Question

Integrate :
∫(2x^2 ln⁡8)dx

Answer 1

since ln8 = 3ln2 is just a number, you have

∫(2x^2 ln⁡8)dx
= ∫2x^2*3ln2 dx
= 6ln2∫x^2 dx
= 2ln2 x^3
= ln4 x^3 + C

Maybe you had a typo, I'm guessing...

If so, recall how to do integration by parts:

∫x lnx dx

u = lnx
du = 1/x dx

dv = x dx
v = 1/2 x^2

∫u dv = uv - ∫v du, so
∫x lnx dx = 1/2 x^2 lnx - ∫x/2 dx