Talk:List of integrals of rational functions

Using Safari 1.2.3 (v125.9) on Mac OS X, the HTML-based math formatting is much less clear than the TeX-based images. The integral signs are too small, the fractions are too widely spaced, and so forth.

I do not know by what rule Wikipedia chooses to render using images or HTML, but the Italian version, with only images, displays much more clearly on this setup than this English version.

I hope that someone who knows more than I do about the workings of Wikipedia can correct this.

- Jrn 17:02, 17 Oct 2004 (UTC)

This page is not very precise with notation - all of them are missing a constant of integration, most of them are missing 'dx' at the end, and to make this worse, some use 'dx' in a different meaning. guiltyspark 23:47, 18 April 2007 (UTC)

There should not be constants of integration present in equations which have an integral as part of the solution because the integral includes a constant of integration. —Preceding unsigned comment added by 96.241.227.12 (talk) 05:09, 28 December 2010 (UTC)

This is not this?

'(forgive my wrong speling ness)' The List of rational fractions are not that accurate. please help in correcting stupidity here... The first integral of the said function is a complete noncence and is not the integral of the said definition of that function... I suggest this article be rewriten or in other case case... Deleted... —Preceding unsigned comment added by Kendelarosa5357 (talk • contribs) 09:53, 10 June 2008 (UTC)

Some Inaccuracy Is Due to

Some of the inaccuracy is due to the flaw of foluma starting with

$\int\frac{x}{(ax + b)^2} dx$,

because, this equation is applied several times. --Chenchiheshang (talk) 15:18, 26 May 2010 (UTC)

Concerning this integral, both the older version[1] and your revised version[2] are correct. They just differ by a constant 1/a², which simply changes the constant of integration.

$\frac{b}{a^{2} (a x + b)} = \frac{1}{a^{2}} - \frac{x}{a (a x + b)}$

This is probably true for the other integrals, but I haven't checked. --catslash (talk) 21:55, 7 July 2010 (UTC)

Differentiating the integrals given for $\scriptstyle{{x^2}/{(a x + b)^2}}$, $\scriptstyle{{x^2}/{(a x + b)^3}}$ and $\scriptstyle{{x^2}/{(a x + b)^n}}$ in the older version[3] shows that they are all correct. Differentiating the integrals given in the later version[4] shows that the integral of $\scriptstyle{{x^2}/{(a x + b)^3}}$ is still correct though it has changed by a constant term. However, something has gone wrong with the integrals of $\scriptstyle{{x^2}/{(a x + b)^2}}$ and $\scriptstyle{{x^2}/{(a x + b)^n}}$. I think that the simplest fix is just to revert these edits.

Regarding the integrals of $\scriptstyle{\frac{1}{x (a x + b)}}$ and $\scriptstyle{\frac{1}{x^{2} (a x + b)}}$, a factor of $\scriptstyle{1/a}$ has been removed from arguments of the logarithms. This simply has the effect of subtracting a constant multiple of $\scriptstyle{\ln(1/a)}$, and so does not affect the correctness. Since these edits make the expressions slightly simpler, I will try to preserve these last two edits. --catslash (talk) 23:42, 7 July 2010 (UTC)