The value of the integral I=∫((logx)^3)/xdx is :

The correct answer is Option (2) → $\frac{(logx)^4}{4}+C,$ where C is a constant

$I=\int\frac{(\log x)^3}{x}dx$

Let $y=\log x$, $dy=\frac{dx}{x}$

$⇒I=\int y^3dy$

$⇒\frac{y^4}{4}+C=\frac{(\log x)^4}{4}+C$