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Chapter 5: Q. 33 (page 417)

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)

鈭�sec2xtan2xdx

Short Answer

Expert verified

The solution of the given integral is 鈭�sec2xtan2xdx=12sec2x+C .

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�sec2xtan2xdx

02

Step 2. Solving the given integral using substitution method. 

Let

u=2xdudx=2du=2dx12du=dx

03

Step 3. This substitution changes the integral into 

鈭�sec2xtan2xdx=12鈭�secutanudu鈭�sec2xtan2xdx=12secu+C鈭�sec2xtan2xdx=12sec2x+C

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