Find the most general antiderivative or indefinite integral. $$ \int \frac{\csc 6\theta}{\csc 6\theta - \sin 6\theta} d\theta $$
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The integral is: $$ I = \int \frac{\csc 6\theta}{\csc 6\theta - \sin 6\theta} d\theta $$ First, we can rewrite $\csc 6\theta$ in terms of $\sin 6\theta$. We know that $\csc x = \frac{1}{\sin x}$. So, $\csc 6\theta = \frac{1}{\sin 6\theta}$. Substitute this into Show more…
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