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Question Number 120703 by bobhans last updated on 02/Nov/20

$$\int \frac{\mathrm{dx}}{{\mathrm{x}}^2\sqrt{9+{\mathrm{x}}^2}}?$$

Answered by john santu last updated on 02/Nov/20

$$letx=3\tan r\Rightarrow dx=3\sec {}^{2}rdr$$$$\int \frac{3\sec {}^{2}rdr}{9\tan {}^{2}r.3\sec r}=\frac{1}{9}\int \frac{1}{\cos r}.\cot {}^{2}rdr$$$$=\frac{1}{9}\int \frac{\cos rdr}{\sin {}^{2}r}=\frac{1}{9}\int \frac{d\left(\sin r\right)}{\sin {}^{2}r}$$$$=-\frac{1}{9\sin r}+c=-\frac{\sqrt{9+x^2}}{9x}+c$$

Commented by malwaan last updated on 04/Nov/20

$$yessir$$$$youareright$$

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