Tabular Integration by Parts Repeated

In summary, the conversation discusses the use of the tabular method for solving integration by parts problems, and the question of what to do when the two parts of the integral continuously repeat. The speaker is familiar with using repeated integration by parts to solve this type of problem, but is unsure if it is possible to solve it using the tabular method due to the endless repetition of derivatives and integrals. The response explains that tabular integration by parts is a useful way to organize the process and that one can stop and solve for the integral when reaching a previously encountered form.
  • #1
benjaug
1
0
So, in my class we are learning how to use the tabular method to solve an integration by parts problem... but what happens if the two parts of the integral continuously repeat?
The example I have in mind is
[tex]\int e^x sin(x) dx[/tex].
I know how to solve this using repeated integration by parts... solve it until the integrand is e^x sinx again and then add to both sides and divide by 2... that makes sense to me. But when you use the tabular method for it, the derivatives of u and the integrals of v just continue endlessly... is it impossible to solve that way?

Thanks for the help!
 
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  • #2
Tabular integration by parts is just a way to organize integration by parts when it may be repeated. In particular upon reaching a form previously encountered (without having merely undone a step) one can stop and solve for the integral.
 

1. What is tabular integration by parts repeated?

Tabular integration by parts repeated is a method of integration that uses the product rule to solve integrals. It involves creating a table to systematically compute the integral by repeatedly applying the integration by parts formula.

2. When should I use tabular integration by parts repeated?

This method is useful when the integral involves a product of two functions and the first function cannot be easily integrated. It can also be used when the integral involves a function that repeats with a constant coefficient.

3. How do I set up the tabular integration by parts repeated table?

The table is set up by listing the functions in the integral in the first column, and then repeatedly applying the integration by parts formula to the functions in the subsequent columns until the integral is solved.

4. What are the advantages of using tabular integration by parts repeated over other integration methods?

Tabular integration by parts repeated can be more efficient and less prone to error compared to other integration methods, especially when the integral involves a product of functions with repeating patterns.

5. Are there any limitations to using tabular integration by parts repeated?

This method may not work for all types of integrals, especially if the integral involves complex functions or functions that do not follow a repeating pattern. It is important to try other integration methods if tabular integration by parts repeated does not yield a solution.

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