Can the Indefinite Integral of 1/(1+x^4) be Simplified?

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In summary, an integral is a mathematical concept used to find the total amount of a quantity over a given range by calculating the area under a curve in a graph. Common problems with integrals include finding the correct limits of integration and dealing with discontinuous functions. To solve these problems, one must identify the type of integral and use the appropriate integration method. Technology can also be used to solve integrals, but it is important to understand the concepts behind integration. Integrals are important in science for calculating important quantities and are used in various fields such as physics, chemistry, and engineering.
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hellais
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We are having problems solving the indefinite integral of the following function:
[tex]\frac{dx}{\sqrt[4]{1+x^4}}[/tex]
We tried the substitution [tex]t^4=x^4+1[/tex], but we got stuck.

Our professor tried solving it, but he also encountered difficulties.
Any suggestion is apreciated.

(wolfram alpha says that the integral is a hypergeometric function, but it must be simpler)
 
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  • #3
Hi hellais! :smile:

I think you just have to keep substituting again and again …

x2 = sinhu, a = tanhu … :rolleyes:
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is also known as the antiderivative of a function, and it is used to calculate the total amount of a quantity over a given range.

2. What are some common problems with integrals?

One common problem with integrals is finding the correct limits of integration. This refers to the upper and lower bounds of the range over which the integral is being calculated. Another problem can arise when the function being integrated is not continuous or has discontinuities within the range of integration.

3. How can I solve a problem with an integral?

To solve a problem with an integral, it is important to first identify the type of integral and the appropriate integration method to use. This could include substitution, integration by parts, or using special functions like trigonometric identities. It is also important to carefully choose the limits of integration and to check for any discontinuities in the function being integrated.

4. Can I use technology to solve integrals?

Yes, there are many tools and software available to help solve integrals. These include online calculators, graphing calculators, and computer programs. However, it is important to understand the concepts and methods behind integration before relying solely on technology for solutions.

5. Why are integrals important in science?

Integrals are important in science because they allow us to calculate important quantities such as area, volume, and mass. They are also used in many scientific applications such as physics, chemistry, and engineering to model and analyze real-world phenomena. Integrals are a fundamental tool in understanding and solving complex mathematical problems in science.

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