An effective method of integration is integration by algebraic substitution. In this type of problem dydx can be treated like a fraction.

The key to recognising this type of integration is that one part of the expression to be integrated is often the derivative of another part. Make sure that x is totally removed from the substituted integral.

The best way to illustrate integration by substitution is by six examples of some of the different methods.

Example 1
Example 2
Example 3
Find  (3x − 7)5 dx Find  x(x − 3)4 dx Find  x √(x2 + 9) dx
Y12_Integration_by_Substitution_02.gif Y12_Integration_by_Substitution_03.gif Y12_Integration_by_Substitution_04.gif
Example 4
Example 5
Example 6
Find  8ex4. xdx FindY12_Integration_by_Substitution_05.gif Find Y12_Integration_by_Substitution_06.gif
"Although each example has a similar substitution, each has its own particular features and as always, practice makes perfect!"