How to get simplified, symbolic solutions for definite integrals

Hi,

I have a function:

which I integrate over the whole real line, and then divide by pi. The below code:

syms x w
fn1 = exp(-abs(x))*cos(w*x)
int(fn1, x, [-inf inf])/pi

produces the following output:

Which is probably not incorrect, but I was hoping to see what Python (SymPy) would cleanly give as:

I tried to 'simplify' or to play with format, but, to be honest, I am not even sure what to look for in documentation. My issue is most likely due to trying to run before I can walk. That is to say, after recently having aquired Matlab (student, doing another degree late in life), I never did spend months on learning all of its basics, and am instead relying on 40 years of general programming and math experience. Clearly not enough in this case, though :)

Could I get a few pointers, please, as to how to get Matlab results to be in a fully symbolic, rational (1/3 instead of 0.333333), simplified (cos^2 + sin^2 = 1) kind of mode?

Answer 1

[Paul]

Declare x w to be real

syms x w real
fn1 = exp(-abs(x))*cos(w*x)

fn1 = 

int(fn1, x, [-inf inf])/sym(pi)

ans = 

[Darko Ilic]

Ah, but of course! Thanks a bunch Paul.