Re: arctan(x)/x^2
- From: "turkishmathematician@xxxxxxxxx" <turkishmathematician@xxxxxxxxx>
- Date: Tue, 30 Oct 2007 00:20:55 -0000
Here is my comment:
Integration by parts is a good idea of computing this integral. So,
U = arctan(x) dV = 1/x^2 dx
dU = 1/(1+x^2)dx V = -1/x
Hence, result = - arctan(x)/x + Integral[1/(x(1+x^2))dx].
Now, one can use partial fraction decomposition to write 1/
(x(1+x^2))=(1/x)-(x/(1+x^2)).
Now term by term integration gives, lnx-(1/2)ln(1+x^2)=ln(x/
(Sqrt(1+x^2))).
Hence, result = - arctan(x)/x + ln(x/(Sqrt(1+x^2))) + C where C is
constant which comes since we are computing an indefinite integral.
Turkish Mathematician
.
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- arctan(x)/x^2
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