Q:

Help with $\int{\sin(101x)\sin^{99}(x)}\,dx$

Here's one that is difficult to solve manually, what is the trick involved?
$$\int \sin(101x)\sin^{99}(x)\,dx$$

A:

This question has been asked several times before: 

Need help solving - $ \int (\sin 101x) \cdot\sin^{99}x\,dx $
Evaluate $\Im \bigg (\dfrac{1}{100\times 2^{100}}(e^{2\iota x} -1)^{100}\bigg )$
Integrate $\sin(101x)\cdot \sin^{99}x$

