What is the antiderivative of 3x / ((x-1) ^2)

3 ln (x - 1) - 3 / (x - 1) + C

Step-by-step explanation:

∫ 3x / (x - 1) ² dx

3 ∫ x / (x - 1) ² dx

If u = x - 1, then x = u + 1, and du = dx.

3 ∫ (u + 1) / u² du

3 ∫ (1/u + 1/u²) du

3 (ln u - 1/u + C)

3 ln u - 3/u + C

Substitute back:

3 ln (x - 1) - 3 / (x - 1) + C