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Let g (x) be an antiderivative for f(x)....

Let g (x) be an antiderivative for f(x). Then `ln (1+ (g(x))^2)` is an antiderivative for

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Let f(x)=(9x)/(25)+c, c gt 0 . If the curve y=f^(-1)(x) passes through ((1)/(4), -(5)/(4)) and g(x) is the antiderivative of f^(-1)(x) such that g(0)=(5)/(2) , then the value of [g(1)] is, (where [.] represents the greatest integer function)