/ d / log(4) \\| / /3*x\\ /3*x\
6*|-----|---------||| /3*x\*log|4, cos|---||*sin|---|
cot(3*x) 7 \dxi_2\log(xi_2)//|xi_2=cos|---| \ \ 5 // \ 5 /
16*4 *asin (2*x + 3) \ 5 / cot(3*x) 8 / 2 \
--------------------------- + ------------------------------------------------------------ + 4 *asin (2*x + 3)*\-3 - 3*cot (3*x)/*log(4)
________________ 5
/ 2
\/ 1 - (2*x + 3)
$$4^{\cot{\left(3 x \right)}} \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \log{\left(4 \right)} \operatorname{asin}^{8}{\left(2 x + 3 \right)} + \frac{16 \cdot 4^{\cot{\left(3 x \right)}} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\sqrt{- \left(2 x + 3\right)^{2} + 1}} + \frac{6 \log{\left(4 \right)} \sin{\left(\frac{3 x}{5} \right)} \left. \frac{d}{d \xi_{2}} \frac{\log{\left(4 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\cos{\left(\frac{3 x}{5} \right)} }}}{5}$$
2 2 2/3*x\ / 2 \
/ d / log(4) \\| 2/3*x\ / d / log(4) \\| /3*x\ 18*log (4)*sin |---|*|1 + -------------|
18*|-----|---------||| /3*x\ *sin |---| 18*|-----|---------||| /3*x\*cos|---|*log(4) \ 5 / | / /3*x\\|
\dxi_2\log(xi_2)//|xi_2=cos|---| \ 5 / cot(3*x) 6 2 cot(3*x) 7 \dxi_2\log(xi_2)//|xi_2=cos|---| \ 5 / cot(3*x) 7 / 2 \ | log|cos|---|||
\ 5 / 224*4 *asin (3 + 2*x) cot(3*x) / 2 \ 8 2 32*4 *asin (3 + 2*x)*(3 + 2*x) \ 5 / 96*4 *asin (3 + 2*x)*\1 + cot (3*x)/*log(4) cot(3*x) 8 / 2 \ \ \ \ 5 ///
- ---------------------------------------------- - ---------------------------- + 9*4 *\1 + cot (3*x)/ *asin (3 + 2*x)*log (4) + ------------------------------------- + --------------------------------------------------- - -------------------------------------------------- + 18*4 *asin (3 + 2*x)*\1 + cot (3*x)/*cot(3*x)*log(4) - ----------------------------------------
25 2 3/2 / /3*x\\ ________________ 2/3*x\ 3/ /3*x\\
-1 + (3 + 2*x) / 2\ 25*log|cos|---|| / 2 25*cos |---|*log |cos|---||
\1 - (3 + 2*x) / \ \ 5 // \/ 1 - (3 + 2*x) \ 5 / \ \ 5 //
$$9 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(4 \right)}^{2} \operatorname{asin}^{8}{\left(2 x + 3 \right)} + 18 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(4 \right)} \cot{\left(3 x \right)} \operatorname{asin}^{8}{\left(2 x + 3 \right)} - \frac{96 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(4 \right)} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\sqrt{- \left(2 x + 3\right)^{2} + 1}} - \frac{224 \cdot 4^{\cot{\left(3 x \right)}} \operatorname{asin}^{6}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{2} - 1} + \frac{32 \cdot 4^{\cot{\left(3 x \right)}} \left(2 x + 3\right) \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\left(- \left(2 x + 3\right)^{2} + 1\right)^{\frac{3}{2}}} - \frac{18 \sin^{2}{\left(\frac{3 x}{5} \right)} \left. \frac{d}{d \xi_{2}} \frac{\log{\left(4 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\cos{\left(\frac{3 x}{5} \right)} }}^{2}}{25} + \frac{18 \log{\left(4 \right)} \cos{\left(\frac{3 x}{5} \right)} \left. \frac{d}{d \xi_{2}} \frac{\log{\left(4 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\cos{\left(\frac{3 x}{5} \right)} }}}{25 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}} - \frac{18 \cdot \left(1 + \frac{2}{\log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}}\right) \log{\left(4 \right)}^{2} \sin^{2}{\left(\frac{3 x}{5} \right)}}{25 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}^{3} \cos^{2}{\left(\frac{3 x}{5} \right)}}$$
