Question

x^2/(x^2-1)

Answer 1

This is part of an integral by parts q, which apparently needs long division...

Answer 2

Rearrange the numerator It will become simple then..

Answer 3

I got 1+1/(x^2-1) as the answer, but apparently it's 1- 1/2(x+1) +2/2(x-1)

Answer 4

1 + 1/(x^2 - 1) is your quotient from long div?

Answer 5

\[x^2 \implies x^2 - 1 + 1\]

Answer 6

So it will become:

\[\int\limits 1.dx + \int\limits \frac{1}{x^2 - 1}dx\]

Answer 7

@waterineyes i think the book used PFs..

Answer 8

dont you think so?

Answer 9

hmmm.....

Answer 10

PF ??

Answer 11

partial fractions

Answer 12

There is a special formula for the last part..

Answer 13

well iggy I did x^2- 1 | x^2 and x^2/x^2 = 1 1 * x^2 = x^2 1 * -1 = -1..

Answer 14

since there was nothing else I did what your sheet said and did 1/x^2-1

Answer 15

\[\frac{1}{x^2 - 1} = \frac{A}{x+1} + \frac{B}{x-1}\]
are you familiar with that method?

Answer 16

@KonradZuse you are right...but the book or whoever provided the answer took it a step more

Answer 17

Yes I am.

Answer 18

Oic yeah...

Answer 19

i was referring to konrad lol. i know you're familiar