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Question: integral answer undefined otherwise? and too long.pls help-from japan

Question:integral answer undefined otherwise? and too long.pls help-from japan

difficultmaple 5 Maple
improper-integral
May 21 2013
1
I have a very big problem in answering this equation.>Int(1/sqrt((x-R*cos(theta))^2+(y-R*sin(theta))^2+z^2), theta = 0 .. 2*Pi)+Int(1/sqrt((x+l*cos(alpha)-R*cos(theta))^2+(y-R*sin(theta))^2+(z+l*sin(alpha))^2), theta = 0 .. 2*Pi)I've put the equation. then simplify(%). It becomes like this:Int(1/sqrt(x^2-2*x*R*cos(theta)+R^2+y^2-2*y*R*sin(theta)+z^2), theta = 0 .. 2*Pi)+Int(1/sqrt(x^2+2*x*l*cos(alpha)-2*x*R*cos(theta)-2*l*cos(alpha)*R*cos(theta)+y^2-2*y*R*sin(theta)+R^2+z^2+2*z*l*sin(alpha)+l^2), theta = 0 .. 2*Pi)then, I wrote >value(%). but the answer is something i never met.undefined   (And(-(1/4)*(2*arcsin(x*R/sqrt((y^2+x^2)*R^2))+Pi)/Pi <= floor((1/4)*(3*Pi-2*arcsin(x*R/sqrt((y^2+x^2)*R^2)))/Pi), -(1/4)*(2*arcsin(x*R/sqrt((y^2+x^2)*R^2))+3*Pi)/Pi <= floor((1/4)*(-2*arcsin(x*R/sqrt((y^2+x^2)*R^2))+Pi)/Pi)),undefined    -(1/4)*(2*arcsin(x*R/sqrt((y^2+x^2)*R^2))+Pi)/Pi <= floor((1/4)*(3*Pi-2*arcsin(x*R/sqrt((y^2+x^2)*R^2)))/Pi), undefined     -(1/4)*(2*arcsin(x*R/sqrt((y^2+x^2)*R^2))+3*Pi)/Pi <= floor((1/4)*(-2*arcsin(x*R/sqrt((y^2+x^2)*R^2))+Pi)/Pi) otherwise    -(4*(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2))*sqrt((y^2+x^2)*R^2/(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2))*sqrt(-(y^2+x^2)*R^2/(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2))*(EllipticK(sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2)/(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2)))*sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2)/sqrt((y^2+x^2)*R^2))-sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2)/(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2))*EllipticF(sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2)/(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2)), sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2)/(z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2)))*sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2)/sqrt((y^2+x^2)*R^2)))/((y^2+x^2)*R^2*sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)-2*R^2*y^2-2*R^2*x^2)/sqrt((y^2+x^2)*R^2))*sqrt((z^2*sqrt((y^2+x^2)*R^2)+R^2*sqrt((y^2+x^2)*R^2)+x^2*sqrt((y^2+x^2)*R^2)+y^2*sqrt((y^2+x^2)*R^2)+2*R^2*y^2+2*R^2*x^2)/sqrt((y^2+x^2)*R^2))))4*EllipticK(sqrt((2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z*l*sin(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*l^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x^2+2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x*l*cos(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*y^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*R^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z^2-4*x*R^2*l*cos(alpha)-2*R^2*y^2-2*R^2*x^2+2*R^2*sin(alpha)^2*l^2-2*l^2*R^2)/(2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z*l*sin(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*l^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x^2+2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x*l*cos(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*y^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*R^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z^2+4*x*R^2*l*cos(alpha)+2*R^2*y^2+2*R^2*x^2-2*R^2*sin(alpha)^2*l^2+2*l^2*R^2)))*sqrt(-R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2)/(2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z*l*sin(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*l^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x^2+2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x*l*cos(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*y^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*R^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z^2-4*x*R^2*l*cos(alpha)-2*R^2*y^2-2*R^2*x^2+2*R^2*sin(alpha)^2*l^2-2*l^2*R^2))*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2)/(2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z*l*sin(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*l^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x^2+2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x*l*cos(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*y^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*R^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z^2+4*x*R^2*l*cos(alpha)+2*R^2*y^2+2*R^2*x^2-2*R^2*sin(alpha)^2*l^2+2*l^2*R^2))*(2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z*l*sin(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*l^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x^2+2*sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*x*l*cos(alpha)+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*y^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*R^2+sqrt(R^2*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2))*z^2-4*x*R^2*l*cos(alpha)-2*R^2*y^2-2*R^2*x^2+2*R^2*sin(alpha)^2*l^2-2*l^2*R^2)/(sqrt((2*z*l*sin(alpha)*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))+l^2*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))+x^2*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))+2*x*l*cos(alpha)*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))+y^2*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))+R^2*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))+z^2*sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2))-4*x*R^2*l*cos(alpha)-2*R^2*y^2-2*R^2*x^2-2*l^2*cos(alpha)^2*R^2)/sqrt(R^2*(y^2+x^2+2*x*l*cos(alpha)+l^2*cos(alpha)^2)))*(2*x*l*cos(alpha)+y^2+x^2-sin(alpha)^2*l^2+l^2)*R^2)can anyone help? i really donot know how to solve the integration.thanks in advance.
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