AP EAMCET202316 May 2023Evening ShiftMathematicsIndefinite IntegrationActual
⁻¹ x - ⁻¹ x x ( ⁻¹ x + ⁻¹ x ) d x=
Options
- A2 [ ⁻¹ x (2 x-1)+ x(1-x) ]+x+C
- B8 ( ( x ⁻¹ x - 1-x ) )-2 x +C
- C2 [(2 x-1) ⁻¹ x - x(1-x) ]-x+C
- D2 [(2 x-1) ⁻¹ x - x(1-x) ]+x+C
Correct answer
B. 8 ( ( x ⁻¹ x - 1-x ) )-2 x +C
Step-by-step solution
Let I= ⁻¹ x - ⁻¹ x x ( ⁻¹ x + ⁻¹ x ) d x aligned & Let x = t 1 2 x dx = dt & I =2 ⁻¹ t - ⁻¹ t 2 dt = 4 (2 ⁻¹ t - 2 ) dt & = 8 -1 tdt -2 dt & = 8 [ x ⁻¹ x - 1- x ]-2 x + C aligned