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Integrate the following functions sqrt(x...

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

Text Solution

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`int sqrt(x^2+4x+1) dx`
=`int sqrt(x^2+4x+4-(sqrt3)^2) dx`
=`int sqrt((x+2)^2-(sqrt3)^2) dx`
`(x+2)/2 sqrt((x+2)-(sqrt3)^2-(sqrt)^2/2 log|x+2+sqrt(x^2+4x+1)|+c`
=`(x+2)/2 sqrt(x^2+4x+1)-3/2 log|x+2+sqrt(x^2+4x=1)|+c`
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