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प्रश्न
Integrate the function `1/sqrt((2-x)^2 + 1)`
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उत्तर
Let `I = int 1/sqrt((2 - x)^2 + 1) dx`
Put 2 - x = t
- dx = dt ⇒ dx = - dt
`therefore I = - int dt/sqrt(t^2 + 1) dt`
`= - log [t + sqrt(t^2 + 1)] + C`
`= - log [(2 - x) + sqrt((2 - x)^2 + 1)] + C`
`= log |1/ ((2 - x) + sqrt (x^2 - 4x + 5))| + C`
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