Is this a trig interval?

1. Mar 14, 2013

whatlifeforme

1. The problem statement, all variables and given/known data
Evaluate the integral.

2. Relevant equations
$\displaystyle\int \frac{1}{x^5 + 5} dx$

3. 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.

Last edited: Mar 14, 2013
2. Mar 14, 2013

eumyang

No. If you let u = x5/2, what would du equal, and can you make the substitution work?

3. Mar 15, 2013

whatlifeforme

how would i solve this then?

4. Mar 15, 2013

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?

5. Mar 15, 2013

Dick

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.