- #1
irony of truth
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How do I integrate this? e^[1 / (1 + t)] dt?
Can I Integrate e^[1 / (1 + t)] dt Numerically?
- Thread starter irony of truth
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In summary, The function e^[1 / (1 + t)] dt cannot be integrated nicely and numerically is the best approach. There is a connection between Ei (exp.integral) and Si (sinus integral), and you can refer to the Wolfram website for more information. The code for this function has more characters than "numerically".
- #2
arildno
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Short answer: Numerically.
There exist no nice anti-derivative to this function.
There exist no nice anti-derivative to this function.
- #3
irony of truth
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I see... so this could be the same case as that of (sinx / x) dx...
- #4
- 13,366
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Long answer:
[tex]\allowbreak \left( 1+x\right) e^{\frac 1{1+x}}+\func{Ei}\left( 1,-\frac 1{1+x}\right) +C [/tex]
Daniel.
[tex]\allowbreak \left( 1+x\right) e^{\frac 1{1+x}}+\func{Ei}\left( 1,-\frac 1{1+x}\right) +C [/tex]
Daniel.
- #5
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irony of truth said:
Yes,there is a connection between Ei (exp.integral) and Si (sinus integral).
Daniel.
P.S.Chack the wolfram site for more.
- #6
arildno
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I'd rather say apparently short answer..dextercioby said:
- #7
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Yes,"apparently" is a well placed word...
Daniel.
P.S.Anyways,the # of characters from the code is much bigger than the # of letters from "numerically"...
Daniel.
P.S.Anyways,the # of characters from the code is much bigger than the # of letters from "numerically"...
FAQ: Can I Integrate e^[1 / (1 + t)] dt Numerically?
What is integration?
Integration is the process of combining different parts or elements to create a whole. In science, it can refer to the incorporation of new knowledge or techniques into existing systems or theories.
Why is integration important in science?
Integration allows scientists to connect and build upon existing knowledge and theories, leading to a more comprehensive understanding of a particular subject. It also allows for the development of new ideas and technologies.
What are some challenges with integration in science?
Some challenges with integration in science include finding ways to bridge different disciplines and perspectives, ensuring accurate and consistent data collection and analysis, and addressing potential conflicts between different theories or models.
How can scientists overcome these challenges?
To overcome challenges with integration, scientists can collaborate and communicate with experts from different fields, use standardized methods and protocols for data collection and analysis, and critically evaluate and compare different theories and models.
What are the benefits of successful integration in science?
Successful integration in science can lead to breakthroughs and advancements in research, improved understanding of complex systems, and the development of innovative solutions to real-world problems. It can also promote interdisciplinary collaboration and foster a more holistic approach to scientific inquiry.