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Integrate the following functions (4x+2)...

Integrate the following functions `(4x+2) sqrt(x^2+x+1)`

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(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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