# How to integrate cos^7 x*sinx?

justaguide | Certified Educator

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

Int [(cos x)^7 * sin...

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giorgiana1976 | Student

So, we'll have to calculate the indefinite integral of the function (cos x)^7*sin x.

Int (cos x)^7*sin x dx

We'll solve the indefinite integral using substitution technique.

We'll put cos x = t =>-sin x dx = dt

We'll raise to 7th power cos x:

(cos x)^7  = t^7

We'll re-write the integral:

-Int t^7 dt = -t^8/8 + c

We'll substitute t by cos x:

Int (cos x)^7*sin x dx = -(cos x)^8/8 + C

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