Preliminary steps The following integrals | Ch 7.4 - 58E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 58E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Problem 58E

Preliminary steps

The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals.

Step-by-Step Solution:

Problem 58E

The following integrals require a preliminary step such as long division or a change of variables before using partial fractions.
Evaluate these integral

$\int\limits_{\ }^{\ }\frac{cosx}{si{n}^{3}x-4sinx}dx$
Solution:-

Step 1
To evaluate the integral, first we substitute $sin\ x=t$ ,
Differentiating $sin\ x=t$ , we get $cos\ xdx=dt$

Substituting these in the integral, we get
$I=\ \int\limits_{\ }^{\ }\frac{dt}{{t}^{3}-4t}$
Now, we have rational fraction which we can decompose into partial fraction and then carry on the integral.

Step 2 of 2

Chapter 7.4, Problem 58E is Solved

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

The full step-by-step solution to problem: 58E from chapter: 7.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 58E from 7.4 chapter was answered, more than 269 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Preliminary steps The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals.” is broken down into a number of easy to follow steps, and 25 words. This full solution covers the following key subjects: Integrals, preliminary, partial, evaluate, fractions. This expansive textbook survival guide covers 112 chapters, and 5248 solutions.