Evaluate the integral.

e$4$

ln$($x$)$x

$$dx$1$

Solution

We let

u $=$ ln$($x$)$

because its differential

du $=$

dxx

occurs in the integral. When

x $=1,$

u $=$ ln$(1)=$

$,$

and when

x $=$ e$4,$

u $=$ ln

e$4$

$=4.$

Thus,

e$4$

ln$($x$)$x

$$dx$1$

$=$

$4$u du$0$

$=$

$40$

$=$

$.$