Integrand size = 103, antiderivative size = 28 \[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=e^{-7+x-\left (2 x+x \left (e^{3+x}+x\right )\right ) (2-\log (\log (\log (x))))} \] Output:
exp(x-7-((exp(3+x)+x)*x+2*x)*(2-ln(ln(ln(x)))))
Time = 0.13 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.25 \[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{x \left (2+e^{3+x}+x\right )}(\log (x)) \] Input:
Integrate[(E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2 + (2*x + E^(3 + x)*x + x^2) *Log[Log[Log[x]]])*(2 + E^(3 + x) + x + (-3 + E^(3 + x)*(-2 - 2*x) - 4*x)* Log[x]*Log[Log[x]] + (2 + 2*x + E^(3 + x)*(1 + x))*Log[x]*Log[Log[x]]*Log[ Log[Log[x]]]))/(Log[x]*Log[Log[x]]),x]
Output:
E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*Log[Log[x]]^(x*(2 + E^(3 + x) + x))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (x+e^{x+3}+\left (e^{x+3} (-2 x-2)-4 x-3\right ) \log (x) \log (\log (x))+\left (2 x+e^{x+3} (x+1)+2\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))+2\right ) \exp \left (-2 x^2+\left (x^2+e^{x+3} x+2 x\right ) \log (\log (\log (x)))-2 e^{x+3} x-3 x-7\right )}{\log (x) \log (\log (x))} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {(-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \exp \left (-2 x^2+\left (x^2+e^{x+3} x+2 x\right ) \log (\log (\log (x)))-2 e^{x+3} x-2 x-4\right )}{\log (x) \log (\log (x))}+\frac {(x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \exp \left (-2 x^2+\left (x^2+e^{x+3} x+2 x\right ) \log (\log (\log (x)))-2 e^{x+3} x-3 x-7\right )}{\log (x) \log (\log (x))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{-2 x^2-2 e^{x+3} x-2 x-4} (-2 x \log (x) \log (\log (x))-2 \log (x) \log (\log (x))+x \log (x) \log (\log (\log (x))) \log (\log (x))+\log (x) \log (\log (\log (x))) \log (\log (x))+1) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}+\frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} (x-4 x \log (x) \log (\log (x))+2 x \log (x) \log (\log (x)) \log (\log (\log (x)))-3 \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2) \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x))}{\log (x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{-2 x^2-2 e^{x+3} x-3 x-7} \log ^{x^2+\left (e^{x+3}+2\right ) x-1}(\log (x)) \left (x+e^{x+3}+\log (x) \log (\log (x)) \left (-4 x-2 e^{x+3} (x+1)+\left (e^{x+3}+2\right ) (x+1) \log (\log (\log (x)))-3\right )+2\right )}{\log (x)}dx\) |
Input:
Int[(E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2 + (2*x + E^(3 + x)*x + x^2)*Log[L og[Log[x]]])*(2 + E^(3 + x) + x + (-3 + E^(3 + x)*(-2 - 2*x) - 4*x)*Log[x] *Log[Log[x]] + (2 + 2*x + E^(3 + x)*(1 + x))*Log[x]*Log[Log[x]]*Log[Log[Lo g[x]]]))/(Log[x]*Log[Log[x]]),x]
Output:
$Aborted
Time = 22.39 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18
| method | result | size |
| risch | \(\ln \left (\ln \left (x \right )\right )^{\left ({\mathrm e}^{3+x}+x +2\right ) x} {\mathrm e}^{-7-2 \,{\mathrm e}^{3+x} x -2 x^{2}-3 x}\) | \(33\) |
| parallelrisch | \({\mathrm e}^{\left ({\mathrm e}^{3+x} x +x^{2}+2 x \right ) \ln \left (\ln \left (\ln \left (x \right )\right )\right )-2 \,{\mathrm e}^{3+x} x -2 x^{2}-3 x -7}\) | \(37\) |
Input:
int((((1+x)*exp(3+x)+2*x+2)*ln(x)*ln(ln(x))*ln(ln(ln(x)))+((-2-2*x)*exp(3+ x)-4*x-3)*ln(x)*ln(ln(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2+2*x)*ln(ln(ln( x)))-2*exp(3+x)*x-2*x^2-3*x-7)/ln(x)/ln(ln(x)),x,method=_RETURNVERBOSE)
Output:
ln(ln(x))^((exp(3+x)+x+2)*x)*exp(-7-2*exp(3+x)*x-2*x^2-3*x)
Time = 0.11 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=e^{\left (-2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + {\left (x^{2} + x e^{\left (x + 3\right )} + 2 \, x\right )} \log \left (\log \left (\log \left (x\right )\right )\right ) - 3 \, x - 7\right )} \] Input:
integrate((((1+x)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2 -2*x)*exp(3+x)-4*x-3)*log(x)*log(log(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2 +2*x)*log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x, alg orithm="fricas")
Output:
e^(-2*x^2 - 2*x*e^(x + 3) + (x^2 + x*e^(x + 3) + 2*x)*log(log(log(x))) - 3 *x - 7)
