Integration with Eulers formula.

[cragar]

I want to integrate $\frac{e^x}{cos(x)}$ with eulers formula.
I start by writing $\frac{e^x}{e^{ix}}$
then I integrate that as usual.
So after I integrate I get $\frac{e^{(1-i)x}}{1-i}$
Normally I would multiply and divide by the complex conjugate and then back substitute in
e^(ix) and the take the real part.

can I just back substitute in isin(x)+cos(x) on the bottom and then multiply it by (1-i)
and then take the real part. That seems to easy.
Does anyone have suggestions. This is not a homework problem.

 

[chiro]

Hey cragar.

You should be able to integrate the expression and then take the real part as your answer.