What kind of Integration to use

In summary, the problem is to solve the integral of (x^2)/(e^(x/2)) and the attempt at a solution involves considering u substitution or integration by parts, with a suggestion to rewrite the integrand as (1/e^(x/2))x^2. The suggestion is also made to write (1/e^(ax)) as e^(-ax) when a > 0.
  • #1
jdawg
367
2

Homework Statement


∫(x2)/(ex/2) dx


Homework Equations





The Attempt at a Solution


I'm not completely sure where to start on this one. I don't see any sort of u substitution working, would integration by parts be a good idea? Maybe let u=x2 and dv=(1/ex/2) ?
 
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  • #2
jdawg said:

Homework Statement


∫(x2)/(ex/2) dx


Homework Equations





The Attempt at a Solution


I'm not completely sure where to start on this one. I don't see any sort of u substitution working, would integration by parts be a good idea? Maybe let u=x2 and dv=(1/ex/2) ?

Don't ask: just go ahead and try it for yourself!

BTW: you should always write ##1/e^{ax}## as ##e^{-ax}## whenever ##a > 0##.
 
  • #3
Ray Vickson said:
Don't ask: just go ahead and try it for yourself!

BTW: you should always write ##1/e^{ax}## as ##e^{-ax}## whenever ##a > 0##.

Haha ok, thanks! It doesn't look as scary now with that e rewritten :)
 

Related to What kind of Integration to use

1. What is integration in science?

Integration in science refers to the process of combining different pieces of information or data to form a more complete understanding of a system or phenomenon. It involves incorporating various factors, theories, and perspectives to create a unified picture.

2. What are the different types of integration?

There are several types of integration in science, including mathematical, conceptual, interdisciplinary, and methodological. Mathematical integration involves combining equations or data sets to solve complex problems. Conceptual integration involves merging different theories or ideas to explain a phenomenon. Interdisciplinary integration involves incorporating knowledge and methods from multiple disciplines. Methodological integration involves using various research methods to answer a specific question or problem.

3. How do you decide which type of integration to use?

The type of integration to use depends on the specific research question or problem at hand. For example, if the question involves solving a mathematical equation, mathematical integration would be appropriate. If the question involves understanding a complex phenomenon, conceptual or interdisciplinary integration may be necessary. It is important to carefully consider the different types of integration and determine which would be most effective in addressing the research question.

4. What are the benefits of using integration in scientific research?

Using integration in scientific research allows for a more comprehensive understanding of complex systems or phenomena. It also allows for a more robust and complete analysis, as different perspectives and methods are incorporated. Additionally, integration can lead to new insights and innovations by combining ideas and approaches from different fields.

5. What are some challenges of using integration in scientific research?

One challenge of using integration in scientific research is the potential for conflicting or inconsistent results from different sources. It can also be time-consuming and complex to incorporate multiple factors or perspectives. Additionally, interdisciplinary integration may require collaboration and communication between researchers from different fields, which can present challenges in terms of coordination and understanding of different terminology and methods.

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