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KCET2023MathematicsIndefinite Integration

5-2 x+x^2 d x is equals to

Options

  1. Aaligned & x 2 5-2 x+x^2 +4 (x+1) & + x^2-2 x+5 +C aligned
  2. Baligned x-1 2 5+2 x+x^2 +2 (x-1) + 5+2 x+x^2 +C aligned
  3. Caligned x-1 2 5-2 x+x^2 +2 (x-1) + 5-2 x+x^2 +C aligned
  4. Daligned x-1 2 5-2 x+x^2 +2 (x+1) + x^2+2 x+5 +C aligned

Correct answer

C. aligned x-1 2 5-2 x+x^2 +2 (x-1) + 5-2 x+x^2 +C aligned

Step-by-step solution

Let aligned I & = 5-2 x+x^2 d x I & = (x-1)^2+(2)^2 aligned We know that aligned & [ x^2+a^2 = x 2 x^2+a^2 . & . + a^2 2 |x+ x^2+a^2 | ] & = x-1 2 5-2 x+x^2 & +2 |(x-1)+ 5-2 x+x^2 |+C aligned

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