Integrand size = 83, antiderivative size = 24 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=\frac {x}{-15-16 x^2 (-x+4 x (x+\log (5 x)))} \]
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\[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=\int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2} \, dx \\ & = \int \left (\frac {-45+64 x^3+64 x^4}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2}+\frac {2}{15-16 x^3+64 x^4+64 x^3 \log (5 x)}\right ) \, dx \\ & = 2 \int \frac {1}{15-16 x^3+64 x^4+64 x^3 \log (5 x)} \, dx+\int \frac {-45+64 x^3+64 x^4}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2} \, dx \\ & = 2 \int \frac {1}{15-16 x^3+64 x^4+64 x^3 \log (5 x)} \, dx+\int \left (-\frac {45}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2}+\frac {64 x^3}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2}+\frac {64 x^4}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2}\right ) \, dx \\ & = 2 \int \frac {1}{15-16 x^3+64 x^4+64 x^3 \log (5 x)} \, dx-45 \int \frac {1}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2} \, dx+64 \int \frac {x^3}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2} \, dx+64 \int \frac {x^4}{\left (15-16 x^3+64 x^4+64 x^3 \log (5 x)\right )^2} \, dx \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=-\frac {x}{15-16 x^3+64 x^4+64 x^3 \log (5 x)} \]
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Time = 0.34 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12
method | result | size |
derivativedivides | \(-\frac {625 x}{40000 x^{4}+40000 x^{3} \ln \left (5 x \right )-10000 x^{3}+9375}\) | \(27\) |
default | \(-\frac {625 x}{40000 x^{4}+40000 x^{3} \ln \left (5 x \right )-10000 x^{3}+9375}\) | \(27\) |
risch | \(-\frac {x}{64 x^{3} \ln \left (5 x \right )+64 x^{4}-16 x^{3}+15}\) | \(27\) |
parallelrisch | \(-\frac {x}{64 x^{3} \ln \left (5 x \right )+64 x^{4}-16 x^{3}+15}\) | \(27\) |
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Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=-\frac {x}{64 \, x^{4} + 64 \, x^{3} \log \left (5 \, x\right ) - 16 \, x^{3} + 15} \]
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Time = 0.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=- \frac {x}{64 x^{4} + 64 x^{3} \log {\left (5 x \right )} - 16 x^{3} + 15} \]
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Time = 0.30 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.25 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=-\frac {x}{64 \, x^{4} + 16 \, x^{3} {\left (4 \, \log \left (5\right ) - 1\right )} + 64 \, x^{3} \log \left (x\right ) + 15} \]
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Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=-\frac {x}{64 \, x^{4} + 64 \, x^{3} \log \left (5 \, x\right ) - 16 \, x^{3} + 15} \]
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Time = 8.28 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {-15+32 x^3+192 x^4+128 x^3 \log (5 x)}{225-480 x^3+1920 x^4+256 x^6-2048 x^7+4096 x^8+\left (1920 x^3-2048 x^6+8192 x^7\right ) \log (5 x)+4096 x^6 \log ^2(5 x)} \, dx=-\frac {x}{64\,x^3\,\ln \left (5\,x\right )-16\,x^3+64\,x^4+15} \]
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