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Evaluate: int1/((x+1)sqrt(x))\ dx...

Evaluate: `int1/((x+1)sqrt(x))\ dx`

Text Solution

Verified by Experts

Let, `x=t^2`
`dx=2tdt`

`=int1/((x+1)sqrt(x))\ dx`

`=int1/((t^2+1)t)\ 2tdt`

`=int(2dt)/((t^2+1)`

`=2tan^(-1)t+C`

`=2tan^(-1) sqrt(x)+C`

`(Answer)`
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