Question

How do you find the integral of `18e^(3t) dt`?

Answer 1

`int18e^(3t)dt=18inte^(3t)dt=18/3inte^udu=6e^u+C=6e^(3t)+C`

Explanation:

From laws of integration, the integral of e^t is e^t.
We may substitute u = 3t, which means du = 3 dt and rewrite this integral as
18/3`inte^u du`
This then becomes 6 e^u + C,where C is the constant of integration.
Substituting back we get the answer as 6e^(3t) + C