/ 3 / 2 \\
| 2*x 2*x *\x - 4/|
-|------------ - -------------|
| _________ 3/2|
| / 4 / 4 \ |
\\/ x - 16 \x - 16/ /
--------------------------------
_______________
/ 2
/ / 2 \
/ \x - 4/
/ 1 - ---------
/ 4
\/ x - 16
$$- \frac{- \frac{2 x^{3} \left(x^{2} - 4\right)}{\left(x^{4} - 16\right)^{\frac{3}{2}}} + \frac{2 x}{\sqrt{x^{4} - 16}}}{\sqrt{- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1}}$$
/ 2 \
| / 2 / 2\\ |
| 2 | x *\-4 + x /| / 2\|
| 2*x *|-1 + ------------| *\-4 + x /|
| 4 2 / 2\ 6 / 2\ | 4 | |
| 4*x 3*x *\-4 + x / 6*x *\-4 + x / \ -16 + x / |
-2*|1 - -------- - -------------- + -------------- + -----------------------------------|
| 4 4 2 / 2\ |
| -16 + x -16 + x / 4\ | / 2\ | |
| \-16 + x / | \-4 + x / | / 4\ |
| |1 - ----------|*\-16 + x / |
| | 4 | |
\ \ -16 + x / /
-----------------------------------------------------------------------------------------
________________
/ 2
/ / 2\ __________
/ \-4 + x / / 4
/ 1 - ---------- *\/ -16 + x
/ 4
\/ -16 + x
$$- \frac{2 \cdot \left(\frac{6 x^{6} \left(x^{2} - 4\right)}{\left(x^{4} - 16\right)^{2}} - \frac{4 x^{4}}{x^{4} - 16} + \frac{2 x^{2} \left(x^{2} - 4\right) \left(\frac{x^{2} \left(x^{2} - 4\right)}{x^{4} - 16} - 1\right)^{2}}{\left(x^{4} - 16\right) \left(- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1\right)} - \frac{3 x^{2} \left(x^{2} - 4\right)}{x^{4} - 16} + 1\right)}{\sqrt{x^{4} - 16} \sqrt{- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1}}$$
/ / 2 2\ \
| / 2 / 2\\ | 4 / 2\ 2 / 2\ 6 / 2\ | / 2 / 2\\ / 4 2 / 2\ 6 / 2\\ 3 |
| | x *\-4 + x /| | 2 8*x *\-4 + x / 3*x *\-4 + x / 8*x *\-4 + x / | | x *\-4 + x /| / 2\ | 4*x 3*x *\-4 + x / 6*x *\-4 + x /| / 2 / 2\\ 2|
| |-1 + ------------|*|-4 + 3*x - -------------- - --------------- + ---------------| 2*|-1 + ------------|*\-4 + x /*|1 - -------- - -------------- + --------------| 2 | x *\-4 + x /| / 2\ |
| | 4 | | 4 4 2 | | 4 | | 4 4 2 | 6*x *|-1 + ------------| *\-4 + x / |
| 6 \ -16 + x / | -16 + x -16 + x / 4\ | 4 / 2\ 8 / 2\ \ -16 + x / | -16 + x -16 + x / 4\ | | 4 | |
| 2 18*x \ \-16 + x / / 27*x *\-4 + x / 30*x *\-4 + x / \ \-16 + x / / \ -16 + x / |
4*x*|-12 + 15*x - -------- + ------------------------------------------------------------------------------------ - --------------- + --------------- + -------------------------------------------------------------------------------- + ------------------------------------|
| 4 2 4 2 2 2 |
| -16 + x / 2\ -16 + x / 4\ / 2\ / 2\ |
| \-4 + x / \-16 + x / \-4 + x / | / 2\ | |
| 1 - ---------- 1 - ---------- | \-4 + x / | / 4\ |
| 4 4 |1 - ----------| *\-16 + x / |
| -16 + x -16 + x | 4 | |
\ \ -16 + x / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________________
/ 2
/ / 2\ 3/2
/ \-4 + x / / 4\
/ 1 - ---------- *\-16 + x /
/ 4
\/ -16 + x
$$\frac{4 x \left(\frac{30 x^{8} \left(x^{2} - 4\right)}{\left(x^{4} - 16\right)^{2}} - \frac{18 x^{6}}{x^{4} - 16} - \frac{27 x^{4} \left(x^{2} - 4\right)}{x^{4} - 16} + \frac{6 x^{2} \left(x^{2} - 4\right)^{2} \left(\frac{x^{2} \left(x^{2} - 4\right)}{x^{4} - 16} - 1\right)^{3}}{\left(x^{4} - 16\right) \left(- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1\right)^{2}} + 15 x^{2} + \frac{2 \left(x^{2} - 4\right) \left(\frac{x^{2} \left(x^{2} - 4\right)}{x^{4} - 16} - 1\right) \left(\frac{6 x^{6} \left(x^{2} - 4\right)}{\left(x^{4} - 16\right)^{2}} - \frac{4 x^{4}}{x^{4} - 16} - \frac{3 x^{2} \left(x^{2} - 4\right)}{x^{4} - 16} + 1\right)}{- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1} + \frac{\left(\frac{x^{2} \left(x^{2} - 4\right)}{x^{4} - 16} - 1\right) \left(\frac{8 x^{6} \left(x^{2} - 4\right)^{2}}{\left(x^{4} - 16\right)^{2}} - \frac{8 x^{4} \left(x^{2} - 4\right)}{x^{4} - 16} - \frac{3 x^{2} \left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 3 x^{2} - 4\right)}{- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1} - 12\right)}{\left(x^{4} - 16\right)^{\frac{3}{2}} \sqrt{- \frac{\left(x^{2} - 4\right)^{2}}{x^{4} - 16} + 1}}$$