Sine: Integration (formula 01.06.21.0161)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving algebraic functions

Involving (a z+b)^beta

http://functions.wolfram.com/01.06.21.0161.01

Input Form

Integrate[(a z + b)^\[Beta] Sin[c z + d], z] == (-(1/(2 c))) (((b + a z)^\[Beta] (((I c (b + a z))/a)^\[Beta] Gamma[1 + \[Beta], -((I c (b + a z))/a)] (Cos[(b c)/a - d] - I Sin[(b c)/a - d]) + (-((I c (b + a z))/a))^\[Beta] Gamma[1 + \[Beta], (I c (b + a z))/a] (Cos[(b c)/a - d] + I Sin[(b c)/a - d])))/((c^2 (b + a z)^2)/a^2)^\[Beta])

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