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प्रश्न
Evaluate: `int_0^1 "e"^x/sqrt("e"^x - 1) "d"x`
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उत्तर
`int_0^1 "e"^x/sqrt("e"^x - 1) "d"x = [2sqrt("e"^x - 1)]_0^1` ......`[∵ int ("f'"(x))/sqrt("f"(x)) "d"x = 2sqrt("f"(x)) + "c"]`
= `2(sqrt("e"^1 1) - sqrt("e"^0 - 1))`
= `2(sqrt("e" - 1) - sqrt(1 - 1))`
= `2sqrt("e" - 1)`
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