Integrand size = 255, antiderivative size = 31 \[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=e^{e^{2 x^4} \left (2-\frac {1}{x}+2 x\right )^2 (-\log (2)+\log (x))^2} \]
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\[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=\int \frac {\exp \left (\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}\right ) \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) (\log (2)-\log (x)) \left (-1+2 x-\log (2)+4 x^4 \log (2)-8 x^5 \log (2)-8 x^6 \log (2)-x^2 (-2+\log (4))+\left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log (x)\right )}{x^3} \, dx \\ & = 2 \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) (\log (2)-\log (x)) \left (-1+2 x-\log (2)+4 x^4 \log (2)-8 x^5 \log (2)-8 x^6 \log (2)-x^2 (-2+\log (4))+\left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log (x)\right )}{x^3} \, dx \\ & = 2 \int \left (\frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \log (2) \left (-1+2 x+2 x^2 (1-\log (2))-\log (2)+4 x^4 \log (2)-8 x^5 \log (2)-8 x^6 \log (2)\right )}{x^3}+\frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (1-2 x-8 x^4 \log (2)+16 x^5 \log (2)+16 x^6 \log (2)-2 x^2 (1-\log (4))+\log (4)\right ) \log (x)}{x^3}+\frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (-1+2 x+2 x^2\right ) \left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log ^2(x)}{x^3}\right ) \, dx \\ & = 2 \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (1-2 x-8 x^4 \log (2)+16 x^5 \log (2)+16 x^6 \log (2)-2 x^2 (1-\log (4))+\log (4)\right ) \log (x)}{x^3} \, dx+2 \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (-1+2 x+2 x^2\right ) \left (1+2 x^2-4 x^4+8 x^5+8 x^6\right ) \log ^2(x)}{x^3} \, dx+(2 \log (2)) \int \frac {\exp \left (2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}\right ) \left (1-2 x-2 x^2\right ) \left (-1+2 x+2 x^2 (1-\log (2))-\log (2)+4 x^4 \log (2)-8 x^5 \log (2)-8 x^6 \log (2)\right )}{x^3} \, dx \\ & = 2 \int \left (32 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^2 \log (2) \log (x)-64 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^4 \log (2) \log (x)-32 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^5 \log (2) \log (x)-4 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} (-2+\log (4)) \log (x)+\frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} (1+\log (4)) \log (x)}{x^3}-\frac {2 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} (2+\log (4)) \log (x)}{x^2}-4 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x (-1+\log (16)) \log (x)\right ) \, dx+2 \int \left (4 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log ^2(x)-\frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log ^2(x)}{x^3}+\frac {2 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log ^2(x)}{x^2}+8 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x \log ^2(x)-16 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^2 \log ^2(x)+32 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^4 \log ^2(x)+16 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^5 \log ^2(x)\right ) \, dx+(2 \log (2)) \int \left (\frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} (-1-\log (2))}{x^3}-8 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \left (1-\frac {\log (2)}{2}\right )-16 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^2 \log (2)+32 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^4 \log (2)+16 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^5 \log (2)+4 e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x (-1+\log (4))+\frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} (4+\log (4))}{x^2}\right ) \, dx \\ & = -\left (2 \int \frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log ^2(x)}{x^3} \, dx\right )+4 \int \frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log ^2(x)}{x^2} \, dx+8 \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log ^2(x) \, dx+16 \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x \log ^2(x) \, dx-32 \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^2 \log ^2(x) \, dx+32 \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^5 \log ^2(x) \, dx+64 \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^4 \log ^2(x) \, dx+(64 \log (2)) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^2 \log (x) \, dx-(64 \log (2)) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^5 \log (x) \, dx-(128 \log (2)) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^4 \log (x) \, dx-(8 (2-\log (2)) \log (2)) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \, dx-\left (32 \log ^2(2)\right ) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^2 \, dx+\left (32 \log ^2(2)\right ) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^5 \, dx+\left (64 \log ^2(2)\right ) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x^4 \, dx-(2 \log (2) (1+\log (2))) \int \frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}}}{x^3} \, dx-(8 \log (2) (1-\log (4))) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x \, dx+(8 (2-\log (4))) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log (x) \, dx+(2 (1+\log (4))) \int \frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log (x)}{x^3} \, dx-(4 (2+\log (4))) \int \frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} \log (x)}{x^2} \, dx+(2 \log (2) (4+\log (4))) \int \frac {e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}}}{x^2} \, dx+(8 (1-\log (16))) \int e^{2 x^4+\frac {e^{2 x^4} \left (-1+2 x+2 x^2\right )^2 \log ^2\left (\frac {x}{2}\right )}{x^2}} x \log (x) \, dx \\ \end{align*}
\[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=\int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx \]
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Time = 0.09 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06
\[{\mathrm e}^{\frac {{\mathrm e}^{2 x^{4}} \left (2 x^{2}+2 x -1\right )^{2} \left (-\ln \left (x \right )+\ln \left (2\right )\right )^{2}}{x^{2}}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.74 \[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=e^{\left (\frac {{\left (4 \, x^{4} + 8 \, x^{3} - 4 \, x + 1\right )} e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2} - 2 \, {\left (4 \, x^{4} + 8 \, x^{3} - 4 \, x + 1\right )} e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right ) + {\left (4 \, x^{4} + 8 \, x^{3} - 4 \, x + 1\right )} e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2}}{x^{2}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (26) = 52\).
