AP EAMCET202119 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual
If ∫ ( x - 1 ) 2 x 2 + 1 2 d x = tan - 1 x + g x + k , then g ( x ) is equal to
Options
- Atan − 1 ⁡ x 2
- B1 x 2 + 1
- C1 2 x 2 + 1
- D2 x 2 + 1
Correct answer
B. 1 x 2 + 1
Step-by-step solution
Given that ∫ x - 1 2 x 2 + 1 2 d x =   ∫ x 2 + 1 - 2 x x 2 + 1 2 d x =   ∫ x 2 + 1 x 2 + 1 2 d x   -   ∫ 2 x x 2 + 1 2 d x =   ∫ 1 x 2 + 1 d x   -   ∫ 2 x   x 2 + 1 - 2 d x We know that ∫ f ' x f x n   d x   =   f x n + 1 n + 1 + c =   tan - 1 x   + x 2 + 1 - 1 + c So g x   =   1 x 2 + 1 .