Understanding the Step-By-Step Breakdown of the Math Expression ln |sec u| + c

ln|secu|+c

The expression given is ln |sec u| + c, where ln represents the natural logarithm, sec represents the secant function, u represents the variable, and c represents a constant

The expression given is ln |sec u| + c, where ln represents the natural logarithm, sec represents the secant function, u represents the variable, and c represents a constant.

1. The secant function is reciprocal of the cosine function. It is defined as sec x = 1/cos x. In this case, u represents the angle whose secant is being taken.

2. The absolute value notation (| |) is included in the expression to ensure that the argument of the natural logarithm is always positive. This is important because the natural logarithm is only defined for positive numbers.

3. The natural logarithm function, ln, is the inverse function of the exponential function e^x. It is defined as the power to which e (approximately equal to 2.71828) must be raised to obtain a given number.

4. Adding the constant c at the end of the expression represents the indefinite integral of the given function. This implies that the expression came from an antiderivative, or the reverse process of taking a derivative.

So, ln |sec u| + c represents the antiderivative (or integral) of the function whose secant is u, plus a constant of integration.

To provide a more specific explanation or solve the expression further, we would need additional information or context about the problem or equation it is involved in.

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