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

1 Answer
Jun 15, 2018

2y2y2+4dy=2y4arctan(y2)+C

Explanation:

Lower the degree of the numerator:

2y2y2+4=2(y2+44y2+4)=2(14y2+4)

Now using the linearity of the integral:

2y2y2+4dy=2dy8dyy2+4

2y2y2+4dy=2y82d(y2)4((y2)2+1)

2y2y2+4dy=2y4arctan(y2)+C