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Fun integrals to try

  1. Nov 10, 2015 #1
    Hey folks,

    found a couple of interesting integrals and was able to solve one of them ANALYTICALLY! That means no numerical solutions needed.

    $$\int_{0}^{\frac{\pi}{2}} \frac{1}{1+(tan(x))^{\sqrt{2}}} dx$$

    $$\int \frac{1}{1+e^{\frac{1}{x}}} dx$$

    The first one I solved and will reveal analytic solution if no one can get it (it should be $$\frac{\pi}{4}$$).

    Have fun!

    To moderators: These are not homework or test problems, both of them are either from an old math olympiad and an old research paper.
     
  2. jcsd
  3. Nov 11, 2015 #2

    jedishrfu

    Staff: Mentor

    Interesting integral, I tend to use my math handbook and just look these things up. However a method I learned recently was parametric integration. I don't know if that's what you used but I'll share a reference on it here in the interest of learning about new things:

    http://www.maa.org/sites/default/files/268948443847.pdf
     
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