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COMEDK2017MathematicsIndefinite Integration

The value of d x x + [3] x is

Options

  1. A3 x +3( [3] x )-6 [6] x + ( [6] x +1)+C
  2. B2 x +6( [6] x )-6 ( [6] x +1)+C
  3. C2 x -3( [3] x )+6 [6] x -6 ( [6] x +1)+C
  4. DNone of the above

Correct answer

C. 2 x -3( [3] x )+6 [6] x -6 ( [6] x +1)+C

Step-by-step solution

Let I= d x x + [3] x Put x=t⁶ d x=6 t⁵ d t aligned I &= 6 t⁵ t³+t² d t=6 t³ t+1 d t &=6 (t²-t+1- 1 t+1 ) d t &=2 t³-3 t²+6 t-6 (t+1)+C &=2 x -3( [3] x )+6( [6] x )-6 ( [6] x +1)+C aligned

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