How to find the inverse of this complicated function?

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Hi I've been trying to figure out this algebra problem and have gotten nowhere. I'm trying to find the inverse function of this function.

$f(x)=\dfrac{c^\frac{3}{2}\sqrt{c-\frac{2k}{x}}x-ck\ln\left(\frac{\left|\sqrt{c-\frac{2k}{x}}-\sqrt{c}\right|}{\sqrt{c-\frac{2k}{x}}+\sqrt{c}}\right)}{c^\frac{5}{2}}$

I'm looking to find $f^{-1}(x)$

If it helps $f(x)=\int\frac{1}{\sqrt{\frac{-2k}{x}+c}} dx$

I can find the inverse functions of certain parts of the right side, but I'm unable to do it as a whole. I was wondering if this is even possible to solve!? Thanks!