find-L-sh-3x-x-L-laplace-transform-

Question Number 96659 by mathmax by abdo last updated on 03/Jun/20

find L (\frac{sh (3 x)}{x}) L laplace transform

Answered by Sourav mridha last updated on 07/Jun/20

f (a) = \int_{0}^{\infty} e^{- a x} s h (3 x) d x

= \frac{3}{a^{2} - 9}

n o w L [\frac{s h (3 x)}{x}] = \int_{s}^{\infty} f (a) d a

= \int_{s}^{\infty} \frac{3}{a^{2} - 3^{2}} d a

= \frac{1}{2} {[l n (\frac{a - 3}{a + 3})]}_{s}^{\infty}

= l n {[\frac{s + 3}{s - 3}]}^{\frac{1}{2}} . .