cos-n-mx-dx-

Question Number 84246 by pew_247 last updated on 10/Mar/20

\int \cos^{n} m x d x =

Answered by TANMAY PANACEA last updated on 10/Mar/20

I_{n, m} = \int {c o s}^{n} m x d x = \int {c o s}^{n - 1} m x . c o s m x d x

{c o s}^{n - 1} m x . \frac{s i n m x}{m} + \int (n - 1) {c o s}^{n - 2} m x . m s i n m x . \frac{s i n m x}{m} d x

\frac{{c o s}^{n - 1} m x s i n m x}{m} + (n - 1) \int {c o s}^{n - 2} m x (1 - {c o s}^{2} m x)

I_{n, m} = \frac{{c o s}^{n - 1} m x . s i n m x}{m} + (n - 1) I_{n - 2, m} - (n - 1) I_{n, m}

I_{n, m} = \frac{{c o s}^{n - 1} m x . s i n m x}{m n} + \frac{n - 1}{n} I_{n - 2, m}

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