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MHT CET202314 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

The value of e ^x ( x^2+4 x+4 (x+4)^2 ) d x is

Options

  1. Ae ^x ( x x+4 )+ c , where c is a constant of integration.
  2. Be ^x ( 4 x+4 )+ c , where c is a constant of integration.
  3. Ce ^x ( x (x+4)^2 )+ c , where c is a constant of integration.
  4. De ^x ( 4 (x+4)^2 )+ 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 & e ^x [ x^2+4 x+4 (x+4)^2 ] d x & = e ^x [ x(x+4)+4 (x+4)^2 ] d x & = e ^x [ x x+4 + 4 (x+4)^2 ] d x aligned aligned = e ^x ( x x+4 )+ c & & [ e ^x [ f (x)+ f ^ (x) ] d x= e ^x f (x)+ c ] aligned

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