1.计算$|p|<frac{1}{2}$时
$$int_0^{+infty}left(frac{x^p-x^{-p}}{1-x} ight)^2mathrm{d}x=2(1-2ppicot 2ppi)$$
2. 证明：
$$int_0^{+infty}sinleft(x^3+frac{pi}{4} ight)mathrm{d}x=frac{sqrt{6}+sqrt{2}}{4}int_0^{+infty}e^{-x^3}mathrm{d} x$$