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

1 Answer
Jun 15, 2018

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