(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use

1) [itex]\frac{1}{2\pi}\int\limits_{-\pi}^{\pi} \frac{r_0^2 - r^2}{r_0^2 - 2rr_0cos(\theta-t) + r^2} dt = 1[/itex]

to compute the integral:

2) [itex]\int\limits_{-\pi}^{\pi} \left[1 - acos(x) \right]^{-1} dx[/itex]

for [itex]0<a<1[/itex]

[/itex].

3. The attempt at a solution

I looked on Wolfram for help. I did a tan substitution,

[itex]u = tan\left(\frac{x}{2}\right)[/itex]

and simplified

[itex]\int\limits_{-\pi}^{\pi} \left[1 - acos(x) \right]^{-1} dx \rightarrow \int\limits_{-\pi}^{\pi} \frac{2}{u^2+1-a+au^2}dx[/itex]

It kind of looks like 1)...? I am pretty confused.

Thanks in advance!

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# Poisson integral formula to solve other integrals

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