Find the indefinite integral. $\int\left(2+x+2 x^{2}+e^{x}\right) d x$

Find the indefinite integrals.

$$\int e^{-3 t} d t$$

Use MuPAD to find the first three nonzero terms in the Taylor series for cos x.

Evaluate the indefinite integral.

$$\int t^{3} e^{-t^{4}} d t$$

Use transformations to graph the function.

$$y=3 \cos x+3$$

Add:

$$\frac{1}{x-5}-\frac{2 x-3}{5-x}$$

In the following exercise, evaluate the indefinite integral.

$$\int_1^4 3 d x$$

Let $90^{\circ}<\theta<180^{\circ}$. Determine the sign of the given function value.

$$\tan \frac{\theta}{2}$$

Graph $g(x)=\frac{1}{2} \sqrt{x-1}-3 .$ What transformations of the graph of $f(x)=\sqrt{x}$ produce the graph of $g ?$ What is the effect of the transformations on the domain and range of $g$ ?

(a) identify the claim and state $H_0$ and $H_a$, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. The table shows the numbers of emails sent and the numbers of emails received in a week for a random sample of nine people. At $\alpha=0.01,$ can you conclude that there is a significant correlation between the number of emails sent and the number of emails received?

$$\begin{matrix} \text{Emails sent} & \text{30} & \text{30} & \text{25} & \text{26} & \text{24} & \text{18} & \text{18} & \text{25} & \text{28}\\ \text{Emails received} & \text{32} & \text{36} & \text{21} & \text{22} & \text{20} & \text{20} & \text{22} & \text{23} & \text{23}\\ \end{matrix}$$

Add or subtract, as indicated. $\frac{x+y}{2 x-y}-\frac{2 x}{y-2 x}$

Suppose that $90^{\circ}<\theta<180^{\circ}$. Find the sign of the function value.

$$\tan (\theta +180^\circ)$$

Assume that $a, b$, and $c$ are real numbers and $a<0, b>0$, and $c<0$. Determine the sign of the expression:

$$\frac{a^2 c}{b^4}$$

In this exercise, find the indefinite integral.

$$\displaystyle\int x 5^{-x^2} d x$$