Question

Compute the integral ${\int }_1^{\sqrt{3}}\frac{\sqrt{1+x^2}}{x^2}dx$

• A. $\frac{2}{\sqrt{3}}+\ln \frac{2+\sqrt{3}}{1+\sqrt{3}}$
• B. $\sqrt{2}-\frac{\sqrt{2}}{3}+\ln \frac{2+\sqrt{3}}{1-\sqrt{3}}$
• C. $\sqrt{2}-\frac{2}{\sqrt{3}}+\ln \frac{2+\sqrt{3}}{1+\sqrt{3}}$
• D. $\sqrt{2}+2-\ln \frac{2+\sqrt{3}}{1+\sqrt{3}}$

Answer 1

The correct option is C $\sqrt{2}-\frac{2}{\sqrt{3}}+\ln \frac{2+\sqrt{3}}{1+\sqrt{3}}$