Re: arctan(x)/x^2
- From: "turkishmathematician@xxxxxxxxx" <turkishmathematician@xxxxxxxxx>
- Date: Tue, 30 Oct 2007 00:43:46 -0000
This is the third time I'm posting :) for some reason my post doesn't
appear.
Here is my comment:
Set
U = arctan(x) dV = 1/x^2 dx
dU = 1/(1+x^2)dx V = -1/x
result = -arctan(x)/x + Integral[1/(x(1+x^2))]
Now decompose, 1/(x(1+x^2)) = 1/x - x/(1+x^2) and integrating this
term by term is easy and one gets
lnx-(1/2)ln(1+x^2) + C =ln(x/Sqrt(1+x^2)) + C
Hence, result = -arctan(x)/x + ln(x/Sqrt(1+x^2)) + C where C is just a
constant.
I hope this helps,
Turkish Mathematician
.
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