Definite integral of square root+cube root

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Discussion Overview

The discussion centers around the evaluation of a definite integral involving the square root and cube root functions. Participants explore methods for solving the integral, including substitution and the possibility of expressing the solution in terms of elementary functions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in solving the integral using substitution and questions whether it can be solved using elementary functions.
  • Another participant emphasizes the importance of showing progress in problem-solving to facilitate better assistance.
  • A different participant asserts that the integral cannot be solved using elementary functions.
  • One participant suggests applying a specific formula related to integrals involving square roots.

Areas of Agreement / Disagreement

There is no consensus on the solvability of the integral using elementary functions, as some participants believe it cannot be solved this way while others have not yet expressed a definitive stance on the matter.

Contextual Notes

Participants have not provided detailed steps or assumptions regarding their approaches, and the discussion includes unresolved aspects of the integral's evaluation.

tree21c
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Dear all,

Please solve this integral:

View attachment 7576

I tried integral by substitution, but failed.

Wolframalpha shows the result is 6, but I don't know how to proceed it.

Can it be solved by elementary function?
 

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Hello and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
tree21c said:
Can it be solved by elementary function?

No; I don't think so.
 
Try applying the formula

$$\int\sqrt {x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{a^2}{2}ln(x+\sqrt {x^2+a^2})$$
 

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