1. `int te^t dt`

Integrate by parts.  u = t and dv = e^t.  Then du = 1 and v = e^t

`=te^t-int e^t dt`

`=te^t-e^t+c`

`=e^t(t-1)+c`

2. `int -e^(-2t)dt`

You could use substitution, but I like to just think "what would the derivative of e^-2t be?  -2e^-2t.  So we have half of that:

`1/2 e^(-2t)+c`

3.  `int te^(t^2) dt`

Think "what would the derivative of `e^(t^2)` be?  `2te^(t^2)` . Again, we just have half of that in our integral, so answer is

`1/2e^(t^2)+c`