Solving the Equation: 8x/(x^4+1)dx

[mshiddensecret]

Homework Statement

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

Homework Equations

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.

 

[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!

 

[Mark44]

Homework Statement

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

A bit of LaTeX would be very helpful.
Here's your integral in LaTeX:
$$ \int \frac{8x dx}{x^4 + 1}$$

This is what the LaTeX script I used looks like:

$$ \int \frac{8x dx}{x^4 + 1}$$

Homework Equations

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.

 

[LCKurtz]

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