I know integrate needs to get information, but...
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(%i22) integrate(log(cos(x)),x,0,%pi/2);
Is %pi/2 an ?integer?
n;
Is %pi/4 an ?integer?
n;
Is 2*%pi an ?integer?
n;
Is 4*%pi an ?integer?
n;
(%o22) %i*%pi^2/24-(6*%pi*log(4)+%i*%pi^2)/24
(%i23) ratsimp(%);
(%o23) -%pi*log(4)/4
(%i24) float(%);
(%o24) -1.088793045151801
(%i25) quad(log(cos(x)),x,0,%pi/2);
(%o25) -1.088793045151803
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In the above we get ?integer? instead of
integer? because display2d is false.
quad is a function in nint package, ch. 8.
Ted