Integrand size = 280, antiderivative size = 28 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=2 x+\left (\log (5)-4 \left (x^2+\log \left (e^{e^3}+\log (2+x)\right )\right )^2\right )^2 \]
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\[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=\int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx \\ & = \int \left (\frac {2 \left (2 e^{e^3}+e^{e^3} x+32 x^6+128 e^{e^3} x^7+64 e^{e^3} x^8-8 x^2 \log (5)-32 e^{e^3} x^3 \log (5)-16 e^{e^3} x^4 \log (5)+2 \log (2+x)+x \log (2+x)+128 x^7 \log (2+x)+64 x^8 \log (2+x)-32 x^3 \log (5) \log (2+x)-16 x^4 \log (5) \log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {16 \left (12 x^4-\log (5)\right ) \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {192 x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {64 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx \\ & = 2 \int \frac {2 e^{e^3}+e^{e^3} x+32 x^6+128 e^{e^3} x^7+64 e^{e^3} x^8-8 x^2 \log (5)-32 e^{e^3} x^3 \log (5)-16 e^{e^3} x^4 \log (5)+2 \log (2+x)+x \log (2+x)+128 x^7 \log (2+x)+64 x^8 \log (2+x)-32 x^3 \log (5) \log (2+x)-16 x^4 \log (5) \log (2+x)}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+16 \int \frac {\left (12 x^4-\log (5)\right ) \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+64 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+192 \int \frac {x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx \\ & = 2 \int \frac {32 x^6-8 x^2 \log (5)+e^{e^3} (2+x) \left (1+64 x^7-16 x^3 \log (5)\right )+(2+x) \left (1+64 x^7-16 x^3 \log (5)\right ) \log (2+x)}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+16 \int \frac {\left (12 x^4-\log (5)\right ) \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+64 \int \frac {\left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+192 \int \frac {x^2 \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx \\ & = 2 \int \left (1+64 x^7-16 x^3 \log (5)+\frac {8 x^2 \left (4 x^4-\log (5)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+16 \int \left (-\frac {96 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {48 x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}-\frac {24 x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {12 x^3 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}-\frac {(-192+\log (5)) \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+64 \int \left (\frac {\log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {4 e^{e^3} x \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {2 e^{e^3} x^2 \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {4 x \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}+\frac {2 x^2 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+192 \int \left (-\frac {2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {4 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx \\ & = 2 x+16 x^8-8 x^4 \log (5)+16 \int \frac {x^2 \left (4 x^4-\log (5)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+64 \int \frac {\log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+128 \int \frac {x^2 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+192 \int \frac {x^3 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+192 \int \frac {x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+256 \int \frac {x \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx-384 \int \frac {x^2 \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx-384 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+768 \int \frac {x \left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+768 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx-1536 \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+\left (128 e^{e^3}\right ) \int \frac {x^2 \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+\left (256 e^{e^3}\right ) \int \frac {x \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx+(16 (192-\log (5))) \int \frac {\left (1+4 e^{e^3} x+2 e^{e^3} x^2+4 x \log (2+x)+2 x^2 \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx \\ & = 2 x+16 x^8-8 x^4 \log (5)+16 \log ^4\left (e^{e^3}+\log (2+x)\right )+16 \int \left (-\frac {32 x^2}{e^{e^3}+\log (2+x)}+\frac {16 x^3}{e^{e^3}+\log (2+x)}-\frac {8 x^4}{e^{e^3}+\log (2+x)}+\frac {4 x^5}{e^{e^3}+\log (2+x)}-\frac {128 \left (1-\frac {\log (5)}{64}\right )}{e^{e^3}+\log (2+x)}-\frac {x (-64+\log (5))}{e^{e^3}+\log (2+x)}-\frac {4 (-64+\log (5))}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+128 \int \left (-\frac {2 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {x \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {4 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+192 \int \frac {x^3 \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+192 \int \frac {x \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+256 \int \left (\frac {\log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}-\frac {2 \log (2+x) \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx-384 \int \frac {x^2 \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx-384 \int \frac {\left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+768 \int \frac {x \left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+768 \int \frac {\left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx-1536 \int \frac {\left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)} \, dx+\left (128 e^{e^3}\right ) \int \left (-\frac {2 \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {x \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}+\frac {4 \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+\left (256 e^{e^3}\right ) \int \left (\frac {\log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3}+\log (2+x)}-\frac {2 \log ^3\left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )}\right ) \, dx+(16 (192-\log (5))) \int \frac {\left (1+2 e^{e^3} x (2+x)+2 x (2+x) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )}{(2+x) \left (e^{e^3}+\log (2+x)\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(100\) vs. \(2(28)=56\).
