# Integrating x^4

1. Sep 25, 2014

### mshiddensecret

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

http://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmex10/alpha/144/char5A.png [Broken](8x)/(x4+1)dx

2. Relevant equations
Arctan?

3. The attempt at a solution

I tried using subsitution with x^4+1 but it will only derive to 4x^3 which cannot get rid of the 8x on top.

Last edited by a moderator: May 7, 2017
2. Sep 25, 2014

### Char. Limit

This is slightly tricky, yes. The key is to let $tan(\theta) = x^2$. Then the differential will be $sec^2(\theta) d\theta = 2x dx$ and the rest of it will be some trig identities. You can do it!

3. Sep 25, 2014

### Staff: Mentor

A bit of LaTeX would be very helpful.
$$\int \frac{8x dx}{x^4 + 1}$$

This is what the LaTeX script I used looks like:
Code (Text):
$$\int \frac{8x dx}{x^4 + 1}$$

Last edited by a moderator: May 7, 2017
4. Sep 25, 2014

### LCKurtz

Or you can try $u=x^2$ and if you know the basic arctan formula you are home free.