Laplace transform using the basic integral

[Pietair]

The question:

Find the Laplace transform of f(t)=$$te^2^t$$

I have got:

Though, this will not become f(s) = 1/(s+2)^2

Anyone got an idea about what I am doing wrong?

 

[quantumdude]

Though, this will not become f(s) = 1/(s+2)^2

That's good because it's not supposed to become that! The answer is:

$$\mathcal{L}\left[te^{2t}\right]=\frac{1}{(s-2)^2}$$

This is exactly what you have.