Answer
\[ =\dfrac{1}{12}(4z^2-5)^{3/2}+C
\]
Work Step by Step
In order to integrate this function, we have to use a «u» substitution.
Choose a u, derive it:
$u = 4z^2-5 $
$du = 8zdz $
$\dfrac{1}{8}du=zdz $
Then substitute:
\[ = \dfrac{1}{8}\int u^{1/2} du \]
Then integrate
\[ = \dfrac{1}{8} \bigg( \dfrac {2}{3}\bigg) u^{3/2}+C
=\dfrac{1}{12}u^{3/2}+C
\]
And undo the substitution:
\[ =\boxed{\dfrac{1}{12}(4z^2-5)^{3/2}+C}
\]
