What is the integral of log of x?

Answer 1

Assuming you mean natural logs (as 'log' by itself means logs to any base):

∫ln x dx = x ln x - x + C

let y = ln x → ey = x → ey dy = dy

→ ∫ln x dx = ∫y ey dy

But ∫uv = u∫v - ∫u'∫v

let u = y → u' = 1

let v = ey

→ ∫y ey dy = y∫ey dy - ∫∫ ey dy

= y ey - ey + C

= (ln x) x - x + C

= x ln x - x + C