∫ log(x) dx

Using "Integration by parts" or "reverse chain rule" .
Recall formula for intergration by parts: "∫f'(x) g(x) dx = f(x)g(x) - ∫f(x)g'(x)dx"
Then set f'(x) = 1, g(x) = log(x). Can calculate f(x) = x, g'(x) = 1/x.
Then plug into the formula to get ∫log(x)dx = xlog(x) - ∫1 dx = xlog(x) - x +c