1. (Integration of Trigonometric Powers) Compute the following integrals: a. ( int sin ^{14}(5 x) cos ^{3}(5 x) d x )
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Notice that we have powers of sine and cosine. We can use the substitution method to simplify the integral. Let \( u = \sin(5x) \). Then, \( du = 5 \cos(5x) dx \) or \( \frac{du}{5} = \cos(5x) dx \). Show more…
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