What is the indefinite integral of the function cos^4x*sinx ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To evaluate the integral of the function, we'll have to use substitution method.

Let cos x = t .

We'll differentiate both sides:

-sin x dx = dt => sin x dx = -dt

`int` (cos x)^4*sin x dx = - `int` t^4 dt

`int` - ` ` t^4 dt = - t^5/5 + C

The indefinite integral of the function is `int` (cos x)^4*sin x dx = -(cos x)^5/5 + C

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