For a project I'm working on I need to solve the following integral. Can anyone help me tackle this challenge?
The Integral: $$ \beta \int_{\pi}^{\pi/2} {i k^2 r e^{i \theta} + ikr^2 e^{2i\theta} + ir^3e^{3i\theta} \over cos({a \over 4} ( k + re^{i\theta}))} d\theta$$
Where $\beta$ , $k$ , $r$ , and $a$ are constants and all positive real numbers.
NOTE: k here actually equals $k_{max} = {2 \pi \over a}$
Also, $i$ is the imaginary variable
Thanks for the help!
UPDATE: initial integral: $$ \beta \int_0^{2\pi \over a} {k^2 \over cos({ka \over 4})} dk$$
The variable k here is the true variable. Note: in the first integral k = $k_{max}$