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Integrate : 1/(1+square root x ) square root x

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Solution: We have ,

$I=int frac1(x-1)sqrtxdx$ Put $sqrtx=tRightarrow frac12sqrtxdx=dt$

$I=2int frac1t^2-1dt=2 imes frac12lnleft | fract-1t+1 ight |+c=lnleft | fracsqrtx-1sqrtx+1 ight |+c$

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Deependra Verma

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