COMEDK20269 May 2026Evening ShiftMathematicsIndefinite IntegrationActual
⁻¹ ( 1 - x 1 + x ) , dx =
Options
- A2 x - x^2 4 + C
- B4 - x 4 + C
- C4 x - x^2 2 + C
- D4 x - x^2 4 + C
Correct answer
D. 4 x - x^2 4 + C
Step-by-step solution
⁻¹ ( 1 - x 1 + x ) , dx 1 - x 1 + x = 1 - ( /2 - x) 1 + ( /2 - x) Using the half-angle formulas 1 - = 2 ^2( /2) and 1 + = 2 ^2( /2) : 2 ^2( /4 - x/2) 2 ^2( /4 - x/2) = ^2( /4 - x/2) = ( /4 - x/2) Substituting this back into the integral: ⁻¹ ( ( /4 - x/2) ) , dx = ( 4 - x 2 ) , dx Integrating with respect to x : 4 x - x^2 4 + C Answer: 4 x - x^2 4 + C