Question

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

Answer 1

\[g(t)=\frac{5+t+t^2}{t^\frac{1}{2}}=\frac{5}{t^\frac{1}{2}}+\frac{t}{t^\frac{1}{2}}+\frac{t^2}{t^\frac{1}{2}}=5t^{-\frac{1}{2}}+t^{1-\frac{1}{2}}+t^{2-\frac{1}{2}}\]
\[g(t)=5t^{-\frac{1}{2}}+t^\frac{1}{2}+t^{\frac{3}{2}}\]
Find the antiderivative of each term using
\[f(t)=t^n => F(t)=\frac{t^{n+1}}{n+1} \text{ where } F'=f \text{ and } n \neq -1\]

Answer 2

thanks!