Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 7 - Section 7.1 - Integration by Parts - 7.1 Exercises - Page 491: 58

Answer

$$\displaystyle{\int x^ne^x\ dx=x^ne^x-n\int x^{n-1}e^x\ dx}$$

Work Step by Step

$\displaystyle{I=\int x^ne^x\ dx}$ $\displaystyle \left[\begin{array}{ll} u=x^n & dv=e^x \\ & \\ du=nx^{n-1} & v=e^x \end{array}\right]$ Integration by parts $\displaystyle{I=x^ne^x-\int e^x\times nx^{n-1}\ dx}\\ \displaystyle{I=x^ne^x-n\int x^{n-1}e^x\ dx}$
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.