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प्रश्न
Evaluate `int "x - 1"/sqrt("x + 4")` dx
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उत्तर
Let I = `int "x - 1"/sqrt("x + 4")` dx
= `int (("x + 4") - 5)/sqrt("x + 4")` dx
= `int (sqrt"x + 4" - 5/(sqrt "x + 4"))` dx
`= int [("x + 4")^(1/2) - 5("x + 4")^(- 1/2)]` dx
`= ("x + 4")^(3/2)/(3/2) - 5 ("x + 4")^(1/2)/(1/2)` + c
∴ I = `2/3 ("x + 4")^(3/2) - 10 sqrt("x + 4")` + c
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