kill(all)$

f(x):=1/((x-1)^3*(x+2)^5)^(1/4);

g(u):=substitute(u+1,x,f(x))$ g(u);

G(u):=1/(u^(3/4)*(u+3)^(5/4));

integrate(G(u),u);

substitute(x-1,u,%);