Why is the "universal trigonometric substitution" called "Weierstrass's substitution"?

The universal trigonometric substitution converts a rational function in $sin(x), cos(x) $ into a rational function of a new variable $t$ by the substitution $t = tan(x/2) $. It therefore enables to solve the integral of any function in $R[sin x,cos x] $ by the methods of decomposition into partial fractions.

According to Wikipedia, this method is named after Weierstrass although It was used much earlier by Euler. It seems to me very elementary, and even Euler himself calculated far more difficult integrals, so i’d like to know why the name of a mathematician as modern as Weierstrass is attached to such an elementary technique; did he contribute something to it? did he just popularize it?