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Evaluate: intsqrt((1+x)/x)\ dx...

Evaluate: `intsqrt((1+x)/x)\ dx`

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Verified by Experts

I=`intsqrt((1+x)/x)\ dx`
Let `x=u^2`
`dx=2udu`
`I=int(sqrt(1+u^2)2udu)/u`
`I=2int(sqrt(1+u^2)du`
`I=2(1/2sqrt(u^2+1)+1/2ln(u+sqrt(u^2+1)))+C`
`I=(sqrt(u^2+1)+1/2ln(u+sqrt(u^2+1)))+C`
`I=sqrt(x+1)+1/2ln(sqrt(x)+sqrt(x+1))+C`
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