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int(dx)/(sqrt(x+1)+sqrt(x+2))...

`int(dx)/(sqrt(x+1)+sqrt(x+2))`

Text Solution

Verified by Experts

The correct Answer is:
`2/3 (x+2)^(3//2) - 2/3(x+1)^(3//2) + C`.
`I = int(1)/((sqrt(x+2)+ sqrt(x+1))) xx ((sqrt(x+2) - sqrt(x+1)))/((sqrt(x+2) - sqrt(x+1))) dx`
`= intsqrt(x+2) dx - intsqrt(x+1) dx =2/3 (x+2)^(3//2) - 2/3 (x+1)^(3//2) +C`.
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