91Ó°ÊÓ

Restricted Domain What is a restricted domain? Why are restricted domains necessary to define inverse trigonometric functions?

Reflective Property of Inverse Functions Describe the relationship between the graph of a function and the graph of its inverse function.

Guidelines for lntegration Describe two ways to alter an integrand so that it fits an integration formula.

Logarithmic Differentiation Explain when it is necessary to use logarithmic differentiation to find the derivative of an exponential function.

In Exercises \(5-28\) , find the indefinite integral. $$\int \frac{5}{x} d x$$

In Exercises \(21-26,\) solve for \(x\) (a) \(\log _{3} x=-1\) (b) \(\log _{2} x=-4\)

In Exercises \(33-54,\) find the derivative of the function. $$y=e^{5 x}$$

In Exercises 47-50, find the indefinite integrals, if possible, using the formulas and techniques you have studied so far in the text. $$\begin{array}{l}{\text { (a) } \int \frac{1}{\sqrt{1-x^{2}}} d x} \\ {\text { (b) } \int \frac{x}{\sqrt{1-x^{2}}} d x} \\ {\text { (c) } \int \frac{1}{x \sqrt{1-x^{2}}} d x}\end{array}$$

In Exercises 47-50, find the indefinite integrals, if possible, using the formulas and techniques you have studied so far in the text. $$\begin{array}{l}{\text { (a) } \int \sqrt{x-1} d x} \\ {\text { (b) } \int x \sqrt{x-1} d x} \\ {\text { (c) } \int \frac{x}{\sqrt{x-1}} d x}\end{array}$$

In Exercises \(69-72\) , find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify your result. $$y=2 x-\tan 0.3 x, \quad x=1, \quad x=4, \quad y=0$$