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**Elvis** Say we want to find $\displaystyle \int\sin^m{x}\cos^n{x}\;{dx}$. Then we would make use of the identity $\displaystyle \cos^2{x}+\sin^2{x}= 1$, if either $\displaystyle m$ or $\displaystyle n$ is odd, and $\displaystyle \cos^2x = \dfrac{1+\cos{2x}}{2}$ and $\displaystyle \sin^2x = \dfrac{1-\cos{2x}}{2}$, if m and n are both even. But isn't this impractical when m and n are large? When want to find, for example, $\displaystyle \int\sin^{78}{x}\cos^{36}{x}\;{dx}$? Or am I missing some trick?