Answer
$$\int \frac{dx}{\sqrt{x}+x\sqrt{x}}=2arctan\,\sqrt{x}+C$$
Work Step by Step
$$let\ x=t^{2},\,dx=2t\,dt$$
$$\int \frac{dx}{\sqrt{x}+x\sqrt{x}}=\int \frac{2t}{t+t^{3}}dt=\int \frac{2}{1+t^{2}}dt$$
$$=2arctan\,t+C=2arctan\,\sqrt{x}+C$$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 508: 56
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter 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.
