Integrand size = 289, antiderivative size = 35 \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=-x+\frac {e^4 \left (-5+e^{2 x}-x\right )}{2-4 \left (-e^x+x\right )^2 \log (x)} \]
[Out]
\[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=\int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+4 e^{4+x} x (5+x)+2 e^{4+2 x} \left (-5+x^2\right )-e^4 x \left (1+10 x+2 x^2\right )+2 \left (e^x-x\right ) x \left (4 e^x+2 e^{4+2 x} (-1+x)-4 x+e^4 (10+x)-e^{4+x} (9+2 x)\right ) \log (x)-8 \left (e^x-x\right )^4 x \log ^2(x)}{2 x \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx \\ & = \frac {1}{2} \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+4 e^{4+x} x (5+x)+2 e^{4+2 x} \left (-5+x^2\right )-e^4 x \left (1+10 x+2 x^2\right )+2 \left (e^x-x\right ) x \left (4 e^x+2 e^{4+2 x} (-1+x)-4 x+e^4 (10+x)-e^{4+x} (9+2 x)\right ) \log (x)-8 \left (e^x-x\right )^4 x \log ^2(x)}{x \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx \\ & = \frac {1}{2} \int \left (\frac {e^4-4 x \log ^2(x)}{2 x \log ^2(x)}+\frac {e^4 \left (1-5 \log (x)+2 e^x x \log (x)-x^2 \log (x)-9 x \log ^2(x)-2 e^x x \log ^2(x)-4 x^2 \log ^2(x)+2 e^x x^2 \log ^2(x)+2 x^3 \log ^2(x)\right )}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )}-\frac {e^4 \left (-1+10 \log (x)-4 e^x x \log (x)+2 x^2 \log (x)+20 x \log ^2(x)+4 e^x x \log ^2(x)+8 x^2 \log ^2(x)-12 e^x x^2 \log ^2(x)-40 e^x x \log ^3(x)+40 x^2 \log ^3(x)+32 e^x x^2 \log ^3(x)-32 x^3 \log ^3(x)+16 e^x x^3 \log ^3(x)-16 x^4 \log ^3(x)-8 e^x x^4 \log ^3(x)+8 x^5 \log ^3(x)\right )}{2 x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}\right ) \, dx \\ & = \frac {1}{4} \int \frac {e^4-4 x \log ^2(x)}{x \log ^2(x)} \, dx-\frac {1}{4} e^4 \int \frac {-1+10 \log (x)-4 e^x x \log (x)+2 x^2 \log (x)+20 x \log ^2(x)+4 e^x x \log ^2(x)+8 x^2 \log ^2(x)-12 e^x x^2 \log ^2(x)-40 e^x x \log ^3(x)+40 x^2 \log ^3(x)+32 e^x x^2 \log ^3(x)-32 x^3 \log ^3(x)+16 e^x x^3 \log ^3(x)-16 x^4 \log ^3(x)-8 e^x x^4 \log ^3(x)+8 x^5 \log ^3(x)}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\frac {1}{2} e^4 \int \frac {1-5 \log (x)+2 e^x x \log (x)-x^2 \log (x)-9 x \log ^2(x)-2 e^x x \log ^2(x)-4 x^2 \log ^2(x)+2 e^x x^2 \log ^2(x)+2 x^3 \log ^2(x)}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )} \, dx \\ & = \frac {1}{4} \int \left (-4+\frac {e^4}{x \log ^2(x)}\right ) \, dx-\frac {1}{4} e^4 \int \frac {-1+2 \left (5-2 e^x x+x^2\right ) \log (x)-4 x \left (-5-2 x+e^x (-1+3 x)\right ) \log ^2(x)-8 \left (e^x-x\right ) x \left (5-4 x-2 x^2+x^3\right ) \log ^3(x)}{x \log ^2(x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\frac {1}{2} e^4 \int \frac {-1-\left (-5+2 e^x x-x^2\right ) \log (x)-x \left (-9+2 e^x (-1+x)-4 x+2 x^2\right ) \log ^2(x)}{x \log ^2(x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )} \, dx \\ & = -x+\frac {1}{4} e^4 \int \frac {1}{x \log ^2(x)} \, dx-\frac {1}{4} e^4 \int \left (\frac {20}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {4 e^x}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {8 x}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {12 e^x x}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {1}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {4 e^x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {10}{x \log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {2 x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {40 e^x \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {40 x \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {32 e^x x \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {32 x^2 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {16 e^x x^2 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {16 x^3 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}-\frac {8 e^x x^3 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}+\frac {8 x^4 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}\right ) \, dx+\frac {1}{2} e^4 \int \left (-\frac {9}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)}-\frac {2 e^x}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)}-\frac {4 x}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)}+\frac {2 e^x x}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)}+\frac {2 x^2}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)}+\frac {1}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )}+\frac {2 e^x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )}-\frac {5}{x \log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )}-\frac {x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )}\right ) \, dx \\ & = -x+\frac {1}{4} e^4 \int \frac {1}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\frac {1}{4} e^4 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )-\frac {1}{2} e^4 \int \frac {x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\frac {1}{2} e^4 \int \frac {1}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )} \, dx-\frac {1}{2} e^4 \int \frac {x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )} \, dx-e^4 \int \frac {e^x}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+e^4 \int \frac {e^x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-e^4 \int \frac {e^x}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)} \, dx+e^4 \int \frac {e^x x}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)} \, dx+e^4 \int \frac {x^2}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)} \, dx+e^4 \int \frac {e^x}{\log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )} \, dx-\left (2 e^4\right ) \int \frac {x}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\left (2 e^4\right ) \int \frac {e^x x^3 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\left (2 e^4\right ) \int \frac {x^4 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\left (2 e^4\right ) \int \frac {x}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)} \, dx-\frac {1}{2} \left (5 e^4\right ) \int \frac {1}{x \log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\frac {1}{2} \left (5 e^4\right ) \int \frac {1}{x \log (x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )} \, dx+\left (3 e^4\right ) \int \frac {e^x x}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\left (4 e^4\right ) \int \frac {e^x x^2 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\left (4 e^4\right ) \int \frac {x^3 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\frac {1}{2} \left (9 e^4\right ) \int \frac {1}{-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)} \, dx-\left (5 e^4\right ) \int \frac {1}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\left (8 e^4\right ) \int \frac {e^x x \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\left (8 e^4\right ) \int \frac {x^2 \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\left (10 e^4\right ) \int \frac {e^x \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx-\left (10 e^4\right ) \int \frac {x \log (x)}{\left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx \\ & = -x-\frac {e^4}{4 \log (x)}+\frac {1}{4} e^4 \int \frac {1}{x \log ^2(x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\frac {1}{2} e^4 \int \frac {x}{\log (x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\frac {1}{2} e^4 \int \frac {1}{x \log ^2(x) \left (-1+2 \left (e^x-x\right )^2 \log (x)\right )} \, dx-\frac {1}{2} e^4 \int \frac {x}{\log (x) \left (-1+2 \left (e^x-x\right )^2 \log (x)\right )} \, dx-e^4 \int \frac {e^x}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+e^4 \int \frac {e^x}{\log (x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-e^4 \int \frac {e^x}{-1+2 \left (e^x-x\right )^2 \log (x)} \, dx+e^4 \int \frac {e^x x}{-1+2 \left (e^x-x\right )^2 \log (x)} \, dx+e^4 \int \frac {x^2}{-1+2 \left (e^x-x\right )^2 \log (x)} \, dx+e^4 \int \frac {e^x}{\log (x) \left (-1+2 \left (e^x-x\right )^2 \log (x)\right )} \, dx-\left (2 e^4\right ) \int \frac {x}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\left (2 e^4\right ) \int \frac {e^x x^3 \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\left (2 e^4\right ) \int \frac {x^4 \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\left (2 e^4\right ) \int \frac {x}{-1+2 \left (e^x-x\right )^2 \log (x)} \, dx-\frac {1}{2} \left (5 e^4\right ) \int \frac {1}{x \log (x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\frac {1}{2} \left (5 e^4\right ) \int \frac {1}{x \log (x) \left (-1+2 \left (e^x-x\right )^2 \log (x)\right )} \, dx+\left (3 e^4\right ) \int \frac {e^x x}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\left (4 e^4\right ) \int \frac {e^x x^2 \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\left (4 e^4\right ) \int \frac {x^3 \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\frac {1}{2} \left (9 e^4\right ) \int \frac {1}{-1+2 \left (e^x-x\right )^2 \log (x)} \, dx-\left (5 e^4\right ) \int \frac {1}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\left (8 e^4\right ) \int \frac {e^x x \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\left (8 e^4\right ) \int \frac {x^2 \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\left (10 e^4\right ) \int \frac {e^x \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx-\left (10 e^4\right ) \int \frac {x \log (x)}{\left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx \\ \end{align*}
Time = 0.23 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.14 \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=\frac {1}{2} \left (-2 x-\frac {e^4 \left (-5+e^{2 x}-x\right )}{-1+2 \left (e^x-x\right )^2 \log (x)}\right ) \]
[In]
[Out]
Time = 1.43 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.26
method | result | size |
risch | \(-x +\frac {\left (5+x -{\mathrm e}^{2 x}\right ) {\mathrm e}^{4}}{4 \,{\mathrm e}^{2 x} \ln \left (x \right )-8 x \,{\mathrm e}^{x} \ln \left (x \right )+4 x^{2} \ln \left (x \right )-2}\) | \(44\) |
parallelrisch | \(\frac {-8 x^{3} \ln \left (x \right )+16 x^{2} {\mathrm e}^{x} \ln \left (x \right )-8 \,{\mathrm e}^{2 x} \ln \left (x \right ) x -2 \,{\mathrm e}^{2 x} {\mathrm e}^{4}+2 x \,{\mathrm e}^{4}+10 \,{\mathrm e}^{4}+4 x}{8 \,{\mathrm e}^{2 x} \ln \left (x \right )-16 x \,{\mathrm e}^{x} \ln \left (x \right )+8 x^{2} \ln \left (x \right )-4}\) | \(75\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (33) = 66\).
