7/ 3 ___\
-8*asin \1 - \/ x /
-----------------------------
__________________
/ 2
2/3 / / 3 ___\
3*x *\/ 1 - \1 - \/ x /
$$- \frac{8 \operatorname{asin}^{7}{\left(1 - \sqrt[3]{x} \right)}}{3 x^{\frac{2}{3}} \sqrt{1 - \left(1 - \sqrt[3]{x}\right)^{2}}}$$
/ / 3 ___\ / 3 ___\ / 3 ___\ \
6/ 3 ___\ | 7 \-1 + \/ x /*asin\-1 + \/ x / 2*asin\-1 + \/ x / |
8*asin \-1 + \/ x /*|- ------------------ + ----------------------------- - ----------------------------|
| 2 3/2 __________________|
| / 3 ___\ / 2\ / 2 |
| -1 + \-1 + \/ x / | / 3 ___\ | 3 ___ / / 3 ___\ |
\ \1 - \1 - \/ x / / \/ x *\/ 1 - \1 - \/ x / /
---------------------------------------------------------------------------------------------------------
4/3
9*x
$$\frac{8 \left(- \frac{7}{\left(\sqrt[3]{x} - 1\right)^{2} - 1} + \frac{\left(\sqrt[3]{x} - 1\right) \operatorname{asin}{\left(\sqrt[3]{x} - 1 \right)}}{\left(1 - \left(1 - \sqrt[3]{x}\right)^{2}\right)^{\frac{3}{2}}} - \frac{2 \operatorname{asin}{\left(\sqrt[3]{x} - 1 \right)}}{\sqrt[3]{x} \sqrt{1 - \left(1 - \sqrt[3]{x}\right)^{2}}}\right) \operatorname{asin}^{6}{\left(\sqrt[3]{x} - 1 \right)}}{9 x^{\frac{4}{3}}}$$
/ 2 \
| 2/ 3 ___\ 2/ 3 ___\ / 3 ___\ 2/ 3 ___\ / 3 ___\ / 3 ___\ 2/ 3 ___\ / 3 ___\ / 3 ___\|
5/ 3 ___\ | 42 asin \-1 + \/ x / 10*asin \-1 + \/ x / 42*asin\-1 + \/ x / 6*asin \-1 + \/ x /*\-1 + \/ x / 3*\-1 + \/ x / *asin \-1 + \/ x / 21*\-1 + \/ x /*asin\-1 + \/ x /|
8*asin \-1 + \/ x /*|------------------------ + ------------------------ + --------------------------- + ------------------------- - -------------------------------- + --------------------------------- + --------------------------------|
| 3/2 3/2 __________________ / 2\ 3/2 5/2 2 |
| / 2\ / 2\ / 2 7/3 | / 3 ___\ | / 2\ / 2\ / 2\ |
| 2 | / 3 ___\ | 2 | / 3 ___\ | 8/3 / / 3 ___\ x *\-1 + \-1 + \/ x / / 7/3 | / 3 ___\ | 2 | / 3 ___\ | 2 | / 3 ___\ | |
\x *\1 - \1 - \/ x / / x *\1 - \1 - \/ x / / x *\/ 1 - \1 - \/ x / x *\1 - \1 - \/ x / / x *\1 - \1 - \/ x / / x *\-1 + \-1 + \/ x / / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27
$$\frac{8 \left(\frac{21 \left(\sqrt[3]{x} - 1\right) \operatorname{asin}{\left(\sqrt[3]{x} - 1 \right)}}{x^{2} \left(\left(\sqrt[3]{x} - 1\right)^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(\sqrt[3]{x} - 1 \right)}}{x^{2} \left(1 - \left(1 - \sqrt[3]{x}\right)^{2}\right)^{\frac{3}{2}}} + \frac{42}{x^{2} \left(1 - \left(1 - \sqrt[3]{x}\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(\sqrt[3]{x} - 1\right)^{2} \operatorname{asin}^{2}{\left(\sqrt[3]{x} - 1 \right)}}{x^{2} \left(1 - \left(1 - \sqrt[3]{x}\right)^{2}\right)^{\frac{5}{2}}} + \frac{42 \operatorname{asin}{\left(\sqrt[3]{x} - 1 \right)}}{x^{\frac{7}{3}} \left(\left(\sqrt[3]{x} - 1\right)^{2} - 1\right)} - \frac{6 \left(\sqrt[3]{x} - 1\right) \operatorname{asin}^{2}{\left(\sqrt[3]{x} - 1 \right)}}{x^{\frac{7}{3}} \left(1 - \left(1 - \sqrt[3]{x}\right)^{2}\right)^{\frac{3}{2}}} + \frac{10 \operatorname{asin}^{2}{\left(\sqrt[3]{x} - 1 \right)}}{x^{\frac{8}{3}} \sqrt{1 - \left(1 - \sqrt[3]{x}\right)^{2}}}\right) \operatorname{asin}^{5}{\left(\sqrt[3]{x} - 1 \right)}}{27}$$