Plot[Cos[x]/(1 - Cos[x] + 0.25), {x, 0, 2*Pi}]
The graph is easily seen to be symmetric about $\pi$.
But
Integrate[Cos[x]/(1 - Cos[x] + 0.25), {x, 0, Pi}]
gives the correct answer of 2.0944
but
Integrate[Cos[x]/(1 - Cos[x] + 0.25), {x, Pi, 2*Pi}]
outputs -8.37758
It turns out that
Integrate[Cos[x]/(1 - Cos[x] + 0.25), {x, 0, 2*Pi}]
does work giving double the previous answer: 4.18879
Why??? This is driving me insane.
1/4
, not0.25
. $\endgroup$Integrate[Cos[x]/(1 - Cos[x] + 0.25), {x, 0, Pi}] == Integrate[Cos[x]/(1 - Cos[x] + 0.25), {x, Pi, 2 *Pi}] (* True*)
. $\endgroup$