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Chapter 5: Q 16. (page 495)

Fill in the blanks to complete each of the following integration formulas.

鈭�secxdx=______

Short Answer

Expert verified

The result islntanx+secx+C.

Step by step solution

01

Step 1. Given information.

Consider the given integration,

鈭�secxdx

02

Step 2. Simplify.

Simplify the given expression.

鈭�secxdx=鈭�secxsecx+tanxsecx+tanxdx=鈭�sec2x+secxtanxsecx+tanxdx

03

Step 3. Find the integration. 

Apply the integration method.

鈭�secxdx=鈭�sec2x+secxtanxsecx+tanxdxt=secx+tanx,dt=sec2x+secxtanxdx=鈭�1tdt=lnt+C=lnsecx+tanx+C

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Most popular questions from this chapter

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.

Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

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