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#method

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Félicien Breton 🍉 🔻 🌱

On the neocons all over again – Amir Tibon in Haaretz:
The experiment would ‘go something like this: American companies will begin operating in southern Gaza, under the supervision of the Israeli military, in a "humanitarian compound" surrounded by barbed wire. Two million Gazan citizens will be concentrated in this compound to get food and aid, while Israel will take over the rest of Gaza and use the pressure put on Gaza's population in order to topple the Hamas regime.’
(…)
‘If all this sounds familiar to you, that means you've probably lived through the Iraq War and the "happy" days of American contractors operating under military guidance in an attempt to "separate the local population from the terrorists" and replace the regime, but it's unclear with what exactly.’
(…)
‘Two decades later, they are promoting their Gaza plan in similar fashion – and so far, despite all the rage about the "neocons disrupting his agenda," the president seems to buy it.’

arnongrunberg.com/now/blog/180

www.arnongrunberg.comMany
#GazaMethod#Hamas#neocons
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Emmanuel José García

𝐁𝐢𝐠 𝐔𝐩𝐝𝐚𝐭𝐞 𝐨𝐧 𝐌𝐲 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐓𝐞𝐜𝐡𝐧𝐢𝐪𝐮𝐞!

I'm excited to share the latest development in what I initially called the "Exponential Substitution Method." Moving forward, this approach will be known as the Unified Substitution Method because it unifies several powerful techniques for tackling integrals, including:

𝟏. 𝐂𝐨𝐦𝐩𝐥𝐞𝐱 𝐄𝐱𝐩𝐨𝐧𝐞𝐧𝐭𝐢𝐚𝐥𝐬 𝐟𝐨𝐫 𝐓𝐫𝐢𝐠𝐨𝐧𝐨𝐦𝐞𝐭𝐫𝐢𝐜 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧𝐬: Originally used to simplify integrals by expressing sine and cosine in terms of exponential functions, this technique is extended to handle irrational integrands.

𝟐. 𝐖𝐞𝐢𝐞𝐫𝐬𝐭𝐫𝐚𝐬𝐬 𝐒𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐢𝐨𝐧: Traditionally used to transform rational expressions of trigonometric functions into purely rational ones, this is now extended and incorporated into my method to simplify irrational expressions as well.

𝟑. 𝐄𝐮𝐥𝐞𝐫 𝐒𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐢𝐨𝐧𝐬: These classic substitutions, designed for certain irrational integrands, are also integrated into the Unified Substitution Method. Interestingly, I’ve found that the extended Weierstrass substitution often simplifies integrals into rational forms nearly identical to those obtained through Euler’s substitutions.

By unifying and extending these techniques, this method becomes a comprehensive tool capable of handling a wide variety of integrals, including some of the most challenging irrational ones.

This approach represents a significant step forward in simplifying integral calculus and demonstrates the deep interconnections between these classic methods. I’m excited to see how this can benefit students, researchers, and enthusiasts alike.

To stay tuned for more examples and demonstrations of this method, here is my blog post on it:

geometriadominicana.blogspot.c

#math#calculus#integration
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