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Manipal MET2014MathematicsIndefinite Integration

d x x- x+ 2 is equal to

Options

  1. A- 1 2 ( x 2 + 8 )+C
  2. B1 2 ( x 2 + 8 )+C
  3. C1 2 ( x 2 + 8 )+C
  4. D- 1 2 ( x 2 + 8 )+C

Correct answer

D. - 1 2 ( x 2 + 8 )+C

Step-by-step solution

aligned & Let, I= d x x- x+ 2 & aligned & I= d x 2 ( 1 2 x- 1 2 x )+ 2 &= 1 2 d x 1- (x+ 4 ) = 1 2 d x 2 ^2 ( x 2 + 8 ) &= 1 2 2 d x ^2 ( x 2 + 8 ) = 1 2 2 &= 1 2 2 [ - ( x 2 + 8 ) 1 2 ]+C &=- 1 2 ( x 2 + 8 )+C aligned aligned

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