I wanted maple to calculate the \(\displaystyle 10^th\) taylor series of f(x), while:

\(\displaystyle f(x):=\frac{1}{2\pi}\int^{\pi}_0 e^{xcos(t)} dt\)

and so I wrote :

f := (int(exp(x*cos(t)), t = 0 .. pi))/(2*pi)

p10 := taylor(f, x = 0, 11)

And I got an answer that involved multiplying by \(\displaystyle sin(\pi)\). I must change all these into zeros, so I tried to use the 'subs' command, or to simplify, even 'simplify trig', but it didn't change a thing.

What can I do in order to get a simple answer?

Thank you