The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

integrating a partial fraction HELP!

Could anyone walk me through how to integrate the following please :

2(x^2 + 3x - 1)/(x+1)(2x-1)

thanks in advance :biggrin:
Reply 1
Avatar for BJack
BJack
19
Original post by guitarmike456
Could anyone walk me through how to integrate the following please :

2(x^2 + 3x - 1)/(x+1)(2x-1)

thanks in advance :biggrin:


One approach would be to rewrite the fraction as

(2x−1)(x+1)+...(2x−1)(x+1)\displaystyle \frac{(2x-1)(x+1) + ...}{(2x-1)(x+1)}

and then use that to reach

1+A2x−1+Bx+11 + \displaystyle \frac{A}{2x-1} + \frac{B}{x+1}

where A and B are constants found in the usual way. This is then a simple integration.
Reply 2
Avatar for guitarmike456
guitarmike456
OP
9
Original post by BJack
One approach would be to rewrite the fraction as

(2x−1)(x+1)+...(2x−1)(x+1)\displaystyle \frac{(2x-1)(x+1) + ...}{(2x-1)(x+1)}

and then use that to reach

1+A2x−1+Bx+11 + \displaystyle \frac{A}{2x-1} + \frac{B}{x+1}

where A and B are constants found in the usual way. This is then a simple integration.


I tried that, and got A/x+1 + B/2x-1 = 5x + 1
but that gives nasty numbers forB and A so I'm fairly sure its wrong?
Reply 3
Avatar for guitarmike456
guitarmike456
OP
9
2(x2+3x?1) / (x+1)(2x?1) ?1+A/x+1 +B /2x?1

? 2x2+6x?2?(x+1)(2x?1)+A(2x?1)+B(x+1)

can someone confirm that the above is surely incorrect?
Reply 4
Avatar for BJack
BJack
19
Original post by guitarmike456
I tried that, and got A/x+1 + B/2x-1 = 5x + 1
but that gives nasty numbers forB and A so I'm fairly sure its wrong?


It should be 5x-1.
Reply 5
Avatar for guitarmike456
guitarmike456
OP
9
Original post by BJack
It should be 5x-1.


Thanks :biggrin:

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you