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

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

Answered by Frix last updated on 25/May/23

$$\int \frac{dx}{x^2\sqrt{x^2+a^2}}\stackrel{[t=x+\sqrt{x^2+a^2}]}{=}$$$$=\frac{4}{a^2}\int \frac{t}{{(t^2-1)}^2}dt=-\frac{2}{a^2(t^2-1)}=$$$$=\frac{x-\sqrt{x^2+a^2}}{a^{2}x}+C$$

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