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AP EAMCET201920 Apr 2019Evening ShiftMathematicsIndefinite IntegrationActual

If x -3 2 , then x^2 2 x^2+6 2 x+9 d x=

Options

  1. A1 2 2 [( 2 x+3)-6 | 2 x+3|- 9 2 x+3 ]+c
  2. B1 2 2 [ 2 x+3-6 |( 2 x+3)|+ 9 2 x+3 ]+c
  3. C2 x+3-6 ( 2 x+3)+c
  4. D(2 x^2+6 2 x+9 )+c

Correct answer

A. 1 2 2 [( 2 x+3)-6 | 2 x+3|- 9 2 x+3 ]+c

Step-by-step solution

Given, aligned & x^2 2 x^2+6 2 x+9 d x & 1 2 (2 x^2+6 2 x+9 )- (3 2 x+ 9 2 ) 2 x^2+6 2 x+9 d x & [ x^2= (2 x^2+6 2 x+9 ) 1 2 - (3 2 x+ 9 2 ) ] & ( 1 2 - (3 2 x+ 9 2 ) 2 x^2+6 2 x+9 ) d x & 1 2 d x- 3 2 x+ 9 2 2 x^2+6 2 x+9 d x & aligned 3 2 x+ 9 2 =A d d x (2 x^2+6 2 x+9 )+B On comparison, we get aligned & 4 A=3 2 & 6 2 A+B= 9 2 & A= 3 2 4 & 6 2 3 2 4 +B= 9 2 & B=- 9 2 aligned Substituting values of A, B Eq. (ii) Substituting Eq. (iii) in Eq. (i) gathered x 2 - ( 3 2 4 (4 x+6 2 )- 9 2 ) d x 2 x^2+6 2 x+9 x 2 - 3 2

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