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AP EAMCET20227 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

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

Options

  1. A2 e^ +e
  2. B2 e^ +2 e-2
  3. Ce^ (e+2) 2
  4. De^ ( e-2 2 )

Correct answer

D. e^ ( e-2 2 )

Step-by-step solution

aligned I & = _ +1 ^ e^x( -x) (x- +1)^2 d x= _ +1 ^ e^x( -x-1+1) (x- +1)^2 d x & = _ +1 ^ e^x [ 1 (x- +1)^2 - 1 (x- +1) ] d x & = [- e^x (x- +1) ]_ +1 ^ & =-e^ + e^ +1 2 =e^ [ e-2 2 ] aligned

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