Sine: Integration (formula 01.06.21.1257)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Integration

Indefinite integration

Involving functions of the direct function and algebraic functions

Involving products of the direct function and algebraic functions

Involving products of two direct functions and algebraic functions

Involving (f+e z)^alpha-1sin(d+c z) sin(b+a z)

http://functions.wolfram.com/01.06.21.1257.01

Input Form

Integrate[(Sin[c z + d] Sin[b + a z])/(f + e z), z] == (1/(2 e)) (Cos[(b e - d e - a f + c f)/e] CosIntegral[((a - c) (f + e z))/e] - Cos[b + d - ((a + c) f)/e] CosIntegral[((a + c) (f + e z))/e] - Sin[(b e - d e - a f + c f)/e] SinIntegral[((a - c) (f + e z))/e] + Sin[b + d - ((a + c) f)/e] SinIntegral[((a + c) (f + e z))/e])

Standard Form

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MathML Form

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<cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <plus /> <ci> f </ci> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <cos /> <apply> <plus /> <ci> b </ci> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> c </ci> </apply> <ci> f </ci> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> c </ci> </apply> <apply> <plus /> <ci> f </ci> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> e </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> d </ci> <ci> e </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> f </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> f </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <plus /> <ci> f </ci> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <sin /> 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Rule Form

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

2002-12-18