1. ## Another integration help!

evaulate the integral by substitution
37. $\displaystyle \int^1_{0} \frac{e^z+1}{e^z+z}*dz$
What substitution should I be making?
Any tips in general for choosing substitutions?

2. You need to be able to see an "inner function" and the inner function's derivative as a factor.

Notice that $\displaystyle \displaystyle \frac{d}{dz}(e^z + z) = e^z + 1$.

So what do you think you will use as your substitution?

3. $\displaystyle \displaystyle u=e^z+z=e^z+1$

4. Originally Posted by dwsmith
$\displaystyle \displaystyle u=e^z+z=e^z+1$
$\displaystyle \displaystyle e^z + z$ is NOT always equal $\displaystyle \displaystyle e^z + 1$...

5. I meant to put $\displaystyle \displaystyle du=e^z+1$

6. Thanks! I missed that $\displaystyle e^z' = e^z$
For some reason I thought I would have to use the chain rule for that.

7. Originally Posted by dwsmith
$\displaystyle \displaystyle u=e^z+z=e^z+1$
I hope what you meant to post is $\displaystyle \displaystyle u=e^z+z \Rightarrow du = e^z+1$.