Time = 1.05 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.81 \[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=e^{\frac {\left (- 8 x^{4} - 16 x^{3} + 8 x - 2\right ) e^{2 x^{4}} \log {\left (2 \right )} \log {\left (x \right )} + \left (4 x^{4} + 8 x^{3} - 4 x + 1\right ) e^{2 x^{4}} \log {\left (x \right )}^{2} + \left (4 x^{4} + 8 x^{3} - 4 x + 1\right ) e^{2 x^{4}} \log {\left (2 \right )}^{2}}{x^{2}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 174 vs. \(2 (29) = 58\).
Time = 0.83 (sec) , antiderivative size = 174, normalized size of antiderivative = 5.61 \[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=e^{\left (4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2} - 8 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right ) + 4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2} + 8 \, x e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2} - 16 \, x e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right ) + 8 \, x e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2}}{x} + \frac {8 \, e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right )}{x} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2}}{x} + \frac {e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2}}{x^{2}} - \frac {2 \, e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right )}{x^{2}} + \frac {e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2}}{x^{2}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 174 vs. \(2 (29) = 58\).
Time = 0.63 (sec) , antiderivative size = 174, normalized size of antiderivative = 5.61 \[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=e^{\left (4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2} - 8 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right ) + 4 \, x^{2} e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2} + 8 \, x e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2} - 16 \, x e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right ) + 8 \, x e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2}}{x} + \frac {8 \, e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right )}{x} - \frac {4 \, e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2}}{x} + \frac {e^{\left (2 \, x^{4}\right )} \log \left (2\right )^{2}}{x^{2}} - \frac {2 \, e^{\left (2 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right )}{x^{2}} + \frac {e^{\left (2 \, x^{4}\right )} \log \left (x\right )^{2}}{x^{2}}\right )} \]
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Time = 9.21 (sec) , antiderivative size = 155, normalized size of antiderivative = 5.00 \[ \int \frac {e^{\frac {e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(2)+e^{2 x^4} \left (-2+8 x-16 x^3-8 x^4\right ) \log (2) \log (x)+e^{2 x^4} \left (1-4 x+8 x^3+4 x^4\right ) \log ^2(x)}{x^2}} \left (e^{2 x^4} \left (\left (-2+8 x-16 x^3-8 x^4\right ) \log (2)+\left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(2)\right )+e^{2 x^4} \left (2-8 x+16 x^3+8 x^4+\left (4-8 x-16 x^3-32 x^4+64 x^5-128 x^7-64 x^8\right ) \log (2)\right ) \log (x)+e^{2 x^4} \left (-2+4 x+8 x^3+16 x^4-32 x^5+64 x^7+32 x^8\right ) \log ^2(x)\right )}{x^3} \, dx=\frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^4}\,{\ln \left (2\right )}^2}{x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^4}\,{\ln \left (2\right )}^2}{x}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{2\,x^4}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^{2\,x^4}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^4}\,{\ln \left (x\right )}^2}{x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^4}\,{\ln \left (x\right )}^2}{x}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{2\,x^4}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^{2\,x^4}\,{\ln \left (2\right )}^2}}{x^{\frac {2\,{\mathrm {e}}^{2\,x^4}\,\ln \left (2\right )\,\left (4\,x^4+8\,x^3-4\,x+1\right )}{x^2}}} \]
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