   Chapter 7.R, Problem 39E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 1 / 2 x e 2 x ( 1 + 2 x ) 2 d x

To determine

To Find: 01/2xe2x(1+2x)2dx

Explanation

Formula Used: ex(f(x)+f'(x))dx=exf(x)+C

Calculation:

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:

01/2xe2x(1+2x)2dx=1201/2(1+2x1)e2x(1+2x)2dx=1201/2(11+2x1(1+2x)2)e2xdx

Use substitution 2 x = t to convert the integrand in standard form so that you can use the integration formula mentioned above

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