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Question
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Options
`e^(sin^-1x)*(sin^-1 x - 1) + c`
`e^(sin^-1x)*(1 - sin^-1x) + c`
`e^(sin^-1x)*(sin^-1 x + 1) + c`
`-e^(sin^-1x)*(sin^-1 x + 1) + c`
Solution
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = `underlinebb(e^(sin^-1x)*(sin^-1 x - 1) + c)`.
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