Integrate,
$$ \int{({\sin{x}})^{101}\cdot \sin({99x}})\ dx $$
I have seen this Question and tried to proceed the same way but it doesn't work.
I also tried writing this as,
$$ \int{({\sin{x}})^{99}\cdot \sin({99x}}) - (\cos{x})^2 ({\sin{x}})^{99}\cdot \sin({99x}) $$
I was able to solve the first term using,
$$\sin{99x}=\sin({100x})\cos({x})-cos({100x})\sin({x})$$
But the second term is giving me problem. How should I proceed?