1
1 + ------
3/4 / 4 ___\
4*x 3*\x + \/ x /
---------- + ------------------------
acos(3*x) __________
/ 2 2
\/ 1 - 9*x *acos (3*x)
$$\frac{1 + \frac{1}{4 x^{\frac{3}{4}}}}{\operatorname{acos}{\left(3 x \right)}} + \frac{3 \left(\sqrt[4]{x} + x\right)}{\sqrt{1 - 9 x^{2}} \operatorname{acos}^{2}{\left(3 x \right)}}$$
/ / 4 ___\ / 2 3*x \\
| 1 3*\x + \/ x /*|- --------------------- + -------------||
| 4 + ---- | / 2\ 3/2||
| 3/4 | \-1 + 9*x /*acos(3*x) / 2\ ||
| 1 x \ \1 - 9*x / /|
3*|- ------- + ------------------------- + -------------------------------------------------------|
| 7/4 __________ acos(3*x) |
| 16*x / 2 |
\ 2*\/ 1 - 9*x *acos(3*x) /
---------------------------------------------------------------------------------------------------
acos(3*x)
$$\frac{3 \left(\frac{3 \left(\sqrt[4]{x} + x\right) \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right)}{\operatorname{acos}{\left(3 x \right)}} + \frac{4 + \frac{1}{x^{\frac{3}{4}}}}{2 \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{1}{16 x^{\frac{7}{4}}}\right)}{\operatorname{acos}{\left(3 x \right)}}$$
/ / 2 \ \
| / 4 ___\ | 1 6 27*x 18*x | / 1 \ / 2 3*x \|
| 9*\x + \/ x /*|------------- + ------------------------ + ------------- + ----------------------| 9*|4 + ----|*|- --------------------- + -------------||
| | 3/2 3/2 5/2 2 | | 3/4| | / 2\ 3/2||
| |/ 2\ / 2\ 2 / 2\ / 2\ | \ x / | \-1 + 9*x /*acos(3*x) / 2\ ||
| 7 \\1 - 9*x / \1 - 9*x / *acos (3*x) \1 - 9*x / \-1 + 9*x / *acos(3*x)/ 9 \ \1 - 9*x / /|
3*|-------- + ------------------------------------------------------------------------------------------------- - ------------------------------- + ------------------------------------------------------|
| 11/4 acos(3*x) __________ 4*acos(3*x) |
|64*x 7/4 / 2 |
\ 16*x *\/ 1 - 9*x *acos(3*x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
acos(3*x)
$$\frac{3 \left(\frac{9 \left(4 + \frac{1}{x^{\frac{3}{4}}}\right) \left(\frac{3 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(9 x^{2} - 1\right) \operatorname{acos}{\left(3 x \right)}}\right)}{4 \operatorname{acos}{\left(3 x \right)}} + \frac{9 \left(\sqrt[4]{x} + x\right) \left(\frac{27 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{18 x}{\left(9 x^{2} - 1\right)^{2} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(3 x \right)}}\right)}{\operatorname{acos}{\left(3 x \right)}} - \frac{9}{16 x^{\frac{7}{4}} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{7}{64 x^{\frac{11}{4}}}\right)}{\operatorname{acos}{\left(3 x \right)}}$$