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Question
`int sqrt(1+ x^2) dx` is equal to ______.
Options
`x/2 sqrt(1 + x^2) + 1/2 log abs ((x + sqrt(1 + x^2))) + C`
`2/3 (1 + x^2)^(3/2) + C`
`2/3 x(1 + x^2)^(3/2) + C`
`x^2/2 sqrt(1 + x^2) + 1/2 x^2 log abs (x + sqrt(1 + x^2)) + C`
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Solution
`int sqrt(1+ x^2) dx` is equal to `underline (x/2 sqrt(1 + x^2) + 1/2 log abs ((x + sqrt(1 + x^2))) + C).`
Explanation:
`int sqrt(a^2 + x^2) dx`
`= x/2 sqrt (a^2 + x^2) + a^2/2 log abs (x + sqrt(a^2 + x^2)) + C`
Here, `a^2 = 1`
`therefore int sqrt(1 + x^2) dx = x/2 sqrt(1 + x^2) + 1/2 log abs ((x + sqrt(1 + x^2))) + C`
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