Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Quickie integration question!

Hi, can someone show me how to integrate (x-1)/(x+1) ?? ~ can someone help? thanks very much!! :biggrin:

:biggrin:

use integration by parts. uv- integral udv/dx
(x-1) times (x+1) to the power of -1
v= x-1
dv/dx=1
du/dx=(x+1) to the power of -1
u= in (x+1)
so it becomes (x-1)In (x+1) - integral of In(x+1)
(x-1)In(x+1) - In(x-1) +x
x-2In(x+1)
gosh its so hard typing up things on computer. i couldnt use integral sign or any thing so i just typed up the word.

Integration by parts works, but it's easier to write

(x - 1)/(x + 1)
= 1 - 2/(x + 1)

and integrate 1 and 2/(x + 1) separately.

rockiee

Hi, can someone show me how to integrate (x-1)/(x+1) ?? ~ can someone help? thanks very much!! :biggrin:

:biggrin:

INT (x-1)/(x+1).dx
= INT (x+1-2)/(x+1).dx
= INT (x+1)/(x+1) - 2/(x+1) .dx
= INT 1 - 2/(x+1) .dx
= x - 2ln|x+1| + c

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