Talk:List of integrals of inverse trigonometric functions

Move to "list of integrals of inverse trigonometric functions

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was move. Duja► 12:27, 29 October 2007 (UTC)

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Yea.. thats self explanatory. I've never heard of "arc functions" - its not very standard I would guess. Fresheneesz 02:36, 27 April 2006 (UTC)

I've never heard the term "arc functions" either. I like to use Google to justify my assertions regarding common usage - like this...

Search term	Google hits
"inverse trigonometric functions" OR "inverse trigonometric function" OR "inverse trig functions" OR "inverse trig function"	166,000
"arc functions" OR "arc function"	22,500
"arcus functions" OR "arcus function"	369

...and in the process I discovered "arcus functions"! Anyway that's better than 7:1 for "inverse trig...", so I'm for merging this page into List of integrals of inverse trigonometric functions, rather than (as indicated by the current merge-tags) vice-versa.--catslash 21:53, 12 February 2007 (UTC)

the term 'arc functions' is not used much imo, but instead the functions ARE widely referred to as arcsine, arccosine etc. as such, your google search may not be a fair test. (analogy: Searching for sin^(-1) would yield very, very few results) 220.253.69.119 05:32, 13 July 2007 (UTC)

Yes, I agree arcsine, arccosine etc. are commonly used terms and unlike sin^-1 are unambiguous. It's only the collective term arc functions that I have a problem with --catslash 12:29, 24 October 2007 (UTC)

I've never heard "arc functions" before either. Our our own article on them is at inverse trigonometric function, with arc functions being a redirect to that page. I've merged the content from List of integrals of inverse trigonometric functions into here, since this was a more developed page and had a much longer edit history, but I think the page should now be moved over the top of the redirect at "List of integrals of inverse trigonometric functions". jwillbur 23:57, 23 October 2007 (UTC)

The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Inverse of sine

Representing the inverse of sine by sin^-1 can be confusing because arcsin does not equal 1/sin —Preceding unsigned comment added by 71.166.249.250 (talk) 14:06, 10 October 2007 (UTC)

Vandalism

Is this edit vandalism? Thanks, delldot talk 18:35, 25 November 2007 (UTC)

Indefinite integrals

You forgot to add C. —Preceding unsigned comment added by 76.127.171.222 (talk) 02:47, 15 February 2009 (UTC)

True. However it would be cumbersome to have '+ C' on every line - so perhaps you could add a note at the top? --catslash (talk) 18:50, 15 February 2009 (UTC)

That's a possible solution, but what about the other pages with lists of integrals? Some, like the List of trigonometric integrals (http://en.wikipedia.org/wiki/List_of_integrals_of_trigonometric_functions), do have + C when needed. For consistency, should all the pages have a note of some sort at the top and any + C's removed, should they all have + C, or should only this page be modified, and any + C decisions for the other pages be made on their own discussion page? —Preceding unsigned comment added by 76.127.171.222 (talk) 01:17, 16 February 2009 (UTC)

The article Lists of integrals has a + C on every line, the following have + C on many or most lines

• List of integrals of trigonometric functions
• List of integrals of hyperbolic functions

and the following have no + Cs

• List of integrals of rational functions,
• List of integrals of irrational functions,
• List of integrals of inverse trigonometric functions,
• List of integrals of inverse hyperbolic functions,
• List of integrals of exponential functions,
• List of integrals of logarithmic functions.

The very last of these has a note at the top saying: "...throughout this article, and the constant of integration is omitted for simplicity", which I reckon is the neatest way. Such a note could easily be added to the other pages that don't have + Cs (perhaps with a link on constant of integration) --catslash (talk) 01:57, 16 February 2009 (UTC)

It should be noted that List of integrals of trigonometric functions and List of integrals of hyperbolic functions actually have + C in every case where it is required, as opposed to "many or most" cases, because in all instances where it does not appear on those pages the integral is either definite or contains another indefinite integral, which itself would contain + C.

Although both systems have their own merits, it seems likely that, realistically, a note at the top could be easily overlooked. Additionally, RDBury brings up the point on the Talk:List of integrals of trigonometric functions article discussion page that, without the + C's, one could inadvertently create incorrect proofs, such as $\sin ^{2}x=-\cos ^{2}x$.

I'd be perfectly happy to implement whichever change is agreed upon in all the integration articles in the end.

Oh, also, I changed "constant of integration" to also be a link to the constant's article, as you suggested, in the note on logarithmic functions. Daryl7569 (talk) 08:39, 16 February 2009 (UTC)

None of the printed list of integrals that I have to hand (including Peirce and Abramowitz & Stegun) has + C's (nor any obvious note regarding them), so it may be conventional to omit them. I still think it's cumbersome to repeat + C on every line, but if you are keen to put them in, then I shan't argue any further. --catslash (talk) 10:25, 16 February 2009 (UTC)

Recent edits to Arcsecant function integration formulas

There are some problems with these edits to the Arcsecant function integration formulas section.

1. The rewrite

$\mathrm {arctanh} \left({\sqrt {1-{\frac {1}{a^{2}x^{2}}}}}\right)\to \mathrm {arccosh} (|ax|)$

does simplify the formulae - so ok.

2. The change of $\scriptstyle {a\to {\frac {1}{a}}}$ is arbitrary, makes the section inconsistent with the others and two errors have been introduced in the process (two terms are out by a factor of $\scriptstyle {a}$). The formulae in this section were all correct before, as may be verified by differentiation.

3. The $\scriptstyle {(x^{2}\mathrm {arcsec} (ax))}$ formula is (strictly) redundant given the $\scriptstyle {(x^{m}\mathrm {arcsec} (ax))}$ formula, but the removal of the former of these makes the section inconsistent with the others. Also, the $\scriptstyle {x^{m}}$ formula has an integral on the right hand side, and it is convenient to have this evaluated for small $\scriptstyle {m}$.

So I shall revert some or all of these changes. --catslash (talk) 01:03, 15 October 2015 (UTC)