1.

निम्न फलनों का समाकलन कीजिये - `(1)/(x+sqrt(x))`

Answer» माना `I = int (dx)/(x+sqrt(x)) = int =(dx)/(sqrt(x)(sqrt(x) +1))`
माना `sqrt(x) + 1 = t`
`therefore (1)/(2sqrt(x))dx = dt rArr (dx)/(sqrt(x)) = 2dt`
अतः समी (1 ) से
`I = 2int (dt)/(t) = 2 log t = 2 log(sqrt(x+1))`


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