Integrate: \frac{2x+1}{x^2+1} - Solutions

[tunabeast]

Homework Statement

Compute the following antiderivative $$\int \frac {(2x+1)}{ (x^2+1)} d \ x$$

Homework Equations

The Attempt at a Solution

I tried a method using using substitution of u = x^2+1, but i think this is approaching the question in the complete wrong way. I think maybe some kind of trigonometric function comes into it but I'm not sure which. Thanks in advance for any assistance

 

[neutrino]

I tried a method using using substitution of u = x^2+1, but i think this is approaching the question in the complete wrong way. I think maybe some kind of trigonometric function comes into it but I'm not sure which.

Both are needed, but only after you split the fraction

$$\frac {(2x+1)}{ (x^2+1)}$$ as $$\frac {2x}{ (x^2+1)} + \frac {1}{ (x^2+1)}$$