Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (b)/Solution 2

By the chain rule, we have $(\sqrt{x^2-3}{)}^{\prime }=\frac{1}{2\sqrt{x^2-3}}\cdot (x^2-3{)}^{\prime }=\frac{x}{\sqrt{x^2-3}}$.

Then, by the definition of anti-derivative, we get

$\int \frac{3x}{\sqrt{x^2-3}}=3\int \frac{x}{\sqrt{x^2-3}}=3\int (\sqrt{x^2-3}{)}^{\prime }=3\sqrt{x^2-3}+C$.

Answer: $3\sqrt{x^2-3}+C$