atan(2*x) 12 / 2 \
2*2 *log(2) 4*cot (x)*\-3 - 3*cot (x)/
------------------- + ---------------------------
2 cot(x)
1 + 4*x
$$\frac{2 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}}{4 x^{2} + 1} + \frac{4 \left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{12}{\left(x \right)}}{\cot{\left(x \right)}}$$
/ 2 atan(2*x) 2 atan(2*x) \
| 12 / 2 \ / 2 \ 10 2 *log (2) 4*x*2 *log(2)|
4*|6*cot (x)*\1 + cot (x)/ + 33*\1 + cot (x)/ *cot (x) + ------------------ - ---------------------|
| 2 2 |
| / 2\ / 2\ |
\ \1 + 4*x / \1 + 4*x / /
$$4 \left(- \frac{4 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} x \log{\left(2 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}^{2}}{\left(4 x^{2} + 1\right)^{2}} + 33 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{10}{\left(x \right)} + 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{12}{\left(x \right)}\right)$$
/ 3 2 atan(2*x) 3 atan(2*x) atan(2*x) 2 atan(2*x) 2 \
| / 2 \ 9 / 2 \ 11 13 / 2 \ 2 *log (2) 2*2 *log(2) 12*x*2 *log (2) 32*2 *x *log(2)|
8*|- 165*\1 + cot (x)/ *cot (x) - 102*\1 + cot (x)/ *cot (x) - 6*cot (x)*\1 + cot (x)/ + ------------------ - ------------------- - ----------------------- + -----------------------|
| 3 2 3 3 |
| / 2\ / 2\ / 2\ / 2\ |
\ \1 + 4*x / \1 + 4*x / \1 + 4*x / \1 + 4*x / /
$$8 \left(\frac{32 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} x^{2} \log{\left(2 \right)}}{\left(4 x^{2} + 1\right)^{3}} - \frac{12 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} x \log{\left(2 \right)}^{2}}{\left(4 x^{2} + 1\right)^{3}} - \frac{2 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}^{3}}{\left(4 x^{2} + 1\right)^{3}} - 165 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \cot^{9}{\left(x \right)} - 102 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{11}{\left(x \right)} - 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{13}{\left(x \right)}\right)$$