contour integral comples .. please help me

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salah zetreni 2015-3-14

I write the limits of integration from 0 to 2*pi when he give me a Full Circle ,, but what I write

instead of 2*pi when he give me half circle as show in figure? :

this statement of matlab when he give me a contour for full circle :

q1=quad(@(t) fun(g(t)).*gprime(t),0,2*pi)

I want instead it by contour for half circle ,, what I write instead( 0,2*pi)?

this problem that I want answer it:

find the integral around half contour

∫(x^3+3)/((x^2+1)(x^2+4))

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