Find the integral $\displaystyle \int e^x (4 + e^x)^5 dx$

If we let $u = 4 + e^x$, then $du = e^x dx$. Thus,

$ \begin{equation} \begin{aligned} \int e^x (4 + e^x)^5 dx =& \int (4 + e^x)^5 e^x dx \\ \\ \int e^x (4 + e^x)^5 dx =& \int u^5 du \\ \\ \int e^x (4 + e^x)^5 dx =& \frac{u^{5 + 1}}{5 + 1} + C \\ \\ \int e^x (4 + e^x)^5 dx =& \frac{u^6}{6} + C \\ \\ \int e^x (4 + e^x)^5 dx =& \frac{(4 + e^x)^6}{6} + C \end{aligned} \end{equation} $

Posted on

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now