Published On:Friday 16 December 2011
Posted by Muhammad Atif Saeed
Integration by the Substitution method(or 'changing the variable')
This is best explained with an example:
![substitution problem#1](http://www.a-levelmathstutor.com/images/integration/substitution01.jpg)
![substitution variable](http://www.a-levelmathstutor.com/images/integration/substitution01b.jpg)
Differentiate the equation with respect to the chosen variable.
![substitution derivative](http://www.a-levelmathstutor.com/images/integration/substitution01c.jpg)
![substitution rearrange](http://www.a-levelmathstutor.com/images/integration/substitution01d.jpg)
![substitution dx](http://www.a-levelmathstutor.com/images/integration/substitution01e.jpg)
![substitute chosen variable](http://www.a-levelmathstutor.com/images/integration/substitution01f.jpg)
![integrate with respect to t](http://www.a-levelmathstutor.com/images/integration/substitution01g.jpg)
Restate the original expression and substitute for t.
![final equation](http://www.a-levelmathstutor.com/images/integration/substitution01h.jpg)
NB Don't forget to add the Constant of Integration(C) at the end. Remember this is an indefinite integral.
Example #1
![substitution problem#1](http://www.a-levelmathstutor.com/images/integration/substitutionprob01.jpg)
Example #2
![substitution problem#2](http://www.a-levelmathstutor.com/images/integration/substitutionprob02.jpg)
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Example #3
![substitution problem#3](http://www.a-levelmathstutor.com/images/integration/substitutionprob03.jpg)