Answer
$$
f(x)=4 \sqrt{x}-6 x^{2}+3=4 x^{1 / 2}-6 x^{2}+3
$$
The most general antiderivative of the given function is
$$
F(x)=\frac{8}{3} x^{3 / 2}-2 x^{3}+3 x+C
$$
Work Step by Step
$$
f(x)=4 \sqrt{x}-6 x^{2}+3=4 x^{1 / 2}-6 x^{2}+3
$$
The general anti-derivative of $
f(x)=4 \sqrt{x}-6 x^{2}+3,
$ is
$$
\begin{aligned}
F(x) &=4\left(\frac{2}{3} x^{3 / 2}\right)-6\left(\frac{1}{3} x^{3}\right)+3 x+C \\
& =\frac{8}{3} x^{3 / 2}-2 x^{3}+3 x+C
\end{aligned}
$$
