Evaluate the integral: {eq}\; \int (1 + \sin 5t)^9 \cos 5t \, \mathrm{d}t {/eq}.

Question:

Evaluate the integral: {eq}\; \int (1 + \sin 5t)^9 \cos 5t \, \mathrm{d}t {/eq}.

Indefinite Integrals:

Integration is the opposite of differentiation. When it comes to indefinite integrals, no limits of integration are given. To solve these problems, we apply different rules of integration to integrate a function. Integral of a function {eq}f(x) {/eq} is given by {eq}\int f(x)dx {/eq}.

Answer and Explanation: 1

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{eq}I=\; \int (1 + \sin 5t)^9 \cos 5t \, \mathrm{d}t {/eq}

Put {eq}1 + \sin 5t=u {/eq}

{eq}5\cos 5t dt=du {/eq}

{eq}\cos 5t...

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Integration Problems in Calculus: Solutions & Examples

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Chapter 13 / Lesson 13
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Learn what integration problems are. Discover how to find integration sums and how to solve integral calculus problems using calculus example problems.


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