In mathematics, the logarithmic integral function or integral logarithm li (x) is a special function. It is relevant in problems of physics and has number theoretic significance.

Dec 3, 2025 · Here, PV denotes Cauchy principal value of the integral, and the function has a singularity at . The logarithmic integral defined in this way is implemented in the Wolfram …

The logarithm is a basic function from which many other functions are built, so learning to integrate it substantially broadens the kinds of integrals we can tackle.

May 17, 2025 · Learn AP Calculus AB/BC approaches to integrate logarithmic functions with substitution, integration by parts, and key practice exercises.

Follow the previous example and refer to the rule on integration formulas involving logarithmic functions.

Apr 8, 2025 · Thus, the integration of ∫ x d x 3 + x 2 will be done using the logarithmic form, whereas ∫ x d x (3 + x 2) 2 will be done using the power rule for integration.

What is the Integration of Log x? The integration of log x with base e is equal to xlogx - x + C, where C is the constant integration. The logarithmic function is the inverse of the exponential …

Feb 25, 2021 · The function $ \mathop {\rm li} $ is better known as the logarithmic integral. It can, of course, be defined by the integral (as above) for $ z \in \mathbf C \setminus \ { {x \in \mathbf …

Tutorial to find indefinite integrals involving logarithmic functions, examples with detailed solutions.

The logarithmic integral function Li (x) (or just the “logarithmic integral”) is a locally summable function on the real line. This special function is used in physics and number theory, most …