how can i find the primitive of this function(ignore the bound of the integral) | Mathematics | Page 1

teal nova Nov 10, 2025, 5:40 PM

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the website i found it said this ais a classical form, does anybody recognize it?

rustic bluffBOT Nov 10, 2025, 5:40 PM

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gray vale Nov 10, 2025, 5:43 PM

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teal nova the website i found it said this ais a classical form, does anybody recognize it...

you can google this

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https://math.stackexchange.com/questions/4165124/given-that-int-frac1x-sqrtx2-1dx-arccos-frac1xc-what-is-in?noredirect=1

Mathematics Stack Exchange

Given that $\int \frac{1}{x\sqrt{x^2-1}}dx=\arccos(\frac{1}{x})+C$,...

The following is clear:
$x\sqrt{x^2-a^2}=x\sqrt{a^2}\sqrt{\frac{x^2}{a^2}-1}=ax\sqrt{\frac{x^2}{a^2}-1}= a^2\frac{x}{a}\sqrt{\frac{x^2}{a^2}-1}$.
So I get that $$\int\frac{1}{x\sqrt{x^2-a^2}}dx=\fr...

teal nova Nov 10, 2025, 5:44 PM

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this didn't show when i searches

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thanks anyway!

rustic bluffBOT Nov 10, 2025, 5:44 PM

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teal nova thanks anyway!

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teal nova Nov 10, 2025, 5:45 PM

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.close

#how can i find the primitive of this function(ignore the bound of the integral)