MHT CET202211 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual
( x-1)^2 [1+( x)^2 ]^2 d x= (where C is constant of integration.)
Options
- Ax (1+ x)^2 +C
- Be^ x 1+ x +C
- Cx 1+( x)^2 +C
- Dx 1+( x)^2 +C
Correct answer
C. x 1+( x)^2 +C
Step-by-step solution
aligned & ( x-1)^2 1+( x)^2 ^2 ~d x= ( x)^2+1-2 x 1+( x)^2 ^2 ~d x & = 1 1+( x)^2 - 2 x 1+( x)^2 ^2 d x & x -2 x x (1+( x)^2 )^2 + 1 1+( x)^2 d x & = x 1+( x)^2 +C aligned