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Chapter 5: Q. 57 (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�sin(1/x)x2dx

Short Answer

Expert verified

The solution of the given integral is 鈭�sin(1/x)x2dx=cos(1/x)+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�sin(1/x)x2dx

02

Step 2. Using the substitution method.

Let

u=1xu=x-1dudx=-x-2dudx=-1x2du=-1x2dx-du=1x2dx

03

Step 3. This substitution changes the integral into 

鈭�sin(1/x)x2dx=-鈭�sinudu鈭�sin(1/x)x2dx=-鈭�sinudu鈭�sin(1/x)x2dx=-(-cosu)+C鈭�sin(1/x)x2dx=cosu+C鈭�sin(1/x)x2dx=cos(1/x)+C

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