2 2 / 2 \ /3*x\ 2 3/3*x\ / 2 \ 2 3/3*x\ / 2 \ 3/3*x\ / 2 \ / d / log(4) \\|
/ d / log(4) \\| /3*x\ /3*x\ / d / log(4) \\| /3*x\ 162*log (4)*|1 + -------------|*sin|---| 108*log (4)*sin |---|*|1 + -------------| 108*log (4)*sin |---|*|1 + -------------| 162*sin |---|*|1 + -------------|*|-----|---------||| /3*x\*log(4)
162*|-----|---------||| /3*x\ *cos|---|*sin|---| 2 3/3*x\ 54*|-----|---------||| /3*x\*log(4)*sin|---| 2 | / /3*x\\| \ 5 / \ 5 / | / /3*x\\| \ 5 / | / /3*x\\| \ 5 / | / /3*x\\| \dxi_2\log(xi_2)//|xi_2=cos|---|
cot(3*x) 7 cot(3*x) 5 \dxi_2\log(xi_2)//|xi_2=cos|---| \ 5 / \ 5 / 2 3 cot(3*x) 2 7 cot(3*x) 6 108*log (4)*sin |---| \dxi_2\log(xi_2)//|xi_2=cos|---| \ 5 / 2 cot(3*x) / 2 \ 7 2 cot(3*x) 6 / 2 \ | log|cos|---||| | log|cos|---||| | log|cos|---||| cot(3*x) 7 / 2 \ cot(3*x) 7 / 2 \ | log|cos|---||| \ 5 /
64*4 *asin (3 + 2*x) 2688*4 *asin (3 + 2*x) \ 5 / cot(3*x) / 2 \ 8 cot(3*x) / 2 \ 8 3 192*4 *(3 + 2*x) *asin (3 + 2*x) 1344*4 *asin (3 + 2*x)*(3 + 2*x) \ 5 / \ 5 / cot(3*x) / 2 \ 8 2 cot(3*x) 8 2 / 2 \ 432*4 *\1 + cot (3*x)/ *asin (3 + 2*x)*log (4) 2016*4 *asin (3 + 2*x)*\1 + cot (3*x)/*log(4) \ \ \ 5 /// \ \ \ 5 /// \ \ \ 5 /// 288*4 *asin (3 + 2*x)*\1 + cot (3*x)/*(3 + 2*x)*log(4) 864*4 *asin (3 + 2*x)*\1 + cot (3*x)/*cot(3*x)*log(4) \ \ \ 5 ///
--------------------------- + ----------------------------- - ------------------------------------------------------- - 54*4 *\1 + cot (3*x)/ *asin (3 + 2*x)*log(4) - 27*4 *\1 + cot (3*x)/ *asin (3 + 2*x)*log (4) + --------------------------------------- + --------------------------------------- - ---------------------------- - --------------------------------------------------- - 162*4 *\1 + cot (3*x)/ *asin (3 + 2*x)*log (4)*cot(3*x) - 108*4 *asin (3 + 2*x)*cot (3*x)*\1 + cot (3*x)/*log(4) + ----------------------------------------------------- + ---------------------------------------------------- - ---------------------------------------- - ----------------------------------------- - ----------------------------------------- - ------------------------------------------------------------- + ------------------------------------------------------------ + -------------------------------------------------------------------------
3/2 3/2 125 5/2 2 3/3*x\ 5/ /3*x\\ / /3*x\\ ________________ 2 /3*x\ 3/ /3*x\\ 3/3*x\ 4/ /3*x\\ 3/3*x\ 3/ /3*x\\ 3/2 ________________ 2/3*x\ 2/ /3*x\\
/ 2\ / 2\ / 2\ / 2\ 125*cos |---|*log |cos|---|| 125*log|cos|---|| / 2 -1 + (3 + 2*x) 125*cos|---|*log |cos|---|| 125*cos |---|*log |cos|---|| 125*cos |---|*log |cos|---|| / 2\ / 2 125*cos |---|*log |cos|---||
\1 - (3 + 2*x) / \1 - (3 + 2*x) / \1 - (3 + 2*x) / \-1 + (3 + 2*x) / \ 5 / \ \ 5 // \ \ 5 // \/ 1 - (3 + 2*x) \ 5 / \ \ 5 // \ 5 / \ \ 5 // \ 5 / \ \ 5 // \1 - (3 + 2*x) / \/ 1 - (3 + 2*x) \ 5 / \ \ 5 //
$$- 27 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3} \log{\left(4 \right)}^{3} \operatorname{asin}^{8}{\left(2 x + 3 \right)} - 162 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(4 \right)}^{2} \cot{\left(3 x \right)} \operatorname{asin}^{8}{\left(2 x + 3 \right)} - 108 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(4 \right)} \cot^{2}{\left(3 x \right)} \operatorname{asin}^{8}{\left(2 x + 3 \right)} - 54 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(4 \right)} \operatorname{asin}^{8}{\left(2 x + 3 \right)} + \frac{432 