Head scratching integral calculus hw

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Homework Help Overview

The discussion revolves around integral calculus, specifically focusing on the integral of expressions involving exponential functions and polynomials, such as ∫x^3e^(x^7) dx and ∫xe^(x^7) dx. Participants are exploring the complexities of these integrals and the challenges faced in solving them.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss potential substitutions to simplify the integrals, with one suggesting a substitution involving square roots. There is also a clarification sought regarding the original expression's notation, questioning whether it is ∫3xe^(x^7) dx or ∫x^3e^(x^7) dx. Some express doubts about the straightforwardness of the integrals and mention the use of reduction formulas.

Discussion Status

The conversation is ongoing, with participants offering different approaches and clarifications. There is a recognition of the complexity of the integrals, and while some guidance has been provided, there is no clear consensus on the best method to proceed. The original poster's notation is under scrutiny, suggesting that clarification may be necessary for further progress.

Contextual Notes

There is a mention of potential typos in the original post, which may affect the interpretation of the problem. Additionally, there are implications that the original poster may not be expected to know advanced techniques such as gamma integral transformations, indicating a possible limitation in the scope of the homework assignment.

JasonJo
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hey guys, i need help on my integral calculus hw

2) int(x*3*e^(x^7)) dx
this one is just giving me insane problems
 
Last edited:
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1) Try the substitution:

u = (4-t)1/2

du = -dt / 2(4-t)1/2

Key thing here: you've got some expression of t and square root of some other expression involving t. Make a substitution to so that u is proportional to square root of t, and therefore t is in terms of u^2, and your integral now has u and u^2 in it. Much easier to work with. No square roots. Just polynomials. That's why I chose that substitution.
 
JasonJo said:
2) int(x*3*e^(x^7)) dx
this one is just giving me insane problems
Is this [tex]\int3 x e^x^7{dx}[/tex] or [tex]\int x^3 e^x^7{dx}[/tex]?

As you have it written, it's a very strange order for multiplication. Either way, it doesn't seem to be a simple, straight-forward answer. The only way I seem to have found so far requires a reduction formula.
 
For the integral
[tex]\int x \ e^{x^{7}} dx[/tex]

view the first attachement.

For the integral
[tex]\int x^{3} \ e^{x^{7}} dx[/tex]

view the second...

Daniel.
 

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dextercioby said:
For the integral
[tex]\int x \ e^{x^{7}} dx[/tex]

view the first attachement.

For the integral
[tex]\int x^{3} \ e^{x^{7}} dx[/tex]

view the second...

Daniel.
If he's still doing normal substitutions, it is doubtful that he is expected to know gamma integral transformations. I think there's a typo in the original poster's post.
 
Then let him correct it,else his entire visit to PF has been useless...

Daniel.
 

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