Intergration by substitution

A

Anthonyk2013

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Wondering if the method we used in class is right in the images below. Q 6 (a) I attempted to do this at home before class and the method I used was to divide the polynomials, but that worked out the be nasty and this is the method we did in class.
 

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Anthonyk2013 said:
Wondering if the method we used in class is right in the images below. Q 6 (a) I attempted to do this at home before class and the method I used was to divide the polynomials, but that worked out the be nasty and this is the method we did in class.
Click to expand...

attachment.php
attachment.php


There are lot of mistakes - as presented. Steps (4) and (6) are incorrect. The way it should be done (the way you tried to do at home):

\(\displaystyle \displaystyle{\frac{6x^2 - 5x +3}{12x - 5}}\)

\(\displaystyle \displaystyle{= \frac{x}{2} - \frac{5}{24} + \frac{47}{24(12x - 5)}}\)

Now it should be easy to integrate...
 
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Subhotosh Khan said:
attachment.php
attachment.php


There are lot of mistakes - as presented. Steps (4) and (6) are incorrect. The way it should be done (the way tried to do at home):

\(\displaystyle \displaystyle{\frac{6x^2 - 5x +3}{12x - 5}}\)

\(\displaystyle \displaystyle{= \frac{x}{2} - \frac{5}{24} + \frac{47}{24(12x - 5)}}\)

Now it should be easy to integrate...
Click to expand...

What you have done is divide polynomials?
 
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