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The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.
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. In particular, according to the prime number theorem , it is a very good approximation to the prime-counting function , which is defined as the number of prime numbers ...
In mathematics, the definite integral ()is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.
This can be proved by computing the derivative of the right-hand side of the formula, taking into account that the condition on g is here for insuring the continuity of the integral. This gives the following formulas (where a ≠ 0), which are valid over any interval where f is continuous (over larger intervals, the constant C must be replaced ...
Romberg's method is a Newton–Cotes formula – it evaluates the integrand at equally spaced points. The integrand must have continuous derivatives, though fairly good results may be obtained if only a few derivatives exist.
In mathematics, Frullani integrals are a specific type of improper integral named after the Italian mathematician Giuliano Frullani. The integrals are of the form The integrals are of the form ∫ 0 ∞ f ( a x ) − f ( b x ) x d x {\displaystyle \int _{0}^{\infty }{\frac {f(ax)-f(bx)}{x}}\,{\rm {d}}x}
In mathematics, Dirichlet integrals play an important role in distribution theory. We can see the Dirichlet integral in terms of distributions. One of those is the improper integral of the sinc function over the positive real line,
An aircraft pilot's logbook Typical page layout in aircraft pilot's logbook. A pilot logbook is a record of a pilot's flying hours. It contains every flight a pilot has flown, including flight time, number of landings, and types of instrument approaches made. Pilots also log simulator time, as it counts towards training. [1]: FCL.630.H [2]