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MHT CET20249 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

The value of I = (x-1) e ^x (x+1)^3 ~d x is

Options

  1. A- e ^x (x+1)^2 + C , (where C is a constant of integration)
  2. B-x e ^x (x+1)^2 + C , (where C is a constant of integration)
  3. Cx e ^x (x+1)^2 + C , (where C is a constant of integration)
  4. De ^x (x+1)^2 + C , (where C is a constant of integration)

Correct answer

D. e ^x (x+1)^2 + C , (where C is a constant of integration)

Step-by-step solution

aligned I & = (x-1) e ^x (x+1)^3 ~d x I & = ( x+1-2 (x+1)^3 ) e ^x ~d x & = [ x+1 (x+1)^3 - 2 (x+1)^3 ] e ^x ~d x & = [ 1 (x+1)^2 - 2 (x+1)^3 ] e ^x ~d x & = e ^x ( 1 (x+1)^2 )+ c aligned e ^x ( f (x)+ f ^ (x) ) d x= e ^x f (x)+ c

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