integration by complex exponentials

I have seen that one can use the euler's formula to complexify the integration, and integrate functions like easily.(The method has a wikipedia page:Integration using Euler's formula - Wikipedia, the free encyclopedia)

How can i do using complex exponentials.

PS:I know this can be easily done with standard trig substitutions and might turn out to be longer using complex exponentials, but I want to know if and how can it be done with this method ...(Nod)

Re: integration by complex exponentials

Re: integration by complex exponentials

Re: integration by complex exponentials

Quote:

Originally Posted by

**earthboy** small doubt:

is

or

both are seem to be used in books, but what is the difference?

It's .

Re: integration by complex exponentials

Quote:

Originally Posted by

**HallsofIvy**
That denominator can be factored (though not easily- use the quadratic formula to find the roots). Then it will be of the form

where a and b are the roots. That can be integrated by "partial fracations".

where and

how do I separate the real and imaginary part here to get the answer,especially what to do with the ?

Re: integration by complex exponentials

Quote:

Originally Posted by

**earthboy**
where

and

how do I separate the real and imaginary part here to get the answer,especially what to do with the

?

Any hint on how to separate the real and the imaginary part and find the answer from here?