Consider the definite integral The first step in evaluating this integral is to apply integration by parts: where = and where = Note: Use for .
After integrating by parts, we obtain the integral on the right hand side where = The most appropriate substitution to simplify this integral is where = Note: We are using as variable for angles instead of , since there is no standard way to type on a computer keyboard. After making this substitution and simplifying (using trig identities), we obtain the integral where = = = After evaluating this integral and plugging back into the integration by parts formula we obtain: =
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