Question

What is the integral of 1/x(lnx)^3 dx

Answer 1

Set up the integral and since you have an LN in the integral you see that you may have to use substitution or integration by parts

Answer 2

∫ 1/{x * [ln(x)]^3} dx
= ∫ 1/x * 1/[ln(x)]^3 dx.

So let u = ln(x) <==> du = 1/x dx. Then, applying these substitutions yields:

∫ 1/x * 1/[ln(x)]^3 dx
= ∫ 1/u^3 du
= ∫ u^(-3) du
= u^(-3 + 1)/(-3 + 1) + C
= -1/(2u^2) + C
= -1/{2 * [ln(x)]^2} + C

Answer 3

\[\int\limits_{}^{} \frac{ 1 }{ x } (\ln x )^{3} \]

Answer 4

\[
\int \frac{(\ln x)^3}{x}dx = \int (\ln x)^3d(\ln x)
\]

Answer 5

actually the (lnx)^3 is on the bottom xD

Answer 6

thats what i did..

Answer 7

(inx)^3 as you see is listed below.

Answer 8

thank-you, I was telling wio :)

Answer 9

Oh okay! your welcome. Goodluck!!!

Answer 10

Thanks!!