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AP EAMCET20226 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

( 2 x+1 (2+ x)^2 d x )- x 2+ x =

Options

  1. A1 2+ x +C
  2. Bx+C
  3. C2 2+ x +C
  4. DC

Correct answer

D. C

Step-by-step solution

Let f(x)= x 2+ x aligned f^ (x) & = (2+ x) x- x(- x) (2+ x)^2 & = 2 x+1 (2+ x)^2 aligned x 2+ x is the antiderivatives of 2 x+1 (2+ x)^2 aligned & ( 2 x+1 (2+ x)^2 ) d x= x 2+ x +C & (2 x+1) (2+ x)^2 d x- x 2+ x =C aligned

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