6) A ladder 6 ft long is leaning against a wall, with the foot of ladder 3 ft away from the wall. If the foot of the ladde is being pulled away from the wall at 2 feet per second, how fast is the top of the ladder sliding down the wall?

\( \int \frac { 3 x ^ { 5 } } { \sqrt { 7 - 12 x ^ { 6 } } } d x = \square \)

Given the following velocity function of an object moving aiong a line, find the position function with the given initial position. \[ v(t)=2 \sqrt[3]{t}, s(0)=3 \] The position function is \( s(t)=\square \)

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

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

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