Let f(x) be a polynomial function of degree 2 satisfying ∫f(x)x3−1=ln∣∣x2+x+1x−1∣∣+2√3tan−1(2x+1√3)+c, where c is indefinite integration constant. Let ∫5+f(sinx)+f(cos x)sin x+cos xdx=h(x)+λ, where h(1) = - 1. The value of tan−1[h(2)]+tan−1[h(3)] is equal to (whereλ is indefinite integration constant)

Let f(x) be a polynomial function of degree 2 satisfying ∫f(x)x3−1

1.	Let f(x) be a polynomial function of degree 2 satisfying ∫f(x)x3−1=ln∣∣x2+x+1x−1∣∣+2√3tan−1(2x+1√3)+c, where c is indefinite integration constant. Let ∫5+f(sinx)+f(cos x)sin x+cos xdx=h(x)+λ, where h(1) = - 1. The value of tan−1[h(2)]+tan−1[h(3)] is equal to (whereλ is indefinite integration constant)
Answer» Let f(x) be a polynomial function of degree 2 satisfying $\int \frac{f (x)}{x^{3} - 1} = l n ∣ ∣ \frac{x^{2} + x + 1}{x - 1} ∣ ∣ + \frac{2}{\sqrt{3}} t a n^{- 1} (\frac{2 x + 1}{\sqrt{3}}) + c,$ where c is indefinite integration constant. Let $\int \frac{5 + f (s i n x) + f (c o s x)}{s i n x + c o s x} d x = h (x) + λ,$ where h(1) = - 1. The value of $t a n^{- 1} [h (2)] + t a n^{- 1} [h (3)]$ is equal to (where $λ$ is indefinite integration constant)