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 Tanh

 http://functions.wolfram.com/01.21.21.0200.01

 Input Form

 Integrate[z^n E^(p z) Sin[a z] Sinh[b z] Tanh[c z], z] == (1/4) I n! ((-E^(((-I) a + b + p) z)) Sum[(1/(-j + n)!) ((-1)^j ((-I) a + b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[e, 1], \[Ellipsis], Subscript[e, 1 + j], 1}, {1 + Subscript[e, 1], \[Ellipsis], 1 + Subscript[e, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + E^(((-I) a + b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a + b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[f, 1], \[Ellipsis], Subscript[f, 1 + j], 1}, {1 + Subscript[f, 1], \[Ellipsis], 1 + Subscript[f, 1 + j]}, -E^(2 c z)]), {j, 0, n}] - E^((I a + b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a + b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[g, 1], \[Ellipsis], Subscript[g, 1 + j], 1}, {1 + Subscript[g, 1], \[Ellipsis], 1 + Subscript[g, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + E^((I a + b + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a + b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[h, 1], \[Ellipsis], Subscript[h, 1 + j], 1}, {1 + Subscript[h, 1], \[Ellipsis], 1 + Subscript[h, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + E^(((-I) a - b + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a - b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[i, 1], \[Ellipsis], Subscript[i, 1 + j], 1}, {1 + Subscript[i, 1], \[Ellipsis], 1 + Subscript[i, 1 + j]}, -E^(2 c z)]), {j, 0, n}] - E^(((-I) a - b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a - b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[k, 1], \[Ellipsis], Subscript[k, 1 + j], 1}, {1 + Subscript[k, 1], \[Ellipsis], 1 + Subscript[k, 1 + j]}, -E^(2 c z)]), {j, 0, n}] - E^((I a - b + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a - b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[l, 1], \[Ellipsis], Subscript[l, 1 + j], 1}, {1 + Subscript[l, 1], \[Ellipsis], 1 + Subscript[l, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + E^((I a - b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a - b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[m, 1], \[Ellipsis], Subscript[m, 1 + j], 1}, {1 + Subscript[m, 1], \[Ellipsis], 1 + Subscript[m, 1 + j]}, -E^(2 c z)]), {j, 0, n}]) /; Subscript[e, 1] == Subscript[e, 2] == \[Ellipsis] == Subscript[e, n + 1] == ((-I) a + b + p)/(2 c) && Subscript[f, 1] == Subscript[f, 2] == \[Ellipsis] == Subscript[f, n + 1] == ((-I) a + b + p + 2 c)/(2 c) && Subscript[g, 1] == Subscript[g, 2] == \[Ellipsis] == Subscript[g, n + 1] == (I a + b + p + 2 c)/(2 c) && Subscript[h, 1] == Subscript[h, 2] == \[Ellipsis] == Subscript[h, n + 1] == (I a + b + p)/(2 c) && Subscript[i, 1] == Subscript[i, 2] == \[Ellipsis] == Subscript[i, n + 1] == ((-I) a - b + p)/(2 c) && Subscript[k, 1] == Subscript[k, 2] == \[Ellipsis] == Subscript[k, n + 1] == ((-I) a - b + p + 2 c)/(2 c) && Subscript[l, 1] == Subscript[l, 2] == \[Ellipsis] == Subscript[l, n + 1] == (I a - b + p)/(2 c) && Subscript[m, 1] == Subscript[m, 2] == \[Ellipsis] == Subscript[m, n + 1] == (I a - b + p + 2 c)/(2 c) && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z sin ( a z ) sinh ( b z ) tanh ( c z ) z 1 4 n ! 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 Rule Form

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

 2002-12-18