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Mathematics
Problem
Identify the correct formula for integrating a product of two differentiable functions
u
(
x
)
u(x)
u
(
x
)
and
v
(
x
)
v(x)
v
(
x
)
. a)
∫
u
d
v
=
u
v
+
∫
v
d
u
\displaystyle \int u\,dv = u\,v + \int v\,du
∫
u
d
v
=
u
v
+
∫
v
d
u
b)
∫
u
d
v
=
v
u
+
C
\displaystyle \int u\,dv = v\,u + C
∫
u
d
v
=
v
u
+
C
c)
∫
u
d
v
=
u
v
−
∫
v
d
u
\displaystyle \int u\,dv = u\,v - \int v\,du
∫
u
d
v
=
u
v
−
∫
v
d
u
d)
∫
u
d
v
=
v
u
′
−
∫
v
d
u
\displaystyle \int u\,dv = v\,u' - \int v\,du
∫
u
d
v
=
v
u
′
−
∫
v
d
u
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