Evaluate: `int1/(sqrt(5-4x-2x^2))\ dx`

Explanation

`int1/(sqrt(5-4x-2x^2))\ dx`

`=int frac{dx}{sqrt(-2(x^2+2x-5/2))}`

`=int frac{dx}{sqrt(-2[(x+1)^2-7/2])}`

`=1/(sqrt(2)) int frac{dx}{sqrt((sqrt(frac{7}{2}))^2-(x+1)^2))`

`frac{1}{sqrt 2} sin^(-1)frac{sqrt 2(x+1)}{sqrt 7}+C`