1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral of 1/(x^2 + 36)dx When and how to draw triangle?

  1. Mar 4, 2013 #1
    1. ∫1/(x2 + 36)dx


    2. I started by trying a trig substitution.

    The normal form, "a2 + x2, x=(a)tan(θ)," I thought could be reversed here:

    x2 + 62
    x = 6tan(θ)
    dx= 6sec2θdθ


    ∫1/[(6tanθ)2 + 36] = ∫1/[36(tan2θ + 1)]*6sec2θdθ

    = ∫1/[36sec2θ]*6sec2θdθ

    = ∫1/6dθ

    = (1/6)θ + C

    From before, θ= arctan(1/6(x))

    1/6(arctan(1/6(x))) + C

    In my class, sometimes the professor says we need to draw a triangle to figure out the value...

    I'm a little confused about that. Would I need to draw a triangle here to figure out an exact value?

    Since tan(1/6(x))=θ, do I draw a triangle and say the side opposite θ equals 1, and the adjacent side equals 6?

    And then do I figure out from that what arctanθ equals...?
    Would you help me with the triangle thing?

    Thank you so much! :D
     
  2. jcsd
  3. Mar 4, 2013 #2
    What value do you need to figure out?
     
  4. Sep 20, 2015 #3
    I used partial fractions... But it's a bit odd

    X^2+36=(x+6i)(x-6i)

    1=A(x+6i) + B(x-6i)
    A= -1/12i , B = 1/12i
    1/i= -i
    i/12 Integ 1/(x+6i) -1/(x-6i) dx

    i/12 ln |(x+6i)/(x-6i)| + c
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integral of 1/(x^2 + 36)dx When and how to draw triangle?
Loading...