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## Homework Statement

[tex]\int\frac{dx}{(R^{2}+x^{2})^{3/2}}[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]\mbox{Let }x = R\\tan\theta \Rightarrow dx = R\\sec^{2}d\theta[/tex]

[tex]x^{2} = R^{2}\\tan^{2}\theta[/tex]

[tex]\Rightarrow R^{2} + x^{2} = R^{2}\\( 1 + tan^{2}\theta)[/tex]

[tex]\Rightarrow R^{2} + x^{2} = R^{2}\\sec^{2}[/tex]

[tex]\Rightarrow (R^{2} + x^{2})^{3/2} = R^{3}\\sec^{3}\theta[/tex]

[tex]\mbox{Therefore, }\int\frac{dx}{(R^{2}+x^{2})^{3/2}}[/tex]

[tex]=\int\frac{R\\sec^{2}\theta}{R^{3}\\sec^{3}\theta}\\d\theta[/tex]

[tex]=\frac{1}{R^{2}}\\ \int^{\infty}_{-\infty}cos\theta\\ d\theta[/tex]

[tex]=\frac{1}{R^{2}}\stackrel{lim}{n\rightarrow\infty} \int^{N}_{-N}cos\theta\\ d\theta[/tex]

[tex]=\frac{1}{R^{2}}\stackrel{lim}{n\rightarrow\infty}(sin\theta)\mid^{N}_{-N}[/tex]

[tex]=\frac{1}{R^{2}}\stackrel{lim}{n\rightarrow\infty}(mbox{sin N + sin N})[/tex]

[tex]=\frac{2}{R}\stackrel{lim}{n\rightarrow\infty}mbox{sin N}[/tex]

and then??????????????????????