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

Explanation

Let
`I=intx/(x-sqrt(x^2-1))dx`
`=int (x(x+sqrt(x^2-1)))/((x-sqrt(x^2-1))(x+sqrt(x^2-1)))`
`I=int(x(x+sqrt(x^2-1)))/(x^2-(x^2-1))dx`
`=int(x^2+xsqrt(x^2-1))dx`
`=intx^2dx+intxsqrt(x^2-1))dx`
`=x^3/3+1/3 t^(3/2)+c`
`=x^3/3+1/3(x^2-1)^(3/2)+c`