\( \begin{array}{ll}\text { (2) } \int \frac{d x}{7-3 x} & \text { (3) } \int \sqrt[3]{x+5} d x \\ \text { (5) } \int \frac{d x}{(2 x-5)^{2}} & \text { (6) } \int \sqrt[3]{(5-3 x)^{2}} d x\end{array} \)

\( \int _{}^{} d m \)

If \( f(x)=\frac{7}{x+5} \) and \( g(x)=\frac{x+73}{x^{2}-25} \), determine \( (f+g)(x) \) \( (f+g)(x)=\frac{\pi+32}{x^{2}-25} \) \( (f+g)(x)=\frac{x+32}{x+5} \) \( (f+g)(x)=\frac{8}{x^{2}-25} \) \( (f+g)(x)=\frac{8}{x-5} \)

(c) \( f(x)=5 x(2 x-5)^{2} \) Ralls to the left and rises to the right Rises to the left and falls to the right Falls to the left and falls to the right

8.- Resolver por Integración por fracciones parciales \( \int \frac{1}{x^{2}-4} d x \) Opciones: a) \( \frac{1}{2} \ln |x-2|-\frac{1}{2} \ln |x+2|+C \) b) ln \( |x-2|-\ln |x+2|+C \) c) \( \frac{1}{2} \ln |x+2|-\frac{1}{2} \ln |x-2|+C \) d) \( \left.{ }^{\frac{1}{2}} \ln \left|x+2+\frac{1}{2} \ln \right| x-2 \right\rvert\,+C \)

Find the difference quotient of \( f \); that is, find \( \frac{f(x+h)-f(x)}{h}, h \neq 0 \), for the following function. Be sure to simplify. \( f(x)=3 x^{2}-7 x+8 \) \( \frac{f(x+h)-f(x)}{h}=\square \)