You are Here: Home >< Maths

# yet another integration question watch

1. Right, i'm not really understanding this:

integrate (2x)/(x^2 + 1)

in the example its as follows:

Let I = integral(2x/ x^2 + 1) dx

Consider y = ln|x^2 + 1|

Then dy/dx = [1/(x^2 + 1)]2x

So I = ln|x^2 + 1| + C

Right, what on earth has happened to the 2x. I dont think they've explained it very well
2. Differentiate to see where it came from in the first place :P
Ln|x²+1|.
It's a ln thing, so it goes to (Differential) / (Original function).
Differential is 2x
Original is x²+1
So we get 2x/(x²+1)

It's a sort of standardy patterny thing. I think you can use a substitution to verify it, if you're up for that (take u=x²+1, du/dx = 2x, and sub that in which should destroy the 2x, etc...).

Basically, differentiating more complex functions creates new bits and new expressions (product rule, for example...it just doubles the amount of stuff you have, chain rule creates ex-nihilo the differential of the inner function, etc). So when you integrate, stuff disappears if you're using standard patterns.

My explanation skills at -5 out of 10. So you better try some questions to see how it works :/
3. Yeah, i got the 2x/(x^2 + 1) from differentiating y. Its just, well, you have dy/dx, you the integrate that? It's not making any sense.
4. You could just spot that the derivative of the bottom is on the top. It's one of your standard recognition questions. If you have:

INT [f '(x) / f(x)] dx, then this is equal to ln|f(x)| + c

That's kinda what Rabite was saying..I think.
5. Ah, its clicked now, you're kinda comapring dy/dx to the original function you want to integrate. (in the example above.) Ta people!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 14, 2006
Today on TSR

### University open days

• Southampton Solent University
Sun, 18 Nov '18
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams