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Question
Integrate the function `1/sqrt(x^2 +2x + 2)`
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Solution
Let `I = int 1/ sqrt (x^2 + 2x + 2) dx`
`= dx/ sqrt ((x + 1)^2 + 1)`
∴ `I = log |(x + 1) + sqrt ((x + 1)^2 + 1)| + C` ` ....[∵ int dx/sqrt (a^2 + x^2) = log |x + sqrt (x^2 + a^2)| + C]`
`= log |(x + 1) + sqrt (x^2 + 2x + 2)| +C`
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