Can the Integral of 1/(x^5+5) be Evaluated Analytically?

[whatlifeforme]

Homework Statement

Evaluate the integral.

Homework Equations

\displaystyle\int \frac{1}{x^5 + 5} dx

The Attempt at a Solution

could i turn this into an x^2 + a^2 --> arctan

for example: \frac{1}{x^(5/2)^2 + \sqrt{5}^2} dx

note that is: x^{5/2} squared.

 

[eumyang]

Your thread title says, "Is this a trig interval?"

Homework Statement

Evaluate the integral.

Homework Equations

\displaystyle\int \frac{1}{x^5 + 5} dx

The Attempt at a Solution

could i turn this into an x^2 + a^2 --> arctan

for example: \frac{1}{x^(5/2)^2 + 5} dx

No. If you let u = x^5/2, what would du equal, and can you make the substitution work?

 

[whatlifeforme]

how would i solve this then?

 

[eumyang]

Wolframalpha gives a very complicated answer, so I'm not sure this integral can be evaluated using the usual analytic methods. Maybe you copied the problem wrong?

 

[Dick]

Wolframalpha gives a very complicated answer, so I'm not sure this integral can be evaluated using the usual analytic methods. Maybe you copied the problem wrong?

One analytic way to do it is to factor x^5+5 completely over the complex numbers and then use partial fractions. Then carefully track how the complex parts cancel. It's a MASSIVE pain in the neck. I could start it but I would probably never finish. Certainly wouldn't assign it as a problem.