Evaluate the indefinite integral.

$($ln$($x$))33$x

$$dx

Step $1$

We must decide what to choose for u$.$

If

u $=$ f$($x$),$

then

du $=$ f$\text{'}($x$)$ dx$,$

and so it is helpful to look for some expression in

$($ln$($x$))33$x

$$dx

$=$

$($ln$($x$))33$

$1$x

$$dx

for which the derivative is also present, though perhaps missing a constant factor.

For example,

ln$($x$)$

is part of this integral, and the derivative of

ln$($x$)$

is

$,$ which is also presen