`int(xdx)/((x-1)(x-2))` बराबर है:

Options

A. `log|((x-1)^(2))/(x-2)|+C`
B. `log|((x-2)^(2))|+C`
C. `log|((x-1)^(2))/(x-1)|+C`
D. `log|(x-1)(x-2)|+C`

Answer

B

Explanation

माना `(x)/((x-1)(x-2))=(A)/((x-1))+(B)/((x-2))`
`rArr" "x=A(x-2)+B(x-1)`
`{:(x=1,"तो ",1=A(1-2)+0 ,rArr.,A=-1),(x=2,"तो ", 2=0+B(2-1),rArr., B=2):}`
`therefore" "(x)/((x-1)(x-2))=-(1)/((x-1))+(2)/((x-2))`
`therefore" "int(x)/((x-1)(x-2))dx=int((-1))/(x-1)dx+int(2)/(x-2)dx`
`=-log|x-1|+2log|x-2|+C`
`=-log|x-1|+log|x-2|^(2)+C`
`=log|((x-2)^(2))/(x-1)|+C`
`(because log b - log a = log. (b)/(a))`