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Grade: 12


The integral of the given expression (x m +m x )÷(m-x) is-

The integral of the given expression
(xm +mx )÷(m-x)

2 years ago

Answers : (1)

Tech Xposed
37 Points
The above function cannot be integrated because there are important restriction on antiderivatives that can be expressed as elementary functions
According 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.
2 years ago
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