html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Tanh

 http://functions.wolfram.com/01.21.21.0188.01

 Input Form

 Integrate[E^(p z) Sin[a z]^m Cosh[c z]^\[Mu] Tanh[c z], z] == (Binomial[m, m/2] Cosh[c z]^\[Mu] (1 - Mod[m, 2]) (-(E^(p z) Hypergeometric2F1[(p - c \[Mu])/(2 c), 1 - \[Mu], (1/2) (2 + p/c - \[Mu]), -E^(2 c z)])/(p - c \[Mu]) + (E^((2 c + p) z) Hypergeometric2F1[(p + c (2 - \[Mu]))/(2 c), 1 - \[Mu], (1/2) (4 + p/c - \[Mu]), -E^(2 c z)])/ (p + c (2 - \[Mu]))))/(2^m (1 + E^(2 c z))^\[Mu]) + (Cosh[c z]^\[Mu] Sum[(-1)^k Binomial[m, k] (-(E^((I m Pi)/2 + ((-I) a (-2 k + m) + p) z) Hypergeometric2F1[ ((-I) a (-2 k + m) + p - c \[Mu])/(2 c), 1 - \[Mu], (1/2) (2 + ((-I) a (-2 k + m) + p)/c - \[Mu]), -E^(2 c z)])/ ((-I) a (-2 k + m) + p - c \[Mu]) + (E^((I m Pi)/2 + (2 c - I a (-2 k + m) + p) z) Hypergeometric2F1[ ((-I) a (-2 k + m) + p + c (2 - \[Mu]))/(2 c), 1 - \[Mu], (1/2) (4 + ((-I) a (-2 k + m) + p)/c - \[Mu]), -E^(2 c z)])/ ((-I) a (-2 k + m) + p + c (2 - \[Mu])) - (E^((-(1/2)) I m Pi + (I a (-2 k + m) + p) z) Hypergeometric2F1[ (I a (-2 k + m) + p - c \[Mu])/(2 c), 1 - \[Mu], (1/2) (2 + (I a (-2 k + m) + p)/c - \[Mu]), -E^(2 c z)])/ (I a (-2 k + m) + p - c \[Mu]) + (E^((-(1/2)) I m Pi + (2 c + I a (-2 k + m) + p) z) Hypergeometric2F1[(I a (-2 k + m) + p + c (2 - \[Mu]))/(2 c), 1 - \[Mu], (1/2) (4 + (I a (-2 k + m) + p)/c - \[Mu]), -E^(2 c z)])/(I a (-2 k + m) + p + c (2 - \[Mu]))), {k, 0, Floor[(1/2) (-1 + m)]}])/(2^m (1 + E^(2 c z))^\[Mu]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18