Integrand size = 28, antiderivative size = 20 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=5 \left (4-5 \log \left (\frac {x}{6+x^4-4 \log (x)}\right )\right ) \]
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Time = 0.12 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 5, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {6873, 12, 6874, 6816} \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=25 \log \left (x^4-4 \log (x)+6\right )-25 \log (x) \]
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Rule 12
Rule 6816
Rule 6873
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {25 \left (-10+3 x^4+4 \log (x)\right )}{6 x+x^5-4 x \log (x)} \, dx \\ & = 25 \int \frac {-10+3 x^4+4 \log (x)}{6 x+x^5-4 x \log (x)} \, dx \\ & = 25 \int \left (-\frac {1}{x}+\frac {4 \left (-1+x^4\right )}{x \left (6+x^4-4 \log (x)\right )}\right ) \, dx \\ & = -25 \log (x)+100 \int \frac {-1+x^4}{x \left (6+x^4-4 \log (x)\right )} \, dx \\ & = -25 \log (x)+25 \log \left (6+x^4-4 \log (x)\right ) \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=25 \left (-\log (x)+\log \left (6+x^4-4 \log (x)\right )\right ) \]
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Time = 0.84 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
method | result | size |
norman | \(-25 \ln \left (x \right )+25 \ln \left (6+x^{4}-4 \ln \left (x \right )\right )\) | \(18\) |
risch | \(-25 \ln \left (x \right )+25 \ln \left (-\frac {x^{4}}{4}+\ln \left (x \right )-\frac {3}{2}\right )\) | \(18\) |
parallelrisch | \(-25 \ln \left (x \right )+25 \ln \left (6+x^{4}-4 \ln \left (x \right )\right )\) | \(18\) |
default | \(-25 \ln \left (x \right )+25 \ln \left (-x^{4}+4 \ln \left (x \right )-6\right )\) | \(20\) |
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Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=25 \, \log \left (-x^{4} + 4 \, \log \left (x\right ) - 6\right ) - 25 \, \log \left (x\right ) \]
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Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=- 25 \log {\left (x \right )} + 25 \log {\left (- \frac {x^{4}}{4} + \log {\left (x \right )} - \frac {3}{2} \right )} \]
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Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=25 \, \log \left (-\frac {1}{4} \, x^{4} + \log \left (x\right ) - \frac {3}{2}\right ) - 25 \, \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=25 \, \log \left (-x^{4} + 4 \, \log \left (x\right ) - 6\right ) - 25 \, \log \left (x\right ) \]
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Time = 9.39 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {250-75 x^4-100 \log (x)}{-6 x-x^5+4 x \log (x)} \, dx=25\,\ln \left (x^4-4\,\ln \left (x\right )+6\right )-25\,\ln \left (x\right ) \]
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