Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Practice Exercises - Page 517: 23

Answer

$$\dfrac{x^2}{2}+\dfrac{3\ln |x+1|}{2} -\dfrac{9}{2} \ln |x+3|+C$$

Work Step by Step

Apply the integration by parts formula such follows: $\int a'(x) b(x)=a(x) b(x)-\int a(x) b'(x)dx$ Re-write the integral into partial fractions: $\int \dfrac{x^3+4x^2}{x^2+4x+3}dx=\int (x- \dfrac{3x}{x^2+4x+3})dx$ Now, $$\int (x- \dfrac{3x}{x^2+4x+3})dx=\int x \space dx+(\dfrac{3}{2}) \times \int \dfrac{dx}{x+1}-(\dfrac{9}{2}) \times \int \dfrac{dx}{x+3} \\=\dfrac{x^2}{2}+\dfrac{3\ln |x+1|}{2} -\dfrac{9}{2} \ln |x+3|+C$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.