Integrand size = 197, antiderivative size = 31 \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=\frac {2 e^{2 x}}{x \left (-2+x+\frac {4 e^{-x}}{x (-3+\log (x))}\right )} \]
[Out]
\[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=\int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {4 e^{3 x} \left (2+9 \left (-2+e^x\right ) x-27 e^x x^2+9 e^x x^3-6 x \left (-1+e^x \left (1-3 x+x^2\right )\right ) \log (x)+e^x x \left (1-3 x+x^2\right ) \log ^2(x)\right )}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx \\ & = 4 \int \frac {e^{3 x} \left (2+9 \left (-2+e^x\right ) x-27 e^x x^2+9 e^x x^3-6 x \left (-1+e^x \left (1-3 x+x^2\right )\right ) \log (x)+e^x x \left (1-3 x+x^2\right ) \log ^2(x)\right )}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx \\ & = 4 \int \left (\frac {2 e^{3 x} \left (4+x-3 x^2-2 \log (x)+x^2 \log (x)\right )}{(-2+x) x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {e^{3 x} \left (1-3 x+x^2\right ) (-3+\log (x))}{(-2+x) x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}\right ) \, dx \\ & = 4 \int \frac {e^{3 x} \left (1-3 x+x^2\right ) (-3+\log (x))}{(-2+x) x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx+8 \int \frac {e^{3 x} \left (4+x-3 x^2-2 \log (x)+x^2 \log (x)\right )}{(-2+x) x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx \\ & = 4 \int \left (\frac {e^{3 x} (-3+\log (x))}{4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)}-\frac {e^{3 x} (-3+\log (x))}{2 (-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}-\frac {e^{3 x} (-3+\log (x))}{2 x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}\right ) \, dx+8 \int \left (\frac {e^{3 x} \left (4+x-3 x^2-2 \log (x)+x^2 \log (x)\right )}{2 (-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}-\frac {e^{3 x} \left (4+x-3 x^2-2 \log (x)+x^2 \log (x)\right )}{2 x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}\right ) \, dx \\ & = -\left (2 \int \frac {e^{3 x} (-3+\log (x))}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx\right )-2 \int \frac {e^{3 x} (-3+\log (x))}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx+4 \int \frac {e^{3 x} \left (4+x-3 x^2-2 \log (x)+x^2 \log (x)\right )}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-4 \int \frac {e^{3 x} \left (4+x-3 x^2-2 \log (x)+x^2 \log (x)\right )}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} (-3+\log (x))}{4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)} \, dx \\ & = -\left (2 \int \frac {e^{3 x} (-3+\log (x))}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx\right )-2 \int \left (-\frac {3 e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}+\frac {e^{3 x} \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}\right ) \, dx+4 \int \frac {e^{3 x} (-3+\log (x))}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx-4 \int \frac {e^{3 x} \left (4+x-3 x^2+\left (-2+x^2\right ) \log (x)\right )}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+4 \int \left (\frac {4 e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {e^{3 x} x}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}-\frac {3 e^{3 x} x^2}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}-\frac {2 e^{3 x} \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {e^{3 x} x^2 \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}\right ) \, dx \\ & = -\left (2 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx\right )-2 \int \left (-\frac {3 e^{3 x}}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}+\frac {e^{3 x} \log (x)}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )}\right ) \, dx+4 \int \frac {e^{3 x} x}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} x^2 \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-4 \int \left (\frac {e^{3 x}}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {4 e^{3 x}}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}-\frac {3 e^{3 x} x}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}-\frac {2 e^{3 x} \log (x)}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {e^{3 x} x \log (x)}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}\right ) \, dx+4 \int \left (-\frac {3 e^{3 x}}{4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)}+\frac {e^{3 x} \log (x)}{4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)}\right ) \, dx+6 \int \frac {e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx-8 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-12 \int \frac {e^{3 x} x^2}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+16 \int \frac {e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx \\ & = -\left (2 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx\right )-2 \int \frac {e^{3 x} \log (x)}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx+4 \int \frac {e^{3 x} x}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} x^2 \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-4 \int \frac {e^{3 x}}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-4 \int \frac {e^{3 x} x \log (x)}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} \log (x)}{4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)} \, dx+6 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx+6 \int \frac {e^{3 x}}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )} \, dx-8 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x} \log (x)}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-12 \int \frac {e^{3 x} x^2}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+12 \int \frac {e^{3 x} x}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-12 \int \frac {e^{3 x}}{4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)} \, dx+16 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-16 \int \frac {e^{3 x}}{x \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx \\ & = -\left (2 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx\right )-2 \int \frac {e^{3 x} \log (x)}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx-4 \int \frac {e^{3 x}}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-4 \int \frac {e^{3 x} x \log (x)}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} \log (x)}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx+4 \int \left (\frac {e^{3 x}}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {2 e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}\right ) \, dx+4 \int \left (\frac {2 e^{3 x} \log (x)}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {4 e^{3 x} \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {e^{3 x} x \log (x)}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}\right ) \, dx+6 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx+6 \int \frac {e^{3 x}}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx-8 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x} \log (x)}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+12 \int \frac {e^{3 x} x}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-12 \int \frac {e^{3 x}}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx-12 \int \left (\frac {2 e^{3 x}}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {4 e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}+\frac {e^{3 x} x}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2}\right ) \, dx+16 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-16 \int \frac {e^{3 x}}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx \\ & = -\left (2 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx\right )-2 \int \frac {e^{3 x} \log (x)}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx-4 \int \frac {e^{3 x}}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-4 \int \frac {e^{3 x} x \log (x)}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} \log (x)}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx+4 \int \frac {e^{3 x}}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+4 \int \frac {e^{3 x} x \log (x)}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+6 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx+6 \int \frac {e^{3 x}}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx-8 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x} \log (x)}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x} \log (x)}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+12 \int \frac {e^{3 x} x}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-12 \int \frac {e^{3 x}}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx-12 \int \frac {e^{3 x} x}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx+16 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-16 \int \frac {e^{3 x}}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+16 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-24 \int \frac {e^{3 x}}{\left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx-48 \int \frac {e^{3 x}}{(-2+x) \left (4+6 e^x x-3 e^x x^2-2 e^x x \log (x)+e^x x^2 \log (x)\right )^2} \, dx \\ & = -\left (2 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx\right )-2 \int \frac {e^{3 x} \log (x)}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx+4 \int \frac {e^{3 x} \log (x)}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx+6 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx+6 \int \frac {e^{3 x}}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )} \, dx+8 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x} \log (x)}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-8 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+8 \int \frac {e^{3 x} \log (x)}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-12 \int \frac {e^{3 x}}{4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)} \, dx+16 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-16 \int \frac {e^{3 x}}{x \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx+16 \int \frac {e^{3 x} \log (x)}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-24 \int \frac {e^{3 x}}{\left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx-48 \int \frac {e^{3 x}}{(-2+x) \left (4-3 e^x (-2+x) x+e^x (-2+x) x \log (x)\right )^2} \, dx \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.13 \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=\frac {4 e^{3 x} (-3+\log (x))}{8-6 e^x (-2+x) x+2 e^x (-2+x) x \log (x)} \]
[In]
[Out]
Time = 0.80 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35
method | result | size |
risch | \(\frac {2 \left (\ln \left (x \right )-3\right ) {\mathrm e}^{3 x}}{x^{2} {\mathrm e}^{x} \ln \left (x \right )-2 x \,{\mathrm e}^{x} \ln \left (x \right )-3 \,{\mathrm e}^{x} x^{2}+6 \,{\mathrm e}^{x} x +4}\) | \(42\) |
parallelrisch | \(\frac {2 \,{\mathrm e}^{3 x} \ln \left (x \right )-6 \,{\mathrm e}^{3 x}}{x^{2} {\mathrm e}^{x} \ln \left (x \right )-2 x \,{\mathrm e}^{x} \ln \left (x \right )-3 \,{\mathrm e}^{x} x^{2}+6 \,{\mathrm e}^{x} x +4}\) | \(48\) |
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39 \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=\frac {2 \, {\left (e^{\left (3 \, x\right )} \log \left (x\right ) - 3 \, e^{\left (3 \, x\right )}\right )}}{{\left (x^{2} - 2 \, x\right )} e^{x} \log \left (x\right ) - 3 \, {\left (x^{2} - 2 \, x\right )} e^{x} + 4} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 447 vs. \(2 (26) = 52\).
