What is the integral of sin(x)cos^5(x) ?

The integral of sin(x)cos^5(x) is -(cos^6(x))/6+C

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integral of sin(x)cos^5(x)

\int sin (x) cos^{5} (x) d x

- \frac{cos ^{6} ( x )}{6} + C

Solution steps

\int sin (x) cos^{5} (x) d x

Apply u-substitution

= \int - u^{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{5} d u

Apply the Power Rule

= - \frac{u ^{6}}{6}

Substitute back

u = cos (x)

= - \frac{cos ^{6} ( x )}{6}

Add a constant to the solution

= - \frac{cos ^{6} ( x )}{6} + C

What is the integral of sin(x)cos^5(x) ?
The integral of sin(x)cos^5(x) is -(cos^6(x))/6+C