   Chapter 7.1, Problem 1E

Chapter
Section
Textbook Problem

# Evaluate the integral using integration by parts with the indicated choices of u and dv. ∫ x e 2 x d x ;       u = x ,     d v = e 2 x d x

To determine

To evaluate: The given integral using integration by parts with u and v as indicated.

Explanation

The technique of integration by parts comes in handy when the integrand involves product of two functions. It can be thought of as a rule corresponding to the product rule in differentiation.

Formula used:

The formula for integration by parts in terms of u and v is given by

udv=uvvdu

Given:

The integral, xe2xdx.

The functions, u=x,dv=e2xdx.

Calculation:

The choice for the variables are as shown below:

u=x     dv=e2xdx

Then, the differentiation of u and antiderivative of dv will be

du=1dx     v=12e2x

Substitute for variables in the formula above to get

xe2xdx=x(12e2x)(12e

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