integrals circulars

int[ z = e^{ix}+a ][ (z+a)^{2}(z+(-a))^{q} ] d_{x}[z] d[x] = ...

... int[ z = e^{ix}+a ][ (e^{ix}+2a)^{2}e^{qix} ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+a ][ (e^{2ix}+4ae^{ix}+4a^{2})e^{qix} ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+a ][ ie^{(q+3)ix}+4iae^{(q+2)ix}+4ia^{2}e^{(q+1)ix} ] d[x] = ...

... (1/(q+3))·e^{(q+3)ix}+4a·(1/(q+2))·e^{(q+2)ix}+4a^{2}·(1/(q+1))·e^{(q+1)ix}

int[ z = e^{ix}+(-a) ][ (z+a)^{p}(z+(-a))^{2} ] d_{x}[z] d[x] = ...

... int[ z = e^{ix}+(-a) ][ e^{pix}(e^{ix}+(-2)a)^{2} ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+(-a) ][ e^{pix}(e^{2ix}+(-4)ae^{ix}+4a^{2}) ] ie^{ix} d[x] = ...

... int[ z = e^{ix}+(-a) ][ ie^{(p+3)ix}+(-4)iae^{(p+2)ix}+4ia^{2}e^{(p+1)ix} ] d[x] = ...

... (1/(p+3))·e^{(p+3)ix}+(-4)·a·(1/(p+2))·e^{(p+2)ix}+4a^{2}·(1/(p+1))·e^{(p+1)ix}