[xxzzy]

Hi,
I am attempting to solve an integration problem.

x^2 Numerator
(8 - 3x^2) Denominator.

I would like to see the steps, as textbooks that I have consulted either avoid a question type like this or use various greek letters to show the steps but which are confusing. I realise that substitution must be used but surely this is after you take the lower line (8 - 3x^2) up to the top line and give it a negative power (-1). What then happens to the x^2 does it multiply into bracket (8 - 3x^2)?

Grateful for help.
Regards
Sandy Forrester:( :(

[jiten55]

x^2/(8 - 3 x^2) = 1/3 [8/(8 - 3x^2) - 1]

= A + B

A = (8/3)/(8 - 3x^2), B = -1/3


Integral of B = -1/3 x

For integral of A,

Use formula for Integral of 1/(a^2 - u^2)

= (1/2a) log [(a + u)/(a - u) ]

Without using formula, you can see:

1/(a^2 - u^2) = (1/2a) [1/(a - u) + 1/ (a + u)]

from which you can derive the formula.

I hope the above is clear, if not let me know.