   Chapter 8.2, Problem 19E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral In Exercises 15-34, find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts.) ∫ x e 2 x ( 2 x + 1 ) 2   d x

To determine

To calculate: The indefinite integral xe2x(2x+1)2dx.

Explanation

Given:

The integral is: xe2x(2x+1)2dx.

Formula used:

The formula for integration by parts udv=uvvdu.

Calculation:

Let dv=1(2x+1)2dx.

Now, integrate both the sides in order to find v.

v=1(2x+1)2dx=12(2x+1)

And, let u=xe2x.

Now, differentiate both the sides in order to find u.

du=(e2x+2xe2x)dx=e2x(1+2x)dx

Now, consider the given integral. Apply integration by parts and substitute the values

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