Question

$\int\frac{x\ dx}{(x-1)(x-2)}$ equals
(A)$\log \bigg \arrowvert \frac{(x-1)^2}{x-2}\bigg \arrowvert + C$
(B)$\log \bigg \arrowvert \frac{(x-2)^2}{x-2}\bigg \arrowvert + C$
(C)$\log \bigg \arrowvert \bigg\lgroup \frac{x-1}{x-2}\bigg\rgroup^{2} \bigg \arrowvert + C$
(D)$\log \bigg \arrowvert (x-1)(x-2)\bigg \arrowvert + C$

Answer 1

Answer:

B

Step-by-step explanation:

Hi,

Given integral is

$\int \dfrac{xdx}{(x - 1)(x - 2)}$

Using partial fractions, we can write it as

$\int \dfrac{-dx}{(x - 1)} + \int \dfrac{2dx}{(x - 2)}$

$= -\ln \mid x - 1\mid + 2\ln \mid x - 2\mid + c,$

where c is an arbitrary constant,

We can simplify the above expression as

$= -\ln\mid x - 1\mid + \ln \mid x - 2\mid ^{2} + c,$

$\dfrac{\ln \mid x - 2\mid^{2}}{\ln \mid x - 1\mid} + c,$

There seems to be a typo in Option (B),

Option (B) should be the answer.

Hope, it helps !