Integrating x^4

  • #1

Homework Statement



http://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmex10/alpha/144/char5A.png [Broken](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.
 
Last edited by a moderator:

Answers and Replies

  • #2
Char. Limit
Gold Member
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This is slightly tricky, yes. The key is to let [itex]tan(\theta) = x^2[/itex]. Then the differential will be [itex]sec^2(\theta) d\theta = 2x dx[/itex] and the rest of it will be some trig identities. You can do it!
 
  • #3
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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.
Here's your integral in LaTeX:
$$ \int \frac{8x dx}{x^4 + 1}$$

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

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.
 
Last edited by a moderator:
  • #4
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
Or you can try ##u=x^2## and if you know the basic arctan formula you are home free.
 

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