Quiz on Forward Euler and indefinite integrals

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Total points: 7

Use Forward Euler with time steps of size $\frac{1}{4}$ to approximate the solution of the differential equation $\frac{d x}{d t} = - 8 t^{2} + 8 t + 3$ at time $t=4$, given that $x{\left (3 \right )}=-9$. If rounding, be sure to include at least $5$ significant figures.
Evaluate the integral: $\displaystyle \int 5 t^{5} - 3 t^{2} + 3 t\, dt =$
Solve the pure-time differential equation $\frac{d g}{d t} = - 2 e^{- t}$ with initial condition $g{\left (4 \right )} = -6$.
$g{\left (t \right )}=$
Evaluate the following integral: $\displaystyle\int - 2 e^{t}\, dt=$
Evaluate the following integral: $\displaystyle \int - \frac{9}{- 9 t + 10}\, dt=$