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