# Thread: u substitution help -- lots of e^x

1. ## u substitution help -- lots of e^x

hi there,

I need help solving the following problem using U-substitution:

any idea what I should set my u variable equal to?

any help would be greatly appreciated

thanks so much & all the best
- xecutioner

2. ## Re: u substitution help -- lots of e^x

Originally Posted by xecutioner
hi there,

I need help solving the following problem using U-substitution:

any idea what I should set my u variable equal to?

any help would be greatly appreciated

thanks so much & all the best
- xecutioner
Let \displaystyle \begin{align*} u = e^x + 4 \implies du = e^x\,dx \end{align*} and the integral becomes

\displaystyle \begin{align*} \int{\frac{e^x}{\left(e^x + 4\right)^3}\,dx} &= \int{\frac{1}{u^3}\,du} \\ &= \int{u^{-3}\,du} \end{align*}

I'm sure you can go from here

3. ## Re: u substitution help -- lots of e^x

hi there,

your post has helped me significantly, thanks so much!

all the best,

xecutioner