you need to find the formula for du in terms of dx so that you can replace dx in the original integral by a function of du.

Here we have

u = x^{4}+ 2

du/dx = 4x^{3}

du = 4x^{3}dx

1/4 du = x^{3}dx

the right hand side is what appears in your original integral.

So after substituting you end up with