If ∫dx/(x^2+x+1)^2 = a tan^(-1)((2x+1)/√3) + b((2x+1)(x^2+x+1)) + C,x > 0 where C is the constant of integration,

Question

If \(\int \frac{dx}{(x^2+x+1)^2}\) = a tan^-1(\(\frac{2x+1}{\sqrt3}\))+b(\(\frac{2x+1}{x^2+x+1}\)) + C,x > 0 where C is the constant of integration, then the value of 9 (√3a + b) is equal to____.

∫dx/(x²+x+1)² = a tan^-1((2x+1)/√3) + b((2x+1)(x²+x+1)) + C

Answer 1

Hence,

9(√3a + b) = 15