  We find best constants in several dilation invariant integral inequalities
involving derivatives of functions. Some of these inequalities are new and some
were known without best constants. The contents: 1. Estimate for a quadratic
form of the gradient, 2. Weighted G{\aa}rding inequality for the biharmonic
operator, 3.Dilation invariant Hardy's inequality with remainder term, 4.
Generalized Hardy-Sobolev inequality with sharp constant, 5. Hardy's inequality
with sharp Sobolev remainder term.
