# What's Wrong with My Integration by Parts?

• QuickQThrowaway
In summary, the conversation discusses a discrepancy in the results of an integral, with one method using integration by parts and the other using an online calculator. However, it is concluded that both results are equivalent, with the difference only being in the constant of integration.
QuickQThrowaway
Heya...

I just stumbled upon this integral while doing ODEs...

∫x*(x-2)-2dx

I used integration by parts

u=x
du/dx=1
dv/dx=(x-2)-2
v=-(x-2)-1

Thus

∫x*(x-2)-2dx=-x(x-2)-1-∫1*-(x-2)-1dx=-x*(x-2)-1+ln(x-2)+C

Now... I don't see anything wrong with this...

But every single online integration calculator as well as the ODE solution solves this integral by doing 1/(x-2)+2/(x-2)2 and they all get

-2*(x-2)-1+ln(x-2)+C

as a result...

What am I doing wrong in my integration by parts? What am I missing? Oo

eifphysics
There is nothing wrong. The two results are equivalent.

$\frac{x}{x-2}=\frac{x-2+2}{x-2}=1+\frac{2}{x-2}$.

The difference is only in the constant of integration.

QuickQThrowaway and mrnike992
mathman said:
There is nothing wrong. The two results are equivalent.

$\frac{x}{x-2}=\frac{x-2+2}{x-2}=1+\frac{2}{x-2}$.

The difference is only in the constant of integration.

Thank you!
The maths department screwed up then because the question asked to verify that C=2 but with the above integration it equals 3... So they omitted one result... >.<

## 1. What is a weird integral?

A weird integral is a mathematical expression that cannot be solved using conventional techniques or methods. It often involves complex or unusual functions and can result in unexpected or confusing results.

## 2. Why is the integral considered weird?

The integral may be considered weird because it may not follow the usual rules and properties of integrals, making it difficult to evaluate or understand. It may also have a non-standard form or involve strange functions that are not commonly encountered.

## 3. How do I solve a weird integral?

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## 4. Can a weird integral have a solution?

Yes, a weird integral can have a solution. However, the solution may not be in a simple or familiar form and may require further simplification or manipulation to fully understand its meaning.

## 5. What should I do if I encounter a weird integral?

If you encounter a weird integral, don't panic! Take a step back and analyze the integral carefully. Try to identify any patterns or relationships that may help you solve it. If you are still stuck, seek help from a mathematics expert or use mathematical software to assist you in finding a solution.

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