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?
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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?
$\displaystyle \displaystyle u=e^z+z=e^z+1$
Originally Posted by dwsmith $\displaystyle \displaystyle u=e^z+z=e^z+1$ $\displaystyle \displaystyle e^z + z$ is NOT always equal $\displaystyle \displaystyle e^z + 1$...
I meant to put $\displaystyle \displaystyle du=e^z+1$
Thanks! I missed that $\displaystyle e^z' = e^z$ For some reason I thought I would have to use the chain rule for that.
Originally Posted by dwsmith $\displaystyle \displaystyle u=e^z+z=e^z+1$ I hope what you meant to post is $\displaystyle \displaystyle u=e^z+z \Rightarrow du = e^z+1$.
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