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Chapter 5: Q 17. (page 451)

Describe strategy for solving the type of integral given.
$鈭� s e c^{m} x \tan^{n} x d x, n$ odd

Short Answer

Expert verified

Write $\tan^{n} x = \tan^{2} x \tan^{n - 2} x$

Step by step solution

01

Step 1. Given information

Integral is $鈭� s e c^{m} x \tan^{n} x d x, n$ odd

02

Step 2. Explanation

Consider the integral $鈭� s e c^{m} x \tan^{n} x d x, n$ odd

Write $\tan^{n} x = \tan^{2} x \tan^{n - 2} x$

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Most popular questions from this chapter

Solve given definite integrals.

${鈭�}_{0}^{4} x \sqrt{x^{2} + 4} d x$

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

$u (x) = \frac{1}{x}$

Solve the integral: $鈭� \ln \sqrt{x} d x$

Solve $鈭� \frac{x^{2}}{1 + x^{2}} d x$ the following two ways:

(a) with the substitution $u = \tan^{- 1} x;$

(b) with the trigonometric substitution x = tan u.

Find three integrals in Exercises 39鈥�74 that can be solved without using trigonometric substitution.

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