# Some big numbers

Calculus Level 4

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

If the indefinite integral above equals $\dfrac{\sin(ax) (\sin x)^b}{k} + C$ where $$a,b$$ and $$k$$ are constants and $$C$$ is the arbitrary constant of integration, find $$a+b+k$$.

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