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Integrating tan(^4)x-sec(^4)x

  1. Jul 3, 2012 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    I looked online and it gave a really simple method to solve it and it ended up with the solution
    x-2tan(x)
    I took a really weird approach and I'm not sure if my answer is right, and I'm hoping if someone could take the same approach and confirm if I did it correctly.
    I basically separated the integral into 2 separate integrals and got a solution.
    ∫tan(^4)xdx-∫sec(^4)xdx

    When I was done, I got the answer of
    (tan(^3)x)/3-2tanx-x-(tan(^2)x)/2
     
  2. jcsd
  3. Jul 3, 2012 #2
    You can always differentiate your answer and see if you get the original integrand.
    However, the answer you got isn't equivalent to the answer x - 2tan x.
     
  4. Jul 4, 2012 #3
    You might want to try simplifying tan^4x-sec^4x first.
     
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