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Display information for equation id:math.1199.176 on revision:1199
* Page found: Elektrodynamik Schöll (eq math.1199.176)
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TeX (original user input):
\begin{align}
& W=\int_{{}}^{{}}{{{d}^{3}}r}w(\bar{r})=\frac{{{\varepsilon }_{0}}}{2}{{\left( \frac{q}{4\pi {{\varepsilon }_{0}}} \right)}^{2}}4\pi \int_{0}^{\infty }{{{r}^{2}}dr}\frac{1}{{{r}^{4}}} \\
& \int_{0}^{\infty }{{{r}^{2}}dr}\frac{1}{{{r}^{4}}}=\int_{0}^{\infty }{dr}\frac{1}{{{r}^{2}}}=\left[ \frac{1}{r} \right]_{0}^{\infty }\to \infty \\
\end{align}
TeX (checked):
{\begin{aligned}&W=\int _{}^{}{{{d}^{3}}r}w({\bar {r}})={\frac {{\varepsilon }_{0}}{2}}{{\left({\frac {q}{4\pi {{\varepsilon }_{0}}}}\right)}^{2}}4\pi \int _{0}^{\infty }{{{r}^{2}}dr}{\frac {1}{{r}^{4}}}\\&\int _{0}^{\infty }{{{r}^{2}}dr}{\frac {1}{{r}^{4}}}=\int _{0}^{\infty }{dr}{\frac {1}{{r}^{2}}}=\left[{\frac {1}{r}}\right]_{0}^{\infty }\to \infty \\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>W</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><mi>w</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mn>4</mn><mi>π</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>d</mi><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>d</mi><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup></mrow></mfrac></mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>=</mo><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mo accent="false">→</mo><mi mathvariant="normal">∞</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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