(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Check whether the integral [tex] \int_{0}^{\infty}\frac{arctanx}{xln^{2}x}dx [/tex] converges.

2. Relevant equations

3. The attempt at a solution

The problematic points are: [tex] 0, 1, \infty [/tex] . So I said:

[tex] \int_{0}^{\infty}\frac{arctanx}{xln^{2}x}dx

= \int_{0}^{1}\frac{arctanx}{xln^{2}x}dx+ \int_{1}^{2}\frac{arctanx}{xln^{2}x}dx+ \int_{2}^{\infty}\frac{arctanx}{xln^{2}x}dx[/tex] .

The second integral converges [I've proved this by substition: [tex] x=1+t [/tex] and then comparison to the series [tex]g(x)=\frac{1}{x^{2}}[/tex]... I did it by knowing that in 0:

[tex] ln(1+x)\approx x[/tex]...

I have no idea how to deal with the two other integrals... The ln is my problem...

Hope you'll be able to help

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculus-Infinite Integral

**Physics Forums | Science Articles, Homework Help, Discussion**