№01_010
Пункт №9
\(
\int\frac{dx}{x\sqrt{3+7x^2}}
=\int\frac{dx}{x\cdot{|x|}\cdot\sqrt{\frac{3}{x^2}+7}}
=-\frac{1}{\sqrt{3}}\cdot\int\frac{d\left(\frac{\sqrt{3}}{|x|}\right)}{\sqrt{\left(\frac{\sqrt{3}}{|x|}\right)^2+7}}=\\
=-\frac{1}{\sqrt{3}}\cdot\ln\left|\frac{\sqrt{3}}{|x|}+\sqrt{\frac{3}{x^2}+7}\right|+C
=-\frac{1}{\sqrt{3}}\cdot\ln\frac{\sqrt{3}+\sqrt{3+7x^2}}{|x|}+C
\)