   Chapter 7.5, Problem 36E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 1 + sin x 1 + cos x d x

To determine

To find:

1+sinx1+cosxdx

Explanation

Formula used: 1. csc2xdx=-cotx

2. cscxdx=-lncscx+cotx

3. cotxdx=lnsinx

Calculations: Multiplying the numerator and denominator by (1-cosx), we get I as

I=1+sinx1-cosx1+cosx1-cosxdx=1-cosx+sinx-sinxcosxsin2xdx

Separating the above integral we get

I=1sin2xdx-cosxsin2xdx+1sinxdx

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