- uv}}\right)}
arcoth u ±
arcoth v =
arcoth ( 1 ± u v u ± v ) {\displaystyle \operatorname {
arcoth} u\pm \operatorname {
arcoth} v=\operatorname {
arcoth} \left({\frac...
-
denoted "tanh−1", "atanh" or
sometimes "arctanh") area
hyperbolic cotangent "
arcoth" (also
denoted "coth−1", "acoth" or
sometimes "arccoth") area hyperbolic...
-
arcoth(ax)2a2+x2a+C{\displaystyle \int x\operatorname {
arcoth} (ax)\,dx={\frac {x^{2}\operatorname {
arcoth} (ax)}{2}}-{\frac {\operatorname {
arcoth}...
- 1 2
arcoth [ 1 2 2 cos ( 3 14 π ) cot ( 1 28 π ) + cos ( 1 7 π ) ] } {\displaystyle \tanh {\bigl \{}{\tfrac {1}{2}}\operatorname {
arcoth} {\bigl...
- {\displaystyle 2\sinh x\cosh x=\sinh 2x} , and
arcoth x = 1 2 ln x + 1 x − 1 {\displaystyle \operatorname {
arcoth} x={\tfrac {1}{2}}\ln {\tfrac {x+1}{x-1}}}...
- x=-\operatorname {csch} ^{2}x=1-\coth ^{2}x} d d x
arcoth x = 1 1 − x 2 {\displaystyle {\frac {d}{dx}}\operatorname {
arcoth} x={\frac {1}{1-x^{2}}}} d d x sech ...
- (Also
written as arcsch.)
arcosh –
inverse hyperbolic cosine function.
arcoth –
inverse hyperbolic cotangent function.
arcsch –
inverse hyperbolic cosecant...
- }}|x|<|a|{\mbox{)}}\\[12pt]\displaystyle -{\frac {1}{a}}\,\operatorname {
arcoth} {\frac {x}{a}}+C={\frac {1}{2a}}\ln {\frac {x-a}{x+a}}+C&{\text{(for...
- \int {\frac {dx}{xS}}={\begin{cases}-{\dfrac {2}{\sqrt {b}}}\operatorname {
arcoth} \left({\dfrac {S}{\sqrt {b}}}\right)&{\mbox{(for }}b>0,\quad ax>0{\mbox{)}}\\-{\dfrac...
- B_{\pm }}}\right)=\operatorname {eval} {\frac {x}{\pi }}\operatorname {
arcoth} \left({\frac {\pi B_{\pm }}{x}}\right)=x\coth(x)-1}...
