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Integrate the functionssqrt(1+(x^2)/9)...

Integrate the functions`sqrt(1+(x^2)/9)`

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`" Let " I= int sqrt(1+(x^(2))/(9))dx`
`=int sqrt((9+x^(2))/(9))dx =(1)/(3) int sqrt((3)^(2)+x^(2))dx`
`=(1)/(3) [(x)/(2)sqrt((3)^(2)+x^(2))+(9)/(2)log |x+sqrt(9+x^(2))|]+C`
`=(x)/(6) sqrt(x^(2)+9)+(3)/(2)log |x+sqrt(9+x^(2))|+C`
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