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Integrate the functionssqrt(x^2+4x+6)...

Integrate the functions`sqrt(x^2+4x+6)`

Text Solution

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`x^2+4x+6=(x+2)^2+2=(x+2)^2+(sqrt2)^2`
Let `x+2=t=>dx=dt`
Also we know that, `intsqrt(a^2+x^2)dx=x/2sqrt(a^2+x^2)+a^2/2log|x+sqrt(x^2+a^2)|+c`
`:. int sqrt(x^2+4x+6)dx=intsqrt(((x+2)^2)+(sqrt2)^2)dx`
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