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Chapter 5: Q. 30 (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�x3cosx4dx

Short Answer

Expert verified

The solution of the given integral is 鈭�x3cosx4dx=14sinx4+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�x3cosx4dx

02

Step 2. Solving the given integral using substitution method. 

Let

u=x4dudx=4x3du=4x3dx14du=x3dx

03

Step 3. This substitution changes the integral into 

鈭�x3cosx4dx=14鈭�cosudu鈭�x3cosx4dx=14sinu+C鈭�x3cosx4dx=14sinx4+C

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Most popular questions from this chapter

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withx=asinuor x=atanu? Why do we need to think about the unit circle after trigonometric substitution with x=asecu?

Find three integrals in Exercises 27鈥�70 for which a good strategy is to apply integration by parts twice.

Solve the integral:鈭�xcosxdx.

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.

鈭�sinudu

Solve given definite integrals.

鈭�04xx2+4dx
See all solutions

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