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KCET2017MathematicsDifferentiation

( x²+2 x+5 d x ) is equal to

Options

  1. A( 1 2 (x+1) x²+2 x+5 +2 |x+1+ x²+2 x+5 |+C )
  2. B( (x+1) x²+2 x+5 +2 |x+1+ x²+2 x+5 |+C )
  3. C( (x+1) x²+2 x+5 -2 |x+1+ x²+2 x+5 |+C )
  4. D( (x+1) x²+2 x+5 + 1 2 |x+1+ x²+2 x+5 |+C )

Correct answer

A. ( 1 2 (x+1) x²+2 x+5 +2 |x+1+ x²+2 x+5 |+C )

Step-by-step solution

Given that, ( x²+2 x+5 d x ) [ = x²+2 x+1+4 d x ] [ = (x+1)²+2² d x ] We know that, ( x²+a² d x= x 2 x²+a² +2 |x+ x²+a² |+C ) So, ( x²+2 x+5 d x ) ( = (x+1) 2 x²+2 x+5 +2 |(x+1)+ x²+2 x+5 |+C )

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