Integrand size = 150, antiderivative size = 28 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^5+e^{\left (-1+\left (-2+e^x (5-x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2} \]
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\[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=\int \frac {\exp \left (1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right ) \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\left (1+2 \log \left (\frac {3 x}{2}\right )-5 e^x \log \left (\frac {3 x}{2}\right )+e^x x \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = \int \frac {2 \exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (2+e^x (-5+x)+\left (4+e^{2 x} (-5+x)^2+e^x \left (-20+x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+e^x \left (2+e^x (-5+x)\right ) (-4+x) x \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = 2 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (2+e^x (-5+x)+\left (4+e^{2 x} (-5+x)^2+e^x \left (-20+x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+e^x \left (2+e^x (-5+x)\right ) (-4+x) x \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = 2 \int \left (\frac {2 \exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (1+2 \log \left (\frac {3 x}{2}\right )\right )}{x}+\frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x) \log \left (\frac {3 x}{2}\right ) \left (-5+x-4 x \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )\right )}{x}+\frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-5+x-20 \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )-8 x \log ^2\left (\frac {3 x}{2}\right )+2 x^2 \log ^2\left (\frac {3 x}{2}\right )\right )}{x}\right ) \, dx \\ & = 2 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x) \log \left (\frac {3 x}{2}\right ) \left (-5+x-4 x \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )\right )}{x} \, dx+2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-5+x-20 \log \left (\frac {3 x}{2}\right )+x^2 \log \left (\frac {3 x}{2}\right )-8 x \log ^2\left (\frac {3 x}{2}\right )+2 x^2 \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (1+2 \log \left (\frac {3 x}{2}\right )\right )}{x} \, dx \\ & = 2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-5+x+\left (-20+x^2\right ) \log \left (\frac {3 x}{2}\right )+2 (-4+x) x \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx+2 \int \left (\frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)^2 \log \left (\frac {3 x}{2}\right )}{x}+\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (20-9 x+x^2\right ) \log ^2\left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \left (\frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x}+\frac {2 \exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x}\right ) \, dx \\ & = 2 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)^2 \log \left (\frac {3 x}{2}\right )}{x} \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (20-9 x+x^2\right ) \log ^2\left (\frac {3 x}{2}\right ) \, dx+2 \int \left (\frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)}{x}+\frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-20+x^2\right ) \log \left (\frac {3 x}{2}\right )}{x}+2 \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-4+x) \log ^2\left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx \\ & = 2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-5+x)}{x} \, dx+2 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \left (-20+x^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx+2 \int \left (-10 \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )+\frac {25 \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x}+\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+4 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) (-4+x) \log ^2\left (\frac {3 x}{2}\right ) \, dx+4 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \left (20-18 x+4 x^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx \\ & = 2 \int \left (\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )-\frac {5 \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x}\right ) \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+2 \int \left (-\frac {20 \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x}+\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right )\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+4 \text {Subst}\left (\int \left (20 \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x)-18 \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x)+4 \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x^2 \log ^2(3 x)\right ) \, dx,x,\frac {x}{2}\right )+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx+8 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) (-4+2 x) \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-20 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right ) \, dx+50 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx \\ & = 2 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \, dx+2 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx+8 \text {Subst}\left (\int \left (-4 \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x)+2 \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x)\right ) \, dx,x,\frac {x}{2}\right )-10 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+16 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x^2 \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-40 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-40 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log (3 x) \, dx,x,\frac {x}{2}\right )+50 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-72 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+80 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right ) \\ & = 2 \int \exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+2 \int \exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) x \log \left (\frac {3 x}{2}\right ) \, dx+4 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+4 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \, dx,x,\frac {x}{2}\right )+8 \int \frac {\exp \left (\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-10 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right )}{x} \, dx+16 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+16 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x^2 \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-32 \text {Subst}\left (\int \exp \left (2 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right )-40 \int \frac {\exp \left (x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-40 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log (3 x) \, dx,x,\frac {x}{2}\right )+50 \int \frac {\exp \left (2 x+\left (1+\left (2+e^x (-5+x)\right ) \log \left (\frac {3 x}{2}\right )\right )^2\right ) \log \left (\frac {3 x}{2}\right )}{x} \, dx-72 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) x \log ^2(3 x) \, dx,x,\frac {x}{2}\right )+80 \text {Subst}\left (\int \exp \left (4 x+\left (1+\left (2+e^{2 x} (-5+2 x)\right ) \log (3 x)\right )^2\right ) \log ^2(3 x) \, dx,x,\frac {x}{2}\right ) \\ \end{align*}
\[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=\int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx \]
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Leaf count of result is larger than twice the leaf count of optimal. \(48\) vs. \(2(23)=46\).
