Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    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 :confused:
    Offline

    8
    ReputationRep:
    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 :/
    • Thread Starter
    Offline

    1
    ReputationRep:
    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.
    Offline

    2
    ReputationRep:
    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.
    • Thread Starter
    Offline

    1
    ReputationRep:
    Ah, its clicked now, you're kinda comapring dy/dx to the original function you want to integrate. (in the example above.) Ta people!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: June 14, 2006

University open days

  • Southampton Solent University
    All faculties Undergraduate
    Sun, 18 Nov '18
  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.