Question

integration of

1/(√x+√(x-2))

Answer 1

Answer:

Step-by-step explanation:

$\int {\frac{1}{\sqrt{x}+\sqrt{x-2}}} \, dx \\\\\frac{1}{\sqrt{x}+\sqrt{x-2}}=\frac{1}{\sqrt{x}+\sqrt{x-2}}\times\frac{\sqrt{x}-\sqrt{x-2}}{\sqrt{x}-\sqrt{x-2}}\\\\\;\;\;\;\;= \frac{\sqrt{x}+\sqrt{x-2}}{(\sqrt{x}+\sqrt{x-2})(\sqrt{x}-\sqrt{x-2})}\\\\\;\;\;\;\;=\frac{\sqrt{x}-\sqrt{x-2}}{2}\\\int \frac{1}{2}\times(\sqrt{x}-\sqrt{x-2})\,  dx\\\\=\frac{1}{2}(\int \sqrt{x}\,dx \;-\; \int \sqrt{x-2}\, dx)\\\\=\frac{1}{2}(\frac{1}{2\sqrt{x}}-\frac{1}{2\sqrt{x-2}})+C$

Hope it Helps