When doing Integration By Parts, I know that using LIATE can be a useful guide most of the time. For those not familiar, LIATE is a guide to help you decide which term to differentiate and which term to integrate. L = Log, I = Inverse Trig, A = Algebraic, T = Trigonometric, E = Exponential.

2021年6月7日 · Do we always have to use "LIATE" to do integration by parts? L = logarithms I = inverse trigonometric functions A = algebraic functions T = trigonometric functions E = exponential functions . So basically, an example is a problem like $$\int -(e^x)\sin x\,dx$$ If I use the LIATE order to integrate this, I will get:

$\begingroup$ This isn't about why LIATE is wrong, but a possible problem with using it in teaching. This method doesn't encourage much thinking. This method doesn't encourage much thinking. Many times students will follow the rule blindly without understanding why …

2016年8月16日 · Question about Integration by Parts (LIATE) Ask Question Asked 8 years, 6 months ago.

2014年11月28日 · Popular textbook contain many examples of integrals which can be computed by parts using the LIATE Rule. However there is almost no example of the case LI, that is a logarithmic function times an inverse trigonometric one and computed by parts.

2018年2月28日 · I'm wondering if there are any examples where the integral is a straightforward integration by parts but is difficult or impossible using the LIATE order. calculus integration

2013年6月1日 · In another question of mine users proposed the LIATE or ILATE rule for partial integration. However, I have encountered a problem: $$ e^{-x}\\cos(x)$$ If I use the rule, I eventually get: $$ d(\\c...

2021年5月10日 · Alcantara, E. C.: On the Derivation of Some Reduction Formula through Tabular Integration by Parts. Asia Pacific Journal of Multidisciplinary Research 3 (2015) (1) 80-84 Alcantara, E. C.: Integrals of composite functions through tabular integration by parts. The problem of integration by parts is to make the right choice or to make the wrong ...

2017年2月1日 · It is a practical answer. A rigorous definition of complexity is far above the level of the original question. When I teach freshman calculus the students grasp what my advice about integration by parts means without anyone ever objecting that I did not offer a careful definition of complexity. $\endgroup$ –

In the case of algebraic, trigonometric and exponential functions both integration and differentiation don't change the nature of the function, so they come later in the ILATE order. Of course, this is just intuition and there are examples where you can violate this so called rule and still integrate by parts without any problems.