2. In the following exercises, calculate the exact value of the improper integrals using the Laplace transform.

Solutions:

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I sin(x) dx a) x2 + a2 0, sin(x) b) sin(x) x(x2 + 1) 1- cos(2x) c) d) cos(r) d.x e) x2 + a? 0. I sin(x) dx a) x2 + a2 0, sin(x) b) sin(x) x(x2 + 1) 1- cos(2x) c) d) cos(r) d.x e) x2 + a? 0.