# Homework Help: 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.