Evaluate this indefinite integral!? Please?

Question

Evaluate the integral (((ln(x)^4)/x))

Answer 1

∫ ( [ln(x)]^4 / x dx )

To solve this we're going to use substitution. But first, I'll show you a preliminary step to help you see it in action.

Splitting the integral into a product, we get

∫ ( [ln(x)]^4 (1/x) dx )

Here's where we use substitution.
Let u = ln(x). Then
du = (1/x) dx

Note that (1/x) dx is the tail end of our integral; as a result, du will be the tail end after the substitution.

∫ (u^4 du )

Integrate using the reverse power rule.

(1/5)u^5 + C

But u = ln(x), so back-substituting, we get

(1/5)[ln(x)]^5 + C

Answer 2

Let u = ln x.
Then du = dx/x.
From here it is just integrating u^4 du, which I am sure you are up for.

Answer 3

integral (4lnx) / x

let ln x =u

1/x dx=du

integral 4udu

=2u^2
=2(lnx)^2 + C