Time = 11.06 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=e^{- 2 x^{2} - 2 x e^{x + 3} - 3 x + \left (x^{2} + x e^{x + 3} + 2 x\right ) \log {\left (\log {\left (\log {\left (x \right )} \right )} \right )} - 7} \] Input:
integrate((((1+x)*exp(3+x)+2*x+2)*ln(x)*ln(ln(x))*ln(ln(ln(x)))+((-2-2*x)* exp(3+x)-4*x-3)*ln(x)*ln(ln(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x**2+2*x)*ln (ln(ln(x)))-2*exp(3+x)*x-2*x**2-3*x-7)/ln(x)/ln(ln(x)),x)
Output:
exp(-2*x**2 - 2*x*exp(x + 3) - 3*x + (x**2 + x*exp(x + 3) + 2*x)*log(log(l og(x))) - 7)
Time = 0.17 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54 \[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=e^{\left (x^{2} \log \left (\log \left (\log \left (x\right )\right )\right ) + x e^{\left (x + 3\right )} \log \left (\log \left (\log \left (x\right )\right )\right ) - 2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + 2 \, x \log \left (\log \left (\log \left (x\right )\right )\right ) - 3 \, x - 7\right )} \] Input:
integrate((((1+x)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2 -2*x)*exp(3+x)-4*x-3)*log(x)*log(log(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2 +2*x)*log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x, alg orithm="maxima")
Output:
e^(x^2*log(log(log(x))) + x*e^(x + 3)*log(log(log(x))) - 2*x^2 - 2*x*e^(x + 3) + 2*x*log(log(log(x))) - 3*x - 7)
\[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=\int { \frac {{\left ({\left ({\left (x + 1\right )} e^{\left (x + 3\right )} + 2 \, x + 2\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) \log \left (\log \left (\log \left (x\right )\right )\right ) - {\left (2 \, {\left (x + 1\right )} e^{\left (x + 3\right )} + 4 \, x + 3\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + x + e^{\left (x + 3\right )} + 2\right )} e^{\left (-2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + {\left (x^{2} + x e^{\left (x + 3\right )} + 2 \, x\right )} \log \left (\log \left (\log \left (x\right )\right )\right ) - 3 \, x - 7\right )}}{\log \left (x\right ) \log \left (\log \left (x\right )\right )} \,d x } \] Input:
integrate((((1+x)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2 -2*x)*exp(3+x)-4*x-3)*log(x)*log(log(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2 +2*x)*log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x, alg orithm="giac")
Output:
undef
Time = 3.16 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.36 \[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx={\ln \left (\ln \left (x\right )\right )}^{2\,x+x^2+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{-7}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-2\,x^2} \] Input:
int((exp(log(log(log(x)))*(2*x + x*exp(x + 3) + x^2) - 2*x*exp(x + 3) - 3* x - 2*x^2 - 7)*(x + exp(x + 3) - log(log(x))*log(x)*(4*x + exp(x + 3)*(2*x + 2) + 3) + log(log(x))*log(log(log(x)))*log(x)*(2*x + exp(x + 3)*(x + 1) + 2) + 2))/(log(log(x))*log(x)),x)
Output:
log(log(x))^(2*x + x^2 + x*exp(3)*exp(x))*exp(-3*x)*exp(-7)*exp(-2*x*exp(3 )*exp(x))*exp(-2*x^2)
\[ \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))} \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=\int \frac {\left (\left (\left (x +1\right ) {\mathrm e}^{x +3}+2 x +2\right ) \mathrm {log}\left (x \right ) \mathrm {log}\left (\mathrm {log}\left (x \right )\right ) \mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x \right )\right )\right )+\left (\left (-2-2 x \right ) {\mathrm e}^{x +3}-4 x -3\right ) \mathrm {log}\left (x \right ) \mathrm {log}\left (\mathrm {log}\left (x \right )\right )+{\mathrm e}^{x +3}+2+x \right ) {\mathrm e}^{\left ({\mathrm e}^{x +3} x +x^{2}+2 x \right ) \mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x \right )\right )\right )-2 \,{\mathrm e}^{x +3} x -2 x^{2}-3 x -7}}{\mathrm {log}\left (x \right ) \mathrm {log}\left (\mathrm {log}\left (x \right )\right )}d x \] Input:
int((((1+x)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2-2*x)* exp(3+x)-4*x-3)*log(x)*log(log(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2+2*x)* log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x)
Output:
int((((1+x)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2-2*x)* exp(3+x)-4*x-3)*log(x)*log(log(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2+2*x)* log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x)