Hint: Try letting u = ln(4t) and dv = t^4 instead.
t^4*ln(4t)dt on the interval [2,7]
I'm using substitution by parts so,
u = t^4
u' = 4t^3
v = tln(4t) - t (i think so?!)
v' = ln(4t)
∫t^4*ln(4t)dt = t^4(tln(4t) - t) - ∫(tln(4t) - t)4t^3
and I don't know how to integrate the second term....Am I doing this right?