Consider the rational function:
\[ \frac {21}{(x-4)^2(x+17)} \]
Give the generic partial fraction decomposition of the rational function:
\[ \frac {21}{(x-4)^2(x+17)} = \answer {\frac {A}{(x-4)^2} + \frac {B}{x-4} + \frac {C}{x+17}} \]
(Use \(A\), \(B\), and \(C\) for the constants and list the terms in the order written in the factored
form and write the higher powers of repeated terms first)
Find the values of \(A\), \(B\), and \(C\) above to give the actual partial fraction decomposition:
\[ \frac {21}{(x-4)^2(x+17)} = \frac {\answer {1}}{{(x-4)^2}} + \frac {\answer {-\frac {1}{21}}}{{x-4}} + \frac {\answer {\frac {1}{21}}}{{x+17}} \]
Calculate \(\int \frac {21}{(x-4)^2(x+17)} \d x \):
\[ \int \frac {21}{(x-4)^2(x+17)} \d x = \answer {\frac {1}{21} \ln |x+17|-\frac {1}{21}\ln |x-4|-\frac {1}{x-4}+C} \]
(Use \(C\) for the constant of integration)