Answer
$$F(x) = \frac{5}{49}x^{7/5}-40x^{1/5}+C$$
Work Step by Step
Given $$f(x) =7x^{2/5}+8x^{-4/5}$$
Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$
\begin{align*}
F(x) &=\frac{7x^{7/5}}{7/5}+\frac{8x^{1/5}}{1/5}+C\\
&= \frac{5}{49}x^{7/5}-40x^{1/5}+C
\end{align*}
To check
\begin{align*}
F'(x) &=7x^{2/5}+8x^{-4/5}\\
&=f(x)
\end{align*}
