Simple linear factors Evaluate the following integrals.

\(\int \frac{d x}{(x-1)(x+2)}\)

Step 1 of 3

Proper fraction definition ; In a rational fraction , if the degree of f(x) < the degree of g(x) , then the rational fraction is called a proper fraction.

The sum of two proper fractions is a proper fraction.

Example;

Partial fractions Depending upon the nature of factors of Denominator ;

1) When the denominator has non-repeated linear factors;

A non - repeated linear factor (x-a) of denominator corresponds a partial fraction of the form , where A is a constant to be determined’

If g(x) = (x-a)(x-b)(x-c)............(x-n), then we assume that

= ++ +...............+

Where A, B, C,............N are constants which can be determined by equating the numerator of L.H.Sto the numerator of R.H.S , and substituting x = a,b ,c ….n.