So, please show your work, and explain where u have any difficulty.

In summary, the person is seeking help with three integration by parts problems in calculus. They have successfully solved the first couple but are struggling with the last three. The questions are not provided but the person asks for help and offers to clarify if needed. They also thank the person in advance for their assistance.
  • #1
Integralien
4
0
Integration by Parts HELP!

Hey, I am working on some calculus and I am having some trouble with the last few integration by parts problems. I got the first couple, and i grasp the concept of integration by parts but for some reason I just can't figure these 3. Any help would be greatly appreciated.

1. The integral of (e^2x)sin3xdx

2. The integral of cos(3x+1)cos(5x+6)dx

3. The integral of x²ln²xdx

P.S> Feel free to ask if you can't read the questions, I tried to write them out the best I could.


Thanks in advance,

Brian
 
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  • #2
you already have another post on these questions. These appear now to be homework problems, and u haven't shown what have u tried so far at all!
 

What is integration by parts and how does it work?

Integration by parts is a method of integration used to solve integrals that involve products of functions. It involves the use of the product rule from calculus, where one function is differentiated and the other is integrated. This method is useful for solving integrals that cannot be easily solved using other methods.

When should I use integration by parts?

You should use integration by parts when you encounter an integral with a product of functions, where one function can be easily differentiated and the other can be easily integrated. This method is also useful when other integration techniques, such as substitution or partial fractions, do not work.

What are the steps to use integration by parts?

The steps to use integration by parts are as follows:

  1. Identify the function to be differentiated and the function to be integrated.
  2. Apply the product rule to differentiate the first function.
  3. Integrate the second function.
  4. Combine the results and simplify the integral.

Can integration by parts be used for definite integrals?

Yes, integration by parts can be used for definite integrals. After integrating and differentiating the functions, you can evaluate the definite integral using the limits of integration.

Are there any limitations to using integration by parts?

There are some limitations to using integration by parts. It may not work for all integrals, and it can become more complicated when the functions involved are more complex. Additionally, it may not always provide a solution and may require multiple iterations to solve the integral.

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