What is the result of integrating \frac{x}{x^2 + 1} and applying the limit?

[shamieh]

Suppose:

\(\displaystyle \int^{\infty}_1 \frac{x}{x^2 + 1} \, dx\)

I can't do this can I?

Let \(\displaystyle u = x^2 + 1\)
so \(\displaystyle du = 2x \, dx\)
\(\displaystyle \therefore \frac{du}{2} = x \, dx\) ?

 

[Jameson]

That looks good to me! What do you get for the result of the integral? What happens when you then apply the limit?