AP EAMCET202119 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual
∫ 1 + x + x + x 2 x + 1 + x d x =
Options
- A1 2 1 + x + c
- B2 3 ( 1 + x ) 3 2 + c
- C1 + x + c
- D2 ( 1 + x ) 3 2 + c
Correct answer
B. 2 3 ( 1 + x ) 3 2 + c
Step-by-step solution
∫ 1 + x + x + x 2 x + 1 + x d x = ∫ ( 1 + x ) 2 + x 1 + x x + 1 + x d x = ∫ 1 + x [ 1 + x + x ] x + 1 + x d x = ∫ ( 1 + x ) 1 2 d x Using ∫ x n d x = x n + 1 n + 1 + c , = ( 1 + x ) 3 2 3 2 + c = 2 3 1 + x 3 2 + c .