One of the most powerful integration techniques is that of the change of variable . It is equivalent to the chain rule for integration:

d/dx f(g(x)) = f'(g(x)) g'(x), or,
as it is sometimes written
d f(g(x)) = f'(g(x)) g'(x) dx

Consequently,

integral f(g(x)) g'(x) dx = integral f(u) du,
if we let
u = g(x)

If we have limits of integration, [x=a,x=b] becomes [u=g(a),u=g(b)].

Choosing the right change of variable is largely a matter of experience!

Last modified Mon Dec 2 20:37:01 CST 1996