Evaluate the integral, using a trig identity and substitution.

{eq}\int \sin^5(x) \cos^2(x) dx {/eq}

Question:

Evaluate the integral, using a trig identity and substitution.

{eq}\int \sin^5(x) \cos^2(x) dx {/eq}

Integration By Substitution:

The first step is to convert the integral into a standard integral form. We need to use trigonometric identities to convert the integral into a simple integrable form. The following integral formula and other identities will guide all the way out.

{eq}\begin{align} \cos^2 x + \sin^2 x = 1\\ (a\pm b)^2&=a^2+b^2\pm 2ab \\ \displaystyle \int x^n\, dx&=\frac { x^{n+1}} {n+1}+C\\ \end{align} {/eq}

Where C is a constant of integration.

Answer and Explanation: 1

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Evaluate the integral, using a trig identity and substitution.

{eq}\int \sin^5(x) \cos^2(x) dx {/eq}

{eq}\begin{align} \int \cos^2 x \sin ^5 x dx...

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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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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