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Question
Integrate the function `1/sqrt(7 - 6x - x^2)`
Solution
Let `I = int 1/sqrt(7 - 6x - x^2) dx`
`= dx/sqrt(7 - (x^2 + 6x))`
`= int dx/sqrt(7 - (x^2 + 6x + 9) + 9)`
`= int dx/sqrt(16 - (x + 3)^2)`
`= int dx/sqrt(4^2 - (x + 3)^2)`
`= sin^-1 ((x + 3)/4) + C` `...[because 1/sqrt(a^2 - x^2) dx = sin^-1 x/a + C]`
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