Prove that the integral of cos(xt)/(t²+1) equals πe^(-x)/2

[jakncoke]

Homework Statement

supposed to prove informally that

f(x)=Integral 0-->infinity (cosxt/(t^2+1))dt == Pi/2*Exp[-x]

Homework Equations

The Attempt at a Solution

no clue, need some hints to get started

 

[HallsofIvy]

Is that (cos x) t or cos(xt)?