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