Results 1 to 3 of 3

Math Help - Need help with Trig Integral

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    2

    Need help with Trig Integral

    Hello,

    I've been trying to work the following problem, but I am getting lost from the start. I'm pretty sure if I could get it started I wouldn't have a problem with it.

    (1+4cot(x))/(4-cot(x))

    Thanks for any help you can offer!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
     \frac{1 + 4\cot(x)}{4 - \cot(x) }

     = \frac{ \tan(x) \cdot (1 + 4\cot(x) )}{ \tan(x) \cdot ( 4 - \cot(x))}

     = \frac{ \tan(x) + 4 }{ 4\tan(x) - 1 }

     = -\frac{ \tan(x) + 4}{ 1 - 4\tan(x) }

    then use the formula

     \tan(A + B) = \frac{ \tan(A) + \tan(B) }{ 1 - \tan(A)\tan(B) }

    By substituting  A = x , B = \tan^{-1}(4)

    We obtain  \frac{1 + 4\cot(x)}{4 - \cot(x) } = - \tan( x + \tan^{-1}(4) )


    Wow , it is actually a tagent function so the integral is log. function :

     \ln{ \left [ \cos( x + \tan^{-1}(4) ) \right ]} + C
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    2
    Thank you!

    Multiplying by 1 is something I would've never seen in my life. I always seem to forget that as an option.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig integral.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 13th 2011, 05:08 PM
  2. Trig Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 1st 2010, 06:09 PM
  3. trig integral 1/(1-sin(x)cos(x))
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 26th 2010, 07:29 AM
  4. Integral trig
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 26th 2010, 03:59 AM
  5. Another trig integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 5th 2009, 08:50 PM

Search Tags


/mathhelpforum @mathhelpforum