# Evaluate the integral \int \sin^4(3x) \cos(3x) \,dx

## Question:

Evaluate the integral {eq}\int \sin^4(3x) \cos(3x) \,dx {/eq}

## Integration in Calculus:

There are many techniques to solve integral problems. Sometimes trigonometric identities may be needed to do so.

To solve this problem, we'll use the trig-identity {eq}sin^2 (x) =1- cos^2 (x) {/eq}.

Next, we'll apply integration by substitution, which is also called u-substitution.

## Answer and Explanation:

## Answer and Explanation:

{eq}\displaystyle \int \sin^4(3x) \cos(3x) \,dx {/eq}

Apply u-substitution {eq}u = 3x \rightarrow \ du = 3 \ dx {/eq}

{eq...

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