Double integral problem (pretty basic)

[chexmix]

Good day, all:

We recently hit double/triple integrals in my multivariable calculus course and I have found that my integration abilities are, well, *beyond* rusty ... and so the problem below, which is one of the very first on my current problem set, has me stumped.

Homework Statement

$\int\int_{R}\frac{x}{1+xy} dA$ R = { [0,1]x[0,1] = {(x,y): 0 $\leq$ x $\leq$1, 0 $\leq$ y $\leq$1 }

The Attempt at a Solution

My first and nearly only step was to turn this into an iterated integral:

$\int^{1}_{0}\int^{1}_{0}\frac{x}{1+xy} dx dy$

... and this is where I begin to choke and sputter. I have started to try u-substitution on this with u = 1+xy, but didn't get anything that made sense to me; some hints I have found online seem to indicate that I should be able to perform "polynomial long division" to turn this into a sum or difference of two simpler integrals, but I guess I don't sufficiently understand polynomial long division to carry this out here.

Any hints would be much appreciated. I am considering dropping this course, but I would like to avoid that ... I need some serious integration mojo to be directly infused into my skull asap.

Regards,

Glenn

 

[murmillo]

Did you try integrating with respect to y first?

 

[chexmix]

Did you try integrating with respect to y first?

No. I'll check it out and see what happens. Thank you.

EDIT: That was key, of course. Jeez. ::strikes forehead::