Antiderivative problem [$10 Reward]

[Niggel]

Okay thanks for trying to help me. I am writing an important school test tomorrow and I still have a question which nobody could answer me.

I am looking for the antiderivative (no clue if thats the right word - if you have no idea what I am talking about tell me and I will try to find the right word in English!) of a formula such as this one:

1000
------
1+3x


or

1000x
-------
x²+16

Can you give me the answers and a way to get there?!?!?

I asked 2 friends of mine who are studying math at college and they couldn't help me (one had an answer but couldn't tell me how he got there)! I think this shouldn't be too hard for experts like you so it would be great if you could help!