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int (x dx)/((x-1)(x-2))" equals : "...

`int (x dx)/((x-1)(x-2))" equals : "`

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The correct Answer is:
B
`" Let " (x)/((x-1)(x-2))=(A)/((x-1)) +(B)/((x-2))`
`rArr " " x=A (x-2) +B(x-1)`
x=1 then 1=A (1-2)+0 `rArr` A=-1
x=2 then 2=0 +B(2-1) `rArr` B=2
`:. (x)/((x-1)(x-2))=(1)/((x-1))+(2)/((x-2))`
`:. int (x)/((x-1)(x-2)) dx= int ((-1))/(x-1)dx+ int(2)/(x-2)dx`
` =-log |x-1|+2 log |x-2|+c`
`=- log |x-1|+log |x-2|^(2)+c`
`=log |((x-2)^(2))/(x-1)|+c`
`"(":' Log b- log a = log .(b)/(a)")"`
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