# User:Jason13086

j 03:21, 22 May 2007 (UTC)

${\displaystyle \int {\frac {\text{dy}}{\sqrt {y^{2}+\rho ^{2}}}}={\frac {1}{2}}\ln \left[{\frac {{\sqrt {y^{2}+\rho ^{2}}}+y}{{\sqrt {y^{2}+\rho ^{2}}}-y}}\right]}$

${\displaystyle \int {\frac {\text{dy}}{\sqrt {y^{2}+\rho ^{2}}}}=\ln \left[y+{\sqrt {y^{2}+\rho ^{2}}}\right]}$

${\displaystyle E={\frac {Q}{4\pi \epsilon _{0}zR}}\tan ^{-1}\left({\frac {R}{z}}\right){\hat {z}}}$

${\displaystyle E=\int {\frac {dq{\hat {z}}}{\rho ^{2}+z^{2}}}{\text{, }}dq={\frac {A}{\rho }}\rho d\rho d\phi }$

${\displaystyle \left({\begin{array}{c}{\frac {x^{2}}{2}}\\{\frac {x^{3}}{3}}\\\sin(x)\\-\cos(x)\\x\log(x)-x\\\sinh ^{-1}(x)\end{array}}\right)}$

## -

${\displaystyle \int _{0}^{1}{\frac {1}{\left(1-x^{4}\right)^{1/3}}}\,dx{\text{//}}N=1.16279}$ \text{Series}\left[\frac{1}{\left(1-x^4\right)^{1/3}},\{x,0,30\}\right]

${\displaystyle 1+{\frac {x^{4}}{3}}+{\frac {2x^{8}}{9}}+{\frac {14x^{12}}{81}}+{\frac {35x^{16}}{243}}+{\frac {91x^{20}}{729}}+{\frac {728x^{24}}{6561}}+{\frac {1976x^{28}}{19683}}+O[x]^{31}}$