Evaluate the following integrals: ∫ (log x)/x^n dx

Question

Evaluate the following integrals:

\(\int \frac{log\, x}{x^n}dx\)

∫ (log x)/xⁿ dx

Answer 1

We can write it as ∫ x^-n . log x dx

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here log x is the first function, and x^{- n} is the second function.