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Calculate the following integral
$$\int\limits_0^1\frac{(1-x)e^x}{x+e^x}dx$$
$$\int\limits_0^1\frac{(1-x)e^x}{x+e^x}dx$$
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An integral is a mathematical concept used to calculate the area under a curve. It is a fundamental tool in calculus and is used to solve a wide range of problems in mathematics and science.
The integral of this function is being calculated to find the area under the curve defined by the function. This can help in solving various problems in physics, engineering, and economics.
The integral of this function can be calculated using techniques from calculus, such as integration by parts or substitution. In this specific case, the integral can be solved using the substitution method.
The limits of integration define the range over which the area under the curve is being calculated. In this case, the limits of integration are 0 and 1, meaning the area under the curve is being calculated between the points x=0 and x=1.
The integral of this function has applications in various fields such as physics, engineering, and economics. For example, it can be used to calculate the work done by a force, the growth rate of a population, or the value of an investment over time.