   Chapter 7.1, Problem 56E

Chapter
Section
Textbook Problem

# Use Exercise 52 to find ∫ x 4 e x d x .

To determine

To evaluate: the given integral using reduction formula

Explanation

The reduction formula is obtained using the technique of integration by parts. 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 reduction formula to be used is given below:

xnexdx=xnexnxn1exdx

Given:

The integral, x4exdx.

Calculation:

Evaluate the given integral by substituting n=4 in the reduction formula:

x4exdx=x4ex4x41exdx=x4ex4x3exdx …… (1)

Solve the integral x3exdx by again applying the reduction formula with n as 3.

x3exdx=x3ex3x31exdx=x3ex3x2exdx …… (2)

Once again apply the reduction formula to solve the integral x2exdx. Substitute n as 2 in the reduction formula to get

x2exdx=x2ex2x21exdx=x2ex2xexdx …… (3)

Solve integral xexdx by substituting n as 1 in the reduction formula:

x1exdx=

### 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

#### Find more solutions based on key concepts 