What is the integral of 9sin^2(x)cos(x) ?

The integral of 9sin^2(x)cos(x) is 3sin^3(x)+C

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integral of 9sin^2(x)cos(x)

\int 9 sin^{2} (x) cos (x) d x

3 sin^{3} (x) + C

Solution steps

\int 9 sin^{2} (x) cos (x) d x

Take the constant out:

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

= 9 \cdot \int sin^{2} (x) cos (x) d x

Apply u-substitution

: \int u^{2} d u

= 9 \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= 9 \cdot \frac{u ^{3}}{3}

Substitute back

u = sin (x)

= 9 \cdot \frac{sin ^{3} ( x )}{3}

Simplify

9 \cdot \frac{sin ^{3} ( x )}{3} : 3 sin^{3} (x)

= 3 sin^{3} (x)

Add a constant to the solution

= 3 sin^{3} (x) + C

f (x) = 4 x + 5

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

f (θ) = 2 sin (θ)

\int_{1}^{e} 2 x ln (x) d x

\int \frac{2 sin ( ln ( x ) )}{x} d x

What is the integral of 9sin^2(x)cos(x) ?
The integral of 9sin^2(x)cos(x) is 3sin^3(x)+C