Evaluate an integral using Laplace transform – math.stackexchange.com

Evaluate an integral using Laplace transform – math.stackexchange.com

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Evaluate the following integral using Laplace transform $$\int_0^\infty\frac{e^{-ax}\sin bx}{x}\,dx$$ I obtained this partial result $$=\int_0^\infty \frac{1}{p+1} \frac{b}{p^2+b^2}\,dp$$ and I am ...

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