Solving an Integral: Tips and Tricks for Evaluating ∫dx/(x√(x² - a²))

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In summary, the conversation is about evaluating the integral of dx/(x√(x² - a²)). The person is struggling to manipulate the integral into a standard form and asks for suggestions. Another person suggests substituting x = au to simplify the integral. Eventually, they realize that it is a standard integral for arcsec and thank the person for their help.
  • #1
insynC
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Homework Statement



Trying to evaluate the following integral:

∫dx/(x√(x² - a²))

The Attempt at a Solution



I think I'm missing something simple. I know:

∫dx/(x√(x² + a²)) = - 1/a arccsch|u/a| + C

&

∫dx/(x√(a² - x²)) = - 1/a arcsech(u/a) + C

But I'm not exactly sure how to manipulate my integral into one of these forms.

Any suggestions? Thanks
 
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  • #2
[tex]\frac{1}{x(x^2-a^2)^{\frac{1}{2}}}[/tex]

Does that help?
 
  • #3
Let x = au, then dx = adu. Can you take it from there?
 
  • #4
It's just a standard integral for arcsec... :S don't know how I missed that.

Thanks for the help
 

Related to Solving an Integral: Tips and Tricks for Evaluating ∫dx/(x√(x² - a²))

What is an Integral question?

An Integral question is a type of question that requires a comprehensive understanding and knowledge of a topic in order to answer it. It often involves synthesizing various concepts and ideas to provide a comprehensive response.

What makes an Integral question different from other types of questions?

Unlike other types of questions that may have a single correct answer, an Integral question does not have a specific right or wrong answer. It requires critical thinking and the ability to connect different ideas and perspectives to provide a well-rounded response.

How can I improve my ability to answer Integral questions?

To improve your ability to answer Integral questions, it is important to have a strong understanding of the subject matter and to practice critical thinking skills. You can also break down the question into smaller parts and analyze each part separately before combining them to form a comprehensive answer.

Can Integral questions be used in different fields of study?

Yes, Integral questions can be used in various fields of study, such as science, mathematics, social sciences, and humanities. They are often used in higher-level education and are a crucial part of critical thinking and problem-solving skills.

What are some examples of Integral questions?

Some examples of Integral questions include "How does climate change impact global ecosystems?", "What are the ethical implications of genetic engineering?", and "What factors contribute to economic inequality?" These questions require a deep understanding of the topics and the ability to analyze and synthesize information from various sources.

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