Time = 241.78 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75
method | result | size |
parallelrisch | \({\mathrm e}^{\left (\left (x^{2}-10 x +25\right ) {\mathrm e}^{2 x}+\left (4 x -20\right ) {\mathrm e}^{x}+4\right ) \ln \left (\frac {3 x}{2}\right )^{2}+\left (\left (2 x -10\right ) {\mathrm e}^{x}+4\right ) \ln \left (\frac {3 x}{2}\right )+1}\) | \(49\) |
risch | \(\left (\frac {3 x}{2}\right )^{2 \,{\mathrm e}^{x} x -10 \,{\mathrm e}^{x}+4} {\mathrm e}^{\ln \left (\frac {3 x}{2}\right )^{2} {\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{x} \ln \left (\frac {3 x}{2}\right )^{2} x -10 \ln \left (\frac {3 x}{2}\right )^{2} {\mathrm e}^{2 x} x -20 \,{\mathrm e}^{x} \ln \left (\frac {3 x}{2}\right )^{2}+25 \ln \left (\frac {3 x}{2}\right )^{2} {\mathrm e}^{2 x}+4 \ln \left (\frac {3 x}{2}\right )^{2}+1}\) | \(88\) |
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Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (21) = 42\).
Time = 0.29 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^{\left ({\left ({\left (x^{2} - 10 \, x + 25\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x - 5\right )} e^{x} + 4\right )} \log \left (\frac {3}{2} \, x\right )^{2} + 2 \, {\left ({\left (x - 5\right )} e^{x} + 2\right )} \log \left (\frac {3}{2} \, x\right ) + 1\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (22) = 44\).
Time = 1.13 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^{\left (\left (2 x - 10\right ) e^{x} + 4\right ) \log {\left (\frac {3 x}{2} \right )} + \left (\left (4 x - 20\right ) e^{x} + \left (x^{2} - 10 x + 25\right ) e^{2 x} + 4\right ) \log {\left (\frac {3 x}{2} \right )}^{2} + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 388 vs. \(2 (21) = 42\).
Time = 2.04 (sec) , antiderivative size = 388, normalized size of antiderivative = 13.86 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=81 \cdot 2^{-8 \, \log \left (3\right ) - 4} x^{4} e^{\left (x^{2} e^{\left (2 \, x\right )} \log \left (3\right )^{2} - 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (2\right ) + x^{2} e^{\left (2 \, x\right )} \log \left (2\right )^{2} + 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (x\right ) - 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (2\right ) \log \left (x\right ) + x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 10 \, x e^{\left (2 \, x\right )} \log \left (3\right )^{2} + 4 \, x e^{x} \log \left (3\right )^{2} + 20 \, x e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (2\right ) - 8 \, x e^{x} \log \left (3\right ) \log \left (2\right ) - 10 \, x e^{\left (2 \, x\right )} \log \left (2\right )^{2} + 4 \, x e^{x} \log \left (2\right )^{2} - 20 \, x e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (x\right ) + 8 \, x e^{x} \log \left (3\right ) \log \left (x\right ) + 20 \, x e^{\left (2 \, x\right )} \log \left (2\right ) \log \left (x\right ) - 8 \, x e^{x} \log \left (2\right ) \log \left (x\right ) - 10 \, x e^{\left (2 \, x\right )} \log \left (x\right )^{2} + 4 \, x e^{x} \log \left (x\right )^{2} + 2 \, x e^{x} \log \left (3\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (3\right )^{2} - 20 \, e^{x} \log \left (3\right )^{2} - 2 \, x e^{x} \log \left (2\right ) - 50 \, e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (2\right ) + 40 \, e^{x} \log \left (3\right ) \log \left (2\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (2\right )^{2} - 20 \, e^{x} \log \left (2\right )^{2} + 2 \, x e^{x} \log \left (x\right ) + 50 \, e^{\left (2 \, x\right )} \log \left (3\right ) \log \left (x\right ) - 40 \, e^{x} \log \left (3\right ) \log \left (x\right ) - 50 \, e^{\left (2 \, x\right )} \log \left (2\right ) \log \left (x\right ) + 40 \, e^{x} \log \left (2\right ) \log \left (x\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 20 \, e^{x} \log \left (x\right )^{2} - 10 \, e^{x} \log \left (3\right ) + 4 \, \log \left (3\right )^{2} + 10 \, e^{x} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 10 \, e^{x} \log \left (x\right ) + 8 \, \log \left (3\right ) \log \left (x\right ) - 8 \, \log \left (2\right ) \log \left (x\right ) + 4 \, \log \left (x\right )^{2} + 1\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (21) = 42\).
