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based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Integral Transforms

LaplaceTransform[expr,t,s]find the Laplace transform of expr
InverseLaplaceTransform[expr,s,t]
find the inverse Laplace transform of expr

Laplace transforms.

This computes a Laplace transform.
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Here is the inverse transform.
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FourierTransform[expr,t,w]find the symbolic Fourier transform of expr
InverseFourierTransform[expr,w,t]
find the inverse Fourier transform of expr

Fourier transforms.

This computes a Fourier transform.
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Here is the inverse transform.
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Note that in the scientific and technical literature many different conventions are used for defining Fourier transforms. The setup for specifying different conventions is described in FourierTransform.