Question: $\color{green}{question}$:

How do you evaluate this integral?

> 
> $$\int \frac{y^2}{y^2+d^2}dy=y-d\,{\tan}^{-1}\left ( \frac{y}{d} \right )+\mathrm{constant}$$
> 
> 
> 

$\color{green}{I~know}$ I should use the change of variables, But I do not know how to do.

Thank you for any hint.

Answer: 
$$\frac{y^2}{y^2+d^2} = \frac{y^2 + d^2}{y^2+d^2} - \frac{d^2}{y^2+d^2}$$

The latter is an arctangent integral.
Maple code with(Student[Calculus1]):IntTutor$(y^2/(y^2 +d^2),y$); produced the output which can be seen [here](http://rapidshare.com/files/1020936765/screen2.24.08.13.docx). It coincides with the excellent answer by Eric Auld.