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

[shamieh]

Suppose:

$$\int^{\infty}_1 \frac{x}{x^2 + 1} \, dx$$

I can't do this can I?

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

 

[Jameson]

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