AP EAMCET202422 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
1 (1+x^2 ) x^2+2 d x=
Options
- A- ⁻¹ x^2+2 |x| +c
- B- ⁻¹ x^2+2 +c
- C⁻¹ x^2+1 x^2+2 +c
- D- ⁻¹ x^2+2 x^2+1 +c
Correct answer
A. - ⁻¹ x^2+2 |x| +c
Step-by-step solution
I= 1 (1+x^2 ) x^2+2 d x Let x= 2 u d x= 2 ^2 u d v aligned & I = 2 ^2 u (2 ^2 u+1 ) 2 ^2 u+2 d u & I = u 2 ^2 u+1 d u aligned I = - u cosec u (- 1 cosec ^2 u+1 ) d u Let v = cosec u d v=- u cosec u d u aligned & I =- 1 v^2+1 d v=- ⁻¹ v+c & I =- ⁻¹( cosec u)+ c =- ⁻¹ x^2+2 |x| +c aligned