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AP EAMCET202420 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

2 x^2-3 (x^2-4 ) (x^2+1 ) d x= Atan ⁻¹ x+ B (x-2)+ C (x+2) then 6 A+7 B-5 C=

Options

  1. A9
  2. B10
  3. C6
  4. D8

Correct answer

A. 9

Step-by-step solution

(2 x^2-3 ) (x^2-4 ) (x^2+1 ) d x= (2 (x^2+1 )-5 ) (x^2-4 ) (x^2+1 ) d x= 2 x^2-4 d x- ( 1 x^2-4 - 1 x^2+1 ) d x= 1 x^2-4 d x+ 1 x^2+1 d x= 1 4 ( x-2 x+2 )+ ⁻¹ x= 1 4 (x-2)- 1 4 (x+2)+ ⁻¹ xA=1 ; B= 1 4 ; C=- 1 4 6 A+7 B-5 C=6+ 7 4 + 5 4 =9

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