/atan(1 + 2*x) 1 1 + 2*x \
8*|------------- - --------------------------- - -----------------|
| 2 / 2\ 2|
| (-1 + 2*x) \1 + (1 + 2*x) /*(-1 + 2*x) / 2\ |
\ \1 + (1 + 2*x) / /
-------------------------------------------------------------------
-1 + 2*x
$$\frac{8 \left(- \frac{2 x + 1}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} - \frac{1}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)} + \frac{\operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{2}}\right)}{2 x - 1}$$
/ 2 \
| 4*(1 + 2*x) |
|-1 + -------------- |
| 2 |
| 1 + (1 + 2*x) 3*atan(1 + 2*x) 3 3*(1 + 2*x) |
16*|------------------- - --------------- + ---------------------------- + ----------------------------|
| 2 3 / 2\ 2 2 |
| / 2\ (-1 + 2*x) \1 + (1 + 2*x) /*(-1 + 2*x) / 2\ |
\ \1 + (1 + 2*x) / \1 + (1 + 2*x) / *(-1 + 2*x)/
--------------------------------------------------------------------------------------------------------
-1 + 2*x
$$\frac{16 \left(\frac{\frac{4 \left(2 x + 1\right)^{2}}{\left(2 x + 1\right)^{2} + 1} - 1}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(2 x + 1\right)}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)^{2}} + \frac{3}{\left(2 x - 1\right)^{2} \left(\left(2 x + 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{3}}\right)}{2 x - 1}$$