   Chapter 8.1, Problem 99E

Chapter
Section
Textbook Problem

# Methods of Integration Show that the following results are equivalent. (You will learn about integration by tables in Section 8.7.)Integration by tables: ∫ x 2 + 1 d x = 1 2 ( x x 2 + 1 + ln | x + x 2 + 1 | ) + c Integration by computer algebra system: ∫ x 2 + 1 d x = 1 2 [ x x 2 + 1 + arcsinh ( x ) ] + c

To determine

To prove: The results derived are equivalent.

Explanation

Given: We are given with the Indefinite Integral x2+1dx

Formula used:

secnθdθ=secn2θtanθn1+n2n1secn2θdθ

Proof:

Consider the given integral,

x2+1dx

Substitute to get:

x=tanθdu=sec2θdθ

Thus,

x2+1dx=sec2θtan2θ+1dθ=sec2θsecθdθ=sec3θdθ …… (1)

Use the reduction formula,

secnθdθ=secn2θtanθn1+n2n1secn2θdθ

Hence,

sec3θdθ=sec32θtanθ31+3231sec32<

### 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 