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Question
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
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Solution
Let `I = int (4x + 2) sqrt(x^2 + x + 1)` dx
or `I = 2 int (2x + 1) sqrt ((x^2 + x + 1))` dx
Taking x2 + x + 1 = t
2x + 1 = dt
Hence, `I = 2 int sqrt t dt`
`= 2 int t^(1/2) dt = 2. 2/3 t^(3/2) + C`
`= 4/3 (x^2 + x + 1)^(3/2) + C`
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