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Re: help with integration


Assuming[r > 0, 
 Integrate[
  r^2*ArcCos[x/r] - x*Sqrt[r^2 - x^2], {x, Sqrt[3] y, 
   Sqrt[r^2 - y^2]}]]

ConditionalExpression[
 y^3/3 + 2/3 r^2 Sqrt[r^2 - 3 y^2] + y^2 Sqrt[r^2 - 3 y^2] - 
  r^2 y (1 + Sqrt[3] ArcCos[(Sqrt[3] y)/r]) + 
  r^2 Sqrt[(r - y) (r + y)] ArcSec[r/Sqrt[r^2 - y^2]], 
 y > 0 && r > 2 y]




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