Q:

Compute $\iint\limits_R\frac{y}{x+y^2}dA$ where $R=[0,1]\times[1,2]$

Compute $\displaystyle\iint\limits_R\frac{y}{x+y^2}dA$ where $R=[0,1]\times[1,2]$
$\displaystyle\int_0^1\int_1^2\frac{y}{x+y^2}dydx=\int_0^1\int_1^2y(x+y^2)^{-1}dydx$
How do I integrate the denominator if the superscript is $-1$?  
Hints are appreciated! 

A:

Hint 1: notice that $\frac{d}{dy}(x+y^2) = 2y$ so $\int y/(x+y^2) \, dy = (\ln{|x+y^2|})/2$. 
Hint 2: you may also want to take advantage of Fubini's theorem and write your integral as follows:
$$I = \int^2_1 \int^1_0 f(x,y) \, dxdy,$$
so it becomes a little bit easier.