If x+1 x^2+1 dx = ⁻¹x + g(x) + c , where c is constant of integration, then the function g(x) is monotonically increasing in the interval

Step-by-step solution

x+1 x^2+1 dx = x x^2+1 dx + 1 x^2+1 dx = 1 2 (x^2+1) + ⁻¹x + c Comparing with the given equation, we get: g(x) = 1 2 (x^2+1) For g(x) to be monotonically increasing, g'(x) 0 . g'(x) = x x^2+1 0 Since x^2+1 > 0 for all x R , we must have x 0 . Thus, g(x) is monotonically increasing in R^+ . Answer: R^+