Question

integrate
(1-x^2)/[x(1-2x)]dx

Answer 1

\[\int\frac{1-x^2}{x(1-2x)}dx\]
Have you tried partial fraction decomposition?

Answer 2

partial fraction cannot work, for that degree of numerator must be strictly less than degree of denom.

Answer 3

So long division first, then PFD.

Answer 4

yes.

Answer 5

I'd suggest rewriting as
\[\int\frac{x^2-1}{2x^2-x}dx\]
That should help with the long division

Answer 6

k

Answer 7

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

Answer 8

if you wantt o avoid long division....

Answer 9

got that ? ^ :P

Answer 10

hmmm..i have solveed it acc to 2 u @hartnn and i got
1/2[1+(1/2x-1)-(2/2x^2-x)]

Answer 11

you got that as final answer ?
and where is +c ?

Answer 12

nahi yaar
till now i have only put value

Answer 13

yup i got the answer and have checked it from wolfram
Thank You so much @hartnn

Answer 14

ohh...i was verifying manually :P
welcome ^_^