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प्रश्न
Integrate the following with respect to x.
`sqrt(1 + x + x^2)`
उत्तर
`int sqrt(1 + x + x^2) "d"x = int sqrt((x + 1/2)^2 - 1/4 + 1) "d"x`
= `int sqrt((x + 1/2)^2 + 3/4) "d"x`
= `int sqrt((x + 1/2)^2 + (sqrt(3)/2)^2) "d"x`
= `((x + 1/2))/2 sqrt(1 + x + x^2) + 3/8 log|(x + 1/2) + sqrt(1 + x + x^2)| + "c"`
{Using the formula for `int sqrt(x2 + "a"^2) "d"x` with 'x' as `x + 1/2` and 'a' as `sqrt(3)/2`}
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