/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 69 Solve each of the integrals in E... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 69 (page 465)

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
鈭�lnx2+1dx

Short Answer

Expert verified

The value isxlnx2+1-2x+2tan-1x+C

Step by step solution

01

Step 1. Given information

An expression is given as鈭�lnx2+1dx

02

Step 2. Solving Integral

Let

u=lnx2+1du=2xx2+1dxv=鈭�1dx=x

Now substitute the value and simplify as,

鈭�lnx2+1dx=lnx2+1x-鈭�x脳2xx2+1dx=xlnx2+1-鈭�2x2x2+1dx=xlnx2+1-2鈭�1-1x2+1dx=xlnx2+1-2x+2tan-1x+C

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

u(x)=x2+x+1

Why don鈥檛 we ever have cause to use the trigonometric substitution x=cosu?

Explain why, if x=asinu, then a2鈭�x2=acosu. Your explanation should include a discussion of domains and absolute values.

Show by differentiating (and then using algebra) that 鈭�cot鈦�sin鈭�1鈦�xand 鈭�1鈭�x2xare both antiderivatives of 1x21鈭�x2. How can these two very different-looking functions be an antiderivative of the same function?

Describe two ways in which the long-division algorithm for polynomials is similar to the long-division algorithm for integers and then two ways in which the two algorithms are different.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.