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If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 x...

`If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x))^2)dx` equal. (A)`1/(x^2-f(x))+c` (B) `1/(x^2+f(x))+c` (C) `1/(x-f(x))+c` (D) `1/(x+f(x))+c`

A

`(1)/(x^(2)-f(x))+c`

B

`(1)/(x^(2)+f(x))+c`

C

`(1)/(x-f(x))+c`

D

`(1)/(x+f(x))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
`f'(x)=(f(x))/(6f(x)-x)`
Now, `I= int(2x^(2)-12xf(x)+f(x))/((6f(x)-x)(x^(2)-f(x))^(2))dx`
`= -int(2x-f'(x))/((x^(2)-f(x))^(2))dx`
`=(1)/(x^(2)-f(x))+C`
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