Thread: Integration by Parts with ln...

Hi guys,

Integrate:

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?

Thank you!

Hey UBCBOY.

Hint: Try letting u = ln(4t) and dv = t^4 instead.

Originally Posted by chiro

Hey UBCBOY.

Hint: Try letting u = ln(4t) and dv = t^4 instead.

Alright, so then I would be left with:

t^4*u du/4t is that right?
Which becomes... 1/4 ∫t^3*u du ?

But how would I be able to integrate that?