List of Integration Formulas

A list of integrals (integral table) and a compilation of integral calculus techniques was published in 1810 by the German mathematician Meyer Hirsch [de] (also known as Meyer Hirsch [de]). These tables were republished in the United Kingdom in 1823. The extensive table was edited by the Dutch mathematician David Bierens de Haan in 1858 for his Tables d`intégrales définies, with the addition of the Supplément aux tables d’intégrales définies around 1864. Dutch. These tables mainly contained elementary function integrals and continued to be used until the mid-20th century. Then they were replaced by the much more voluminous Gradshteyn and Ryzhik tables. In Gradshteyn and Ryzhik, the integrals taken from Bierens de Haan’s book are expressed in BI.

Integration by parts formula:

 Part integration is one of the most important methods of integration. Used when the function to be integrated is described as the product of two or more functions. This is also known as the product rule of integrals and the uv integral method. If f (x) and g (x) are two functions and you want to consolidate their products, the formula to consolidate f (x). g (x) with the parts method is: 

 ∫f (x). g (x) dx = f (x) ∫g (x) dx − ∫ (f ′ (x) [∫g (x) dx)] dx + C 

 Where f (x) Is the first function and g (x) is the second function. For integration with 

parts, the first features are selected in the following order: This method, also commonly referred to as the ILATE or LIATE integral method, is abbreviated as follows: 

• I = Inverse trigonometric function 

• L = logarithmic function 

• A = Algebraic function 

• T = trigonometric function 

• E = exponential function

Application-Suppose the integrand is the product of two functions, an exponential function and a logarithmic function. Compared to the ILATE preferred form, the logarithmic function is chosen as the first function and the exponential function can be used as the second function for ease of evaluation. Therefore, to solve ∫ (ex) log (4×2) dx, you can easily get the result by choosing log (4×2) as the first function and ex as the second function.

Integration by substitution formula: 

The permutation method is also commonly referred to as the integral permutation method. This way you can change the integral variables to simplify the function. This is similar to the reverse chain rule. For example, there is an integral of the form ∫g (f (x)) dx. You can then replace f (x) with another variable, assuming f (x) = u. Distinguish f (x) = u. This means f` (x) dx = du ⇒ dx = du / h (u). Where h (u) = f'(x), f (x) = substitution. Keep in mind that if you change the integral variable, you need to change it for the entire integral. Therefore, the integral formula by the permutation method is as follows. 

 ∫g (f (x)) dx = ∫g (u) / h (u) du

Important note on how to integrate 

• Functions to be integrated can be decomposed into sums or differences of functions for which individual integrals are known. 

• Whenever you find the integral of a function, be sure to add the constant of integration.

Integration by partial fractions formula: 

This integral method is used to integrate rational functions. It is used to decompose the denominator of a rational function and transform it into simpler rational functions. Partial fraction decomposition integration is an important integration method. The formula that integrates rational functions of the form f (x) / g (x) is: 

 ∫ [f (x) / g (x)] dx = ∫ [p (x) / q (x)] dx + ∫ [r (x) / s (x)] dx 

 Where 

 f (x) / g (x) = p (x) / q (x) + r (x) / s (x) and 

 g (x) = q (x). s (x) 

 Now, various forms of rational functions are decomposed using specific forms of partial fractions, making calculations simpler and easier. See the Partial Fraction Integration page for details on each shape and how to simplify the function.

This method relies on the fact that the integral of a function of the form f (x), (f (x) is a linear function with an exponent) is fairly easy to perform. Therefore, integrands that include polynomial functions in the numerator and denominator are first reduced to partial fractions to facilitate the integration process.

Conclusion: 

C is used for any constant of integration. This can only be determined if at some point something is known about the value of the integral. Therefore, every function has an infinite number of indefinite integrals. These expressions reflect the assertiveness of the derived table only in different formats. Integration is a way to add slices and find the whole thing. Areas, volumes, centre points, and many useful things can be found through integration. But the easiest way to get started is to find the area under the curve of the function: the integral area.