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

Let . Then , so . Rewrite using and .
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.
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

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