Homework Help is Here – Start Your Trial Now!
Math
Calculus
Use partial fractions to find the indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) x² + 2x -x²+x-1 x3 dx

Use partial fractions to find the indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) x² + 2x -x²+x-1 x3 dx

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 54CR
See similar textbooks
icon
Related questions
Question
### Integration Using Partial Fractions **Problem Statement:** Use partial fractions to find the indefinite integral. (Use \( C \) for the constant of integration. Remember to use absolute values where appropriate.) \[ \int \frac{x^2 + 2x}{x^3 - x^2 + x - 1} \, dx \] **Step-by-Step Solution:** 1. **Factor the Denominator:** Factor the denominator \( x^3 - x^2 + x - 1 \). 2. **Set Up Partial Fractions:** Decompose the rational function \( \frac{x^2 + 2x}{x^3 - x^2 + x - 1} \) into partial fractions. 3. **Integrate Each Term:** Integrate each term separately and combine the results. 4. **Include the Constant of Integration:** Don't forget to add the constant of integration \( C \) at the end. **Explanation and Graphs (if applicable):** In this example, a graph is not necessary. Focus on the algebraic manipulation through partial fraction decomposition and integration techniques. **Note:** For accurate and complete solutions, students should ensure they follow algebraic steps meticulously to simplify and integrate. --- By following the detailed steps and principles outlined in this guide, you will be able to solve similar integral problems using partial fractions effectively.
Transcribed Image Text:### Integration Using Partial Fractions **Problem Statement:** Use partial fractions to find the indefinite integral. (Use \( C \) for the constant of integration. Remember to use absolute values where appropriate.) \[ \int \frac{x^2 + 2x}{x^3 - x^2 + x - 1} \, dx \] **Step-by-Step Solution:** 1. **Factor the Denominator:** Factor the denominator \( x^3 - x^2 + x - 1 \). 2. **Set Up Partial Fractions:** Decompose the rational function \( \frac{x^2 + 2x}{x^3 - x^2 + x - 1} \) into partial fractions. 3. **Integrate Each Term:** Integrate each term separately and combine the results. 4. **Include the Constant of Integration:** Don't forget to add the constant of integration \( C \) at the end. **Explanation and Graphs (if applicable):** In this example, a graph is not necessary. Focus on the algebraic manipulation through partial fraction decomposition and integration techniques. **Note:** For accurate and complete solutions, students should ensure they follow algebraic steps meticulously to simplify and integrate. --- By following the detailed steps and principles outlined in this guide, you will be able to solve similar integral problems using partial fractions effectively.
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer