parametric double integral, 3 cases

[maxandri]

Hi everybody,
I have to find for which Alpha exists
$\displaystyle \int \frac{x^2}{(x+y)^\alpha}$
1) defined on y=tanx and $\displaystyle \pi/4<x<\pi/2$
2) defined on x<=1 and $\displaystyle \frac{(x^3-1)}{x}<y<x^2$
3) in the triangle (-1,0), (0,1), (1,0) with this similar integral $\displaystyle \int \frac{x^2}{(x^2+y^2)}$

In the first case I can integrate dy between 1 and tanx and I get
$\displaystyle \int \frac{x^2((x+tanx)^{-\alpha +1}-(x+1)^{-\alpha +1})}{(1-\alpha)}$
Now is it enough to say that tan is limited and integrate only x^2 between $\displaystyle \pi/4<x<\pi/2$?

In the second case $\displaystyle \frac{(x^3-1)}{x}<y<x^2$ is asintotic to x^2<y<x^2 and dy become 0? (it sounds bad...)

In the third case should I divide with x^2 and I get arctgy/x? And then?

Sorry, it si a thread a bit long but it is what I have to do... Thank you to anyone will answer me