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Integrate the following functions (4x+2) sqrt(x^2+x+1) |
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Answer» Solution :(4x+2)SQRT(x^2+x+1)` =`2(2x+1)sqrt(x^2+x+1)` Put t = `x^2+x+1`. Then DT = (2x+1)DX therefore `INT (4x+2)sqrt(x^2+x+1) dx` =`int 2(2x+1) sqrt(x^2+x+1) dx` =`2intsqrtt dt` =`2 t^(1/2+1)/(1/2+1) +c = 4/3 t^(3/2) +c` =`4/3 (x^2+x+1)^(3/2) +c` |
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