∫ dU / U
The integral of dU/U can be simplified as:
∫ dU / U = ln|U| + C
where C is the constant of integration
The integral of dU/U can be simplified as:
∫ dU / U = ln|U| + C
where C is the constant of integration.
To understand this, we need to remember the basic properties of logarithms. The natural logarithm, ln(x), is the inverse function of the exponential function, e^x. It is defined as the power to which the base e (approximately 2.71828) must be raised to obtain a specific number x.
In the context of the integral ∫ dU/U, we can see that the denominator U is a variable, so we treat it as a constant. Integrating with respect to U means we are finding an expression that, when differentiated with respect to U, yields 1/U.
The integral of 1/U is ln|U| + C, where |U| represents the absolute value of U. The absolute value ensures that our expression remains valid for negative values of U as well.
So, in summary, the integral of dU/U is ln|U| + C.
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