Integration of (3x^2+1)^(3/2) - Step-by-Step Solution

In summary, integration evaluation is a process used by scientists to assess the effectiveness of integrating new information or systems into existing ones. It is important because it allows scientists to determine the success of an integration and make decisions about future integrations. Methods used in integration evaluation include surveys, interviews, case studies, and quantitative data analysis. The success of integration is evaluated based on its effectiveness, impact on the existing system, and stakeholder satisfaction. However, challenges in integration evaluation include collecting reliable and valid data, measuring impact, and determining causality due to the dynamic and complex nature of scientific research.
  • #1
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Homework Statement



[tex]\int x(3x^2+1)^\frac{3}{2}[/tex]

Homework Equations



The Attempt at a Solution



[tex]u=3x^2+1[/tex]

[tex]du=6x dx[/tex]

[tex]\frac{dx}{6}=xdx[/tex]

[tex]\int\frac{du}{6} u^\frac{3}{2}[/tex]

[tex]\frac{1}{6}\int u^\frac{3}{2}du[/tex]

[tex]\frac{1}{6} \frac{u^\frac{5}{2}}{\frac{5}{2}}[/tex]

[tex]\frac{5}{12}u^\frac{5}{2}[/tex]

[tex]\frac{5}{12}(3x^2+1)^\frac{5}{2}[/tex]
 
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  • #2
[tex]\frac{1}{6} \frac{u^\frac{5}{2}}{\frac{5}{2}}[/tex] =/= [tex]\frac{5}{12}u^\frac{5}{2}[/tex]
 
  • #3
[tex]\frac{2}{30}u^\frac{5}{2}[/tex] ?
 
  • #4
Yeah looks right
 

1. What is integration evaluation?

Integration evaluation is a process used by scientists to assess the effectiveness of integrating new information or systems into existing ones. It helps determine whether the integration has been successful and whether it has achieved its intended goals.

2. Why is integration evaluation important?

Integration evaluation is important because it allows scientists to determine whether the integration has been successful and whether it has achieved its intended goals. This information is crucial in making decisions about future integrations and can help improve the overall effectiveness of scientific research.

3. What are some methods used in integration evaluation?

There are various methods used in integration evaluation, including surveys, interviews, case studies, and quantitative data analysis. Each method has its own strengths and limitations, and scientists may use a combination of methods to get a comprehensive understanding of the integration.

4. How is the success of integration evaluated?

The success of integration is evaluated based on its effectiveness in achieving the intended goals, its impact on the existing system, and the satisfaction of stakeholders involved in the integration. This includes considering factors such as cost, time, and user experience.

5. What are some challenges in integration evaluation?

Some challenges in integration evaluation include collecting reliable and valid data, measuring the impact of integration on different aspects, and determining the causality between the integration and its outcomes. Additionally, the dynamic and complex nature of scientific research can make it difficult to fully evaluate the success of an integration.

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