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(4 \right)}^{2} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\sqrt{- \left(2 x + 3\right)^{2} + 1}} + \frac{864 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(4 \right)} \cot{\left(3 x \right)} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\sqrt{- \left(2 x + 3\right)^{2} + 1}} + \frac{2016 \cdot 4^{\cot{\left(3 x \right)}} \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(4 \right)} \operatorname{asin}^{6}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{2} - 1} - \frac{288 \cdot 4^{\cot{\left(3 x \right)}} \left(2 x + 3\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(4 \right)} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\left(- \left(2 x + 3\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{1344 \cdot 4^{\cot{\left(3 x \right)}} \left(2 x + 3\right) \operatorname{asin}^{6}{\left(2 x + 3 \right)}}{\left(\left(2 x + 3\right)^{2} - 1\right)^{2}} + \frac{64 \cdot 4^{\cot{\left(3 x \right)}} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\left(- \left(2 x + 3\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{192 \cdot 4^{\cot{\left(3 x \right)}} \left(2 x + 3\right)^{2} \operatorname{asin}^{7}{\left(2 x + 3 \right)}}{\left(- \left(2 x + 3\right)^{2} + 1\right)^{\frac{5}{2}}} - \frac{162 \sin{\left(\frac{3 x}{5} \right)} \cos{\left(\frac{3 x}{5} \right)} \left. \frac{d}{d \xi_{2}} \frac{\log{\left(4 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\cos{\left(\frac{3 x}{5} \right)} }}^{2}}{125} + \frac{2688 \cdot 4^{\cot{\left(3 x \right)}} \operatorname{asin}^{5}{\left(2 x + 3 \right)}}{\left(- \left(2 x + 3\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{162 \cdot \left(1 + \frac{2}{\log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}}\right) \log{\left(4 \right)} \sin^{3}{\left(\frac{3 x}{5} \right)} \left. \frac{d}{d \xi_{2}} \frac{\log{\left(4 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\cos{\left(\frac{3 x}{5} \right)} }}}{125 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}^{2} \cos^{2}{\left(\frac{3 x}{5} \right)}} - \frac{54 \log{\left(4 \right)} \sin{\left(\frac{3 x}{5} \right)} \left. \frac{d}{d \xi_{2}} \frac{\log{\left(4 \right)}}{\log{\left(\xi_{2} \right)}} \right|_{\substack{ \xi_{2}=\cos{\left(\frac{3 x}{5} \right)} }}}{125 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}} - \frac{108 \cdot \left(1 + \frac{2}{\log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}}\right) \log{\left(4 \right)}^{2} \sin^{3}{\left(\frac{3 x}{5} \right)}}{125 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}^{3} \cos^{3}{\left(\frac{3 x}{5} \right)}} - \frac{162 \cdot \left(1 + \frac{2}{\log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}}\right) \log{\left(4 \right)}^{2} \sin{\left(\frac{3 x}{5} \right)}}{125 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}^{3} \cos{\left(\frac{3 x}{5} \right)}} - \frac{108 \cdot \left(1 + \frac{2}{\log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}}\right) \log{\left(4 \right)}^{2} \sin^{3}{\left(\frac{3 x}{5} \right)}}{125 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}^{4} \cos^{3}{\left(\frac{3 x}{5} \right)}} - \frac{108 \log{\left(4 \right)}^{2} \sin^{3}{\left(\frac{3 x}{5} \right)}}{125 \log{\left(\cos{\left(\frac{3 x}{5} \right)} \right)}^{5} \cos^{3}{\left(\frac{3 x}{5} \right)}}$$