User:X!/math

1. ${\sqrt {\frac {5}{3}}}\times {\sqrt {\frac {3}{5}}}=1$
2. $3{\sqrt {\frac {4}{16}}}\div 18{\sqrt {{\frac {3}{5}}x}}=(86.4x)^{-{\frac {1}{2}}}$
3. $\int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx={\frac {4}{9}}e^{3}$
4. $\textstyle \int \limits _{-N}^{N}e^{x}\,dx=2\sinh N$
5. $\textstyle \lim _{n\to \infty }\sum _{x=1}^{N}x^{2}={\frac {N(N+1)(2N+1)}{6}},n\neq N$
6. ${\begin{bmatrix}\int _{x}^{x^{2}}\sum _{i=1}^{8}0\end{bmatrix}}=0$