Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.

Consider the indefinite integral $\displaystyle \int \frac{5 x^3+7 x^2+ 100 x + 75}{x^4+25 x^2}\, dx$
Then the integrand has partial fractions decomposition $$\frac{a}{x^2} + \frac{b}{x} + \frac{cx + d}{x^2+25}$$ where
$a$ =
$b$ =
$c$ =
$d$ =
Integrating term by term, we obtain that
$\displaystyle \int \frac{5 x^3+7 x^2+ 100 x + 75}{x^4+25 x^2}\, dx =$
$+C$