What is the integral of 18cos^5(x)sin(x) ?

The integral of 18cos^5(x)sin(x) is -3cos^6(x)+C

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integral of 18cos^5(x)sin(x)

\int 18 cos^{5} (x) sin (x) d x

- 3 cos^{6} (x) + C

Solution steps

\int 18 cos^{5} (x) sin (x) d x

Take the constant out:

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

= 18 \cdot \int cos^{5} (x) sin (x) d x

Apply u-substitution

= 18 \cdot \int - u^{5} d u

Take the constant out:

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

= 18 (- \int u^{5} d u)

Apply the Power Rule

= 18 (- \frac{u ^{6}}{6})

Substitute back

u = cos (x)

= 18 (- \frac{cos ^{6} ( x )}{6})

Simplify

18 (- \frac{cos ^{6} ( x )}{6}) : - 3 cos^{6} (x)

= - 3 cos^{6} (x)

Add a constant to the solution

= - 3 cos^{6} (x) + C

What is the integral of 18cos^5(x)sin(x) ?
The integral of 18cos^5(x)sin(x) is -3cos^6(x)+C