/ ___ \
1 acos(x) ___ |acos(x) \/ x |
----------- + ------- + \/ x *|------- - -----------|
_______ 2 | ___ ________|
2*\/ 1 - x |2*\/ x / 2 |
\ \/ 1 - x /
$$\sqrt{x} \left(- \frac{\sqrt{x}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2 \sqrt{x}}\right) + \frac{\operatorname{acos}{\left(x \right)}}{2} + \frac{1}{2 \sqrt{1 - x}}$$
___
acos(x) 2*\/ x
- ------- + -----------
___ ________
/ 3/2 \ \/ x / 2
1 2 ___ |acos(x) 4 4*x | \/ 1 - x
---------- - ----------- - \/ x *|------- + ----------------- + -----------| - -----------------------
3/2 ________ | 3/2 ________ 3/2| ___
(1 - x) / 2 | x ___ / 2 / 2\ | \/ x
\/ 1 - x \ \/ x *\/ 1 - x \1 - x / /
------------------------------------------------------------------------------------------------------
4
$$\frac{- \sqrt{x} \left(\frac{4 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4}{\sqrt{x} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{\frac{3}{2}}}\right) - \frac{2}{\sqrt{1 - x^{2}}} + \frac{1}{\left(1 - x\right)^{\frac{3}{2}}} - \frac{\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{\sqrt{x}}}{\sqrt{x}}}{4}$$
___ / 3/2 \
acos(x) 2*\/ x |acos(x) 4 4*x |
- ------- + ----------- 2*|------- + ----------------- + -----------|
___ ________ | 3/2 ________ 3/2|
\/ x / 2 / ___ 5/2 \ | x ___ / 2 / 2\ |
3 \/ 1 - x ___ | 6 3*acos(x) 20*\/ x 24*x | 4*x \ \/ x *\/ 1 - x \1 - x / /
---------- + ----------------------- - \/ x *|- ---------------- - --------- + ----------- + -----------| - ----------- - ---------------------------------------------
5/2 3/2 | ________ 5/2 3/2 5/2| 3/2 ___
(1 - x) x | 3/2 / 2 x / 2\ / 2\ | / 2\ \/ x
\ x *\/ 1 - x \1 - x / \1 - x / / \1 - x /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------
8
$$\frac{- \sqrt{x} \left(\frac{24 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{20 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6}{x^{\frac{3}{2}} \sqrt{1 - x^{2}}} - \frac{3 \operatorname{acos}{\left(x \right)}}{x^{\frac{5}{2}}}\right) - \frac{4 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x\right)^{\frac{5}{2}}} - \frac{2 \left(\frac{4 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4}{\sqrt{x} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{\sqrt{x}} + \frac{\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{\sqrt{x}}}{x^{\frac{3}{2}}}}{8}$$