6  Integration by Parts
In this section, we describe one more method of integration, that is found quite useful in
integrating products of functions If u and v are any two differentiable functions of a single variable x (say) Then, by
the product rule of differentiation, we have
(
)
d
uv
dx
 =
dv
du
u
v
dx
dx
+
Integrating both sides, we get
uv =
dv
du
u
dx
v
dx
dx
dx
+
∫
∫
or
udv
dx
∫dx
 =
uv – vdu
dx
∫dx (1)
Let
u = f (x) and dv
dx = g(x)