Time = 0.38 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.31 \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=\frac {{\left (x + 5\right )} e^{12} + 2 \, x e^{8} - 4 \, {\left (x^{3} e^{8} - 2 \, x^{2} e^{\left (x + 8\right )} + x e^{\left (2 \, x + 8\right )}\right )} \log \left (x\right ) - e^{\left (2 \, x + 12\right )}}{2 \, {\left (2 \, {\left (x^{2} e^{8} - 2 \, x e^{\left (x + 8\right )} + e^{\left (2 \, x + 8\right )}\right )} \log \left (x\right ) - e^{8}\right )}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (26) = 52\).
Time = 0.23 (sec) , antiderivative size = 95, normalized size of antiderivative = 2.71 \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=- x - \frac {e^{4}}{4 \log {\left (x \right )}} + \frac {2 x^{2} e^{4} \log {\left (x \right )} - 4 x e^{4} e^{x} \log {\left (x \right )} + 2 x e^{4} \log {\left (x \right )} + 10 e^{4} \log {\left (x \right )} - e^{4}}{8 x^{2} \log {\left (x \right )}^{2} - 16 x e^{x} \log {\left (x \right )}^{2} + 8 e^{2 x} \log {\left (x \right )}^{2} - 4 \log {\left (x \right )}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (33) = 66\).
Time = 0.31 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.97 \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=-\frac {4 \, x^{3} \log \left (x\right ) - 8 \, x^{2} e^{x} \log \left (x\right ) - x {\left (e^{4} + 2\right )} + {\left (4 \, x \log \left (x\right ) + e^{4}\right )} e^{\left (2 \, x\right )} - 5 \, e^{4}}{2 \, {\left (2 \, x^{2} \log \left (x\right ) - 4 \, x e^{x} \log \left (x\right ) + 2 \, e^{\left (2 \, x\right )} \log \left (x\right ) - 1\right )}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 842 vs. \(2 (33) = 66\).
Time = 0.85 (sec) , antiderivative size = 842, normalized size of antiderivative = 24.06 \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=\text {Too large to display} \]
[In]
[Out]
Timed out. \[ \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx=\int -\frac {\left (8\,x\,{\mathrm {e}}^{4\,x}-32\,x^4\,{\mathrm {e}}^x-32\,x^2\,{\mathrm {e}}^{3\,x}+48\,x^3\,{\mathrm {e}}^{2\,x}+8\,x^5\right )\,{\ln \left (x\right )}^2+\left ({\mathrm {e}}^4\,\left (2\,x^3+20\,x^2\right )-{\mathrm {e}}^x\,\left ({\mathrm {e}}^4\,\left (4\,x^3+20\,x^2+20\,x\right )-16\,x^2\right )-{\mathrm {e}}^{2\,x}\,\left (8\,x-{\mathrm {e}}^4\,\left (4\,x^3+18\,x\right )\right )-8\,x^3+{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4\,\left (4\,x-4\,x^2\right )\right )\,\ln \left (x\right )+2\,x-2\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^4+{\mathrm {e}}^4\,\left (2\,x^3+10\,x^2+x\right )-{\mathrm {e}}^4\,{\mathrm {e}}^x\,\left (4\,x^2+20\,x\right )+4\,x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4\,\left (2\,x^2-10\right )}{\left (8\,x\,{\mathrm {e}}^{4\,x}-32\,x^4\,{\mathrm {e}}^x-32\,x^2\,{\mathrm {e}}^{3\,x}+48\,x^3\,{\mathrm {e}}^{2\,x}+8\,x^5\right )\,{\ln \left (x\right )}^2+\left (16\,x^2\,{\mathrm {e}}^x-8\,x\,{\mathrm {e}}^{2\,x}-8\,x^3\right )\,\ln \left (x\right )+2\,x} \,d x \]
[In]
[Out]