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AP EAMCET202422 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

x^2-1 x^3 2 x^4-2 x^2+1 d x

Options

  1. A1+2 x^2+2 x^4 2 x^2 +c
  2. B(1+2 x^2+2 x^4 )^ 1 2 2 x^2 +c
  3. C1-2 x^2+2 x^4 2 x^2 +c
  4. D(1-2 x^2+2 x^4 )^ 1 2 2 x^2 +c

Correct answer

D. (1-2 x^2+2 x^4 )^ 1 2 2 x^2 +c

Step-by-step solution

Let I= x^2-1 x^3 2 x^4-2 x^2+1 d x Divide numerator and denominator by x^5 . aligned & I= 1 x^3 - 1 x^5 2- 2 x^2 + 1 x^4 d x & Let 2- 2 x^2 + 1 x^4 =t ( 4 x^3 - 4 x^5 ) d x=d t & I= 1 4 1 t d t I= t 2 +c & I= (1-2 x^2+2 x^4 )^ 1 2 2 x^2 +c . aligned

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