I was trying to develop a random integral transform, but things happened, and I'm kinda confused as to what I can do. Anyway, here's an example of my in-development transform: $$\int e^{\sin t}\csc(t)dt$$ I just need to place the transform bounds, but here's the main idea as to what I wish to accomplish: $$\int^b_a f(t)e^{\sin t}dt$$ where $f(t)$ can be any function, and I need to add the boundaries, and maybe I could change it up later. Of course, it would evaluate to $e^{\sin t}$ if $f(t)=\cos(t)$.
Anyway, I would really like if someone could help out with the development of this transform. I just need help with stuff like this.