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
- A( 3 8 , 1 8 )
- B( 5 8 , 1 8 )
- C(- 3 8 , 1 8 )
- 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