Evaluate ∫$$1+xxdx$$

Correct option is 3x2+x+12log⁡x+12+x2+x+C

Questions

$Evaluate \int \sqrt{\frac{1 + x}{x}} d x$

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x2+x+log⁡x+12+x2+x+C

x2+x+12log⁡x+12-x2+x+C

x2+x+12log⁡x+12+x2+x+C

None of these

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detailed solution

Correct option is C

∫1+xxdx=∫1+xx1+x1+xdx=∫1+xx2+xdx=12∫2x+1x2+xdx+12∫1x2+xdx=12∫1tdt+12∫1x+122−122dx, where t=x2+x=t+12log⁡x+12+x2+x+C=x2+x+12log⁡x+12+x2+x+C

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Evaluate ∫1+xxdx

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$Evaluate \int \sqrt{\frac{1 + x}{x}} d x$