1) Assuming they converge, the definite integral has a specific value. Call the value "A". The subsequent anti-derivative, then, would be Ax + C.
2) Can you prove that they converge? I'm worried about that first one around x = 0.
3) That last one is kind of an Error Function, isn't it? Maybe its complement?
4) What is your assignment and why do you believe either anti-derivative can be determined?