432 x^{2}+9215 x \right ) x\) | \(18\) |
parts | \(\ln \left (9216 x^{3}-18432 x^{2}+9215 x \right ) x\) | \(18\) |
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Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x \log \left (9216 \, x^{3} - 18432 \, x^{2} + 9215 \, x\right ) \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x \log {\left (9216 x^{3} - 18432 x^{2} + 9215 x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 47 vs. \(2 (15) = 30\).
Time = 0.28 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.76 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=\frac {1}{96} \, {\left (96 \, x - 95\right )} \log \left (96 \, x - 95\right ) + \frac {1}{96} \, {\left (96 \, x - 97\right )} \log \left (96 \, x - 97\right ) + x \log \left (x\right ) + \frac {95}{96} \, \log \left (96 \, x - 95\right ) + \frac {97}{96} \, \log \left (96 \, x - 97\right ) \]
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Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x \log \left (9216 \, x^{3} - 18432 \, x^{2} + 9215 \, x\right ) \]
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Time = 9.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {9215-36864 x+27648 x^2+\left (9215-18432 x+9216 x^2\right ) \log \left (9215 x-18432 x^2+9216 x^3\right )}{9215-18432 x+9216 x^2} \, dx=x\,\ln \left (x\,\left (9216\,x^2-18432\,x+9215\right )\right ) \]
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