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MHT CET202211 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual

( x-1)^2 [1+( x)^2 ]^2 d x= (where C is constant of integration.)

Options

  1. Ax (1+ x)^2 +C
  2. Be^ x 1+ x +C
  3. Cx 1+( x)^2 +C
  4. 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

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