   Chapter 7.1, Problem 24E

Chapter
Section
Textbook Problem

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

To determine

To evaluate: The given integral using the technique of integration by parts.

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 for definite integral is given by

abf(x)g(x)dx=f(x)g(x)]ababg(x)f(x)dx

Given:

The integral, 01(x2+1)exdx.

Calculation:

Make the choice for u and dv such that the resulting integration from the formula above is easier to integrate. Let

u=x2+1      dv=exdx

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

du=2xdx      v=ex

Using the formula above, the given integration will become

01(x2+1)exdx=(x2+1)(ex)]0101(ex)(2x)dx=(x2+1)(ex)]01+201xexdx …… (1)

Integrate the last term using integration by parts with the following substitution:

u=x     dv=exdx

Then

du=dx

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 5-8, graph the given function or equation. 2x3y=12

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 69-74, rationalize the numerator. 72. 2x3y3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th 