Question

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

Answer 1

Answer:

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