Not sure how to proceed with uv-vdu integral

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In summary, a UV-VDU integral is an integral that involves both ultraviolet and vacuum ultraviolet regions of the electromagnetic spectrum. It differs from a regular integral in that it includes a wider range of frequencies and is more complex. UV-VDU integrals are important in scientific research as they allow for accurate calculations of energy levels in atoms and molecules. Common techniques for solving these integrals include perturbation theory, variational methods, and numerical methods such as Monte Carlo simulations. There are various resources available for learning more about UV-VDU integrals, but a strong foundation in mathematics is necessary for understanding them.
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mushroomyo
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hi, I am trying to find the integral of x^3sqrt(1+x^4)dx
i set it up like this:

u=x^3 dv=sqrt(1+x^4)
du = 3x^2dx v=2/3(1+x^4)^(3/2)

and using uv-integralvdu i get

(2/3x^3(1+x^4)^3/2) - 2/3integral((1+x^4)^(3/2)3x^2)dx

i know that in the end, the integral should equal 1/6(x^4+1)^(3/2) but i don't know how to get there from where i stopped...

help?
 
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  • #2
Integration by parts is not the best way to do this integral. Try a simple u-substitution:

u = 1 + x4.
 

1. What is a UV-VDU integral?

A UV-VDU integral is an integral that involves both ultraviolet (UV) and vacuum ultraviolet (VDU) regions of the electromagnetic spectrum. It is commonly used in physics and chemistry to calculate the energy of a system.

2. How is a UV-VDU integral different from a regular integral?

A UV-VDU integral differs from a regular integral in that it involves a wider range of frequencies, including both the UV and VDU regions. This makes it more complex and requires specialized techniques to solve.

3. What is the importance of UV-VDU integrals in scientific research?

UV-VDU integrals are important in scientific research because they allow scientists to accurately calculate the energy levels of atoms and molecules. This information is crucial in understanding the behavior of matter and can lead to advancements in various fields, such as material science and pharmaceuticals.

4. What are some common techniques for solving UV-VDU integrals?

Some common techniques for solving UV-VDU integrals include perturbation theory, variational methods, and numerical methods such as Monte Carlo simulations. These techniques involve breaking down the integral into smaller, more manageable parts and approximating the solution.

5. Are there any resources available for learning more about UV-VDU integrals?

Yes, there are many resources available for learning more about UV-VDU integrals. These include textbooks, online courses, and scientific journals. It is important to have a strong foundation in mathematics, particularly calculus and differential equations, before attempting to understand UV-VDU integrals.

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