- uv}}\right)}
arcoth u ±
arcoth v =
arcoth ( 1 ± u v u ± v ) {\displaystyle \operatorname {
arcoth} u\pm \operatorname {
arcoth} v=\operatorname {
arcoth} \left({\frac...
-
arcoth ( a x ) d x = x
arcoth ( a x ) + ln ( a 2 x 2 − 1 ) 2 a + C {\displaystyle \int \operatorname {
arcoth} (ax)\,dx=x\operatorname {
arcoth}...
-
denoted "tanh−1", "atanh" or
sometimes "arctanh") area
hyperbolic cotangent "
arcoth" (also
denoted "coth−1", "acoth" or
sometimes "arccoth") area hyperbolic...
- {\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}}}...
-
artanh x a + C = 1 2 a ln a − x a + x + C (for | x | < | a | ) − 1 a
arcoth x a + C = 1 2 a ln x − a x + a + C (for | x | > | a | ) {\displaystyle...
- {\displaystyle \int {\frac {dx}{S}}={\frac {2S}{a}}} ∫ d x x S = { − 2 b
arcoth ( S b ) (for b > 0 , a x > 0 ) − 2 b
artanh ( S b ) (for b > 0 , a...
- 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}}}}...
- (Also
written as arcsch.)
arcosh –
inverse hyperbolic cosine function.
arcoth –
inverse hyperbolic cotangent function.
arcsch –
inverse hyperbolic cosecant...
- n ⩾ m ⩾ 2 {\displaystyle n\geqslant m\geqslant 2} J ( n , m ) := ∫ 1 ∞
arcoth n x x m d x = ∫ 1 ∞ log n / 2 ( x + 1 x − 1 ) d x x m = ∫ 0 ∞ z n tanh...
- cosh ( 2 x B ± ) − 1 ) = eval x π
artanh ( x π B ± ) = eval x π
arcoth ( π B ± x ) = x coth ( x ) − 1 {\displaystyle \operatorname {eval} \left(\cosh...
