derivative/integral of trig functions :|

[coreyiscold]

Eek.  I have two homework questions left, and then I'm done for the year besides the final.  My only problem? I'm stumped.

Derivative of 5e^tanx

Integral of e^x tan e^x

The only thing I'm confused about is E.  Can I just get rid of it, or is it like a normal derivative/integral problem?

Comments

[korean_guy_01]

1) d/dx eu = u' * eu

2) ∫ u dv = uv - ∫ v du

I would let u = tan(ex) & dv = ex dx (in the future, don't forget to put your d_ with your integration problem). Use the Chain Rule to find du. v is a trivial integration of dv.

[kanato]

hmm it looks like the second one could be done with a single substitution

u = e^x
du = e^x dx

[niminy_piminy]

hmm. wouldn't it be easier for #2 if you let u=e^x. then you get ∫ tan u du. then ∫ sinu/cos u du. let cos u=v. ∫ dv/v = ln |cos (e^x)| + C

for 1, you can use chain rule. (5e^tanx)(sec^2 x)

[kalieris]

Could the problems be referring to Euler's number?

http://en.wikipedia.org/wiki/E_(mathematical_constant)