I don't like memorizing

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]
 
Last edited:

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.
 
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.
 

Dick

Science Advisor
Homework Helper
26,249
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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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