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

x3cosx4dx

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

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 

x3cosx4dx=14cosudux3cosx4dx=14sinu+Cx3cosx4dx=14sinx4+C

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