The value of ₀^ / 2 3 x+1 2 x-1 d x is

Step-by-step solution

Let aligned I= ₀^ / 2 3 x+1 2 x-1 d x &= ₀^ / 2 3 x- 3 3 2 ( x- 3 ) d x = ₀^ / 2 (4 ³ x-3 x )- (4 ³ 3 -3 3 ) 2 ( x- 3 ) d x =& 2 ₀^ / 2 ( ³ x- ³ 3 x- 3 ) d x = 3 2 ₀^ / 2 ( x- 3 x- 3 ) d x =& ₀^ / 2 (1+ 2 x+ 1 2 + x ) d x- 3 4 =& 3 4 +1- 3 4 =1 aligned