wolfram mathematica - Integrating Norm of vectors -


i have 2 vectors want integrate in matematica. let vectors be

r = {x, y}; q = {x1, y1};

then write command

integrate[  1/norm[-((a*q)/c) + r],  {a, 0, 1},   assumptions -> (a*x1)/c > x && x ->     real && (a*x1)/c ->      real && x > 0 && (a*y1)/c -> real && (a*y1)/c > y && y > 0  ]

where c positive constant. output yields same

integrate[1/norm[-((a q)/c) + r], {a, 0, 1},   assumptions -> (a x1)/c > 0 && (a x1)/c > x && x ->     real && (a x1)/c -> real && x > 0 && (a y1)/c > y && y > 0]

could please tell me making mistake? grateful if me, thanks

r = {x, y}; q = {x1, y1};  integrate[1/sqrt[(-((a*q)/c) + r).(-((a*q)/c) + r)], {a, 0, 1},            assumptions -> element[{x, y, x1, y1, a, c}, reals]]

returns:

(* (1/sqrt[x1^2 + y1^2])c (-log[c (-x x1 - y y1 +sqrt[(x^2 + y^2) (x1^2 + y1^2)])]+   log[x1^2 + y1^2 - c (x x1 + y y1) +   (c sqrt[(x1^2 + y1^2) (x1^2 + c^2 (x^2 + y^2) + y1^2 - 2 c (x x1 + y y1))])/ abs[c]])  *)

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