Integrand size = 74, antiderivative size = 25 \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=\frac {2}{3 \left (\frac {e^{625 x^6}}{x}-2 x-\log (4)\right )} \]
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\[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=\int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 \left (e^{625 x^6}-x (2 x+\log (4))\right )^2} \, dx \\ & = \frac {1}{3} \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{\left (e^{625 x^6}-x (2 x+\log (4))\right )^2} \, dx \\ & = \frac {1}{3} \int \left (\frac {2 \left (-1+3750 x^6\right )}{-e^{625 x^6}+2 x^2+x \log (4)}-\frac {2 x \left (-4 x+7500 x^7-\log (4)+3750 x^6 \log (4)\right )}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}\right ) \, dx \\ & = \frac {2}{3} \int \frac {-1+3750 x^6}{-e^{625 x^6}+2 x^2+x \log (4)} \, dx-\frac {2}{3} \int \frac {x \left (-4 x+7500 x^7-\log (4)+3750 x^6 \log (4)\right )}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx \\ & = -\left (\frac {2}{3} \int \left (-\frac {4 x^2}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}+\frac {7500 x^8}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}-\frac {x \log (4)}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}+\frac {3750 x^7 \log (4)}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}\right ) \, dx\right )+\frac {2}{3} \int \left (\frac {1}{e^{625 x^6}-2 x^2-x \log (4)}+\frac {3750 x^6}{-e^{625 x^6}+2 x^2+x \log (4)}\right ) \, dx \\ & = \frac {2}{3} \int \frac {1}{e^{625 x^6}-2 x^2-x \log (4)} \, dx+\frac {8}{3} \int \frac {x^2}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx+2500 \int \frac {x^6}{-e^{625 x^6}+2 x^2+x \log (4)} \, dx-5000 \int \frac {x^8}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx+\frac {1}{3} (2 \log (4)) \int \frac {x}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx-(2500 \log (4)) \int \frac {x^7}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=\frac {2 x}{3 \left (e^{625 x^6}-2 x^2-x \log (4)\right )} \]
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Time = 1.61 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
method | result | size |
norman | \(-\frac {2 x}{3 \left (2 x \ln \left (2\right )+2 x^{2}-{\mathrm e}^{625 x^{6}}\right )}\) | \(25\) |
risch | \(-\frac {2 x}{3 \left (2 x \ln \left (2\right )+2 x^{2}-{\mathrm e}^{625 x^{6}}\right )}\) | \(25\) |
parallelrisch | \(-\frac {2 x}{3 \left (2 x \ln \left (2\right )+2 x^{2}-{\mathrm e}^{625 x^{6}}\right )}\) | \(25\) |
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Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=-\frac {2 \, x}{3 \, {\left (2 \, x^{2} + 2 \, x \log \left (2\right ) - e^{\left (625 \, x^{6}\right )}\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=\frac {2 x}{- 6 x^{2} - 6 x \log {\left (2 \right )} + 3 e^{625 x^{6}}} \]
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Time = 0.31 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=-\frac {2 \, x}{3 \, {\left (2 \, x^{2} + 2 \, x \log \left (2\right ) - e^{\left (625 \, x^{6}\right )}\right )}} \]
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Time = 0.32 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=-\frac {2 \, x}{3 \, {\left (2 \, x^{2} + 2 \, x \log \left (2\right ) - e^{\left (625 \, x^{6}\right )}\right )}} \]
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Timed out. \[ \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (4)\right )} \, dx=-\int \frac {{\mathrm {e}}^{625\,x^6}\,\left (7500\,x^6-2\right )-4\,x^2}{3\,{\mathrm {e}}^{1250\,x^6}+12\,x^2\,{\ln \left (2\right )}^2+24\,x^3\,\ln \left (2\right )-{\mathrm {e}}^{625\,x^6}\,\left (12\,x^2+12\,\ln \left (2\right )\,x\right )+12\,x^4} \,d x \]
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