**The Laplace Transform**

Part 13: Transform of the Logarithm

Now, let us find the Laplace transform of the natural logarithm. From the definition of the Laplace transform,

.

Making the u-substitution *u*=*st*, we get

.

Now, one may recall that we found the remaining integral here:

, where *γ* is the Euler-Mascheroni constant. Thus,

.

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Tags: Euler-Mascheroni, Laplace Transform, Logarithms, Math, Monday Math

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