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AP EAMCET202125 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

If 2 x+3 x(x+1)(x+2)(x+3)+1 d x= -1 a x^2+b x+c + , then value of a+b+c is equal to

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

C. 5

Step-by-step solution

We have, aligned & 2 x+3 x(x+1)(x+2)(x+3)+1 d x= -1 a x^2+b x+c + & LHS = 2 x+3 x(x+3)(x+1)(x+2)+1 d x & = (2 x+3) d x (x^2+3 x ) (x^2+3 x+2 )+1 aligned Put x^2+3 x=t (2 x+3) d x=d t aligned & LHS = d t t^2+2 t+1 &= d t (t+1)^2 =- 1 t+1 + &= -1 x^2+3 x+1 + & a=1, b=3, c=1 & a+b+c=1+3+1=5 aligned

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