Try and intergrate this

  • Thread starter thomas49th
  • Start date
In summary, when integrating \frac{x}{\sqrt(1-4x^{2})}dx, a change of variable u=1-4x^2 can be used to simplify the integration process. It can be spotted by looking for a multiple of the derivative of something else in the numerator.
  • #1
[tex]\int \frac{x}{\sqrt(1-4x^{2})}dx[/tex]
If it was just a constant on top I could turn it into an arcsin, but there is a stupid x there, so not to sure. I though about intergrating by parts, but their must be an easier method than that?

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  • #2
Well, you could make the x above "disappear" by doing a change of variable u=4x².
  • #3
Try the substitution u=1-4x^2.
  • #4
cheers thanks got it!

btw, how do you spot a substitution? There is a rule(s) for it. When somthingis the product or differential of somthing else?

Thanks :)
  • #5
When you see a multiple of the derivative of something else in the numerator, it's a dead giveaway for a substitution.

1. What is the purpose of integrating this?

The purpose of integrating this is to combine different elements or components into a cohesive whole in order to achieve a desired outcome or result.

2. How do you determine which parts to integrate?

The process of determining which parts to integrate involves conducting research, analyzing data, and evaluating the potential benefits and drawbacks of each component. It also involves considering the overall goals and objectives of the integration.

3. What are the benefits of integrating this?

Integrating this can lead to increased efficiency, improved functionality, and better overall performance. It can also help to streamline processes and reduce costs.

4. What challenges may arise during the integration process?

Some challenges that may arise during the integration process include compatibility issues between different components, technical limitations, and potential conflicts between different systems or processes.

5. What are some best practices for successful integration?

Some best practices for successful integration include clearly defining the goals and objectives, conducting thorough testing and troubleshooting, and involving all relevant stakeholders in the process. It is also important to have a contingency plan in case any issues arise during the integration.

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