\( \begin{array}{ll}5 \cdot \int_{2}^{3} \frac{3 x^{2}-7 x-2}{x^{3}-x} d x & \text { usando solo el método de } \\ & \begin{array}{l}\text { fracción simple. usted debe hallar: } \\ \text { el área }\end{array}\end{array} \)

Find the following limit or state that it does not exist \[ \lim _{x \rightarrow-1} \frac{4(2 x-2)^{2}-64}{x+1} \]

Resuelve la ecuación diferencial \( \frac{dy}{dx} = 3y^{2} \) dado que \( y(0) = 1 \).

Find the point(s) at which the function \( f(x)=10-|x| \) equals its average value on the interval \( [-10,10] \) The function equals its average value at \( x=\square \) (Type an integer or a fraction. Use a comma to separate answers as needed.)

\( \int _ { - 1 } ^ { 1 } \frac { x \cos ^ { 2 } x } { 1 + x ^ { 2 } } d x \)

Given the following velocity function of an object moving along a line, find the position function with the given initial position.