Time = 1.96 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.36 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=e^{\left (x^{2} e^{\left (2 \, x\right )} \log \left (\frac {3}{2} \, x\right )^{2} - 10 \, x e^{\left (2 \, x\right )} \log \left (\frac {3}{2} \, x\right )^{2} + 4 \, x e^{x} \log \left (\frac {3}{2} \, x\right )^{2} + 2 \, x e^{x} \log \left (\frac {3}{2} \, x\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (\frac {3}{2} \, x\right )^{2} - 20 \, e^{x} \log \left (\frac {3}{2} \, x\right )^{2} - 10 \, e^{x} \log \left (\frac {3}{2} \, x\right ) + 4 \, \log \left (\frac {3}{2} \, x\right )^{2} + 4 \, \log \left (\frac {3}{2} \, x\right ) + 1\right )} \]
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Time = 13.37 (sec) , antiderivative size = 429, normalized size of antiderivative = 15.32 \[ \int \frac {e^{1+\left (4+e^x (-10+2 x)\right ) \log \left (\frac {3 x}{2}\right )+\left (4+e^x (-20+4 x)+e^{2 x} \left (25-10 x+x^2\right )\right ) \log ^2\left (\frac {3 x}{2}\right )} \left (4+e^x (-10+2 x)+\left (8+e^x \left (-40+2 x^2\right )+e^{2 x} \left (50-20 x+2 x^2\right )\right ) \log \left (\frac {3 x}{2}\right )+\left (e^x \left (-16 x+4 x^2\right )+e^{2 x} \left (40 x-18 x^2+2 x^3\right )\right ) \log ^2\left (\frac {3 x}{2}\right )\right )}{x} \, dx=\frac {81\,2^{40\,{\mathrm {e}}^x\,\ln \left (3\right )}\,2^{10\,{\mathrm {e}}^x}\,2^{20\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,3^{2\,x\,{\mathrm {e}}^x}\,x^{20\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )}\,x^{40\,{\mathrm {e}}^x\,\ln \left (2\right )}\,x^{2\,x\,{\mathrm {e}}^x}\,x^{8\,\ln \left (3\right )}\,x^{2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,x^4\,x^{50\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,x^{8\,x\,{\mathrm {e}}^x\,\ln \left (3\right )}\,{\mathrm {e}}^{4\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-10\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{-10\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{25\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2}\,\mathrm {e}\,{\mathrm {e}}^{-20\,{\mathrm {e}}^x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{-20\,{\mathrm {e}}^x\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{4\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{4\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-10\,x\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{25\,{\mathrm {e}}^{2\,x}\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{25\,{\mathrm {e}}^{2\,x}\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^x\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-20\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2}}{16\,2^{2\,x\,{\mathrm {e}}^x}\,2^{8\,\ln \left (3\right )}\,2^{2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,2^{50\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,2^{8\,x\,{\mathrm {e}}^x\,\ln \left (3\right )}\,3^{10\,{\mathrm {e}}^x}\,x^{10\,{\mathrm {e}}^x}\,x^{20\,x\,{\mathrm {e}}^{2\,x}\,\ln \left (3\right )}\,x^{40\,{\mathrm {e}}^x\,\ln \left (3\right )}\,x^{8\,\ln \left (2\right )}\,x^{2\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )}\,x^{50\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )}\,x^{8\,x\,{\mathrm {e}}^x\,\ln \left (2\right )}} \]
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