Integrand size = 192, antiderivative size = 28 \[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\log \left (-\frac {e^5}{x}+x+4 x \left (-e^{\frac {x}{\log (4)}}+x\right )^4\right ) \]
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\[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-\left (\left (e^5+x^2+20 x^6\right ) \log (4)\right )-e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )-e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )-e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )-e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{x \left (e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6\right ) \log (4)} \, dx \\ & = \frac {\int \frac {-\left (\left (e^5+x^2+20 x^6\right ) \log (4)\right )-e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )-e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )-e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )-e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{x \left (e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6\right )} \, dx}{\log (4)} \\ & = \frac {\int \left (\frac {4 x+\log (4)}{x}-\frac {2 \left (-2 e^5 x+2 x^3-8 e^{\frac {3 x}{\log (4)}} x^4+24 e^{\frac {2 x}{\log (4)}} x^5-24 e^{\frac {x}{\log (4)}} x^6+8 x^7-e^5 \log (4)+8 e^{\frac {3 x}{\log (4)}} x^3 \log (4)-24 e^{\frac {2 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {x}{\log (4)}} x^5 \log (4)-8 x^6 \log (4)\right )}{x \left (-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6\right )}\right ) \, dx}{\log (4)} \\ & = \frac {\int \frac {4 x+\log (4)}{x} \, dx}{\log (4)}-\frac {2 \int \frac {-2 e^5 x+2 x^3-8 e^{\frac {3 x}{\log (4)}} x^4+24 e^{\frac {2 x}{\log (4)}} x^5-24 e^{\frac {x}{\log (4)}} x^6+8 x^7-e^5 \log (4)+8 e^{\frac {3 x}{\log (4)}} x^3 \log (4)-24 e^{\frac {2 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {x}{\log (4)}} x^5 \log (4)-8 x^6 \log (4)}{x \left (-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6\right )} \, dx}{\log (4)} \\ & = \frac {\int \left (4+\frac {\log (4)}{x}\right ) \, dx}{\log (4)}-\frac {2 \int \left (\frac {2 e^5}{e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6}+\frac {2 x^2}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}-\frac {8 e^{\frac {3 x}{\log (4)}} x^3}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}+\frac {24 e^{\frac {2 x}{\log (4)}} x^4}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}-\frac {24 e^{\frac {x}{\log (4)}} x^5}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}+\frac {8 x^6}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}+\frac {e^5 \log (4)}{x \left (e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6\right )}+\frac {8 e^{\frac {3 x}{\log (4)}} x^2 \log (4)}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}-\frac {24 e^{\frac {2 x}{\log (4)}} x^3 \log (4)}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}+\frac {24 e^{\frac {x}{\log (4)}} x^4 \log (4)}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}-\frac {8 x^5 \log (4)}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6}\right ) \, dx}{\log (4)} \\ & = \frac {4 x}{\log (4)}+\log (x)-16 \int \frac {e^{\frac {3 x}{\log (4)}} x^2}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx+16 \int \frac {x^5}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx+48 \int \frac {e^{\frac {2 x}{\log (4)}} x^3}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx-48 \int \frac {e^{\frac {x}{\log (4)}} x^4}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx-\left (2 e^5\right ) \int \frac {1}{x \left (e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6\right )} \, dx-\frac {4 \int \frac {x^2}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx}{\log (4)}+\frac {16 \int \frac {e^{\frac {3 x}{\log (4)}} x^3}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx}{\log (4)}-\frac {16 \int \frac {x^6}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx}{\log (4)}-\frac {48 \int \frac {e^{\frac {2 x}{\log (4)}} x^4}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx}{\log (4)}+\frac {48 \int \frac {e^{\frac {x}{\log (4)}} x^5}{-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6} \, dx}{\log (4)}-\frac {\left (4 e^5\right ) \int \frac {1}{e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6} \, dx}{\log (4)} \\ \end{align*}
\[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx \]
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Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(27)=54\).
