1. \( \int \frac{x^{3}+2 x^{2}+x+3}{x^{2}+2 x} d x \)

b) \( f(x)=-2 \sqrt[4]{x} \) a. \( \frac{2}{3} x^{\frac{-1}{3}} \) b. \( \frac{2}{3} x^{2} \) c. \( -2 \cdot \frac{1}{4} x^{\frac{-3}{4}} \)

Sketch the region enclosed by \( y=e^{2 x}, y=e^{4 x} \), and \( x=1 \). Find the area of the region.

Find the area of the region between the curve and the \( x \)-axis. \( f(x)=4-x^{2} \), from -6 to 6 The area is \( \square \) square units. (Type an integer or a simplified fraction.)

A factory selling cell phones has a marginal cost function \( C(x)=0.01 x^{2}-3 x+229 \), where \( x \) represents the number of cell phones, and a marginal revenue function given by \( R(x)=429-2 x \). Find the area between the graphs of these curves and \( x=0 \).

Set up the definite integral required to find the area of the region between the graph of \( y=13-x^{2} \) and \( y=24 x+148 \) over the interval \( -5 \leq x \leq 3 \).