Stuck on an integration question… $$\int x^{-\frac{1}{2}}\cosh^{-1}(\frac{x}{2}+1)dx$$
The answer I should get is $$2x^{\frac{1}{2}}\cosh^{-1}(\frac{x}{2}+1)-4(x+4)^{\frac{1}{2}}$$
but I keep going wrong.
Can someone show me how to get this solution? 
Thanks.

The form of the answer suggests integration by parts with the choice $$u = \cosh^{-1} \left( \frac{x}{2} + 1 \right), \quad dv = x^{-1/2} \, dx.$$  Then compute the derivative $$du = \ldots?$$ and the integral $$v = \ldots?$$  If you have trouble computing $du$, you can obtain it by writing $$x = \cosh u, \quad \frac{dx}{du} = \sinh u,$$ hence $$\frac{du}{dx} = \frac{1}{\sinh u} = \ldots.$$
