My result contains 'limit' value

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pando
pando 2020 年 4 月 23 日
My code is
clc;
syms x t X omega
a = 2; b = 2;
x = exp(-a*t)*sin(b*pi*t);
X = simplify(int(x*exp(-j*omega*t),t,0,inf))
in books, its result is
X =
2*pi/(4-w^2+4*pi^2+4*i*w)
however I got
X =
(2*pi)/((2 + omega*1i)^2 + 4*pi^2) - limit(exp(- 2*t - t*omega*1i)*(sin(2*t*pi)*(2 + omega*1i) + 2*pi*cos(2*t*pi)), t, Inf)/((2 + omega*1i)^2 + 4*pi^2)
how can I get the answer on the book?

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