سیگما

`Q=int (dx)/(sin^2x+3sinxcosx-cos^2x)`
`Q=2/3 int (dx)/(2/3(sin^2x-cos^2x)+sin2x)`
`Q=2/3 int (dx)/(2/3(-cos2x)+sin2x)`
`Q=2/3 int (dx)/(sin2x-2/3cos2x)`
`2x=u`
`2dx=du`
`Q= int (du)/(3sinu-2cosu)`
`t=tan(u/2)`
`sinu=(2t)/(1+t^2)`
`cosu=(1-t^2)/(1+t^2)`
`du=(2dt)/(1+t^)`
`Q= int ((2)/(1+t^2))/(3(2t)/(1+t^2)-2(1-t^2)/(1+t^2)) dt`
`Q= int (dt)/(t^2+3t-1)`
`Q= int (dt)/((t+3/2)^2-13/4)`
`Q=2/sqrt(13)arctanh((2t+3)/sqrt(13))`
`|t=tanx`