Sine: Integration (formula 01.06.21.0934)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving (a+b sin²(c z))^beta

http://functions.wolfram.com/01.06.21.0934.01

Input Form

Integrate[(a + b Sin[c z]^2)^(5/2), z] == (16 a (23 a^2 + 23 a b + 8 b^2) Sqrt[(2 a + b - b Cos[2 c z])/a] EllipticE[c z, -(b/a)] - 64 a (2 a^2 + 3 a b + b^2) Sqrt[(2 a + b - b Cos[2 c z])/a] EllipticF[c z, -(b/a)] - Sqrt[2] b (88 a^2 + 88 a b + 25 b^2 - 28 b (2 a + b) Cos[2 c z] + 3 b^2 Cos[4 c z]) Sin[2 c z])/(240 c Sqrt[2 a + b - b Cos[2 c z]])

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)

2002-12-18