For trigometric if the integrand inside the integral (i.e., the function to be integrated in theta )is ODD.
How do we approach the problem? is there a way ?
If the function can be transformed to this form :
$\displaystyle g(\theta) = \sin(a\theta)f(\cos(a\theta)) $
For finding the anti-derivative , we just sub.
$\displaystyle x = \cos(a\theta) ,~~ \sin(a\theta) ~ d\theta = -\frac{1}{a}dx$
$\displaystyle I = -\frac{1}{a} \int f(x) ~dx $
We can always find out such function but hardly transform it to that form ( not impossible )
For example ,
$\displaystyle g(\theta) = \sin^{2n+1}(\theta) $
we have $\displaystyle f(\cos(\theta)) = \sin^{2n}(\theta)$
so $\displaystyle f(x) = (1-x^2)^n $