Time = 0.61 (sec) , antiderivative size = 447, normalized size of antiderivative = 14.42 \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=\frac {\left (- 8 x^{2} + 16 x\right ) e^{x} + \left (2 x^{4} \log {\left (x \right )} - 6 x^{4} - 8 x^{3} \log {\left (x \right )} + 24 x^{3} + 8 x^{2} \log {\left (x \right )} - 24 x^{2}\right ) e^{2 x}}{x^{6} \log {\left (x \right )} - 3 x^{6} - 6 x^{5} \log {\left (x \right )} + 18 x^{5} + 12 x^{4} \log {\left (x \right )} - 36 x^{4} - 8 x^{3} \log {\left (x \right )} + 24 x^{3}} - \frac {128}{4 x^{6} \log {\left (x \right )}^{2} - 24 x^{6} \log {\left (x \right )} + 36 x^{6} - 24 x^{5} \log {\left (x \right )}^{2} + 144 x^{5} \log {\left (x \right )} - 216 x^{5} + 48 x^{4} \log {\left (x \right )}^{2} - 288 x^{4} \log {\left (x \right )} + 432 x^{4} - 32 x^{3} \log {\left (x \right )}^{2} + 192 x^{3} \log {\left (x \right )} - 288 x^{3} + \left (x^{8} \log {\left (x \right )}^{3} - 9 x^{8} \log {\left (x \right )}^{2} + 27 x^{8} \log {\left (x \right )} - 27 x^{8} - 8 x^{7} \log {\left (x \right )}^{3} + 72 x^{7} \log {\left (x \right )}^{2} - 216 x^{7} \log {\left (x \right )} + 216 x^{7} + 24 x^{6} \log {\left (x \right )}^{3} - 216 x^{6} \log {\left (x \right )}^{2} + 648 x^{6} \log {\left (x \right )} - 648 x^{6} - 32 x^{5} \log {\left (x \right )}^{3} + 288 x^{5} \log {\left (x \right )}^{2} - 864 x^{5} \log {\left (x \right )} + 864 x^{5} + 16 x^{4} \log {\left (x \right )}^{3} - 144 x^{4} \log {\left (x \right )}^{2} + 432 x^{4} \log {\left (x \right )} - 432 x^{4}\right ) e^{x}} + \frac {32}{9 x^{6} - 54 x^{5} + 108 x^{4} - 72 x^{3} + \left (- 6 x^{6} + 36 x^{5} - 72 x^{4} + 48 x^{3}\right ) \log {\left (x \right )} + \left (x^{6} - 6 x^{5} + 12 x^{4} - 8 x^{3}\right ) \log {\left (x \right )}^{2}} \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.19 \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (\log \left (x\right ) - 3\right )} e^{\left (3 \, x\right )}}{{\left (3 \, x^{2} - {\left (x^{2} - 2 \, x\right )} \log \left (x\right ) - 6 \, x\right )} e^{x} - 4} \]
[In]
[Out]
none
Time = 0.33 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.52 \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=\frac {2 \, {\left (e^{\left (3 \, x\right )} \log \left (x\right ) - 3 \, e^{\left (3 \, x\right )}\right )}}{x^{2} e^{x} \log \left (x\right ) - 3 \, x^{2} e^{x} - 2 \, x e^{x} \log \left (x\right ) + 6 \, x e^{x} + 4} \]
[In]
[Out]
Timed out. \[ \int \frac {e^{3 x} (8-72 x)+e^{4 x} \left (36 x-108 x^2+36 x^3\right )+\left (24 e^{3 x} x+e^{4 x} \left (-24 x+72 x^2-24 x^3\right )\right ) \log (x)+e^{4 x} \left (4 x-12 x^2+4 x^3\right ) \log ^2(x)}{16 x+e^x \left (48 x^2-24 x^3\right )+e^{2 x} \left (36 x^3-36 x^4+9 x^5\right )+\left (e^x \left (-16 x^2+8 x^3\right )+e^{2 x} \left (-24 x^3+24 x^4-6 x^5\right )\right ) \log (x)+e^{2 x} \left (4 x^3-4 x^4+x^5\right ) \log ^2(x)} \, dx=-\int -\frac {{\mathrm {e}}^{4\,x}\,\left (4\,x^3-12\,x^2+4\,x\right )\,{\ln \left (x\right )}^2+\left (24\,x\,{\mathrm {e}}^{3\,x}-{\mathrm {e}}^{4\,x}\,\left (24\,x^3-72\,x^2+24\,x\right )\right )\,\ln \left (x\right )+{\mathrm {e}}^{4\,x}\,\left (36\,x^3-108\,x^2+36\,x\right )-{\mathrm {e}}^{3\,x}\,\left (72\,x-8\right )}{{\mathrm {e}}^{2\,x}\,\left (x^5-4\,x^4+4\,x^3\right )\,{\ln \left (x\right )}^2+\left (-{\mathrm {e}}^x\,\left (16\,x^2-8\,x^3\right )-{\mathrm {e}}^{2\,x}\,\left (6\,x^5-24\,x^4+24\,x^3\right )\right )\,\ln \left (x\right )+16\,x+{\mathrm {e}}^x\,\left (48\,x^2-24\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (9\,x^5-36\,x^4+36\,x^3\right )} \,d x \]
[In]
[Out]