Time = 0.25 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.57 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=2 \left (x+8 x^8-4 x^4 \log (5)+8 x^2 \left (4 x^4-\log (5)\right ) \log \left (e^{e^3}+\log (2+x)\right )+4 \left (12 x^4-\log (5)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+32 x^2 \log ^3\left (e^{e^3}+\log (2+x)\right )+8 \log ^4\left (e^{e^3}+\log (2+x)\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(90\) vs. \(2(41)=82\).
Time = 4.78 (sec) , antiderivative size = 91, normalized size of antiderivative = 3.25
method | result | size |
risch | \(16 \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{4}+64 x^{2} \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{3}+\left (96 x^{4}-8 \ln \left (5\right )\right ) \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{2}+\left (64 x^{6}-16 x^{2} \ln \left (5\right )\right ) \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )+16 x^{8}-8 x^{4} \ln \left (5\right )+2 x\) | \(91\) |
parallelrisch | \(16 x^{8}+64 \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right ) x^{6}+96 \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{2} x^{4}-8 x^{4} \ln \left (5\right )+64 x^{2} \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{3}-16 \ln \left (5\right ) \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right ) x^{2}+16 \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{4}-8 \ln \left (5\right ) \ln \left (\ln \left (2+x \right )+{\mathrm e}^{{\mathrm e}^{3}}\right )^{2}-8+2 x\) | \(108\) |
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Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (28) = 56\).
Time = 0.34 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.29 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=16 \, x^{8} - 8 \, x^{4} \log \left (5\right ) + 64 \, x^{2} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{3} + 16 \, \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{4} + 8 \, {\left (12 \, x^{4} - \log \left (5\right )\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} + 16 \, {\left (4 \, x^{6} - x^{2} \log \left (5\right )\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 2 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (27) = 54\).
Time = 0.45 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.54 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=16 x^{8} - 8 x^{4} \log {\left (5 \right )} + 64 x^{2} \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )}^{3} + 2 x + \left (96 x^{4} - 8 \log {\left (5 \right )}\right ) \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )}^{2} + \left (64 x^{6} - 16 x^{2} \log {\left (5 \right )}\right ) \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )} + 16 \log {\left (\log {\left (x + 2 \right )} + e^{e^{3}} \right )}^{4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (28) = 56\).
Time = 0.35 (sec) , antiderivative size = 111, normalized size of antiderivative = 3.96 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=16 \, x^{8} - 8 \, x^{4} \log \left (5\right ) + 64 \, x^{2} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{3} + 16 \, \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{4} + 8 \, {\left (12 \, x^{4} - \log \left (5\right )\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} + 4 \, {\left (16 \, x^{6} - 4 \, x^{2} \log \left (5\right ) - e^{\left (e^{3}\right )}\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 4 \, e^{\left (e^{3}\right )} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 2 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (28) = 56\).
Time = 0.46 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.79 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=16 \, x^{8} + 64 \, x^{6} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 96 \, x^{4} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} - 8 \, x^{4} \log \left (5\right ) + 64 \, x^{2} \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{3} - 16 \, x^{2} \log \left (5\right ) \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right ) + 16 \, \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{4} - 8 \, \log \left (5\right ) \log \left (e^{\left (e^{3}\right )} + \log \left (x + 2\right )\right )^{2} + 2 \, x \]
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Time = 15.82 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.29 \[ \int \frac {64 x^6-16 x^2 \log (5)+e^{e^3} \left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right )+\left (4+2 x+256 x^7+128 x^8+\left (-64 x^3-32 x^4\right ) \log (5)\right ) \log (2+x)+\left (192 x^4-16 \log (5)+e^{e^3} \left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right )+\left (768 x^5+384 x^6+\left (-64 x-32 x^2\right ) \log (5)\right ) \log (2+x)\right ) \log \left (e^{e^3}+\log (2+x)\right )+\left (192 x^2+e^{e^3} \left (768 x^3+384 x^4\right )+\left (768 x^3+384 x^4\right ) \log (2+x)\right ) \log ^2\left (e^{e^3}+\log (2+x)\right )+\left (64+e^{e^3} \left (256 x+128 x^2\right )+\left (256 x+128 x^2\right ) \log (2+x)\right ) \log ^3\left (e^{e^3}+\log (2+x)\right )}{e^{e^3} (2+x)+(2+x) \log (2+x)} \, dx=2\,x+16\,{\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )}^4+64\,x^2\,{\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )}^3-\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )\,\left (16\,x^2\,\ln \left (5\right )-64\,x^6\right )-8\,x^4\,\ln \left (5\right )+16\,x^8-{\ln \left (\ln \left (x+2\right )+{\mathrm {e}}^{{\mathrm {e}}^3}\right )}^2\,\left (8\,\ln \left (5\right )-96\,x^4\right ) \]
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