## ln |u| + c

### In mathematics, ln (pronounced “natural logarithm”) refers to the natural logarithm function with a base of “e,” where e is a mathematical constant approximately equal to 2

In mathematics, ln (pronounced “natural logarithm”) refers to the natural logarithm function with a base of “e,” where e is a mathematical constant approximately equal to 2.71828.

The expression ln |u| + c represents the antiderivative of the absolute value of function u, plus a constant c. This expression can also be referred to as the indefinite integral of ln |u|.

To understand this expression further, let’s break it down:

1. The absolute value of a function |u| is a mathematical notation that represents the positive magnitude of the function, regardless of its sign. This ensures that the resulting value is always non-negative.

2. ln |u| represents the natural logarithm of the absolute value of function u. This means that the value of u inside the logarithm can be positive or negative, but it must not be zero. The natural logarithm function ln is the inverse of the exponential function e^x, where x is the input.

3. The “+ c” at the end of the expression represents the constant of integration. When finding the antiderivative of a function, we add this constant to account for all possible solutions.

In summary, ln |u| + c represents the antiderivative of the absolute value of function u, where the logarithm is applied to the magnitude of u, regardless of its sign. The constant c accounts for all potential solutions.

It is important to note that to find the specific solution for a given function u, additional information or constraints are necessary. This could include initial conditions or specific boundaries.

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