Compute the following integral.
Since the denominator is already factored into linear terms we can proceed directly with the partial fraction decomposition. We write,
This gives us the equation
First, we can find the values of and by evaluating at and , respectively. This gives us
Then using these values of and we evaluate at and (these are just convenient values, there isn’t anything special about them) to obtain the two equations
Solving these two equations we obtain and . Therefore, we have the following partial fraction decomposition:
We can now evaluate the integral,