I posted this in the homework section, but I haven't received any help, so hopefully putting it in this section won't be an issue. I'm trying to compute the integral
$$ \int_0^ \infty \frac{ \cos xt}{1 + t^2} \, dt $$
using the Laplace transform. The first thing that catches my eye is the 1 /(1 + t^2) factor, which is equal to the Laplace transform of sin x:
$$ = \int_0^\infty \cos xt \, L[ \sin x ] \, dt $$
Any ideas?
$$ \int_0^ \infty \frac{ \cos xt}{1 + t^2} \, dt $$
using the Laplace transform. The first thing that catches my eye is the 1 /(1 + t^2) factor, which is equal to the Laplace transform of sin x:
$$ = \int_0^\infty \cos xt \, L[ \sin x ] \, dt $$
Any ideas?
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