Is there any notation for representing $L(t\sin t)$ at $s=2$?

Question

I know that, in order to evaluate $\large\large\int_0^\infty te^{-2t}\sin t\;dt$ I should evaluate $L(t\sin t)$ where $L$ is the laplace transformation and then plug in $s=2$. But I'm wondering is there any mathematical notation to represent, the integral is equal to $L(t\sin t)$ at $s=2$? For example, does $L(t\sin t)\vert_{s=2}$ make sense?

Answer 1

Well, you can use:

$$\text{F}\left(2\right):=\left.{\mathscr{L}_x\left[x\sin\left(x\right)\right]_{\left(\text{s}\right)}}\right|_{\;\text{s}\space=\space2}=\int\limits_0^\infty x\sin\left(x\right)\exp\left(-2x\right)\space\text{d}x=\frac{4}{25}\tag1$$