Calculus Help!?

Question

Anyone pls help. I need to find the integral of:
((ln(x))^5)/x

Answer 1

∫ (lnx)^5 · 1/x · dx = ...

Use substitution.
Put lnx = u. Differentiate both sides to get
=> 1/x dx = du

So we replace lnx by u and 1/x dx by du

... = ∫ u^5 du =
(u^6)/6 + C =
([lnx]^6)/6 + C

Hope this helps.

Answer 2

∫ln⁵ x/x dx

Make the substitution u=ln x, du=1/x dx. Then this becomes:

∫u⁵ du

Integrate:

u⁶/6 + C

Substitute:

ln⁶ x/6 + C

And we are done.

Answer 3

((ln(x))^6)/6 + c

just let u = ln(x) and then use the power rule