Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202316 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

aligned & If 3 x+2 4 x^2+4 x+5 d x=A (4 x^2+4 x+5 )+B Tan ⁻¹ & (x+ 1 2 )+C, then (A, B)= aligned

Options

  1. A( 3 8 , 1 8 )
  2. B( 5 8 , 1 8 )
  3. C(- 3 8 , 1 8 )
  4. D(- 5 8 , 1 8 )

Correct answer

A. ( 3 8 , 1 8 )

Step-by-step solution

Let I= 3 x+2 4 x^2+4 x+5 d x aligned & = 3 8 8 x+4 4 x^2+4 x+5 d x+ 1 2 1 4 x^2+4 x+5 d x & = 3 8 (4 x^2+4 x+5 )+ 1 2 1 (2 x+1)^2+2^2 d x & = 3 8 (4 x^2+4 x+5 )+ 1 2 1 4 ⁻¹ ( 2 x+1 2 )+C & = 3 8 (4 x^2+4 x+5 )+ 1 8 ⁻¹ (x+ 1 2 )+C aligned

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