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Maths for Engineers - 2
Laplace Transforms Of Standard Function
Laplace Transforms of Standard Function-1:
4. Laplace Transform of cos h at
We have 
5. Laplace Transformation of sin at and cos at.
We know by Euler's formula that,
On equating the Real and Imaginary parts, we obtain;
6. Laplace Transformation of tn
Let f (t) = tn , where n is non-negative real number or n is a negative non-integer. Then from the definition;
Substitute st = x, so that dt = dx/s and
Where n is non- negative integers.