   Chapter 7.5, Problem 6E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 1 x ( 2 x + 1 ) 3 d x

To determine

To find:

01xdx2x+13

Explanation

Formula used:dxn dx=nxn-1

Calculations: In the given integral let 2x+1=t, such that 2dx=dt, the limit for t is 1,3. Also xdx=(dt/2)(t-1)/2=(t-1)dt4

So the integral can be written as

I=13(t-1)dt4t3=13tdt4t3-13dt4t3=13

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