Question

Solve: $\int \sqrt{x^2-4}dx$

• A. $\sqrt{x^2-4}-2\log |x+\sqrt{x^2-4}|+C$
• B. $\frac{x}{2}\sqrt{x^2-4}+\frac{4}{2}\log |x-\sqrt{x^2-4}|+C$
• C. $\frac{x}{2}\sqrt{x^2-4}-\frac{4}{2}\log |x+\sqrt{x^2-4}|+C$
• D. None of these

Answer 1

The correct option is C $\frac{x}{2}\sqrt{x^2-4}-\frac{4}{2}\log |x+\sqrt{x^2-4}|+C$

We know that,

$\int \sqrt{x^2-a^2}dx=\frac{x}{2}\sqrt{x^2-a^2}-\frac{a^2}{2}\log |x+\sqrt{x^2-a^2}|+C$

If we put $a=2$ in the formula, we get

$\int \sqrt{x^2-4}dx=\frac{x}{2}\sqrt{x^2-4}-\frac{4}{2}\log |x+\sqrt{x^2-4}|+C$