Need Help with Hard Indefinite Integral

In summary, the conversation involves a person seeking help with a difficult integral and trying various steps and software to solve it. They are given advice to continue with a substitution and breaking down the integral into smaller parts before integrating.
  • #1
dapias09
29
0
Hello, I need help with a very hard integral, I was trying several steps and I tried in the software "derive" but the answer didn't like to me.

It is ψ(x,t)= [b^2-(x-vt)^2]^(-2) . I must integrate it with respect to x .

Thanks in advance for any help!

PD: I tried x-vt = u like the first step du=dx. My teacher adviced to me continue with [b^2-u^2]^(-2) = z but I don't know how to continue in the best way.
 
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  • #2
dapias09 said:
My teacher adviced to me continue with [b^2-u^2]^(-2) = z but I don't know how to continue in the best way.
Find A, B, C , D so that :
1/(b²-u²)² = A/(b+u) +B/(b-u) +C/(b+u)² +D/(b-u)²
Then you can easily integrate.
 

1. What is an indefinite integral?

An indefinite integral is an operation used in calculus to find the antiderivative of a function. It is essentially the reverse process of differentiation.

2. Why is it called a "hard" indefinite integral?

A "hard" indefinite integral refers to an integration problem that is difficult to solve using basic integration techniques. These problems often require advanced techniques such as substitution, integration by parts, or trigonometric identities.

3. How do I know when to use which integration technique?

There is no set rule for which integration technique to use for a given problem. It often requires trial and error, and practice to develop an intuition for which technique will be most effective. However, certain clues such as the form of the integral or the presence of specific types of functions can help guide your approach.

4. Can indefinite integrals be solved using a calculator?

Yes, some calculators have the ability to solve indefinite integrals. However, it is important to note that the calculator may not always give the most efficient or accurate solution. It is still important to understand the concepts and techniques behind indefinite integration in order to verify the results.

5. Are there any tips for approaching difficult indefinite integrals?

One tip is to try rewriting the integral in a different form or manipulating it algebraically before attempting any integration techniques. It may also be helpful to break the integral into smaller, more manageable parts. Additionally, practicing and becoming familiar with different integration techniques can make solving difficult integrals easier.

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