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AP EAMCET20225 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

1 x^2 (2 x+1)^3 d x is equal to

Options

  1. A4 x^2+12 x+6 x- 1 x +C
  2. B4 x^2+12 x-6 x- 2 x +C
  3. C2 x^2+8 x+3 x- 2 x +C
  4. D8 x^2+6 x+6 x+ 2 x +C

Correct answer

A. 4 x^2+12 x+6 x- 1 x +C

Step-by-step solution

We have, 1 x^2 (2 x+1)^3 d x aligned & = (8 x^3+1+12 x^2+6 x ) x^2 d x & = (8 x+12+ 6 x + 1 z^2 ) d x aligned [ array c x^n d x= x^ n+1 n+1 +c, n -1 d x x = x+c, x>0 array ]=4 x^2+12 x+6 x- 1 x +C

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