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Integrate the functions(4x+2)sqrt(x^2+x+...

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

Text Solution

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Let `x^2+x+1=t`
=`(2x+1)dx=dt`
`∫(4x+2)sqrt(x^2+x+1) ​dx`
=`∫2sqrt(t) ​dt`
=`2((t)^(3/2​​))/(3/2)+C`
=`4/3(x^2+x+1)^(1/2)​+C`
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