2/ 2 ___ \ / 1 \ / 1 \ / 2 ___ \
log \x + \/ x , 5/*|------- + 2*x| + 2*|------- + 2*x|*log\x + \/ x , 5/
| ___ | | ___ |
\2*\/ x / \2*\/ x /
$$\left(2 x + \frac{1}{2 \sqrt{x}}\right) \log{\left(x^{2} + \sqrt{x} \right)}^{2} + 2 \cdot \left(2 x + \frac{1}{2 \sqrt{x}}\right) \log{\left(x^{2} + \sqrt{x} \right)}$$
2 2
/ 1 \ 2/ ___ 2\ / 1 \ / 1 \ / ___ 2\ / 1 \ / ___ 2\
2*|----- + 4*x| log \\/ x + x /*|8 - ----| 2*|8 - ----|*log\\/ x + x / 2*|----- + 4*x| *log\\/ x + x /
| ___ | | 3/2| | 3/2| | ___ |
\\/ x / \ x / \ x / \\/ x /
---------------- + --------------------------- + ---------------------------- + --------------------------------
___ 2 2 log(5) / ___ 2\
\/ x + x log (5) \\/ x + x /*log(5)
----------------------------------------------------------------------------------------------------------------
4
$$\frac{\frac{\left(8 - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(x^{2} + \sqrt{x} \right)}^{2}}{\log{\left(5 \right)}^{2}} + \frac{2 \cdot \left(8 - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(x^{2} + \sqrt{x} \right)}}{\log{\left(5 \right)}} + \frac{2 \left(4 x + \frac{1}{\sqrt{x}}\right)^{2} \log{\left(x^{2} + \sqrt{x} \right)}}{\left(x^{2} + \sqrt{x}\right) \log{\left(5 \right)}} + \frac{2 \left(4 x + \frac{1}{\sqrt{x}}\right)^{2}}{x^{2} + \sqrt{x}}}{4}$$
/ 2 2 \
|/ 1 \ / 1 \ / ___ 2\ / 1 \ / ___ 2\|
||----- + 4*x| |8 - ----|*log\\/ x + x / |----- + 4*x| *log\\/ x + x /|
3 || ___ | | 3/2| | ___ | | 3
/ 1 \ / 1 \ / 1 \ / 1 \ |\\/ x / \ x / \\/ x / | / 1 \ / ___ 2\
6*|----- + 4*x| 6*|8 - ----|*|----- + 4*x| 6*|----- + 4*x|*|-------------- + -------------------------- - ------------------------------| 4*|----- + 4*x| *log\\/ x + x /
| ___ | 2/ ___ 2\ / ___ 2\ | 3/2| | ___ | | ___ | | ___ 2 log(5) / ___ 2\ | | ___ |
\\/ x / 3*log \\/ x + x / 6*log\\/ x + x / \ x / \\/ x / \\/ x / \ \/ x + x \\/ x + x /*log(5) / \\/ x /
- ---------------- + ------------------ + ----------------- + -------------------------- + ---------------------------------------------------------------------------------------------- + --------------------------------
2 5/2 2 5/2 ___ 2 ___ 2 2
/ ___ 2\ x *log (5) x *log(5) \/ x + x \/ x + x / ___ 2\
\\/ x + x / \\/ x + x / *log(5)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
8
$$\frac{\frac{4 \left(4 x + \frac{1}{\sqrt{x}}\right)^{3} \log{\left(x^{2} + \sqrt{x} \right)}}{\left(x^{2} + \sqrt{x}\right)^{2} \log{\left(5 \right)}} + \frac{6 \cdot \left(8 - \frac{1}{x^{\frac{3}{2}}}\right) \left(4 x + \frac{1}{\sqrt{x}}\right)}{x^{2} + \sqrt{x}} + \frac{6 \cdot \left(4 x + \frac{1}{\sqrt{x}}\right) \left(\frac{\left(8 - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(x^{2} + \sqrt{x} \right)}}{\log{\left(5 \right)}} - \frac{\left(4 x + \frac{1}{\sqrt{x}}\right)^{2} \log{\left(x^{2} + \sqrt{x} \right)}}{\left(x^{2} + \sqrt{x}\right) \log{\left(5 \right)}} + \frac{\left(4 x + \frac{1}{\sqrt{x}}\right)^{2}}{x^{2} + \sqrt{x}}\right)}{x^{2} + \sqrt{x}} - \frac{6 \left(4 x + \frac{1}{\sqrt{x}}\right)^{3}}{\left(x^{2} + \sqrt{x}\right)^{2}} + \frac{3 \log{\left(x^{2} + \sqrt{x} \right)}^{2}}{x^{\frac{5}{2}} \log{\left(5 \right)}^{2}} + \frac{6 \log{\left(x^{2} + \sqrt{x} \right)}}{x^{\frac{5}{2}} \log{\left(5 \right)}}}{8}$$