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Evaluate the integral ∫ (1+x-(1)/(x))e^(x+1/x) dx.

1. (x+1)e^(x+1/x)+c
2. -x e^(x+1/x)+c
3. (x-1)e^(x+1/x)+c
4. x e^(x+1/x)+c

Correct answer: x e^(x+1/x)+c

Solution

The integral can be solved using integration by parts, where the derivative of the exponent, which is a function of both x and 1/x, simplifies the expression. This leads to the result of the integral being x multiplied by the exponential function, plus a constant of integration.

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