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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=1/3 int sqrt (9+x^2)dx=1/3 sqrt((3)^2+x^2)dx`
We know that, `int sqrt(x^2+a^2)dx=x/2 sqrt(x^2+a^2)+(a^2)/2 log∣x+sqrt(x^2+a^2)∣+C`
`∴I=1/3[x/2 sqrt(x^2+9)+9/2 log∣x+ sqrt(x^2+9)∣]+C`
`=x/6 sqrt(x^2+9)+3/2 log∣x+sqrt (x^2+9)∣+C`
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