AP EAMCET2016MathematicsIndefinite Integration
x (x^2+2 x+2 )^2 d x is equal to
Options
- Ax^2+2 x^2+2 x+2 - 1 2 ⁻¹(x+1)+C
- Bx^2+2 2 (x^2+2 x+2 ) - 1 2 ⁻¹(x-1)+C
- Cx^2-2 4 (x^2+2 x+2 ) - 1 2 ⁻¹(x+1)+C
- D2(x-1) (x^2+2 x+2 ) + 1 2 ⁻¹(x+1)+C
Correct answer
C. x^2-2 4 (x^2+2 x+2 ) - 1 2 ⁻¹(x+1)+C
Step-by-step solution
aligned & Let, l= x (x^2+2 x+2 )^2 d x & l= x [(x+1)^2+1 ]^2 d x aligned Put x+1= aligned & d x= ^2 d l & = ( -1) ^2 ( ^2 +1 )^2 d & = ( -1) ^2 ^4 d aligned aligned & = ( ^2 - 1 ^2 ) d & = ( - ^2 ) d & = 1 2 (2 -2 ^2 ) d & = 1 2 ( 2 -1- 2 ) d & = 1 2 ( - 2 2 - - 2 2 )+C & =- 1 4 [ 2 + ^ 2 ]- 1 2 +C & =- 1 4 [ 1- ^2 1- ^2 + 2 1+ ]- 1 2 ⁻¹(x+1)+C & =- 1 4 [ 1- ^2 +2 1+ ^2 ]- 1 2 ⁻¹(x+1)+C & l=- 1 4 [ x^2-2 x^2+2 x+2 ]- 1 2 ⁻¹(x+1)+C aligned