Answer
$-\dfrac{1}{\sqrt7}\ln |\dfrac{\sqrt7+\sqrt{7+x^2}}{x} |+C$
Work Step by Step
Apply formula : $\int \dfrac{dx}{x\sqrt{a^2+x^2}}=-\dfrac{1}{a}\ln |\dfrac{a+\sqrt{a^2+x^2}}{x} |+C$
Consider $I=\int\dfrac{dx}{x\sqrt{7+x^2}}=-\dfrac{1}{\sqrt7}\ln |\dfrac{\sqrt7+\sqrt{7+x^2}}{x} |+C$
