please solve this(it is from Laplace transformation) showing STEPS:
integrate((e^(-st))*t^(-1/2))dt from 0 to infinity
The answer given in the book is sqrt(pi/s)

Question

please solve this(it is from Laplace transformation) showing STEPS:
integrate((e^(-st))*t^(-1/2))dt from 0 to infinity
The answer given in the book is sqrt(pi/s)

amistre64 · Answer

you do an integration by parts i believe

.sam. · Answer

From wolfram ,$$\int\limits_0^{\infty } e^{-s t} \frac{1}{\sqrt{t}} \, dt=\frac{\sqrt{\pi }}{\sqrt{s}} \text{for} ~\Re(s)>0$$

amistre64 · Answer

there are tables of laplace transforms that might be useful for this as well

anonymous · Answer

from wolframalpha i got the answer as sqrt(pi/s) but i want to know the steps as knowing how to solve a problem is important to me.
thanks