Question

integral e^(-2x)tan(e^-2x)dx
please give me some hints...

Answer 1

\[\huge \int\limits e^{-2 x} \left(\tan [e^{-2 x}]\right) \, dx\]
Try u-sub

Answer 2

u=-2x
du=-2dx
\[-\frac{du}{2}=dx\]
\[\large =\int\limits e^u(\tan(e^u))(-\frac{du}{2})\]
\[\large =-\frac{1}{2} \int\limits \left(e^u \tan (e^u)\right) \, du\]

Answer 3

very detailed, thank u so much ^^

Answer 4

yw :)

Answer 5

Hmm wouldn't you rather set the entire exponential as your u?
I mean unless you don't mind doing a second substitution.

Answer 6

can i let u=e^-2x
then it will be
\[\int\limits -\frac{ 1 }{ 2} \tan u du\]
is it right?

Answer 7

Yah that looks good! :)

Answer 8

tysm ^^