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KCET2017MathematicsThree Dimensional Geometry

( (x+3) e^ x (x+4)² d x ) is eqal to

Options

  1. A( 1 (x+4)² +C )
  2. B( e^ x (x+4)² +C )
  3. C( e^ x (x+4) +C )
  4. D( e^ x (x+3) +C )

Correct answer

C. ( e^ x (x+4) +C )

Step-by-step solution

Given that ( (x+3) e^ x (x+4)² d x ) ( = e^ x (x+4-1) (x+4)² d x ) ( = e^ x [ 1 x+4 - 1 (x+4)² ] d x ) Since, ( e^ x (f(x)+f^ (x) ) d x=e^ x f(x)+c . ) So, ( (x+3) e^ x (x+4)² d x= e^ x x+4 +c )

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