Log Sine Function

Author

Eric W. Weisstein
April 19, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/LogSineFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/LogSineFunction.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Function

Integral

Table[Plot[Through[{Re,Im}[Log[Sin[x]]^n]],{x,0,π},Evaluated->True,PlotStyle->{Directive[Thick,Red],Directive[Thick,Yellow]}],{n,3}]

Plot[Table[Log[Sin[x]]^n,{n,5}],{x,0,π},Evaluated->True,PlotStyle->{Red,Orange,Yellow,Green,Blue},AxesLabel->{x,Log[Sin[x]]^n}]

V5

Integrate[Log[Sin[x]]^n,{x,0,π}]

V7

Integrate[Log[Sin[x]]^n,{x,0,π}]

Integrate[Log[Sin[x]]^n,{x,0,π},Assumptions->n>0]

V8

Integrate[Log[Sin[x]]^n,{x,0,π},Assumptions->n>0]

Special Cases

<<Utilities`Simplify`

V8

Table[Integrate[Log[Sin[x]]^n,{x,0,π}],{n,3}]//LogExpand//Expand