How can I easily derive this tricky integral?

  • Thread starter orthovector
  • Start date
In summary, the conversation discusses different methods for deriving the integral \int \frac{dx}_{\sqrt{x^2 + a^2}} and mentions the benefits of memorizing certain techniques. The speaker suggests using hyperbolic or trigonometric substitutions to solve the integral. Corrections are also made to a previous incorrect solution.
  • #1
orthovector
115
0
does anybody know how to derive this integral?

[tex] \int \frac{dx}_{\sqrt{x^2 + a^2}} [/tex] [tex] = ln(x+ \sqrt{x^2 + a^2}) [/tex]
 
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  • #2
Looks like you already took it, wrongly. Looks more to me like an arctan. Some things are worth memorizing. Not all, but some.
 
  • #3
Dick said:
Looks like you already took it, wrongly. Looks more to me like an arctan. Some things are worth memorizing. Not all, but some.

corrections are made above.
 
  • #4
The easy way is to use hyperbolic functions. Substitute x=a*sinh(t). Then figure out what the arcsinh function looks like by solving a quadratic. Otherwise a trig substitution like x=a*tan(t).
 

1. Why is memorization important in science?

Memorization is important in science because it allows scientists to recall important information quickly and accurately. It also helps them to make connections between different concepts and build a strong foundation of knowledge.

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Memorization helps scientists to develop a deep understanding of concepts and theories, which can then be applied to new situations and problems. It also allows for easier communication and collaboration with other scientists.

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