/*! 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} Problem 4 Use the indicated formula from t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 4

Use the indicated formula from the table of integrals in this section to find the indefinite integral. $$ \int \frac{4}{x^{2}-9} d x, \text { Formula } 29 $$

Short Answer

Expert verified
The integral \( \int \frac{4}{x^{2}-9} d x \) equals \( \frac{2}{3} ln|\frac{x - 3}{x + 3}| + C \)

Step by step solution

01

Identify the Integral Form

The given integral is \( \int \frac{4}{x^{2}-9} d x \). This falls into the integral form of \( \int \frac{A}{n^{2}-a^{2}} d n \) as given in formula 29. Here, A=4 and a=3 (since \((-3)^2\) equals 9).
02

Apply the formula

In formula 29, it is stated that \( \int \frac{A}{n^{2}-a^{2}} d n = \frac{A}{2a}ln|\frac{n - a}{n + a}| + C \), where C is the constant of integration. Applying this formula gives \( \frac{4}{2*3} ln|\frac{x - 3}{x + 3}| + C \).
03

Simplify the expression

The expression simplifies to \( \frac{2}{3} ln|\frac{x - 3}{x + 3}| + C \).

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

Approximate the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of \(n\). (Round your answers to three significant digits.) $$ \int_{0}^{1} \sqrt{1-x^{2}} d x, n=4 $$

Population Growth \(\ln\) Exercises 57 and 58, use a graphing utility to graph the growth function. Use the table of integrals to find the average value of the growth function over the interval, where \(N\) is the size of a population and \(t\) is the time in days. $$ N=\frac{375}{1+e^{4.20-0.25 t}}, \quad[21,28] $$

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{0}^{\infty} \frac{5}{e^{2 x}} d x $$

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{-\infty}^{\infty} x^{2} e^{-x^{3}} d x $$

MAKE A DECISION: CHARITABLE FOUNDATION A charitable foundation wants to help schools buy computers. The foundation plans to donate \(\$ 35,000\) each year to one school beginning one year from now, and the foundation has at most \(\$ 500,000\) to start the fund. The foundation wants the donation to be given out indefinitely. Assuming an annual interest rate of \(8 \%\) compounded continuously, does the foundation have enough money to fund the donation?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.