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We need to determine the integral of (cos x)^7 * sin x.

Int [(cos x)^7 * sin x dx]

let cos x = u => - du = sin x dx

=> Int [ -u^7 du]

=> -u^8 / 8 + C

substitute u  = cos x

=> - (cos x)^8 / 8 + C

The required integral is - (cos x)^8 / 8 + C

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