________________
/ 2
8*\/ - 64*x - 16*x (-8 - 64*x)*asin(8*x + 1)
--------------------- + -------------------------
________________ ________________
/ 2 / 2
\/ 1 - (8*x + 1) \/ - 64*x - 16*x
$$\frac{\left(- 64 x - 8\right) \operatorname{asin}{\left(8 x + 1 \right)}}{\sqrt{- 64 x^{2} - 16 x}} + \frac{8 \sqrt{- 64 x^{2} - 16 x}}{\sqrt{1 - \left(8 x + 1\right)^{2}}}$$
/ 2\
| (1 + 8*x) |
|16 - -----------|*asin(1 + 8*x) ______________
\ x*(1 + 4*x)/ 32*(1 + 8*x) 256*\/ -x*(1 + 4*x) *(1 + 8*x)
- -------------------------------- - ------------------------------------ + ------------------------------
______________ ________________ 3/2
\/ -x*(1 + 4*x) ______________ / 2 / 2\
\/ -x*(1 + 4*x) *\/ 1 - (1 + 8*x) \1 - (1 + 8*x) /
$$\frac{256 \sqrt{- x \left(4 x + 1\right)} \left(8 x + 1\right)}{\left(1 - \left(8 x + 1\right)^{2}\right)^{\frac{3}{2}}} - \frac{\left(16 - \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)}\right) \operatorname{asin}{\left(8 x + 1 \right)}}{\sqrt{- x \left(4 x + 1\right)}} - \frac{32 \left(8 x + 1\right)}{\sqrt{- x \left(4 x + 1\right)} \sqrt{1 - \left(8 x + 1\right)^{2}}}$$
/ / 2 \ \
| / 2\ ______________ | 3*(1 + 8*x) | / 2\ |
| | (1 + 8*x) | 2048*\/ -x*(1 + 4*x) *|-1 + ---------------| | (1 + 8*x) | |
| 24*|16 - -----------| 2 | 2| 3*(1 + 8*x)*|16 - -----------|*asin(1 + 8*x)|
| \ x*(1 + 4*x)/ 384*(1 + 8*x) \ -1 + (1 + 8*x) / \ x*(1 + 4*x)/ |
-|------------------------------------ + ------------------------------------ + -------------------------------------------- + --------------------------------------------|
| ________________ 3/2 3/2 3/2 |
| ______________ / 2 ______________ / 2\ / 2\ 2*(-x*(1 + 4*x)) |
\\/ -x*(1 + 4*x) *\/ 1 - (1 + 8*x) \/ -x*(1 + 4*x) *\1 - (1 + 8*x) / \1 - (1 + 8*x) / /
$$- (\frac{2048 \sqrt{- x \left(4 x + 1\right)} \left(\frac{3 \left(8 x + 1\right)^{2}}{\left(8 x + 1\right)^{2} - 1} - 1\right)}{\left(1 - \left(8 x + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{24 \left(16 - \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)}\right)}{\sqrt{- x \left(4 x + 1\right)} \sqrt{1 - \left(8 x + 1\right)^{2}}} + \frac{384 \left(8 x + 1\right)^{2}}{\sqrt{- x \left(4 x + 1\right)} \left(1 - \left(8 x + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(16 - \frac{\left(8 x + 1\right)^{2}}{x \left(4 x + 1\right)}\right) \left(8 x + 1\right) \operatorname{asin}{\left(8 x + 1 \right)}}{2 \left(- x \left(4 x + 1\right)\right)^{\frac{3}{2}}})$$