Question

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

Answer 1

Hello,

$\int\limits{ \dfrac{ln(x^3)}{x}} \, dx = 3*\int\limits{\frac{ln(x)}{x}} \, dx \\\\=3*\dfrac{ln^2(x)}{2} +C$

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