Find $\int 4x{e}^{4x}dx$.

Find $\int 4x^2\sin xdx$, with $x$ in radians.

For $\frac{dP}{dt}=0.4P\left(1-\frac{P}{1000}\right)$, with $P$ in students and $t$ in days, at what population is the population growing FASTEST, and how fast is it growing then?

Find $\int \frac{3}{\left(x-3\right)\left(x-1\right)}dx$.

Let $\frac{dy}{dx}=2x-y$ with $y(0)=3$. Use Euler's Method with TWO steps of size $h=0.25$ to approximate $y(0.5)$.

Find $\int \frac{3}{\left(x+4\right)\left(x-4\right)}dx$.

Evaluate ${\int }_0^{\infty }4e^{-x}dx$.

Let $\frac{dy}{dx}=x^2+y$ with $y(2)=1$. Use Euler's Method with TWO steps of size $h=0.5$ to approximate $y(3)$.

A particle moves along a line with velocity $v(t)=t^2-16$ for $0\le t\le 6$, in meters per second. What is the TOTAL DISTANCE traveled?

Find $\int \frac{3}{\left(x-3\right)\left(x+1\right)}dx$.

For $\frac{dP}{dt}=0.4P\left(1-\frac{P}{600}\right)$, with $P$ in deer and $t$ in years, at what population is the population growing FASTEST, and how fast is it growing then?

Evaluate ${\int }_0^{\infty }2e^{-x}dx$.

Find $\int 8x^2{e}^{x}dx$.

Find $\int 4x{e}^{3x}dx$.

Find $\int \frac{5}{\left(x-1\right)\left(x+1\right)}dx$.

For $\frac{dP}{dt}=0.2P\left(1-\frac{P}{3000}\right)$, with $P$ in deer and $t$ in years, at what population is the population growing FASTEST, and how fast is it growing then?

Evaluate ${\int }_3^{\infty }\frac{1}{x^4}dx$.

Let $\frac{dy}{dx}=x+2y$ with $y(2)=4$. Use Euler's Method with TWO steps of size $h=0.5$ to approximate $y(3)$.

Evaluate ${\int }_0^{\infty }4e^{-4x}dx$.

Let $\frac{dy}{dx}=x+y$ with $y(1)=1$. Use Euler's Method with TWO steps of size $h=0.25$ to approximate $y(1.5)$.

Find $\int 5x{e}^{3x}dx$.

Let $\frac{dy}{dx}=y+1$ with $y(1)=4$. Use Euler's Method with TWO steps of size $h=0.5$ to approximate $y(2)$.

Evaluate ${\int }_0^{\infty }6e^{-4x}dx$.

Find $\int \frac{2}{\left(x+2\right)\left(x+3\right)}dx$.