Integrating term by term \( \int \frac{y}{(y+4)(y-4)(y+5)} \mathrm{d} y= \) plus a constant of integration. (Do not specify another constant of integration in your answer

Find the derivative of the following function by first expanding the expression. \[ h(x)=\left(x^{5}+1\right)^{2} \] The expanded expression is \( h(x)=\square \) (Simplify your answer.)

Calculate the derivative of the following function. \( y=\sqrt{17 x+4} \)

Calcular el área de las siguientes regiones que están delimitadas por las siguientes curvas cuyas ecuaciones son: A) \( \mathrm{y}=\mathrm{x}+6 \quad ; \quad \mathrm{y}=\mathrm{x}^{3} \quad ; 2 \mathrm{y}+\mathrm{x}=0 \)

A. ctangle initially has dimensions 2 cm by 7 cm . All sides begin increasing in length at a rate of \( 2 \mathrm{~cm} / \mathrm{s} \). At what rate is the area of the rectangle increasing after 16 s ? Let \( \mathrm{A}, \mathrm{b} \), and h be the area, base, and height of a rectangle, respectively. Write an equation relating \( \mathrm{A}, \mathrm{b} \), and h . \( \mathrm{A}=\mathrm{b} \times \mathrm{h} \) Differentiate both sides of the equation with respect to t . \( \mathrm{dA}= \)

Find the following limit or state that it does not exist. \( \lim _{h \rightarrow 0} \frac{\sqrt{225+h}-15}{h} \)