Antiderivative of 50/(25+x²)

[Vagabond7]

Homework Statement

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.)

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?

 

[Dick]

Homework Statement

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.)

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?

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

 

[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.

 

[Dick]

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.

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

 

[SteamKing]

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

Hint: They're not real.