Q. 46 Solve each of the integrals in E... [FREE SOLUTION]

Chapter 5: Q. 46 (page 417)

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
$鈭� \frac{{(\cos x + 1)}^{3 / 2}}{\csc x} d x$

Short Answer

Expert verified

The solution of the given integral is $鈭� \frac{{(\cos x + 1)}^{3 / 2}}{\csc x} d x = - \frac{2}{5} {(\cos x + 1)}^{5 / 2} + C$ .

Step by step solution

Step 1. Given Information

Solving the given integrals.

$鈭� \frac{{(\cos x + 1)}^{3 / 2}}{\csc x} d x$

Step 2. Solving the given integral using substitution method.

$u = \cos x + 1 \frac{d u}{d x} = - \sin x \frac{d u}{d x} = - \frac{1}{\csc x} - d u = \frac{1}{\csc x} d x$

Step 3. This substitution changes the integral into

$鈭� \frac{{(\cos x + 1)}^{3 / 2}}{\csc x} d x = - 鈭� u^{3 / 2} du 鈭� \frac{{(cosx + 1)}^{3 / 2}}{cscx} dx = - [\frac{u^{3 / 2 + 1}}{3 / 2 + 1}] + C 鈭� \frac{{(cosx + 1)}^{3 / 2}}{cscx} dx = - \frac{u^{5 / 2}}{5 / 2} + C 鈭� \frac{{(cosx + 1)}^{3 / 2}}{cscx} dx = - \frac{2}{5} u^{5 / 2} + C 鈭� \frac{{(cosx + 1)}^{3 / 2}}{cscx} dx = - \frac{2}{5} {(cosx + 1)}^{5 / 2} + C$

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
$鈭� \frac{{(\cos x + 1)}^{3 / 2}}{\csc x} d x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the given integral using substitution method.

Step 3. This substitution changes the integral into

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)鈭�(cosx+1)3/2cscxdx

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the given integral using substitution method.

Step 3. This substitution changes the integral into

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
$鈭� \frac{{(\cos x + 1)}^{3 / 2}}{\csc x} d x$