/*! 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. 53 Solve each of the integrals in E... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 53 (page 452)

Solve each of the integrals in Exercises 21鈥�66. Some of the integrals require the methods presented in this section, and some do not. (The last four exercises involve hyperbolic functions.)

鈭�sinxsecxdx

Short Answer

Expert verified

The solution of the integral is-lncosx+C.

Step by step solution

01

Step 1. Given Information

The given integral is鈭�sinxsecxdx.

02

Step 2. Rewrite and substitute

  • Rewrite the integral using the trigonometric identities.

鈭�sinxsecxdx=鈭�sinxcos(x)dx

  • Assume that cos(x)=u. So, role="math" localid="1649043729428" -sin(x)dx=du.
  • Substitute the values into the obtained integral and simplify.

role="math" localid="1649043740338" 鈭�sinxcos(x)dx=-鈭�1udu

03

Step 3. Integrate

  • Integrate the simplified integral.

-鈭�1udu=-logu+C

  • Substitute u=cos(x)to find the solution of the given integral.

鈭�sinxsecxdx=-logcos(x)+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

Solve the integral

鈭�4-xx-2dx

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

Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

x2鈭�4x鈭�8

Consider the integral 鈭�x(x2鈭�1)2dx.

(a) Solve this integral by using u-substitution.

(b) Solve the integral another way, using algebra to multiply out the integrand first.

(c) How must your two answers be related? Use algebra to prove this relationship.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.