evaluate-the-integral-1x225-dx-int-frac1sqrtx2-25-dx-where-x-and-gt5-x-and-gt-5-

Question

Evaluate the integral ∫1x2−25 dx \int \frac{1}{\sqrt{$$x^2 - 25$$}}\, dx , where  5 "\u003ex\u003e5 x \u003e 5 , using trigonometric substitution.

Accepted Answer

ln⁡(x+x2−25)+C\ln\left(x+\sqrt{$$x^2 - 25$$}\right)+C

Answer

ln⁡(x2−25x)+C\ln\left(\frac{\sqrt{$$x^2-25$$}}{x}\right)+C

Answer

ln⁡(xx2−25)+C\ln\left(x\sqrt{$$x^2 - 25$$}\right)+C

Answer

ln⁡(x2−25)+C\ln\left(\sqrt{$$x^2 - 25$$}\right)+C

Evaluate the integral ∫1x2−25dx \(\int\) \(\frac{1}{\sqrt{x^2 - 25}\)}\, dx , where x>5 x > 5 , using trigonometric substitution.