Evaluate the integral ∫2x√(x^2 +1) dx

The first step is deciding on the method of integration. For this integral it makes the most sense to use substitution.Let u = x² + 1Differentiate w.r.t x => du/dx = 2xRearrange for dx=> du/2x = dx Substitute into the Original integral ∫2x√(u) du/2x= ∫√(u) du= (2/3) u^2/3 + c= (2/3 )(x² + 1)^2/3 + c