I’m working through Bender and Orzag’s asymptotic methods and perturbation theory and I’m stuck on the following example:
Show that if $f(x)\sim a(x-x_o)^{-b}$ as $x\rightarrow x_0+$ then
$$\int_x fdx \sim [a/(1-b)](x-x_0)^{1-b}$$ as $x\rightarrow x_0$ if $b>0$ and the path of integration does not pass through $x_0$
There’s a couple more of these cases in the example. I’m not really sure how to start here. The only mention about integration in the main text is where the proof gets sent to this problem. I feel like I’m missing a tool I can tackle this with…
Thank you in advance.