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

Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
The derivative of with respect to is .
Rewrite the problem using 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 .
Evaluate integral of sin(x)cos(cos(x)) with respect to x

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