If xf(x) = 3f 2(x) + 2, then (\integral\_{}^{}\frac{2x^{2} -... | MATH - INTEGRATION BY SUBSTITUTION | SolveeIt | Solveeit

Today, August 24

Question

If xf(x) = 3f ²(x) + 2, then $\int_{}^{}\frac{2x^{2} - 12xf(x) + f(x)}{(6f(x) - x)(x^{2} - f(x))^{2}}$ dx equals-

A

$\frac{1}{x^{2} - f(x)}$ + c

B

$\frac{1}{x^{2} + f(x)}$ + c

C

$\frac{1}{x - f(x)}$ + c

D

$\frac{1}{x + f(x)}$ + c

Answer

$\frac{1}{x^{2} - f(x)}$ + c

Explanation

Solution

f ¢ (x) = $\frac { f ( x ) } { 6 f ( x ) - x }$

Now I = dx

̃ I = –dx = $\frac { 1 } { x ^ { 2 } - f ( x ) }$ + C