Question

Integrate 2y^2/y^2+4?

Answer 1

`int (2y^2)/(y^2+4)dy = 2y -4 arctan(y/2)+C`

Explanation:

Lower the degree of the numerator:

`(2y^2)/(y^2+4) = 2( (y^2+4-4)/(y^2+4)) = 2(1-4/(y^2+4))`

Now using the linearity of the integral:

`int (2y^2)/(y^2+4)dy = 2int dy -8 intdy/(y^2+4)`

`int (2y^2)/(y^2+4)dy = 2y -8int (2d(y/2))/(4((y/2)^2+1)`

`int (2y^2)/(y^2+4)dy = 2y -4 arctan(y/2)+C`