Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 86


$3e^{x^{1/3}}+c $

Work Step by Step

Recall that $(e^x)'=e^x$ Let $ u= x^{1/3}$, then $ du=\frac{1}{3} x^{-2/3}dx $ and hence we have $$ \int x^{-2/3}e^{x^{1/3}} dx=3\int e^{u} du\\ =3e^u+c=3e^{x^{1/3}}+c . $$
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.