I am trying to solve the following integral:
$\int \frac{\gamma F ^ {-3/2} + F ^ {-\beta/2}} {3\gamma F^ {-3/2} + \beta F^ {-\beta/2}} d\varphi$
where $\beta$, $\gamma$ are constant and $F$ is:
$F=1+\frac{\beta-3}{3}\bigg(2\gamma(\beta-1)e^{-(\frac{1+\beta}{\sqrt{6}})\varphi}+\frac{2}{3}(\beta-2)(\beta+3)e^{2(\frac{1-\beta}{\sqrt{6}})\varphi}\bigg)$
does anyone has a solution for this integration?