# Double Integral

1. Oct 4, 2004

### Blast0

Hi, I've tried to solve this problem over and over and always end up with an enormous second integral that seems to never reduce to simpler terms.

$$\int\int(x^2+xy+1)dydx$$

Where the bounds of the inner integral are $$[x-1,xcos(2(\pi)x)]$$ and the outer integral are $$[1,0]$$

Thank you for any help in advance. Any would be great.

2. Oct 4, 2004

### Tide

I get

$$-\frac {116 \pi^2 + 153}{192 \pi^2}$$

The inner integral came out to be

$$x(x^2+1) \cos {2\pi x} - \frac {x^3 \sin^2 2\pi x}{2} -x^3 + 2x^2-\frac {3x}{2} + 1$$

3. Oct 4, 2004

### Blast0

Thank you Tide.

For the inner integral I get:

$$x^3\cos^2(2(\pi)x)+(x(\cos^2(2(\pi)x)))/2+x\cos^2(2(\pi)x)-x(x-1)-((x(x-1)^2)/2)-x+1$$

I can simplify the second half but not the first. Is there some trick like a substitution to going further from this point, because I've tried integrating this and it was a monster... 2 pages and I couldnt reach a solution.

4. Oct 4, 2004