MHT CET202122 Sep 2021Morning ShiftMathematicsIndefinite IntegrationActual
⁻¹ ( 2 x 1+x^2 ) d x=( where |x| < 1)
Options
- A2 ⁻¹ x- |1+x^2 |+c
- Bx ⁻¹ x+ |1+x^2 |+c
- C⁻¹ x+ |1+x^2 |+c
- D2 x ⁻¹ x- |1+x^2 |+c
Correct answer
D. 2 x ⁻¹ x- |1+x^2 |+c
Step-by-step solution
Let I= ⁻¹ ( 2 x 1+x^2 ) d x When x= , ⁻¹ ( 2 x 1+x^2 )= ⁻¹( 2 )=2 and aligned & dx = ^2 d & I = 2 ^2 d & =2 ^2 d =2 [[ ]- d ] & =2[ tran + | |]+ c & =2 ( ⁻¹ x )( x )+2 | 1 1+ ^2 |+ c & =2 x ⁻¹ x+2 | 1 1+x^2 |+c & =2 x ⁻¹ x+2 |1+x^2 |^ - 1 2 +c=2 x ⁻¹ x- |1+x^2 |+c & aligned