2
3 3*cot (3*x)
- - - ----------- 3 2/ 4\
2 2 12*x *acos \x /
----------------- - ---------------
__________ ________
\/ cot(3*x) / 8
\/ 1 - x
$$- \frac{12 x^{3} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} + \frac{- \frac{3 \cot^{2}{\left(3 x \right)}}{2} - \frac{3}{2}}{\sqrt{\cot{\left(3 x \right)}}}$$
/ 2 \
| / 2 \ 6 / 4\ 10 2/ 4\ 2 2/ 4\|
| __________ / 2 \ 3*\1 + cot (3*x)/ 32*x *acos\x / 16*x *acos \x / 12*x *acos \x /|
3*|3*\/ cot(3*x) *\1 + cot (3*x)/ - ------------------ - -------------- - ---------------- - ---------------|
| 3/2 8 3/2 ________ |
| 4*cot (3*x) -1 + x / 8\ / 8 |
\ \1 - x / \/ 1 - x /
$$3 \left(- \frac{16 x^{10} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{32 x^{6} \operatorname{acos}{\left(x^{4} \right)}}{x^{8} - 1} - \frac{12 x^{2} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{4 \cot^{\frac{3}{2}}{\left(3 x \right)}} + 3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \sqrt{\cot{\left(3 x \right)}}\right)$$
/ 3 2 \
| 9 / 2 \ / 2 \ 5 / 4\ 9 2/ 4\ 17 2/ 4\ 2/ 4\ 13 / 4\|
| 128*x 3/2 / 2 \ 27*\1 + cot (3*x)/ 9*\1 + cot (3*x)/ 288*x *acos\x / 208*x *acos \x / 192*x *acos \x / 24*x*acos \x / 384*x *acos\x /|
3*|- ----------- - 18*cot (3*x)*\1 + cot (3*x)/ - ------------------- + ------------------ - --------------- - ---------------- - ----------------- - -------------- + ----------------|
| 3/2 5/2 __________ 8 3/2 5/2 ________ 2 |
| / 8\ 8*cot (3*x) 2*\/ cot(3*x) -1 + x / 8\ / 8\ / 8 / 8\ |
\ \1 - x / \1 - x / \1 - x / \/ 1 - x \-1 + x / /
$$3 \left(- \frac{192 x^{17} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{5}{2}}} + \frac{384 x^{13} \operatorname{acos}{\left(x^{4} \right)}}{\left(x^{8} - 1\right)^{2}} - \frac{208 x^{9} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{128 x^{9}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{288 x^{5} \operatorname{acos}{\left(x^{4} \right)}}{x^{8} - 1} - \frac{24 x \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{8 \cot^{\frac{5}{2}}{\left(3 x \right)}} + \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{2 \sqrt{\cot{\left(3 x \right)}}} - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot^{\frac{3}{2}}{\left(3 x \right)}\right)$$