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Chapter 5: Q 18. (page 451)

Describe strategy for solving the type of integral given.

鈭�secmxtannxdx,m odd andneven

Short Answer

Expert verified

Taketan2x=sec2x-1

Step by step solution

01

Step 1. Given information

Integral is鈭�secmxtannxdx

02

Step 2. Explanation

Consider the integral 鈭�secmxtannxdx

Usetan2x=sec2x-1

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Most popular questions from this chapter

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�13-x2dx

Solve the integral鈭�x3x2-1dxthree ways:

(a) with the substitution u=x2-1,followed by back substitution;

(b) with integration by parts, choosing localid="1648814744993" u=x2anddv=xx2-1dx;

(c) with the trigonometric substitution x = sec u.

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

u(x)=x2+1

What is a rational function? What does it mean for a rational function to be proper? Improper?

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

u(x)=1x
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