Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202119 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual

Which of the following is a partial fraction of - x 2 + 6 x + 13 ( 3 x + 5 ) x 2 + 4 x + 4 =

Options

  1. A3 3 x + 5 + − 1 x + 2 + 2 ( x + 2 ) 2
  2. B2 3 x + 5 + − 1 x + 2 + 3 ( x + 2 ) 2
  3. C− 1 3 x + 5 + 2 x + 2 + 3 ( x + 2 ) 2
  4. D3 3 x + 5 + 2 x + 2 + − 1 ( x + 2 ) 2

Correct answer

B. 2 3 x + 5 + − 1 x + 2 + 3 ( x + 2 ) 2

Step-by-step solution

Given, - x 2 + 6 x + 13 ( 3 x + 5 ) x 2 + 4 x + 4 = - x 2 + 6 x + 13 ( 3 x + 5 ) x + 2 2 Using Partial fraction rules, we get - x 2 + 6 x + 13 ( 3 x + 5 ) x + 2 2 = A 3 x + 5 + B x + 2 + C x + 2 2 ⇒ - x 2 + 6 x + 13 = A x + 2 2 + B x + 2 3 x + 5 + C 3 x + 5 Putting x = - 2 , we get C = 3 Putting x = - 5 3 , we get A = 2 and on comparing coefficients of x 2 , we get B = - 1 i.e. - x 2 + 6 x + 13 ( 3 x + 5 ) x + 2 2 = 2 3 x + 5 - 1 x + 2 + 3 x + 2 2

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

If 5 x x -2 dx = ax + b | x -2 x |+ c , then a + b = 2025x Cos ⁻¹ ( 1-x^2 1+x^2 ) d x(x>0)= 2025d x (1+ x ) x-x^2 = 2025If x x x+1 ~d x= f (x)+ k , then f ( 4 )= 2025If x^4+1 x^2+1 d x=A x^3+B x^2+C x+D Tan ⁻¹ x+E , then A+B+C+D= 2025If x^2-x+2 x^2+x+2 d x=x- (f(x))+ 2 7 Tan ⁻¹(g(x))+c , then f (-1)+ 7 ~g (-1)= 2025(x- 3 ) (x+ 6 ) d x= 2025If a x+3 x 5 x+2 x d x= 26 29 x- k 29 |5 x+2 x|+c , then |a+k|= 2025 Full Indefinite Integration list All AP EAMCET PYQs