ILATE Rule
The ILATE rule tells us about how to choose the first function and the second function while solving the integration of the product of two functions. Suppose we have two functions of x u and v and we have to find the integration of their product then we choose the first function and the by ILATE rule.
The ILATE full form is discussed in the image below,
The ILATE rules give us the hierarchy of taking the first function, i.e. if in the given product of the function, one function is a Logarithmic function and another function is a Trigonometric function. Now we take the Logarithmic function as the first function as it comes above in the hierarchy of the ILATE rule similarly, we choose the first and second functions accordingly.
NOTE: It is not always appropriate to use the ILATE rule sometimes other rules are also used to find the first function and the second function.
Integration by Parts
Integration by Parts: Integration by parts is a technique used in calculus to find the integral of the product of two functions. It’s essentially a reversal of the product rule for differentiation.
Integrating a function is not always easy sometimes we have to integrate a function that is the multiple of two or more functions in this case if we have to find the integration we have to use integration by part concept, which uses two products of two functions and tells us how to find their integration.
Now let’s learn about Integration by parts, its formula, derivation, and others in detail in this article.
Table of Content
- What is Integration by Parts?
- What is Partial Integration?
- Integration By Parts Formula
- Derivation of Integration By Parts Formula
- ILATE Rule
- How to Find Integration by Part?
- Repeated Integration by Parts
- Applications of Integration by Parts
- Integration by Parts Formulas
- Integration By Parts Examples
- Practice Problems
- FAQs
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