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प्रश्न
Integrate the function:
`sqrt(x^2 + 4x - 5)`
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उत्तर
Let `I = int sqrt(x^2 + 4x - 5)` dx
`= int sqrt(x^2 + 4x - 9)` dx
`= int sqrt((x + 2)^2 - (3)^2)` dx
`= ((x + 2)/2) sqrt((x + 2)^2 - (3)^2) - 9/2 log [(x + 2) + sqrt((x + 2)^2 - (3)^2] + C` `...[int sqrt (x^2 - a^2) dx = x/2 sqrt (x^2 - a^2) - a^2/2 log |x + sqrt (x^2 - a^2)| + C]`
`= ((x + 2)/2) sqrt(x^2 + 4x - 5) = 9/ 2 log [x + 2 + sqrt(x^2 + 4x - 5)] + C`
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