How do I get the integral of (ln(x))^2/x?

∫ [((ln(x))^2 / x] dx

Perform a u-substitution with the natural logarithm: u = ln(x)

Thus the derivative of u: du = [1 / x] dx

∫ u^2 du

Perform power rule of integration: add one to the power and divide by the new power:

= u^3 / 3 + C

Undo the substitution:

= [ln(x)]^3 / 3 + C

... while C is the constant of integration.

u = ln(x)

---> integral of u^2 du = (u^3)/3 + C = (lnx)^3/3+C