compute-dx27x2-int-fracdx27-x2-for-x-and-gt33-x-and-gt-3sqrt3

Question

Compute ∫dx27−x2 \int \frac{dx}{27 - $$x^2$$} , for  3\sqrt{3} "\u003ex\u003e33 x \u003e 3\sqrt{3} .

Accepted Answer

318ln⁡(x+33x−33)+C\frac{\sqrt3}{18}\ln\left(\frac{x+3\sqrt3}{x-3\sqrt3}\right)+C

Answer

312ln⁡(x+33x−33)+C\frac{\sqrt3}{12}\ln\left(\frac{x+3\sqrt3}{x-3\sqrt3}\right)+C

Answer

318ln⁡(x−33x+33)+C\frac{\sqrt3}{18}\ln\left(\frac{x-3\sqrt3}{x+3\sqrt3}\right)+C

Answer

36ln⁡(x−33x+33)+C\frac{\sqrt3}{6}\ln\left(\frac{x-3\sqrt3}{x+3\sqrt3}\right)+C

Compute ∫dx27−x2 \(\int\) \(\frac{dx}{27 - x^2}\) , for x>33 x > 3\(\sqrt{3}\) .