/*! 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 66. Solve the integral:聽鈭玸ec4x聽d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q 66. (page 429)

Solve the integral:鈭�sec4xdx

Short Answer

Expert verified

The required answer istanx+13tan3(x)+c.

Step by step solution

01

Step 1. Given information.

We have given integral is鈭�sec4xdx.

02

Step 2. Solve the integration by parts.

We have,

u=tanxdu=sec2xdx

and

鈭�sec4xdx=鈭�tan2(x)+1sec2(x)dx=鈭�u2+1du=鈭�1du+鈭�u2du=u+u33+c=tanx+13tan3x+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 integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.

鈭�sinudu

Solve the integral:鈭�3x+1secxdx

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withx=asinuor x=atanu? Why do we need to think about the unit circle after trigonometric substitution with x=asecu?

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

u(x)=sinx

Find three integrals in Exercises 21鈥�70 in which the denominator of the integrand is a good choice for a substitution u(x).
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.