dx-x-2-9-x-2-

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

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

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

l e t x = 3 \tan r \Rightarrow d x = 3 \sec^{2} r d r

\int \frac{3 \sec^{2} r d r}{9 \tan^{2} r . 3 \sec r} = \frac{1}{9} \int \frac{1}{\cos r} . \cot^{2} r d r

= \frac{1}{9} \int \frac{\cos r d r}{\sin^{2} r} = \frac{1}{9} \int \frac{d (\sin r)}{\sin^{2} r}

= - \frac{1}{9 \sin r} + c = - \frac{\sqrt{9 + x^{2}}}{9 x} + c

Commented by malwaan last updated on 04/Nov/20

y e s s i r

y o u a r e r i g h t

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