91Ó°ÊÓ

Evaluate the following integrals. $$\int \frac{16 x^{2}}{(x-6)(x+2)^{2}} d x$$

Evaluate the following integrals. $$\int \frac{d x}{\left(x^{2}-36\right)^{3 / 2}}, x>6$$

Use a table of integrals to determine the following indefinite integrals. These integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. $$\int \frac{d x}{\sqrt{x^{2}-6 x}}, x>6$$

Evaluate the following integrals. $$\int_{-1}^{1} \frac{x}{(x+3)^{2}} d x$$

The amount of drug in the blood of a patient (in \(m g\) ) due to an intravenous line is governed by the initial value problem \(y^{\prime}(t)=-0.02 y+3, \quad y(0)=0 \quad\) for \(t \geq 0\), where \(t\) is measured in hours. a. Find and graph the solution of the initial value problem. b. What is the steady-state level of the drug? c. When does the drug level reach 90\% of the steady-state value?

Evaluate the following integrals. $$\int \frac{x+2}{x+4} d x$$

Evaluate the following integrals. $$\int x^{2} \sin 2 x d x$$

Integrals of \(\tan x\) or cot \(x\) Evaluate the following integrals. $$\int 20 \tan ^{6} x d x$$

Evaluate the following integrals. $$\int \frac{x^{2}}{\sqrt{16-x^{2}}} d x$$

Use a table of integrals to determine the following indefinite integrals. These integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. $$\int \frac{d x}{\sqrt{x^{2}+10 x}}, x>0$$