Techniques of integration: Partial Fractions: Distinct Linear Factors: Find

We shall decompose the fraction, F, in the integrand by factoring and rewriting it as partial fractions:

We can determine A and B by combining the terms on the right hand side:

We know that this can be satisfied by all values of x, and that the numerators must be equal.

In particular, we can use convenient values of x: -3 and +4.

Try . Then

, or

, or

Now try :

, or

, or

Now we can substitute these values into the original fraction, F:

, and accordingly, the original integral becomes

With , ; , , we get

. We can use the integral leading to the natural log:

. As a final step, we convert back to expressions in x: