   Chapter 7.4, Problem 44E

Chapter
Section
Textbook Problem

# Make a substitution to express the integrand as a rational function and then evaluate the integral. ∫ d x ( 1 + x ) 2

To determine

Make a substitution to express the integrand as a rational function and then evaluate the integral dx(1+x)2

Explanation

Calculation: Put x=t12xdx=dtdx=2tdt

dx(1+x)2=2tdt(1+t)2=2t(1+t)2dt

t(1+t)2=t+11(t+1)2=1t+11

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