# Integrating x^4

## Homework Statement

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

Arctan?

## 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.

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Char. Limit
Gold Member
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!

Mark44
Mentor

## Homework Statement

http://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmex10/alpha/144/char5A.png [Broken](8x)/(x4+1)dx
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:
$$\int \frac{8x dx}{x^4 + 1}$$
mshiddensecret said:

Arctan?

## 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:
LCKurtz