TRIGONOMETRIC functionsLOGARITHMIC functionsANALYTIC functionsSPECIAL functionsMATHEMATICAL constantsGAMMA functionsWe present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof ...
The integrals of thefunctions(log t)−1and e−t2define the logarithmic integral. These cannot be integrated in terms ofelementary functions[3]. Applications of the Logarithmic Integral Function The logarithmic integral function is used primarily in physics and number theory. In number theory, the...
series courtesy of Ramanujan【Ramanujan提供的一个很好的无限系列】 09:11 A wonderful integral with a stunning result【完美的积分带来惊人的结果】 09:40 欧拉对巴塞尔问题的杰出解决方案 11:56 An absolute beast of an integral solved using Feynman's awesome technique 17:39 A savage logarithmic integral...
When dealing with logarithm functions several properties are useful to reduce the expressions: {eq}\bullet {/eq}Sum, the sum of logarithms equals the logarithm of their arguments' product, {eq}\log_a x+\log_a y=\log_a (xy) {/eq}. ...
series courtesy of Ramanujan【Ramanujan提供的一个很好的无限系列】 09:11 A wonderful integral with a stunning result【完美的积分带来惊人的结果】 09:40 欧拉对巴塞尔问题的杰出解决方案 11:56 An absolute beast of an integral solved using Feynman's awesome technique 17:39 A savage logarithmic integral...
Integration of Exponential and Logarithmic Functions: Methods and formulas to integrate functions like e^x, ln(x), etc. Integration of Hyperbolic Functions: Techniques for integrating functions like sinh(x), cosh(x), etc. Linearity of the Integral: The principle that the integral of a sum is ...
This is done based on a preferential list of functions: inverse, logarithmic, algebraic, trigonometric, exponential. The formula of by parts can be written as: $$\int f(x) g(x) \ dx = f(x) \int g(x) - \int \left ( f'(x) \int g(x) \right ) \ dx $$ where f(x)...
series courtesy of Ramanujan【Ramanujan提供的一个很好的无限系列】 09:11 A wonderful integral with a stunning result【完美的积分带来惊人的结果】 09:40 欧拉对巴塞尔问题的杰出解决方案 11:56 An absolute beast of an integral solved using Feynman's awesome technique 17:39 A savage logarithmic integral...
One of the standard integrals comes from the differentiation formula involving the logarithmic function: ddxln|v(x)|=v′(x)v(x) Integrating the right-hand side gives usln(v(x)), so we have the following formula: ∫v′(x)v(x)dx=ln|v(x)|+C ...
Integral formulas are listed along with the classification based on the types of functions involved. Also, get the downloadable PDF of integral formulas for different functions like trigonometric functions, rational functions, etc.