Join TSR now and get all your revision questions answeredSign up now

How do you integrate x^2 / (x^3 + 2) ? Watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    I'm going through the core 3 specimin paper as I'm retaking the exam this summer and on my teachers workthrough of the question she integrates the equation in the title as 1/3 ( ln(x^3 + 2) ). What happend to the x in the x^2? I got it as x^3 /3 ( ln(x^3 + 2) ).


    Posted from TSR Mobile
    Offline

    0
    ReputationRep:
    Use integration by substitution, setting u = x^3 +2. That simplifies it nicely, so the integrand is easy to evaluate, and it'll pop out exactly as your teacher has said! Hope this helps.
    Offline

    2
    ReputationRep:
    (Original post by mattjpye)
    Use integration by substitution, setting u = x^3 +2. That simplifies it nicely, so the integrand is easy to evaluate, and it'll pop out exactly as your teacher has said! Hope this helps.
    But the numerator is a derivative of the denominator, so all the OP has to do is adjust for the the 3x^2 by putting the 1/3 in.
    Offline

    0
    ReputationRep:
    If you haven't done integration by substitution, notice that the top is (sort of) the derivative of the bottom. This happens when differentiating ln(f(x)). So d(ln(x^3+2)/dx is equal to 3x^2/(x^3 +2). In your example the top isn't quite the derivative of the bottom, but if you imagine 3*1/3 x^2 on the top the 3's will cancel and you will get 1/3ln(x^3 +2)+c. To check your answer is right you can always differentiate this using the chain rule. Good luck in C3 in summer
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ah! Thank you all! I have done all this, I just forgot about it, this is the first time I've picked p core 3 since the exam so a few things have slipped my mind, thanks.


    Posted from TSR Mobile
 
 
 
Poll
Which pet is the best?
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

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

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