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JEE Main201912 Apr 2019Morning ShiftMathematicsIndefinite IntegrationActual

The integral ∫ 2 x 3 - 1 x 4 + x d x , is equal to

Options

  1. A1 2 l o g e ( x 3 + 1 ) 2 | x 3 | + C
  2. Bl o g e | x 3 + 1 | x 2 + C
  3. Cl o g e x 3 + 1 x + C
  4. D1 2 l o g e | x 3 + 1 | x 2 + C

Correct answer

C. l o g e x 3 + 1 x + C

Step-by-step solution

I = ∫ 2 x 3 - 1 x 4 + x d x ⇒ I = ∫ 2 x - 1 x 2 x 2 + 1 x d x Put, x 2 + 1 x = t ⇒ 2 x - 1 x 2 d x = d t ∴ I = ∫ d t t = l o g e t + C = l o g e x 2 + 1 x + C = l o g e x 3 + 1 x + C

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