Cosine: Integration (formula 01.07.21.0166)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving algebraic functions

Involving (a z+b)^beta

http://functions.wolfram.com/01.07.21.0166.01

Input Form

Integrate[(a z + b)^(3/2) Cos[c z], z] == (1/(4 c^3)) (-3 a^2 Sqrt[c/a] Sqrt[2 Pi] (Cos[(b c)/a] FresnelC[Sqrt[c/a] Sqrt[2/Pi] Sqrt[b + a z]] + FresnelS[Sqrt[c/a] Sqrt[2/Pi] Sqrt[b + a z]] Sin[(b c)/a]) + Sqrt[b + a z] (6 a c Cos[c z] + 4 c^2 (b + a z) Sin[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