00:01
In this question, the laplace transform of the function f t equals to laplace transform of 2 n t into e raised to the power 3 t.
00:11
So, this is equals to integration from 0 to infinity t into e raised to the power 3 t into e raised to the power minus s t dt.
00:24
So, this is equals to integration from 0 to infinity t into e raised to the power minus s minus 3 t dt.
00:36
Now here using integration by parts using integration by parts because there are 2 functions.
00:49
This is first function and this is the second.
00:53
So, this implies this is equals to leaving first function t as it is integration from 0 to infinity e raised to the power minus s minus 3 dt then minus derivative of t.
01:09
So, derivative of t is 1 and integration of this function.
01:14
So, that will be e raised to the power minus s minus 3 dt upon minus s minus 3.
01:23
Now here dt.
01:25
So, after simplifying this will be equals to this will be equals to t and here it will be e raised to the power minus s minus 3 s minus 3 t and here upon minus s minus 3 and here it will be minus minus plus taking 1 upon s minus 3 common...