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The integral of the given expression (x m +m x )÷(m-x) is-
The above function cannot be integrated because there are important restriction on antiderivatives that can be expressed as elementary functionsAccording to the Liouville's theorem for differential algebra:-The antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions. A standard example of such a function is e^{{-x^{2}}}, whose antiderivative is (with a multiplier of a constant) the error function, familiar from statistics. Other examples include the functions {\frac {\sin(x)}{x}} and x^{x}.Liouville's theorem states that elementary antiderivatives if they exist, must be in the same differential field as the function, plus possibly a finite number of logarithms.Hope it helps.
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