I've seen huge amounts of seemingly impossible integrals. A lot have no nice answer while some have very nice answers. 

I don't want to remove these answers as many are (IMO) quite beautiful. However I do want to somehow contain these a bit, and keep quality up (some integrals can't be computed in any nice way). Should we do anything about these? Other than some really pretty answers, I don't see people getting too much out of it for future reference. 

Would it be wise to have some giant CW thread? 

Examples:

[Integral $\int\_0^1\frac{\arctan^2x}{\sqrt{1-x^2}}\mathrm dx$](https://math.stackexchange.com/questions/555882/integral-int-01-frac-arctan2x-sqrt1-x2-mathrm-dx?rq=1)

[Integral $ \int\_0^\infty \frac{\ln(1+\sigma x)\ln(1+\omega x^2)}{x^3}dx$](https://math.stackexchange.com/questions/713836/integral-int-0-infty-frac-ln1-sigma-x-ln1-omega-x2x3dx?rq=1)

[Integrate $ \int\_0^\infty \frac{ \ln^2(1+x)}{x^{3/2}} dx=8\pi \ln 2$](https://math.stackexchange.com/questions/730869/integrate-int-0-infty-frac-ln21xx3-2-dx-8-pi-ln-2?rq=1)

[Integral $ \int\_0^\infty \frac{x^n\ln x}{(x^2+\alpha^2)^2(e^x-1)}dx$](https://math.stackexchange.com/questions/747429/integral-int-0-infty-fracxn-ln-xx2-alpha22ex-1dx?rq=1)

[Integral $\int\_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$](https://math.stackexchange.com/questions/759513/integral-int-0-pi-2-theta2-log-42-cos-theta-d-theta-frac33-pi7?rq=1)