# Math Help - Laplace

1. ## Laplace

COULD YOU SHOW ME THE STEP BY STEP SOLUTION IN HOW THE UPPER FUNCTION (1/T)SIN(AT)BECOME THE LAPLACE OF LOWER FUNCTION ARCTAN(A/S)

plsssssssssssssssss I REALY NEED IT FOR MAY ADVANCE MATH SUBJECT

2. ## Re: Laplace

$L\left\{\frac{1}{t}\sin(\alpha t)\right\} = \int_0^\infty e^{-st}\frac{1}{t}\sin(\alpha t) dt$

Do integration by parts with the two functions $u(t)=e^{-st}$ and $v'(t)=\frac{\sin(\alpha t)}{t}$

You could also try this: rewrite the above integral as $\int_0^\infty e^{-st}\frac{1}{t}e^{i\alpha t} dt$, solve and take the imaginary part of your answer.