2 2 3
3*acos (x)*log (3*x) 2*acos (x)*log(3*x)
- -------------------- + -------------------
________ x
/ 2
\/ 1 - x
$$- \frac{3 \log{\left(3 x \right)}^{2} \operatorname{acos}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{2 \log{\left(3 x \right)} \operatorname{acos}^{3}{\left(x \right)}}{x}$$
/ 2 \
| 2 / 2 x*acos(x) \ 2*acos (x)*(-1 + log(3*x)) 12*acos(x)*log(3*x)|
-|3*log (3*x)*|------- + -----------| + -------------------------- + -------------------|*acos(x)
| | 2 3/2| 2 ________ |
| |-1 + x / 2\ | x / 2 |
\ \ \1 - x / / x*\/ 1 - x /
$$- \left(3 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} - 1}\right) \log{\left(3 x \right)}^{2} + \frac{12 \log{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{x \sqrt{1 - x^{2}}} + \frac{2 \left(\log{\left(3 x \right)} - 1\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{acos}{\left(x \right)}$$
/ 2 x*acos(x) \
18*|------- + -----------|*acos(x)*log(3*x)
| 2 3/2|
/ 2 2 2 \ 3 |-1 + x / 2\ | 2
2 | 2 acos (x) 6*x*acos(x) 3*x *acos (x)| 2*acos (x)*(-3 + 2*log(3*x)) \ \1 - x / / 18*acos (x)*(-1 + log(3*x))
- 3*log (3*x)*|----------- + ----------- - ----------- + -------------| + ---------------------------- - ------------------------------------------- + ---------------------------
| 3/2 3/2 2 5/2 | 3 x ________
|/ 2\ / 2\ / 2\ / 2\ | x 2 / 2
\\1 - x / \1 - x / \-1 + x / \1 - x / / x *\/ 1 - x
$$- 3 \left(\frac{3 x^{2} \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x \operatorname{acos}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(3 x \right)}^{2} - \frac{18 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} - 1}\right) \log{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{x} + \frac{18 \left(\log{\left(3 x \right)} - 1\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \left(2 \log{\left(3 x \right)} - 3\right) \operatorname{acos}^{3}{\left(x \right)}}{x^{3}}$$