/b\
a*b*cosh|-|
/b\ \x/
a*sinh|-| - -----------
\x/ x / /b\\
----------------------- + log|a*x*sinh|-||
/b\ \ \x//
a*sinh|-|
\x/
$$\log{\left(a x \sinh{\left(\frac{b}{x} \right)} \right)} + \frac{- \frac{a b \cosh{\left(\frac{b}{x} \right)}}{x} + a \sinh{\left(\frac{b}{x} \right)}}{a \sinh{\left(\frac{b}{x} \right)}}$$
/b\ / /b\\
b*cosh|-| | b*cosh|-||
/b\ \x/ | /b\ \x/| /b\
2 - sinh|-| + --------- b*|- sinh|-| + ---------|*cosh|-|
b \x/ x \ \x/ x / \x/
-- - --------------------- - ---------------------------------
2 /b\ 2/b\
x sinh|-| x*sinh |-|
\x/ \x/
--------------------------------------------------------------
x
$$\frac{\frac{b^{2}}{x^{2}} - \frac{b \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right) \cosh{\left(\frac{b}{x} \right)}}{x \sinh^{2}{\left(\frac{b}{x} \right)}} - \frac{\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}}{\sinh{\left(\frac{b}{x} \right)}}}{x}$$
/b\ / /b\\ / /b\\ / /b\\
b*cosh|-| | b*cosh|-|| | b*cosh|-|| | b*cosh|-||
/b\ \x/ 2 | /b\ \x/| 3 /b\ | /b\ \x/| /b\ 2 2/b\ | /b\ \x/|
- sinh|-| + --------- 2 b *|- sinh|-| + ---------| b *cosh|-| b*|- sinh|-| + ---------|*cosh|-| 2*b *cosh |-|*|- sinh|-| + ---------|
\x/ x 2*b \ \x/ x / \x/ \ \x/ x / \x/ \x/ \ \x/ x /
--------------------- - ---- + -------------------------- + ---------- + --------------------------------- - -------------------------------------
/b\ 2 2 /b\ 3 /b\ 2/b\ 2 3/b\
sinh|-| x x *sinh|-| x *sinh|-| x*sinh |-| x *sinh |-|
\x/ \x/ \x/ \x/ \x/
--------------------------------------------------------------------------------------------------------------------------------------------------
2
x
$$\frac{\frac{b^{3} \cosh{\left(\frac{b}{x} \right)}}{x^{3} \sinh{\left(\frac{b}{x} \right)}} + \frac{b^{2} \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right)}{x^{2} \sinh{\left(\frac{b}{x} \right)}} - \frac{2 b^{2} \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right) \cosh^{2}{\left(\frac{b}{x} \right)}}{x^{2} \sinh^{3}{\left(\frac{b}{x} \right)}} - \frac{2 b^{2}}{x^{2}} + \frac{b \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right) \cosh{\left(\frac{b}{x} \right)}}{x \sinh^{2}{\left(\frac{b}{x} \right)}} + \frac{\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}}{\sinh{\left(\frac{b}{x} \right)}}}{x^{2}}$$