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**Bart** In my book I have a proof for this integral: $\displaystyle \int\frac{dx}{\sqrt{a^2+x^2}}$

$\displaystyle \int\frac{dx}{\sqrt{a^2+x^2}}$ = $\displaystyle \int\frac{d\frac{x}{a}}{\sqrt{1+\frac{x^2}{a^2}}}$ = $\displaystyle ln(\frac{x}{a}+\sqrt{1+\frac{x^2}{a^2}})$

$\displaystyle {\frac {d}{dx}}ln(\frac{x}{a}+\sqrt{1+\frac{x^2}{a^2}})$ = $\displaystyle \frac{\frac{x}{a^2\sqrt{\frac{x^2}{a^2}+1}}+\frac{ 1}{a}}{\sqrt{\frac{x^2}{a^2}+1}+\frac{x}{a}}$

How can I simplify = $\displaystyle \frac{\frac{x}{a^2\sqrt{\frac{x^2}{a^2}+1}}+\frac{ 1}{a}}{\sqrt{\frac{x^2}{a^2}+1}+\frac{x}{a}}$ into $\displaystyle \frac{d\frac{x}{a}}{\sqrt{1+\frac{x^2}{a^2}}}$ ?