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Chapter 5: Q 10. (page 451)

Describe strategies for solving the types of integrals given.
$\int co t^{k} x d x, k$ odd

Short Answer

Expert verified

Take $c o t x = u$

Step by step solution

01

Step 1. Given information

Integral is $\int c o t^{k} x d x$

02

Step 2. Explanation

Consider the integral $\int c o t^{k} x d x$

Take $c o t x = u$

Also, use the formula: $(c o t x)' = - c s c^{2} x$

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Most popular questions from this chapter

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

Solve the integral: $\int \ln (x^{3}) d x$ .

Explain why, if $x = a \sin u$ , then $\sqrt{a^{2} - x^{2}} = a \cos u$ . Your explanation should include a discussion of domains and absolute values.

Explain why $\int \frac{2 x}{x^{2} + 1} d x$ and $\int \frac{1}{x \ln x} d x$ are essentially the same integral after a change of variables.

Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).

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