Sine: Integration (formula 01.06.21.0909)

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 sin(c z))^betaand rational function of sin(c z)

http://functions.wolfram.com/01.06.21.0909.01

Input Form

Integrate[Sin[c z]/((d + e Sin[c z]) Sqrt[a + b Sin[c z]]), z] == -(2 I ((b d - a e) EllipticF[I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Sin[c z]]], (a + b)/(a - b)] - b d EllipticPi[((a + b) e)/((-b) d + a e), I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Sin[c z]]], (a + b)/(a - b)]) Sec[c z] Sqrt[(b (1 + Sin[c z]))/(-a + b)] Sqrt[(b - b Sin[c z])/(a + b)])/(b Sqrt[-(1/(a + b))] c e (b d - a e))

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