Using $x=\sqrt5\sec\theta$, find $\displaystyle\int \sqrt{x^2-5}\,\mathrm{d}x$ for \(x\

Question

Using $x=\sqrt5\sec\theta$, find $\displaystyle\int \sqrt{x^2-5}\,\mathrm{d}x$ for $x>\sqrt5$.

Accepted Answer

$\dfrac{x}{2}\sqrt{x^2-5}-\dfrac{5}{2}\ln|x+\sqrt{x^2-5}|+C$

Mixed Integration Techniques