Integral Of Te^t

1. 
te^t dt

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

 

2.
-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:

e^(-2t)+c

 

3. 

Think "what would the derivative of be?  . Again, we just
have half of that in our integral, so answer is