Integrand size = 159, antiderivative size = 29 \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=\frac {10}{-x+2 \left (2+2 (x-5 \log (4))-\log \left (x^2+\log (x)\right )\right )} \]
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Time = 0.23 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6, 6820, 12, 6818} \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=\frac {10}{-2 \log \left (x^2+\log (x)\right )+3 x+4 (1-5 \log (4))} \]
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Rule 6
Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+x^3 \left (16+400 \log ^2(4)\right )+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx \\ & = \int \frac {10 \left (2+4 x^2-3 x^3-3 x \log (x)\right )}{x \left (x^2+\log (x)\right ) \left (3 x+4 (1-5 \log (4))-2 \log \left (x^2+\log (x)\right )\right )^2} \, dx \\ & = 10 \int \frac {2+4 x^2-3 x^3-3 x \log (x)}{x \left (x^2+\log (x)\right ) \left (3 x+4 (1-5 \log (4))-2 \log \left (x^2+\log (x)\right )\right )^2} \, dx \\ & = \frac {10}{3 x+4 (1-5 \log (4))-2 \log \left (x^2+\log (x)\right )} \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=\frac {10}{4+3 x-20 \log (4)-2 \log \left (x^2+\log (x)\right )} \]
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Time = 2.49 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.79
method | result | size |
default | \(-\frac {10}{40 \ln \left (2\right )+2 \ln \left (\ln \left (x \right )+x^{2}\right )-3 x -4}\) | \(23\) |
risch | \(-\frac {10}{40 \ln \left (2\right )+2 \ln \left (\ln \left (x \right )+x^{2}\right )-3 x -4}\) | \(23\) |
parallelrisch | \(-\frac {10}{40 \ln \left (2\right )+2 \ln \left (\ln \left (x \right )+x^{2}\right )-3 x -4}\) | \(23\) |
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Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=\frac {10}{3 \, x - 40 \, \log \left (2\right ) - 2 \, \log \left (x^{2} + \log \left (x\right )\right ) + 4} \]
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Time = 0.15 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=- \frac {5}{- \frac {3 x}{2} + \log {\left (x^{2} + \log {\left (x \right )} \right )} - 2 + 20 \log {\left (2 \right )}} \]
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Time = 0.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=\frac {10}{3 \, x - 40 \, \log \left (2\right ) - 2 \, \log \left (x^{2} + \log \left (x\right )\right ) + 4} \]
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Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=\frac {10}{3 \, x - 40 \, \log \left (2\right ) - 2 \, \log \left (x^{2} + \log \left (x\right )\right ) + 4} \]
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Timed out. \[ \int \frac {20+40 x^2-30 x^3-30 x \log (x)}{16 x^3+24 x^4+9 x^5+\left (-160 x^3-120 x^4\right ) \log (4)+400 x^3 \log ^2(4)+\left (16 x+24 x^2+9 x^3+\left (-160 x-120 x^2\right ) \log (4)+400 x \log ^2(4)\right ) \log (x)+\left (-16 x^3-12 x^4+80 x^3 \log (4)+\left (-16 x-12 x^2+80 x \log (4)\right ) \log (x)\right ) \log \left (x^2+\log (x)\right )+\left (4 x^3+4 x \log (x)\right ) \log ^2\left (x^2+\log (x)\right )} \, dx=-\int \frac {30\,x\,\ln \left (x\right )-40\,x^2+30\,x^3-20}{1600\,x^3\,{\ln \left (2\right )}^2-\ln \left (\ln \left (x\right )+x^2\right )\,\left (16\,x^3-160\,x^3\,\ln \left (2\right )+12\,x^4+\ln \left (x\right )\,\left (16\,x-160\,x\,\ln \left (2\right )+12\,x^2\right )\right )+{\ln \left (\ln \left (x\right )+x^2\right )}^2\,\left (4\,x\,\ln \left (x\right )+4\,x^3\right )-2\,\ln \left (2\right )\,\left (120\,x^4+160\,x^3\right )+\ln \left (x\right )\,\left (16\,x-2\,\ln \left (2\right )\,\left (120\,x^2+160\,x\right )+1600\,x\,{\ln \left (2\right )}^2+24\,x^2+9\,x^3\right )+16\,x^3+24\,x^4+9\,x^5} \,d x \]
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