Re: arctan(x)/x^2
- From: David W. Cantrell <DWCantrell@xxxxxxxxxxx>
- Date: 30 Oct 2007 00:07:04 GMT
tommy1729 <tommy1729@xxxxxxxxx> wrote:
tommy1729 <tommy1729@xxxxxxxxx> wrote:
[snip]Hello all..
I have a problem ... I�´m suppost to fiind the
intergral for:
arctan(x) / x^2
...please :)
ln(x)-(1/2)ln(x^2+1)-(arctan(x)/x)
Presumably, the antiderivative is to be real, valid
for nonzero x, and so
I don't give your result full marks. [Note that, for
x < 0, your result is
not real.] My result is
- ln(1 + 1/x^2) - arctan(x)/x + C
where C is an arbitrary real constant.
David W. Cantrell
funny
I suppose that by "funny" you mean strange, as opposed to humorous. But
it's not strange. It's the same sort of thing as giving ln|x| + C, rather
than ln(x) + C, in elementary calculus for the antiderivative of 1/x.
David
.
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