Do you know how to integrate by parts? If not here's a khan academy vid explaining how it's done https://www.khanacademy.org/math/cal...-parts-formula

I don't know how useful this will be but I find this technique is useful when you have to integrate the product of 2 or more different things like (x^2)*ln(x)

EDIT: I just realized that your problem has 3 variables, and I'm not used to solving stuff like that...