What is the integral of 3cos^2(x)sin(x) ?

The integral of 3cos^2(x)sin(x) is -cos^3(x)+C

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integral of 3cos^2(x)sin(x)

\int 3 cos^{2} (x) sin (x) d x

- cos^{3} (x) + C

Solution steps

\int 3 cos^{2} (x) sin (x) d x

Take the constant out:

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

= 3 \cdot \int cos^{2} (x) sin (x) d x

Apply u-substitution

= 3 \cdot \int - u^{2} d u

Take the constant out:

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

= 3 (- \int u^{2} d u)

Apply the Power Rule

= 3 (- \frac{u ^{3}}{3})

Substitute back

u = cos (x)

= 3 (- \frac{cos ^{3} ( x )}{3})

Simplify

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

= - cos^{3} (x)

Add a constant to the solution

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

What is the integral of 3cos^2(x)sin(x) ?
The integral of 3cos^2(x)sin(x) is -cos^3(x)+C