dx-x-2-x-2-a-2-

Question Number 192715 by mustafazaheen last updated on 25/May/23

\int \frac{dx}{x^{2} \sqrt{x^{2} + a^{2}}} = ?

Answered by Frix last updated on 25/May/23

\int \frac{d x}{x^{2} \sqrt{x^{2} + a^{2}}} \overset{[t = x + \sqrt{x^{2} + a^{2}}]}{=}

= \frac{4}{a^{2}} \int \frac{t}{{(t^{2} - 1)}^{2}} d t = - \frac{2}{a^{2} (t^{2} - 1)} =

= \frac{x - \sqrt{x^{2} + a^{2}}}{a^{2} x} + C

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