Question

What is the indefinite integral of 1/xln(x^3) dx?

Answer 1

Hello,


`\int\limits{ (ln(x^3))/(x)} \, dx = 3*\int\limits{(ln(x))/(x)} \, dx \\\\=3*(ln^2(x))/(2) +C`

Answer 2

We are asked to evaluate the integral of the given function:
∫ 1 / x(lnx)³ dx
Let u = lnx,
du / dx = 1 / x
dx = du(x)
∫ 1 / xu³ du(x)
∫ 1 / u³ du
-1 / 2u² + C
Since u = lnx,
-1 / 2(lnx)² + C
-1 / 2ln²x + C