Chapter 5: Q 16. (page 495)

Fill in the blanks to complete each of the following integration formulas.
$\int \sec x d x =______$

Short Answer

Expert verified

The result is $\ln |\tan (x) + \sec (x)| + C$ .

Step by step solution

Step 1. Given information.

Consider the given integration,

$\int \sec x d x$

Step 2. Simplify.

Simplify the given expression.

$\begin{array}{rcl} \int \sec x d x & = & \int \frac{\sec x (\sec x + \tan x)}{\sec x + \tan x} d x \\ = & \int \frac{\sec^{2} x + \sec x \tan x}{\sec x + \tan x} d x \end{array}$

Step 3. Find the integration.

Apply the integration method.

$\begin{array}{rcl} \int \sec x d x & = & \int \frac{\sec^{2} x + \sec x \tan x}{\sec x + \tan x} d x [t = \sec x + \tan x, d t = (\sec^{2} x + \sec x \tan x) d x] \\ = & \int \frac{1}{t} d t \\ = & \ln |t| + C \\ = & \ln |\sec x + \tan x| + C \end{array}$

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Fill in the blanks to complete each of the following integration formulas.
$\int \sec x d x =______$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify.

Step 3. Find the integration.

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Fill in the blanks to complete each of the following integration formulas. ∫secxdx=______

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify.

Step 3. Find the integration.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Logic and Functions

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following integration formulas.
$\int \sec x d x =______$