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Question
Integrate the function:
`sqrt(x^2 + 4x + 6)`
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Solution
Let `I = int sqrt(x^2 + 4x + 6)`
`= int sqrt(x^2 + 4x + 4 + 2)` dx
`= int sqrt ((x + 2)^2 + (sqrt(2))^2)`
`= ((x + 2))/2 sqrt ((x + 2)^2 + 2) + 2/2 log abs((x + 2) + sqrt((x + 2)^2 + 2)) + C`
`= ((x + 2))/2 sqrt(x^2 + 4x + 6) + log abs ((x + 2) + sqrt(x^2 + 4x + 6)) + C` `...[∵ int sqrt (a^2 + x^2) dx = x/2 sqrt (a^2 + x^2) + a^2/2 log |x + sqrt (a^2 + x^2)| + C]`
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