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