How do I evaluate the following indefinite integral using u-substitution?
cos(5x)/e^sin(5x) dx

Question

How do I evaluate the following indefinite integral using u-substitution?
cos(5x)/e^sin(5x) dx

lυἶცἶ0210 · Answer

Have you tried sin(5x) as a sub?

anonymous · Answer

so far I have picked sin(5x) to be my u and then I get cos(5x)5 dx for my du and then I multiply 1/5 to get rid of the 5

lυἶცἶ0210 · Answer

Actually, maybe changing it to something like this might help: 

$\LARGE \int ~e^{-sin(5x)} * cos(5x) dx$

lυἶცἶ0210 · Answer

Now we can sub in -sin5x instead: 

$ u=-sin(5x) $ and $du=-5cos(5x) $

anonymous · Answer

oh ok I see and I actually tried that but my negative was in the wrong place that might be why I'm struggling

lυἶცἶ0210 · Answer

Yea, after the u sub we end up with this little thing :P

$\LARGE -\frac{1}{5} \int e^u du $

lυἶცἶ0210 · Answer

Think you can finish it from here?

anonymous · Answer

yes thank you very much :D

lυἶცἶ0210 · Answer

You're welcome, and welcome to Openstudy btw :) $\Huge \color{red}{\star^{\star^{\color{green}{\star}}}} $

anonymous · Answer

Thanks (: