Question

Find: `int 1/(x(x^2-1))  dx.`

Answer 1

`int 1/(x(x^2-1))  dx.`

`= int x/(x^2(x^2-1))  dx`

`= 1/2 int dt/(t(t-1))             ...[(x^2 = t),(2x  dx = dt)]`

`= 1/2 [intdt/(t-1) - int dt/t]`

`= 1/2 [log(t-1)-log(t)]+c`

`= 1/2 log ((x^2-1)/x^2)+c`