9E- separation of variables


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7G- Using partial fractions with integration

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objectives: you need to be familiar with the partial fractions techniques. There are 4 cases to consider: when the denominator consists of single factors (x+a)(x+b) when the denominator consists of a single factor (x+a) and a repeated factor, usually a perfect square (x+b)^2. This gives you three partial fractions when the denominator consists of a factor (x+a) and an irreducible quadratic expression. When you have P(x)/Q(x); division of two polynomials. It is wise to apply long division ( click here to revise on long division ) AND THEN apply partial fractions to simplify them.  Question 2b) three partial fractions
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7h- Further techniques and miscellaneous exercises

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in this exercise, you will get to revise on the different integration techniques learned in this chapter. The example below is similar to the problems you've done in Maths methods ( Exercise 11H ). This is where you first derive a function, then use the dy/dx to antidiff one of the terms in the derivative function.
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