Math 129 Section 005H
Lecture 2: Integration by parts
1
1
1
This document is licensed under a
Creative Commons Attribution 3.0 United States License
Math 129 Section 005H
Lecture 2: Integration by parts
1
1
1
This document is licensed under a
Creative Commons Attribution 3.0 United States License
How to pick
u
and
v
′
?
Integration by parts is the product rule “in reverse”
(Wednesday, August 25, 2021)
Recall the product rule for differentiation:
d
d
x
(
u
(
x
)
v
(
x
)
)
=
u
′
(
x
)
v
(
x
)
+
u
(
x
)
v
′
(
x
)
.
This implies
∫
(
u
′
(
x
)
v
(
x
)
+
u
(
x
)
v
′
(
x
)
)
𝑑
x
=
u
(
x
)
v
(
x
)
+
C
.
More useful form:
∫
u
(
x
)
v
′
(
x
)
𝑑
x
=
u
(
x
)
v
(
x
)
-
∫
u
′
(
x
)
v
(
x
)
𝑑
x
.
or
∫
u
v
′
=
u
v
-
∫
u
′
v
.