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MHT CET20243 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

The value of (x-1) e ^x (x+1)^3 ~d x is equal to

Options

  1. Ae ^x (x+1) + c , (where c is constant of integration)
  2. Be ^x (x+1)^2 + c , (where c is constant of integration)
  3. C- e ^x (x+1) + c , (where c is constant of integration)
  4. D- e ^x (x+1)^2 + c , (where c is constant of ' integration)

Correct answer

B. e ^x (x+1)^2 + c , (where c is constant of integration)

Step-by-step solution

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

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