Solve Integral [xln(x^2+9)] Using Tabular Method

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In summary, the conversation is about solving an integral using the tabular method. The individual has attempted to solve it but is facing difficulties as their method yields a trigonometric function in the final answer, while the given answer does not. They have tried a different approach, but it did not solve the issue. They are seeking guidance on where they may have gone wrong.
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Homework Statement


Solve the integral of [xln(x^2+9)] wrt x using the tabular method.


Homework Equations


By parts using the tabular method.


The Attempt at a Solution



u:
1. ln(x^2+9)
2. 2x/(x^2+9)

dv:
1. x
2. (1/2)x^2
3. (1/6)x^3

The answer for now is : ((1/2)x^2)ln(x^2+9) -(1/3)[integral of](x^4/(x^2+9))dx

dividing x^4/(x^2+9) gives (x^2)-9+(81/x^2+9)

however integrating 1/(x^2+9) would give a trig function whereas the answer given contains to trig function at all. Where have I gone wrong in my method? Thanks in advance!
 
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  • #2
It's easier to integrate x^4 than it is to integrate 1/(x^2+9). Set your u and dv values differently and apply tabular integration once again.
 
  • #3
Hi thanks for the reply. I've tried your method but it gives back the same problem. As in the exponent of x in the numerator is greater than that of the exponent of x in the denominator. My initial approach to this was to carry out long division however I got a [81/(x^2+9)] which yields a trig function when integrated. However the ans to this question does not contain any trig function. Where have I gone wrong? Thanks.
 

1. What is the Tabular Method used for in solving integrals?

The Tabular Method, also known as the Tabular Integration Method, is a technique used to solve integrals that involve products of functions. It involves creating a table and systematically integrating different parts of the product function until the entire integral is solved.

2. How do I know when to use the Tabular Method to solve an integral?

The Tabular Method is typically used when the integrand (the function inside the integral) is a product of two functions, one of which can be easily integrated while the other cannot. In these cases, the Tabular Method can simplify the integration process.

3. Can you walk me through the steps of solving Integral [xln(x^2+9)] Using Tabular Method?

Sure! To solve this integral using the Tabular Method, you would first create a table with two columns. In the first column, you would list the two functions in the integral (x and ln(x^2+9)), and in the second column, you would list their corresponding derivatives (1 and 2x/(x^2+9)). Then, you would integrate the derivative in the second column and multiply it by the function in the first column. You would continue this process until the integral is completely solved.

4. Are there any restrictions or limitations when using the Tabular Method to solve integrals?

Yes, there are a few limitations to keep in mind when using the Tabular Method. First, this method can only be used for integrals with products of functions. It cannot be used for other types of integrals, such as trigonometric or exponential functions. Additionally, the Tabular Method may not always work for integrals with complicated functions or multiple variables.

5. Are there any tips or tricks for using the Tabular Method effectively?

One helpful tip is to always start by choosing the function in the integral that will be easiest to integrate. This will make the process more efficient. Additionally, it can be helpful to rearrange the terms in the integral to make them easier to work with. Lastly, practice and familiarity with the method will also improve your speed and accuracy in using the Tabular Method.

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