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Chapter 5: Q. 65 (page 418)

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�excscexdx

Short Answer

Expert verified

The solution of the given integral is 鈭�excscexdx=-cosex+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�excscexdx

02

Step 2. Using the substitution method.

u=exdudx=exdu=exdx

03

Step 3. This substitution changes the integral into 

鈭�excscexdx=鈭�1cscudu鈭�excscexdx=鈭�sinudu鈭�excscexdx=-cosu+C鈭�excscexdx=-cosex+C

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