1
1 + -------
___ / ___\
2*\/ x 3*\x + \/ x /
----------- + ------------------------
acos(3*x) __________
/ 2 2
\/ 1 - 9*x *acos (3*x)
$$\frac{1 + \frac{1}{2 \sqrt{x}}}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(\sqrt{x} + x\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}^{2}{\left(3 x \right)}}$$
/ ___\ / 2 3*x \
/ 1 \ 9*\x + \/ x /*|- --------------------- + -------------|
3*|2 + -----| | / 2\ 3/2|
| ___| | \-1 + 9*x /*acos(3*x) / 2\ |
1 \ \/ x / \ \1 - 9*x / /
- ------ + ----------------------- + -------------------------------------------------------
3/2 __________ acos(3*x)
4*x / 2
\/ 1 - 9*x *acos(3*x)
--------------------------------------------------------------------------------------------
acos(3*x)
$$\frac{\frac{9 \left(\sqrt{x} + x\right) \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right)}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(2 + \frac{1}{\sqrt{x}}\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{1}{4 x^{\frac{3}{2}}}}{\operatorname{acos}{\left(3 x \right)}}$$
/ / 2 \ \
| / ___\ | 1 6 27*x 18*x | / 1 \ / 2 3*x \|
| 9*\x + \/ x /*|------------- + ------------------------ + ------------- + ----------------------| 9*|2 + -----|*|- --------------------- + -------------||
| | 3/2 3/2 5/2 2 | | ___| | / 2\ 3/2||
| |/ 2\ / 2\ 2 / 2\ / 2\ | \ \/ x / | \-1 + 9*x /*acos(3*x) / 2\ ||
| 1 \\1 - 9*x / \1 - 9*x / *acos (3*x) \1 - 9*x / \-1 + 9*x / *acos(3*x)/ 3 \ \1 - 9*x / /|
3*|------ + ------------------------------------------------------------------------------------------------- - ------------------------------ + -------------------------------------------------------|
| 5/2 acos(3*x) __________ 2*acos(3*x) |
|8*x 3/2 / 2 |
\ 4*x *\/ 1 - 9*x *acos(3*x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
acos(3*x)
$$\frac{3 \left(\frac{9 \left(2 + \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right)}{2 \operatorname{acos}{\left(3 x \right)}} + \frac{9 \left(\sqrt{x} + x\right) \left(\frac{27 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{18 x}{\left(9 x^{2} - 1\right)^{2} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(3 x \right)}}\right)}{\operatorname{acos}{\left(3 x \right)}} - \frac{3}{4 x^{\frac{3}{2}} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{8 x^{\frac{5}{2}}}\right)}{\operatorname{acos}{\left(3 x \right)}}$$