Evaluate the indefinite integral.

{eq}\int \sin^3 x \cos^2 x dx {/eq}


Evaluate the indefinite integral.

{eq}\int \sin^3 x \cos^2 x dx {/eq}


Suppose that {eq}u=g(x) {/eq}. The integral {eq}\int f(g(x))g'(x)\, dx {/eq} is equal to {eq}\int f(u)\, du {/eq}. This is known as substitution and undoes a chain rule.

We will often combine this with algebra before or after the substitution in order to evaluate.

Answer and Explanation: 1

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We first recall that {eq}\sin^2 x+\cos^2 x=1 {/eq} or {eq}\sin^2 x=1-\cos^2 x {/eq}. This gives us

{eq}\begin{align} \int \sin^3 x\cos^2 x\,...

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Learn more about this topic:

How to Solve Integrals Using Substitution


Chapter 13 / Lesson 5

Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.

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