Mathematics

Evaluate $$\int \dfrac {1}{\sqrt {7-6x-{x}^{2}}}$$


SOLUTION
$$\int {\cfrac{1}{{\sqrt {7 - 6x - {x^2}} }}dx} $$
$$\int {\cfrac{1}{{\sqrt { - {x^2} - 6x + 7} }}} $$
$$\int {\cfrac{{dx}}{{\sqrt { - \left( {{x^2} + 6x - 7} \right)} }}} $$
$$\int {\cfrac{{dx}}{{\sqrt { - 1\left[ {{x^2} + 6x + 9 - 9 - 7} \right]} }}} $$
$$\int {\cfrac{{dx}}{{\sqrt { - 1\left[ {{{\left( {x + 3} \right)}^2} - 16} \right]} }}} $$
$$\int {\cfrac{{dx}}{{\sqrt {{{\left( 4 \right)}^2} - {{\left( {x + 3} \right)}^2}} }}} $$
$$={\sin ^{ - 1}}\left( {\cfrac{{x + 3}}{4}} \right) + c$$
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Subjective Medium Published on 17th 09, 2020
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