Question

Find the most general antiderivative of the function.
g(t) = (5 + t + t^2)/ square root of t

Answer 1

g(t) = (5 + t + t^2) / √t = 5/√t + √t + t√t
∫g(t)dt = ∫(5√t + √t + t√t)dt = 5(t)^3/2 / 3/2 + t^3/2 / 3/2 + t^5/2 / 5/2 + c = 10/3 t√t + 2/3 t√t + 2/5 t^2√t + c