/ 2 2 x\ / x ___ \
|----- + -------- + e |*cos\e + 4*\/ x + atan(2*x)/
| ___ 2 |
\\/ x 1 + 4*x /
$$\left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right) \cos{\left(\left(4 \sqrt{x} + e^{x}\right) + \operatorname{atan}{\left(2 x \right)} \right)}$$
/ 2 \
|/ 2 2 x\ / ___ x\ / 1 x 16*x \ / ___ x\|
-||----- + -------- + e | *sin\4*\/ x + atan(2*x) + e / + |---- - e + -----------|*cos\4*\/ x + atan(2*x) + e /|
|| ___ 2 | | 3/2 2| |
|\\/ x 1 + 4*x / |x / 2\ | |
\ \ \1 + 4*x / / /
$$- (\left(\frac{16 x}{\left(4 x^{2} + 1\right)^{2}} - e^{x} + \frac{1}{x^{\frac{3}{2}}}\right) \cos{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)} + \left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right)^{2} \sin{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)})$$
/ 2 \
| 32 x 3 512*x | / ___ x\
|- ----------- + 2*e + ---- + -----------|*cos\4*\/ x + atan(2*x) + e /
| 2 5/2 3|
| / 2\ x / 2\ | 3
\ \1 + 4*x / \1 + 4*x / / / 2 2 x\ / ___ x\ / 1 x 16*x \ / 2 2 x\ / ___ x\
------------------------------------------------------------------------- - |----- + -------- + e | *cos\4*\/ x + atan(2*x) + e / + 3*|---- - e + -----------|*|----- + -------- + e |*sin\4*\/ x + atan(2*x) + e /
2 | ___ 2 | | 3/2 2| | ___ 2 |
\\/ x 1 + 4*x / |x / 2\ | \\/ x 1 + 4*x /
\ \1 + 4*x / /
$$3 \left(\frac{16 x}{\left(4 x^{2} + 1\right)^{2}} - e^{x} + \frac{1}{x^{\frac{3}{2}}}\right) \left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right) \sin{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)} - \left(e^{x} + \frac{2}{4 x^{2} + 1} + \frac{2}{\sqrt{x}}\right)^{3} \cos{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)} + \frac{\left(\frac{512 x^{2}}{\left(4 x^{2} + 1\right)^{3}} + 2 e^{x} - \frac{32}{\left(4 x^{2} + 1\right)^{2}} + \frac{3}{x^{\frac{5}{2}}}\right) \cos{\left(4 \sqrt{x} + e^{x} + \operatorname{atan}{\left(2 x \right)} \right)}}{2}$$