How do you evaluate $\int \frac{y^2}{y^2+d^2}dy$? $\color{green}{question}$:
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.

Hint


*

*$$\frac{y^2}{y^2+d^2}=\frac{y^2+d^2-d^2}{y^2+d^2}=1-\frac{d^2}{y^2+d^2}$$

*$$\frac{d^2}{y^2+d^2}=\frac{1}{(y/d)^2+1}=\frac{1}{t^2+1}$$

*$$\int\frac{dt}{t^2+1}=\arctan t+C$$

