I don't like memorizing

  • #1
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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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Answers and Replies

  • #2
Dick
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Looks like you already took it, wrongly. Looks more to me like an arctan. Some things are worth memorizing. Not all, but some.
 
  • #3
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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
Dick
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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).
 

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