3
_________ 2 / 2 \ cot (4*x)
\/ asin(x) *cot (4*x)*\-12 - 12*cot (4*x)/ + -------------------------
________
/ 2 _________
2*\/ 1 - x *\/ asin(x)
$$\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \sqrt{\operatorname{asin}{\left(x \right)}} + \frac{\cot^{3}{\left(4 x \right)}}{2 \sqrt{- x^{2} + 1} \sqrt{\operatorname{asin}{\left(x \right)}}}$$
/ 2 / 1 2*x \ \
| cot (4*x)*|----------------- + -----------| |
| |/ 2\ 3/2| |
| |\-1 + x /*asin(x) / 2\ | / 2 \ |
| _________ / 2 \ / 2 \ \ \1 - x / / 12*\1 + cot (4*x)/*cot(4*x)|
|96*\/ asin(x) *\1 + cot (4*x)/*\1 + 2*cot (4*x)/ + ------------------------------------------- - ---------------------------|*cot(4*x)
| _________ ________ |
| 4*\/ asin(x) / 2 _________ |
\ \/ 1 - x *\/ asin(x) /
$$\left(96 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \sqrt{\operatorname{asin}{\left(x \right)}} + \frac{\left(\frac{2 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) \cot^{2}{\left(4 x \right)}}{4 \sqrt{\operatorname{asin}{\left(x \right)}}} - \frac{12 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)}}{\sqrt{- x^{2} + 1} \sqrt{\operatorname{asin}{\left(x \right)}}}\right) \cot{\left(4 x \right)}$$
/ 2 \
3 | 4 3 12*x 6*x | 2 / 2 \ / 1 2*x \
cot (4*x)*|----------- + -------------------- + ----------- - ------------------| 9*cot (4*x)*\1 + cot (4*x)/*|----------------- + -----------|
| 3/2 3/2 5/2 2 | |/ 2\ 3/2|
/ 2 \ |/ 2\ / 2\ 2 / 2\ / 2\ | |\-1 + x /*asin(x) / 2\ | / 2 \ / 2 \
_________ / 2 \ |/ 2 \ 4 2 / 2 \| \\1 - x / \1 - x / *asin (x) \1 - x / \-1 + x / *asin(x)/ \ \1 - x / / 144*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*cot(4*x)
- 384*\/ asin(x) *\1 + cot (4*x)/*\\1 + cot (4*x)/ + 2*cot (4*x) + 7*cot (4*x)*\1 + cot (4*x)// + --------------------------------------------------------------------------------- - ------------------------------------------------------------- + ----------------------------------------------
_________ _________ ________
8*\/ asin(x) \/ asin(x) / 2 _________
\/ 1 - x *\/ asin(x)
$$- \frac{9 \cdot \left(\frac{2 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)}}{\sqrt{\operatorname{asin}{\left(x \right)}}} - 384 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{4}{\left(4 x \right)} + 7 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} + \left(\cot^{2}{\left(4 x \right)} + 1\right)^{2}\right) \sqrt{\operatorname{asin}{\left(x \right)}} + \frac{\left(- \frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{12 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{4}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}}\right) \cot^{3}{\left(4 x \right)}}{8 \sqrt{\operatorname{asin}{\left(x \right)}}} + \frac{144 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)}}{\sqrt{- x^{2} + 1} \sqrt{\operatorname{asin}{\left(x \right)}}}$$