Thread: laplace transform with powers of t*exponential

Hi all,
I have a question.

f(t) =t^3*e^-4t using theorm 1 and 2.

what im wondering is can I take the t^3 outside the integral as a constant


t^3| e^-st * e^-4t (between 0 and infinity)

then

t^3 [ e-st/-s + e^-4t/s] (between 0 and infinity) or should I be thinking of partial fractions all of which are kind of new to me.

by the way I need to show all steps rather than refering to the tables, according to which I should end up with


6/s^4 * 4/s+4

Originally Posted by tolka

Hi all,
I have a question.

f(t) =t^3*e^-4t using theorm 1 and 2.

what im wondering is can I take the t^3 outside the integral as a constant

No, you can't, because it is NOT a constant. The Lalace transform is, by definition

Do that "by parts" three times.

t^3| e^-st * e^-4t (between 0 and infinity)

then

t^3 [ e-st/-s + e^-4t/s] (between 0 and infinity) or should I be thinking of partial fractions all of which are kind of new to me.

Do you mean partial fractions or int by parts?