Ace school

with brainly

  • Get help from millions of students
  • Learn from experts with step-by-step explanations
  • Level-up by helping others

A community for students.

How to integrate this

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
|dw:1356849576104:dw|
seems it doesn't have any closed form... http://www.wolframalpha.com/input/?i=integral+%28x%5E%281%2Fn%29-1%2Fx%5En%29%5En
are we assuming n is a constant?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

\[=\int\limits \left( \frac{x^{\frac{n^2+1}{n}}-1}{x^n} \right)^ndx\]
I see 2 approaches. Either do something like: u=x^(n^2+1)/n - 1 and solve for x in terms of u; then find dx, etc. Or try integration by parts by letting u=(...)^(n-1), dv=(...)^1dx; from there you could try to establish a pattern for n. But it is more than likely unable to be solved in closed form.
@abb0t We know \(n\) is constant... but it would help to know if \(n\) is just a natural number or any real number.
For some reason things like this want me to try binomial theorem, lol I'm just a bit crazy I guess.
crazy
If you assume \(n \in \mathbb{N}\) you can just use binomial theorem and get an answer in summation notation.
Then if you're lucky, you might be able to simplify it from there, into something algebraic, but there is no guarantee it will happen.
There is no reason to be afraid of summations when it comes to certain integrals... there is no guarantee the function isn't transcendental.
=\[\int\limits \sum_{k=0}^{\infty} \left(\begin{matrix}n \\ k\end{matrix}\right)(x^{\frac{1}{n}})^{n-k}x^{-nk}dx\] My only question with doing this is that in the binomial theorem the don't make mention of things of the form: \[(\alpha(n)+\beta(n))^n\] Where alpha and beta are numbers that depend on n.
I would assume it doesn't matter.
And that last x should have an (-1)^k also.

Not the answer you are looking for?

Search for more explanations.

Ask your own question