# Evaluate integral of cos(x)^2 with respect to x

Use the half-angle formula to rewrite as .

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

Split the single integral into multiple integrals.

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 .

Combine and .

Apply the distributive property.

Combine and .

Multiply .

Multiply and .

Multiply by .

Reorder terms.

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