Let . Find .

Rewrite.

Divide by .

Rewrite the problem using and .

Combine and .

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

Use the half–angle formula to rewrite as .

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

Multiply and .

Multiply by .

Split the single integral into multiple integrals.

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

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

Let . Find .

Rewrite.

Divide by .

Rewrite the problem using and .

Combine and .

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

The integral of with respect to is .

Simplify.

Replace all occurrences of with .

Replace all occurrences of with .

Replace all occurrences of with .

Simplify each term.

Multiply by .

Combine and .

Apply the distributive property.

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply .

Multiply and .

Multiply by .

Reorder terms.

Evaluate integral of sin(3x)^2 with respect to x