# Dumb integral question, can be answered (or hinted) in 2 seconds no doubt.

1. Jan 22, 2013

### Vagabond7

1. The problem statement, all variables and given/known data

Ok, so I am doing areas between curves, but one of the functions is y=50/(25+x^2)

This is stupid, but I THINK I am having trouble finding the anti-derivative (I just know my final answer is wrong, but I'm pretty sure it is related to this.)

3. The attempt at a solution

Ok, so obvious I can't rewrite as a negative power, leads to division by 0. I don't think u substitution works here because the derivative of u is not there (or there but off by a constant factor). Integrating as a natural log seems fine, but does that make the anti-derivative 50 ln (25+x^2)? That doesn't seem right.

In all the problems I did for log anti-derivatives I don't remember what to do if the 1/x is multiplied by a constant. Suggestions?

2. Jan 22, 2013

### Dick

If you want to integrate y you need a trig substitution. Like x=5*tan(t).

3. Jan 22, 2013

### Vagabond7

So you're saying that I can't find the antiderivative of 50/(25+x^2) without using some kind of trig substitution? I don't think I've ever even encountered that in my classes yet.

4. Jan 22, 2013

### Dick

I'm afraid not. The antiderivative is an arctangent.

5. Jan 22, 2013

### SteamKing

Staff Emeritus
For what values of x does the expression (25+x^2) = 0?

Hint: They're not real.