Time = 0.31 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.43
method | result | size |
risch | \(\ln \left (x \right )+\ln \left ({\mathrm e}^{\frac {2 x}{\ln \left (2\right )}}-4 x \,{\mathrm e}^{\frac {3 x}{2 \ln \left (2\right )}}+6 x^{2} {\mathrm e}^{\frac {x}{\ln \left (2\right )}}-4 x^{3} {\mathrm e}^{\frac {x}{2 \ln \left (2\right )}}-\frac {-4 x^{6}-x^{2}+{\mathrm e}^{5}}{4 x^{2}}\right )\) | \(68\) |
parallelrisch | \(-\frac {\ln \left (2\right ) \ln \left (x \right )-\ln \left ({\mathrm e}^{\frac {2 x}{\ln \left (2\right )}} x^{2}-4 \,{\mathrm e}^{\frac {3 x}{2 \ln \left (2\right )}} x^{3}+6 \,{\mathrm e}^{\frac {x}{\ln \left (2\right )}} x^{4}-4 x^{5} {\mathrm e}^{\frac {x}{2 \ln \left (2\right )}}+x^{6}+\frac {x^{2}}{4}-\frac {{\mathrm e}^{5}}{4}\right ) \ln \left (2\right )}{\ln \left (2\right )}\) | \(88\) |
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Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (27) = 54\).
Time = 0.28 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\log \left (x\right ) + \log \left (\frac {4 \, x^{6} - 16 \, x^{5} e^{\left (\frac {x}{2 \, \log \left (2\right )}\right )} + 24 \, x^{4} e^{\frac {x}{\log \left (2\right )}} - 16 \, x^{3} e^{\left (\frac {3 \, x}{2 \, \log \left (2\right )}\right )} + 4 \, x^{2} e^{\left (\frac {2 \, x}{\log \left (2\right )}\right )} + x^{2} - e^{5}}{x^{2}}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (22) = 44\).
Time = 0.50 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.43 \[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\log {\left (x \right )} + \log {\left (- 4 x^{3} e^{\frac {x}{2 \log {\left (2 \right )}}} + 6 x^{2} e^{\frac {x}{\log {\left (2 \right )}}} - 4 x e^{\frac {3 x}{2 \log {\left (2 \right )}}} + e^{\frac {2 x}{\log {\left (2 \right )}}} + \frac {4 x^{6} + x^{2} - e^{5}}{4 x^{2}} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (27) = 54\).
Time = 0.32 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.68 \[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=2 \, \log \left (x\right ) + \log \left (-\frac {4 \, x^{6} - 16 \, x^{5} e^{\left (\frac {x}{2 \, \log \left (2\right )}\right )} + 24 \, x^{4} e^{\frac {x}{\log \left (2\right )}} - 16 \, x^{3} e^{\left (\frac {3 \, x}{2 \, \log \left (2\right )}\right )} + 4 \, x^{2} e^{\left (\frac {2 \, x}{\log \left (2\right )}\right )} + x^{2} - e^{5}}{16 \, x^{3}}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (27) = 54\).
Time = 0.58 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.50 \[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\log \left (4 \, x^{6} - 16 \, x^{5} e^{\left (\frac {x}{2 \, \log \left (2\right )}\right )} + 24 \, x^{4} e^{\frac {x}{\log \left (2\right )}} - 16 \, x^{3} e^{\left (\frac {3 \, x}{2 \, \log \left (2\right )}\right )} + 4 \, x^{2} e^{\left (\frac {2 \, x}{\log \left (2\right )}\right )} + x^{2} - e^{5}\right ) - \log \left (x\right ) \]
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Timed out. \[ \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx=\int \frac {2\,\ln \left (2\right )\,\left (20\,x^6+x^2+{\mathrm {e}}^5\right )+{\mathrm {e}}^{\frac {2\,x}{\ln \left (2\right )}}\,\left (16\,x^3+8\,\ln \left (2\right )\,x^2\right )-{\mathrm {e}}^{\frac {3\,x}{2\,\ln \left (2\right )}}\,\left (48\,x^4+64\,\ln \left (2\right )\,x^3\right )-{\mathrm {e}}^{\frac {x}{2\,\ln \left (2\right )}}\,\left (16\,x^6+128\,\ln \left (2\right )\,x^5\right )+{\mathrm {e}}^{\frac {x}{\ln \left (2\right )}}\,\left (48\,x^5+144\,\ln \left (2\right )\,x^4\right )}{2\,\ln \left (2\right )\,\left (4\,x^7+x^3-{\mathrm {e}}^5\,x\right )+8\,x^3\,{\mathrm {e}}^{\frac {2\,x}{\ln \left (2\right )}}\,\ln \left (2\right )+48\,x^5\,{\mathrm {e}}^{\frac {x}{\ln \left (2\right )}}\,\ln \left (2\right )-32\,x^4\,{\mathrm {e}}^{\frac {3\,x}{2\,\ln \left (2\right )}}\,\ln \left (2\right )-32\,x^6\,{\mathrm {e}}^{\frac {x}{2\,\ln \left (2\right )}}\,\ln \left (2\right )} \,d x \]
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