Partial Fractoin Integration Check

• Procrastinate
In summary, the user had a question about their partial fraction integration and shared their working and final answer. Another user pointed out an error in the integration and the first user fixed it, resulting in the correct final answer. The conversation ended with the first user thanking the second user for their help.
Procrastinate
Partial Fraction Integration Check

Hello, I was just wondering whether my answer for my partial fraction integration question was right. Attached are three pages of my working but the answer is at the bottom of the third page (027) and the question is at the top of the first page (025).

Thanks.

Attachments

• scan0025.jpg
27.3 KB · Views: 343
• scan0026.jpg
27 KB · Views: 360
• scan0027.jpg
17.1 KB · Views: 363
Last edited:
You have a mistake, give me a second to pinpoint where it is.
Oh and by the way, you integrated the fraction at the end with the squared denominator wrong.

$$\int \frac{1}{x^2}dx=\frac{-1}{x}$$

Ok your arithmetic was wrong when you substituted x=-1/3.

Mentallic said:
Ok your arithmetic was wrong when you substituted x=-1/3.

Ok. I fixed that up (as well as my other small integration error.)

$$\frac{22}{25}\ln|x+2|+-\frac{4}{5(x+2)}+-\frac{2}{75}\ln|3x+1| + C$$.

Is this correct?

The ln(3x+1) term is incorrect. I get -16/75 as the constant multiplier.

Oh yes, that is right. I just accidentally copied it down wrong. Thanks for your help.

Mentallic said:
The ln(3x+1) term is incorrect. I get -16/75 as the constant multiplier.

$$\frac{22}{25}\ln|x+2|+-\frac{4}{5(x+2)}+-\frac{16}{75}\ln|3x+1| + C$$

No problem

1. What is Partial Fraction Integration?

Partial Fraction Integration is a mathematical technique used to break down a complex rational function into smaller, simpler fractions to make integration easier. It is typically used in calculus and is an alternative method to integration by substitution.

2. When is Partial Fraction Integration used?

Partial Fraction Integration is used when integrating rational functions that cannot be easily integrated using other techniques such as substitution or integration by parts. It is also used in solving differential equations and in finding the inverse Laplace transform.

3. How do you perform Partial Fraction Integration?

To perform Partial Fraction Integration, the rational function must first be in the form of a proper or improper rational function. Then, the fraction must be decomposed into simpler fractions using a systematic method. Once the fractions are found, the integral of each fraction can be evaluated separately.

4. What are the advantages of using Partial Fraction Integration?

Partial Fraction Integration allows for the integration of complex rational functions that may not be solvable using other techniques. It also simplifies the integration process and can make solving differential equations and finding inverse Laplace transforms easier.

5. Are there any limitations to Partial Fraction Integration?

Partial Fraction Integration can only be used for rational functions, meaning functions that are a ratio of two polynomials. It also cannot be used for functions with repeated roots or irreducible quadratic factors in the denominator. In some cases, the decomposition process can be time-consuming and complex.

• Calculus and Beyond Homework Help
Replies
6
Views
821
• Calculus and Beyond Homework Help
Replies
6
Views
450
• Calculus and Beyond Homework Help
Replies
3
Views
647
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
16
Views
2K
• Calculus and Beyond Homework Help
Replies
9
Views
789
• Calculus and Beyond Homework Help
Replies
3
Views
2K
• Calculus and Beyond Homework Help
Replies
6
Views
729
• Calculus and Beyond Homework Help
Replies
1
Views
303
• Calculus and Beyond Homework Help
Replies
1
Views
643