   Chapter 7.2, Problem 15E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ cot x   cos 2 x   d x

To determine

To evaluate: The trigonometric integral cotxcos2xdx

Explanation

Trigonometric integral of the form sinmxcosnxdx can be solved using strategies depending on whether m and n are odd or even.

Formula used:

When power of cosine in the integral is odd, save one cosine factor and use the identity cos2x=1sin2x to rewrite other terms in sine function form:

sinmxcos2k+1xdx=sinmx(1sin2x)kcosxdx

Then, use the substitution u=sinx

Given:

The integral, cotxcos2xdx.

Calculation:

Substitute for cot x as cosxsinx in the given integral:

cotxcos2xdx=cosxsinxcos2xdx=cos3xsinxdx

Rewrite the integral in terms of sine, saving one cosine term:

cos3xsinxd

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