Maple Maple procedure

so i'm writing a maple procedure for the variational principle in quantum mechanics.

i have a function [itex]f_1(x,\alpha)=\cos{\alpha x}[/itex] for [itex]|x| \leq \frac{\pi}{2 \alpha}[/itex] and i need to compute [itex]\left \langle f_1 | f_1 \right \rangle[/itex]

i have the code:

restart;
assume(x,real);
assume(hbar,positive);
assume(omega,positive);
assume(e,positive);
assume(alpha,positive);
assume(m,positive);
f1:=cos(alpha*x);
conjf1:=conjugate(f1);
normaliseint:=int(conjf1*f1,-Pi/(2*alpha)..Pi/(2*alpha));

now the andwer should be [itex]\frac{\pi}{2}[/itex] (i did it by hand) but Maple keeps giving me

[itex]1/2\, \left( 2\,\cos \left( 1/2\,{\frac {\pi }{{\it \alpha}}} \right)
\sin \left( 1/2\,{\frac {\pi }{{\it \alpha}}} \right) {\it \alpha}+\pi
\right) {{\it \alpha}}^{-1}[/itex]

any ideas?
thanks.
 

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