- #1
junt
- 18
- 1
Homework Statement
Can this function be integrated analytically?
##f=\exp \left(-\frac{e^{-2 \theta } \left(a \left(b^2 \left(e^{2 \theta }-1\right)^2 L^2+16\right)-32
\sqrt{a} e^{\theta }+16 e^{2 \theta }\right)}{b L^4}\right),##
where ##a##, ##b## and ##L## are some real positive constants.
Homework Equations
This is the integral I am looking at:
##I=\int_{-\infty}^{\infty}\exp \left(-\frac{e^{-2 \theta } \left(a \left(b^2 \left(e^{2 \theta }-1\right)^2 L^2+16\right)-32
\sqrt{a} e^{\theta }+16 e^{2 \theta }\right)}{b L^4}\right) d\theta##
The Attempt at a Solution
One can change the coordinates ##u## to ##e^{-\theta}##, but then Jacobian will be inverse in ##x##, as result introduced a pole at ##x=0##. Does anyone know a better solution to it?