Integration, where have i gone wrong?

• Dell
In summary, the conversation discusses the problem of finding the integral of arctan(sqrt(x)) and the mistake made in solving it. It also proposes a possible solution using the substitution method.
Dell
$$\int$$arctg$$\sqrt{x}$$dx

using$$\int$$udv=uv-$$\int$$vdu

dv=dx
v=x

u=arctg$$\sqrt{x}$$
du=u'dx=[1/(1+x)]dx

$$\int$$arctg$$\sqrt{x}$$dx=xarctg$$\sqrt{x}$$ - $$\int$$x*[1/(1+x)]dx
=xarctg$$\sqrt{x}$$ - $$\int$$[x/(1+x)]dx
=xarctg$$\sqrt{x}$$ - $$\int$$1-[1/(1+x)]dx
=xarctg$$\sqrt{x}$$ - x+ln|x+1|+c
but this is wrong, where have i made the mistake?

The derivative of arctan(sqrt(x)) is (1/(1+x))*1/2(sqrt(x)), you can still solve this question by looking at:
sqrt(x)/(1+x)dx=2/3(d(x^3/2))/(1+(x^3/2)^(2/3))
sqrt(x)dx=2/3d(x^3/2)
and the integral of dy/(1+y^2/3)
can be solved by writing y^1/3=sinh(t).

I am not sure this will work, but I think that there is no easy way here.

thanks

1. What is integration and why is it important?

Integration is the process of bringing together different parts to form a whole. In science, it is often used to combine different data or theories to gain a comprehensive understanding of a phenomenon. It is important because it allows us to make connections and draw conclusions that may not be apparent when looking at individual components.

2. How do I know if I have made a mistake in my integration process?

Mistakes in integration can manifest in different ways, such as inconsistent data, illogical conclusions, or incomplete understanding. It is important to carefully check your work and make sure all the pieces fit together logically. If you are unsure, seeking feedback from peers or consulting with experts can help identify any errors.

3. What are some common challenges in integration and how can I overcome them?

Some common challenges in integration include dealing with complex or conflicting data, finding the right balance between simplicity and complexity, and ensuring all aspects are considered. To overcome these challenges, it is important to approach integration with a clear and organized plan, critically evaluate all data and sources, and be open to revising and adjusting your approach as needed.

4. How can I ensure that my integration is accurate and reliable?

To ensure accuracy and reliability in integration, it is important to use credible and reputable sources, carefully evaluate and analyze all data, and consider alternative explanations or perspectives. Additionally, seeking feedback and validation from other experts in the field can help ensure the accuracy of your integration.

5. How can I effectively communicate my integration to others?

Effective communication of integration involves clearly and concisely presenting your findings and conclusions, using visuals or examples to aid understanding, and addressing any potential questions or criticisms. It is also important to consider the audience and tailor your communication to their level of understanding and familiarity with the topic.

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