AP EAMCET202318 May 2023Morning ShiftMathematicsIndefinite IntegrationActual
x^2 (x^2-1 ) (x^2+1 ) d x=
Options
- A1 4 | x+1 x-1 |- 1 2 Tan ⁻¹ x+c
- B1 4 | x-1 x+1 |+ 1 2 Tan ⁻¹ x+c
- C1 4 | x-1 x+1 |- 1 2 Tan ⁻¹ x+c
- D1 4 | x+1 x-1 |+ 1 2 Tan ⁻¹ x+c
Correct answer
B. 1 4 | x-1 x+1 |+ 1 2 Tan ⁻¹ x+c
Step-by-step solution
Let x^2 (x^2-1 ) (x^2+1 ) d x=I I= 1 2 ( 1 x^2-1 + 1 x^2+1 ) d x aligned & = 1 2 1 2 | x-1 x+1 |+ 1 2 ⁻¹ x+c & = 1 4 | x-1 x+1 |+ 1 2 ⁻¹ x+c aligned