Let . Find .

Differentiate .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Since is constant with respect to , the derivative of with respect to is .

Move to the left of .

Differentiate using the Power Rule which states that is where .

Multiply by .

Rewrite the problem using and .

Combine and .

Since is constant with respect to , move out of the integral.

By the Power Rule, the integral of with respect to is .

Simplify.

Simplify.

Combine and .

Multiply and .

Multiply by .

Replace all occurrences of with .

Reorder terms.

Evaluate integral of sin(3x)cos(3x) with respect to x