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Question
Integrate the function:
`sqrt(1+ x^2/9)`
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Solution
Let `I = int sqrt (1 + x^2/9) dx`
`= 1/3 int sqrt (9 + x^2) dx`
`= 1/3 int sqrt (x^2 + 3^2) dx`
`= 1/3 [x/2 sqrt (x^2 + 9) + 9/2 log |x + sqrt (x^2 + 9)|] + 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]`
`= x/6 sqrt (x^2 + 9) + 3/2 log |x + sqrt (x^2 + 9)| + C`
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