Would you still expandthe integrandand then integrateterm by term?That wouldbe impracticaland time-
consuming.A betterway of doingthis is to changethe variables.Changingvariablescan oftenturn a difficult
integral,suchas the one above,into one that is easyto integrate.The methodof doingthis is calledinte-
grationby substitution,or for short,the -substitutionmethod. The examplesbelowwill showyou
how the methodis used.
Example1:
Evaluate
Solution:
Let Then Substitutingfor and we get
Integratingusingthe powerrule,
Since substitutingback,
Example2:
Evaluate
Solution:
Let Then Solvingfor
Substituting,