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Chapter 5: Q 27. (page 452)

Solve each of the integral
$\int s e c 4 x d x$

Short Answer

Expert verified

Answer is $\frac{\ln |s e c 4 x + \tan 4 x|}{4} + C$

Step by step solution

01

Step 1. Given information

Integral is $\int s e c 4 x$

02

Step 2. Explanation

Use the formula: $\int s e c y = \ln |s e c y + \tan y| + C$

Therefore,

\int s e c 4 x = \frac{\ln |s e c 4 x + \tan 4 x|}{4} + C

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Most popular questions from this chapter

Solve the integral: $\int \frac{3 x + 1}{x} d x$

Solve given definite integral.

$\int_{1 / 4}^{1 / 2} \frac{1}{x^{2} \sqrt{1 - x^{2}}} d x$

Suppose $u (x) = x^{2}$ . Calculate and compare the values of the following definite integrals:

role="math" localid="1648786835678" $\int_{- 1}^{5} u^{2} d u, \int_{x = - 1}^{x = 5} u^{2} d u and \int_{u (- 1)}^{u (5)} u^{2} d u$

Consider the integral $\int \frac{1}{x^{2} \sqrt{1 - x^{2}}} d x$ from the reading at the beginning of the section.

(a) Use the inverse trigonometric substitution $u = \sin^{- 1} x$ to solve this integral.

(b) Use the trigonometric substitution $x = \sin u$ to solve the integral.

(c) Compare and contrast the two methods used in parts (a) and (b).

Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial $x^{2} - x + 3$ as the quotient above the top line, and the polynomial 3x − 1 at the bottom as the remainder. Then $p (x) =___a n d \frac{p (x)}{q (x)} =____$

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