Question Detail

To integrate ∫ 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 term by term: ∫ (1 + 1/(x-1)) dx = ∫ 1 dx + ∫ 1/(x-1) dx.The integral of 1 with respect to x is x.The integral of 1/(x-1) with respect to x is ln|x-1|.So, the result is x + ln|x-1| + C.Comparing with the given options, option B matches the result (assuming the constant of integration C is implicit).