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MHT CET202313 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

x-3 (x-1)^3 e ^x ~d x=

Options

  1. Ae ^x ( 1 (x-1)^2 )+ c , where c is constant of integration,
  2. Be ^x ( 1 x+1 )+ c , where c is constant of integration.
  3. Ce ^x ((x-1)^2 )+ c , where c is constant of integration.
  4. De ^x ((x-1)^3 )+ c , where c is constant of integration.

Correct answer

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

Step-by-step solution

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