Answer
$$F(x)= \frac{1}{4.4}x^{4.4}-\sqrt{2} x^{\sqrt{2}}+C$$
Work Step by Step
Given $$f(x) = x^{3.4}-2x^{\sqrt{2}-1}$$
Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$
\begin{align*}
F(x) &=\frac{x^{4.4}}{4.4}-\frac{2x^{\sqrt{2}}}{\sqrt{2}}+C\\
&= \frac{1}{4.4}x^{4.4}-\sqrt{2} x^{\sqrt{2}}+C
\end{align*}
To check
\begin{align*}
F'(x) &=x^{3.4}-2x^{\sqrt{2}-1}\\
&=f(x)
\end{align*}
