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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.)

2xe3x2dx

Short Answer

Expert verified

The solution of the given integral is 2xe3x2dx==13e3x2+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

2xe3x2dx

02

Step 2. Solving the given integral using substitution method.  

Let

u=3x2dudx=6xdu=6xdx16du=xdx

03

Step 3. This substitution changes the integral into 

2xe3x2dx=26eudu2xe3x2dx=13eu+C2xe3x2dx=13e3x2+C

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