1)
x
dx
∫
 = log
1
[
(log ) 1
]
d
x
dx
x
dx dx
dx
−
∫
∫
∫
=
1
(log )
–
log
C
x
x
x dx
x
x – x
x
⋅
=
+
∫ Example 19 Find 
x
x e dx
∫
Solution Take first function as x and second function as ex The integral of the second
function is ex Therefore,
x
∫x e dx
 =
1
x
x
x e
e dx
−
∫⋅
 = xex – ex + C