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Calculus
Find the Integral xe^xdx
x
e
x
d
x
x
e
x
d
x
Step 1
Integrate by parts using the
formula
∫
u
d
v
=
u
v
-
∫
v
d
u
, where
u
=
x
and
d
v
=
e
x
.
x
e
x
-
∫
e
x
d
x
Step 2
The
integral
of
e
x
with respect to
x
is
e
x
.
x
e
x
-
(
e
x
+
C
)
Step 3
Simplify.
x
e
x
-
e
x
+
C
(
(
)
)
|
|
[
[
]
]
√
√
≥
≥
∫
∫
7
7
8
8
9
9
≤
≤
°
°
θ
θ
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
∞
∞
!
!
,
,
0
0
.
.
%
%
=
=
[
x
2
1
2
√
π
∫
x
d
x
]
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