Question

`int 1/sqrt(8 + 2x - x^2) dx` is equal to ______.

पर्याय

• `1/3 sin^-1((x - 1)/3) + c`

• `sin^-1((x + 1)/3) + c`

• `1/3 sin^-1((x + 1)/3) + c`

• `sin^-1((x - 1)/3) + c`

Answer 1

`int 1/sqrt(8 + 2x - x^2) dx` is equal to `underlinebb(sin^-1((x - 1)/3) + c)`.

Explanation:

`int (dx)/sqrt(8 + 2x - x^2)`

= `int (dx)/sqrt(8 + 1 - (x^2 - 2x + 1))`

= `int (dx)/sqrt(3^2 - (x - 1)^2`

= `sin^-1((x - 1)/3) + c`