A tricky integration problem. Save me!

[saksham]

I was asked to integrate( exp(-x) cos(x)) with respect to x with the limits x=0 and x= infinity.
I calculated the indefinite integral to be 0.5 exp(-x) [sin(x)-cos(x)].

I was stuck in the part where we apply limit x approaches infinity of sin(x) and cos x.

Please help me out.

Best,
Saksham

[StatusX]

e^-x goes to zero at infinity, so the other terms arent important, as long as theyre finite, which they clearly are.

[saksham]

Thanks for your reply StatusX. I really appreciate it.
Best,
Saksham