The given integral 
( )
∫f x dx
 can be transformed into another form by changing
the independent variable x to t by substituting x = g (t) Consider
I =
( )
f x dx
∫
Put x = g(t) so that dx
dt  = g′(t) We write
dx = g′(t) dt
Thus
I =
( )
( ( ))
( )
f x dx
f g t
g t dt
=
′
∫
∫
This change of variable formula is one of the important tools available to us in the
name of integration by substitution It is often important to guess what will be the useful
substitution