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MHT CET20242 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

( x+2 x+4 )^2 e^x d x=

Options

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

Correct answer

A. e ^x ( x x+4 )+ c , where c is a constant of integration.

Step-by-step solution

aligned & I = ( x+2 x+4 )^2 e ^x ~d x &= ( x^2+4 x+4 (x+4)^2 ) e ^x ~d x &= e ^x [ x(x+4) (x+4)^2 + 4 (x+4)^2 ] d x &= e ^x [ x (x+4) + 4 (x+4)^2 ] d x &= e ^x ( x x+4 )+ c & [ ( f (x)+ f ^ (x) e ^x ~d x= e ^x f (x)+ c ) ] aligned

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