Evaluate: `intx/(x-sqrt(x^2-1))dx`

Explanation

Let,


`I=int frac{x}{x-sqrt{x^{2}-1}} d x=int x frac{(x+sqrt{x^{2}-1)})}{(x-sqrt{x^{2}-1})(x+sqrt{x^{2}-1})}`



`I=int frac{x(x+sqrt{x^{2}-1})}{x^{2}-(x^{2}-1)} d x `
`
I=int(x^{2}+x sqrt{x^{2}-1}) d x`
`
I=int x^{2} d x+int x sqrt{x^{2}-1} d x `
`
...