Question Detail

To evaluate ∫ (x / (x-1)) dx, we can use algebraic manipulation. Rewrite the integrand as:(x / (x-1)) = ( (x-1) + 1 ) / (x-1) = 1 + (1 / (x-1))Now, integrate each term:∫ (1 + 1/(x-1)) dx = ∫ 1 dx + ∫ (1/(x-1)) dx∫ 1 dx = x∫ (1/(x-1)) dx = ln|x-1|Combining these, we get: x + ln|x-1| + C. Option B matches this result (assuming x-1 > 0).