/ / __________\
| | / 2 |
| 2 |\/ (5 + x) |
|(5 + x) *atanh|-------------|
| \ 2 /
|----------------------------- for And(x > -7, x < -3)
| __________
| / 2
| 2*\/ (5 + x)
<
| oo
| ____
| \ `
| \ -n 2*n
| \ 4 *(5 + x)
| / -------------- otherwise
| / -1 + 2*n
| /___,
\ n = 1
-------------------------------------------------------
5 + x
$$\frac{\begin{cases} \frac{\left(x + 5\right)^{2} \operatorname{atanh}{\left(\frac{\sqrt{\left(x + 5\right)^{2}}}{2} \right)}}{2 \sqrt{\left(x + 5\right)^{2}}} & \text{for}\: x > -7 \wedge x < -3 \\\sum_{n=1}^{\infty} \frac{4^{- n} \left(x + 5\right)^{2 n}}{2 n - 1} & \text{otherwise} \end{cases}}{x + 5}$$
Piecewise(((5 + x)^2*atanh(sqrt((5 + x)^2)/2)/(2*sqrt((5 + x)^2)), (x > -7)∧(x < -3)), (Sum(4^(-n)*(5 + x)^(2*n)/(-1 + 2*n), (n, 1, oo)), True))/(5 + x)