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Integrating x^4

  1. Sep 25, 2014 #1
    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. jcsd
  3. Sep 25, 2014 #2

    Char. Limit

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    Gold Member

    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!
     
  4. Sep 25, 2014 #3

    Mark44

    Staff: Mentor

    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 (Text):
    $$ \int \frac{8x dx}{x^4 + 1}$$
     
    Last edited by a moderator: May 7, 2017
  5. Sep 25, 2014 #4

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

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