   Chapter 7.R, Problem 37E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ ( cos x + sin x ) 2 cos 2 x   d x

To determine

To Find: (cosx+sinx)2cos2xdx

Explanation

Try to rewrite the integrand so that you can integrate it by using one of the known techniques of integration. For that purpose, write the integrand as shown below:

(cosx+sinx)2cos2x=(cos2x+sin2x+2sinxcosx)cos2xdx=(1+2sinxcosx)cos2xdx=(1+sin2x)cos2xdx

Substitute 1+sin2x=t and differentiate it with respect to x to get

2cos2xdx=dt

After substitution, the integral reduces to

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