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1. ### Introduction to Complex Analysis

I think you should be familiar with at least some Calculus before trying to get into Complex Analysis. I don't know if you are by the way, I ain't familiar with european education
2. ### Are certain integrals possible?

If by "integrate" you mean finding its anti derivative as a combinations of the functions we already know, then nope.
3. ### How was e computed?

calculate \lim_{n\to\infty} (1+\frac{1}{n})^n
4. ### So what is it, in that case?

\int (1-x^2)^{1/2} = 1/2 ( x(1-x^2)^{1/2} + \arcsin x)
5. ### Table of Laplace transforms

If it helps, the LT of the error function \frac{2}{\pi^{\frac{1}{2}} }\int_0^t e^{-u^2} du is \frac {1}{s(s+1)^{1/2}} And since you can always work with the N(0,1) distribution instead of the more general N(m, sigma^2) I think you'll find the aforementioned result useful. If you need the...
6. ### Table of Laplace transforms

Schaum's intro to Laplace transforms has like 300 laplace transforms listed on a big table.