x2-4x -dx (x+1)(x²+4)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
100%

Evaluate each of the following integral (photo attached with formula).

The image shows an integral to solve. The integral is given by:

\[
\int \frac{x^2 - 4x}{(x+1)(x^2 + 4)} \, dx
\]

This expression represents the integration of the rational function \(\frac{x^2 - 4x}{(x+1)(x^2 + 4)}\) with respect to \(x\).

The goal is to find the antiderivative or indefinite integral of this expression, which involves techniques such as partial fraction decomposition to simplify the integration process.
Transcribed Image Text:The image shows an integral to solve. The integral is given by: \[ \int \frac{x^2 - 4x}{(x+1)(x^2 + 4)} \, dx \] This expression represents the integration of the rational function \(\frac{x^2 - 4x}{(x+1)(x^2 + 4)}\) with respect to \(x\). The goal is to find the antiderivative or indefinite integral of this expression, which involves techniques such as partial fraction decomposition to simplify the integration process.
Expert Solution
Step 1

I=x2-4xx+1x2+4dxTake the partial fraction of above integral as:-x2-4xx+1x2+4=1x+1-4x2+4I=1x+1-4x2+4dx

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning