/ log(10) \
|------------|
\log(2*x + 1)/ 2*atan(x)*log(10)
-------------- - -----------------------
2 2
1 + x (2*x + 1)*log (2*x + 1)
$$\frac{\log{\left(10 \right)} \frac{1}{\log{\left(2 x + 1 \right)}}}{x^{2} + 1} - \frac{2 \log{\left(10 \right)} \operatorname{atan}{\left(x \right)}}{\left(2 x + 1\right) \log{\left(2 x + 1 \right)}^{2}}$$
/ / 2 \ \
| 2*|1 + ------------|*atan(x)|
| x 2 \ log(1 + 2*x)/ |
2*|- --------- - ------------------------------- + ----------------------------|*log(10)
| 2 / 2\ 2 |
| / 2\ \1 + x /*(1 + 2*x)*log(1 + 2*x) (1 + 2*x) *log(1 + 2*x) |
\ \1 + x / /
----------------------------------------------------------------------------------------
log(1 + 2*x)
$$\frac{2 \left(- \frac{x}{\left(x^{2} + 1\right)^{2}} + \frac{2 \cdot \left(1 + \frac{2}{\log{\left(2 x + 1 \right)}}\right) \operatorname{atan}{\left(x \right)}}{\left(2 x + 1\right)^{2} \log{\left(2 x + 1 \right)}} - \frac{2}{\left(2 x + 1\right) \left(x^{2} + 1\right) \log{\left(2 x + 1 \right)}}\right) \log{\left(10 \right)}}{\log{\left(2 x + 1 \right)}}$$
/ 2 \
| 4*x / 3 3 \ |
|-1 + ------ 8*|1 + ------------ + -------------|*atan(x) / 2 \ |
| 2 | log(1 + 2*x) 2 | 6*|1 + ------------| |
| 1 + x \ log (1 + 2*x)/ 6*x \ log(1 + 2*x)/ |
2*|----------- - -------------------------------------------- + -------------------------------- + --------------------------------|*log(10)
| 2 3 2 / 2\ 2 |
| / 2\ (1 + 2*x) *log(1 + 2*x) / 2\ \1 + x /*(1 + 2*x) *log(1 + 2*x)|
\ \1 + x / \1 + x / *(1 + 2*x)*log(1 + 2*x) /
--------------------------------------------------------------------------------------------------------------------------------------------
log(1 + 2*x)
$$\frac{2 \cdot \left(\frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}} - \frac{8 \cdot \left(1 + \frac{3}{\log{\left(2 x + 1 \right)}} + \frac{3}{\log{\left(2 x + 1 \right)}^{2}}\right) \operatorname{atan}{\left(x \right)}}{\left(2 x + 1\right)^{3} \log{\left(2 x + 1 \right)}} + \frac{6 x}{\left(2 x + 1\right) \left(x^{2} + 1\right)^{2} \log{\left(2 x + 1 \right)}} + \frac{6 \cdot \left(1 + \frac{2}{\log{\left(2 x + 1 \right)}}\right)}{\left(2 x + 1\right)^{2} \left(x^{2} + 1\right) \log{\left(2 x + 1 \right)}}\right) \log{\left(10 \right)}}{\log{\left(2 x + 1 \right)}}$$