What is ILATE Rule?
The ILATE Rule, the acronym for Inverse, Logarithmic, Algebraic, Trigonometric, and Exponential functions, guides the order in which different functions are prioritized during integration or differentiation. The ILATE rule is an acronym commonly used in integral calculus to determine which function should be selected as u and which as dv when employing the integration by parts method.
The ILATE rule is commonly employed when integrating products of two functions where standard integration techniques like substitution or simpler rules do not apply. It serves as a useful strategy for choosing u and dv to simplify the integral in cases involving products of functions.
ILATE stands for
- Inverse functions: Such as logarithmic or exponential functions
- Linear functions: Including polynomials or functions involving algebraic operations
- Algebraic functions: Another reference to algebraic functions
- Transcendental functions: Such as sine, cosine, tangent, etc.
- Exponential functions: Like ex
Using ILATE rule we first find I and II function then we use the formula i.e.
= ∫ (First Function).(Second Function).dx
= First Function ∫ (Second Function) dx – ∫ [ d/dx (First Function) ∫ (Second Function dx) ] dx
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ILATE Rule
ILATE rule stands for Inverse Trigonometric Function, Logarithmic Function, Algebraic Function, Trigonometric Function, and Exponential Function. It tells about the priority order in which functions are selected for their integration. It is an important concept in solving integration problems.
This formula is also called the ‘uv integration formula’. If we have to find the integration of a function that is a product of two functions then we use the ILATE rule of integration. In this article, we will learn about, What the is ILATE Rule, How to Apply the ILATE Rule, ILATE Rule Examples, and others in detail.