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AP EAMCET202124 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual

x+ x 1+ x d x is equal to

Options

  1. Ax ( x 2 )+c
  2. B( x 2 )+c
  3. C( x 2 )+c
  4. Dx ( x 2 )+c

Correct answer

D. x ( x 2 )+c

Step-by-step solution

Let I= x+ x 1+ x d xI= 1 2 (x ^2 x / 2 ) d x+ x / 2 d x aligned I= & x 1 2 ^2 x / 2 d x- & ( d x d x 1 2 ^2 x / 2 d x ) d x+ x / 2 d x aligned I=x x / 2- x / 2 d x+ x / 2 d x+cI=x (x / 2)+c

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