Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 83



Work Step by Step

We have $$ \int \frac{(3 x+2) d x}{x^{2}+4}=\int \frac{3 x}{x^{2}+4}d x+\int \frac{2 }{x^{2}+4}d x\\ =\frac{3}{2}\int \frac{2 x}{x^{2}+4}d x+\int \frac{1 }{(x/2)^{2}+1}d( x/2)\\ =\frac{3}{2}\ln(x^2+4)+\tan^{-1}(x/2)+c. $$
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.