User:Jason13086

j 03:21, 22 May 2007 (UTC)

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

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

$$E = \frac{Q}{4 \pi \epsilon _0 z R}\tan ^{-1}\left(\frac{R}{z}\right) \hat{z}$$

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

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

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$$\int_0^1 \frac{1}{\left(1-x^4\right)^{1/3}} \, dx\text{//}N = 1.16279$$ \text{Series}\left[\frac{1}{\left(1-x^4\right)^{1/3}},\{x,0,30\}\right]

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