Advanced Integration Formulas
Some other advanced integration formulas which are of high importance for solving integrals are discussed below,
- ∫1/(x2 – a2) dx = 1/2a log|(x – a)(x + a| + C
- ∫ 1/(a2 – x2) dx =1/2a log|(a + x)(a – x)| + C
- ∫1/(x2 + a2) dx = 1/a tan-1x/a + C
- ∫1/√(x2 – a2)dx = log |x +√(x2 – a2)| + C
- ∫ √(x2 – a2) dx = x/2 √(x2 – a2) -a2/2 log |x + √(x2 – a2)| + C
- ∫1/√(a2 – x2) dx = sin-1 x/a + C
- ∫√(a2 – x2) dx = x/2 √(a2 – x2) dx + a2/2 sin-1 x/a + C
- ∫1/√(x2 + a2 ) dx = log |x + √(x2 + a2)| + C
- ∫ √(x2 + a2 ) dx = x/2 √(x2 + a2 )+ a2/2 log |x + √(x2 + a2)| + C
Integration Formulas
Integration Formulas are the basic formulas that are used to solve various integral problems. They are used to find the integration of algebraic expressions, trigonometric ratios, inverse trigonometric functions, and logarithmic and exponential functions. These integration formulas are very useful for finding the integration of various functions.
Integration is the inverse process of differentiation, i.e. if d/dx (y) = z, then ∫zdx = y. Integration of any curve gives the area under the curve. We find the integration by two methods Indefinite Integration and Definite Integration. In indefinite integration, there is no limit to the integration whereas in definite integration there is a limit under which the function is integrated.
Let us learn about these integral formulas, and their classification, in detail in this article.
Table of Content
- Integral Calculus
- What are Integration Formulas?
- Integration Formulas of Trigonometric Functions
- Integration Formulas of Inverse Trigonometric Functions
- Advanced Integration Formulas
- Different Integration Formulas
- Application of Integrals
- Definite Integration Formula
- Indefinite Integration Formula