Calculus: ∫ 7*x*(2*x-6)^(-1/4) dx?

Question

Please help get me started on antidifferentiating this problem. I don't need you to solve it for me. Thanks!

Answer 1

I'd try letting u = 2x - 6

Then x = (u - 2) / 6, and du = 2dx

And then you're integrating:

∫ 7/12(u-2)u^(-1/4) du = ∫ 7/12((u^3/4)-2u^(-1/4))du

Answer 2

You'll need to use substitution.
Let u = (2x-6)^(-1/4). (You can also just use u = 2x-6, but I find this way easier.)

Express x in terms of u so that you can substitute for the other x that occurs in the equation. Then differentiate to find dx/du, so you can then substitute dx = du * something.

Then you should have a nice polynomial-style integral in u, so you can integrate and substitute back for x.

Answer 3

you can firsts rewrite it as
integral of 1 / (4th root of 14x^2 - 42x) dx
then use substitution