Definite integral help I'm working on a physics problem and I got to the integral:
$$\int_0^\infty (a+b+x^2)^{-\frac{3}2} dx = \frac{1}{(a+b)}$$
I am just trying to understand how this is achieved. Because the indefinite integral yields
$$x*(a+b)^{-1}*(a+b+x^2)^{-\frac{1}2}$$
Evaluating this from 0 to $\infty$, to me, gives
$$\frac{\infty}{\sqrt{a+b+\infty^2}} - 0$$
Edit: corrected my math

The indefinite integral of $(C+x^2)^{-\frac{3}{2}}$ actually equals $\frac{x}{C\sqrt{C+x^2}}$. If we set $C=a+b$, the answer will coincide with yours.
I guess that in your approach you missed $x$ coming from deriving $x^2$ inside brackets.
