Secant: Integration (formula 01.11.21.0106)

Sec

$Mathematica Notation$

Elementary Functions

Sec[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving ((a+b sec²(c z))ⁿ)^beta

http://functions.wolfram.com/01.11.21.0106.01

Input Form

Integrate[Sec[c z] Sqrt[(a + b Sec[c z]^2)^3], z] == (2 Cos[c z]^3 Sqrt[(a + b Sec[c z]^2)^3] (-2 Sqrt[2] (2 a^2 + 3 a b + b^2) Sqrt[(a + 2 b + a Cos[2 c z])/(a + b)] EllipticE[c z, a/(a + b)] + Sqrt[2] (3 a^2 + 5 a b + 2 b^2) Sqrt[(a + 2 b + a Cos[2 c z])/(a + b)] EllipticF[c z, a/(a + b)] + Tan[c z] (4 a^2 + 11 a b + 4 b^2 + 2 a (2 a + b) Cos[2 c z] + b (a + 2 b) Sec[c z]^2 - a b Tan[c z]^2)))/ (3 c (a + 2 b + a Cos[2 c z])^2)

Standard Form

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MathML Form

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Rule Form

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

2002-10-15