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Evaluate : int dx/(2 sqrtx (x + 1))...

Evaluate : `int dx/(2 sqrtx (x + 1))`

Text Solution

Verified by Experts

Put `x = t^2 rArr dx = 2t dt`
So, `I = int dx/(2 sqrtx (x + 1)) = int (2t dt)/(2t (t^2 +1))`
= `int dt/(1 + t^2) = tan^(-1)t + c`
`= tan^-1 (sqrtx) + c` (where .c. is arbitrary constant)
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