## unimatix one year ago Integral (y^2)/(25+y^2) dy

1. unimatix

I'm tempted to cancel out the y^2 but I feel like that is wrong?

2. freckles

$y^2+25-25=y^2$

3. IrishBoy123

+1 @freckles then a tan sub

4. SolomonZelman

yes $$\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{y^2}{y^2+25}~dy=\int\limits_{~}^{~}\left(1-\frac{25}{y^2+25}\right)~dy}$$ $$u=5\tan(y)$$ $$du=5\sec^2(y)$$