Question

Integral (y^2)/(25+y^2) dy

Answer 1

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

Answer 2

\[y^2+25-25=y^2\]

Answer 3

+1 @freckles

then a tan sub

Answer 4

yes

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{y^2}{y^2+25}~dy=\int\limits_{~}^{~}\left(1-\frac{25}{y^2+25}\right)~dy}\)

\(u=5\tan(y)\)
\(du=5\sec^2(y)\)