Does anyone know the antiderivative of x/(x-1) ?

Question

Anyone know whether the integral x/(x-1) domain: [2, infinity) converges or diverges? Or the antiderivative of the integral?

Answer 1

Hi,
Antiderivative of x/(x-1):
(I'm going to leave out the integral sign until I've finished manipulating the expression.)

∫ x/(x-1)dx
=[x/(x-1) -1/(x-1) +1/(x-1)]dx
=[(x-1)/(x-1) +1/(x-1)dx]
=∫dx +∫dx/(x-1)
= x + ln(x-1) + C

Hope this helps.
FE