Integrating x²/(x² - 1)

Hello, please may someone tell me where I've went wrong on this because the answers say x + 0.5ln((x - 1)/(x + 1)) and i don't know where they've gotten the first term, x, from 🙂

I've posted my workings as well as the question and the answers section whilst I'm at it 😄

Reply 1

DeFreedomWey

OP

11

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189C8592-AB74-4D6F-840F-AD98A7874F13.jpg.jpeg

(14iii)

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Reply 2

zetamcfc

19

Have a think about how you work out your A and B seen as for your values you don't get x^2 =A(x-1) +B(x+1).

Original post by DeFreedomWey

(14iii)

Reply 3

London090

20

Ahaha I'm currently doing math revision at the moment so I've started working out your question but whilst you wait try using this website :smile:

https://www.symbolab.com

Super helpful and it shows you the steps!

Reply 4

London090

20

Actually here's the step by step answer, much faster than me explaining it😂

https://www.symbolab.com/solver/step-by-step/%5Cint%20%5Cfrac%7Bx%5E%7B2%7D%7D%7Bx%5E%7B2%7D-1%7D

Reply 5

Sinnoh

22

Rewrite the integrand as

\dfrac{ x^2 - 1 + 1}{x^2 - 1}

then split it into

\dfrac{x^2 - 1}{x^2 - 1} + \dfrac{1}{x^2 - 1}

(edited 4 years ago)

Reply 6

DeFreedomWey

OP

11

Original post by London090

Actually here's the step by step answer, much faster than me explaining it😂

https://www.symbolab.com/solver/step-by-step/%5Cint%20%5Cfrac%7Bx%5E%7B2%7D%7D%7Bx%5E%7B2%7D-1%7D

How did they do the step directly after "apply the sum rule"? :smile:

what level is this? if its further maths you are given the integral anyway

Reply 8

zetamcfc

19

Original post by DeFreedomWey

How did they do the step directly after "apply the sum rule"? :smile:

Partial fractions on 1/(1-x^2).

Reply 9

Unknown1405

1

Add and subtract 1 to x² so the eqn will be x² 1-1/(x²-1) split it up to (x²-1/x²-1) (1/x²-1) first one will be cancelled hence it will be integral dx which is x and integration of 1/x²-1 will be 0.5ln(x 1/x-1) Hence answer will be x 0.5ln(x 1/x-1) hope u like it ☺☺

Reply 10

username1732133

15

Original post by Unknown1405

Add and subtract 1 to x² so the eqn will be x² 1-1/(x²-1) split it up to (x²-1/x²-1) (1/x²-1) first one will be cancelled hence it will be integral dx which is x and integration of 1/x²-1 will be 0.5ln(x 1/x-1) Hence answer will be x 0.5ln(x 1/x-1) hope u like it ☺☺

Old thread.

Integrating x²/(x² - 1)

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