Tính các tích phân sau:
1. $\int\limits_{1}^{e}\frac{dx}{x(1+\ln^{2}x)}$
2. $\int\limits_{0}^{\ln\sqrt{3}}\frac{e^{x}}{e^{2x}+1}dx$
3. $\int\limits_{0}^{\pi /2}\sin2x\sqrt{1+\sin x}dx$
4. $\int\limits_{0}^{\sqrt{2}}\frac{x^{2}}{\sqrt{2+x^{2}}}dx$
5. $\int\limits_{0}^{\pi /4}x\tan^{2}xdx$
6. $\int\limits_{0}^{\pi /2}\sin2x\ln(1+\cos x)dx$
7. $\int\limits_{0}^{\pi /4}x\sin2x\cos^{2}xdx$
8. $\int\limits_{2}^{3}x\ln\sqrt{\frac{x-1}{x+1}}dx$