If x+1 2x-1dx=f (x ) 2x-1+C where C is a constant of integration, then f (x ) is equal to:

Question

Accepted Answer

Correct answer: D. (c) Let I= x+1 2x-1 dx Put 2x-1=t ∴2x-1=t^2 ⇒ dx= tdt I= (t^2+3)2 dt= t^36+ 3t2+C = (2x-1 )^ 326+ 32 (2x-1 )^ 12+C = 2x-1 ( x+43 )+C =f (x ) 2x-1+C Hence, f (x )= x+43

$If \int \frac{x + 1}{2 x - 1} d x = f (x) 2 x - 1 + C where C is a constant of integration, then f (x) is equal to:$

Solution

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