Results 1 to 9 of 9

Math Help - integration using arctan

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    69

    integration using arctan

    could anyone possibly help me with this problem:

    integral of: 3/((x^2)+2x+5)???

    The only thing I know is that you have to complete the square for the denominator and that gives me:

    (x+1)^2 + 4.

    I also know that this type of integral uses some variation of arctan, but after this, I'm completely lost.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    Next step: make the substitution x+1=2\tan\varphi.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    69
    could you explain why that substitution is made? or is it just common knowledge?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    The standard arctan form is \frac1{1+x^2}, somehow, you just need to turn your integral into that form.

    Forget what I said before, I had my head in another place; the substitution it's actually x+1=2u\implies dx=2\,du so (x+1)^2+4 becomes 4u^2+4=4(u^2+1) and the integral is \frac12\int\frac{du}{1+u^2}=\frac12\arctan u+k.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2008
    Posts
    69
    ok, that all makes sense to me except for the substitution still. I'm sorry if I am bugging you, but I just want to make sure I understand. Why is it 2u and not u?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    I'll put another example to see if you get it:

    \int\frac{dx}{x^2+6x+12}, what's the proper substitution?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Oct 2008
    Posts
    69
    is it: sqrt(3)u = x+3??
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    Jackpot!!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Oct 2008
    Posts
    69
    Cool, ok I get it now. wow thank you sooo much! you really helped me out.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration with arctan
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 10th 2010, 04:35 PM
  2. Integration Into Arctan
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 6th 2010, 12:37 PM
  3. integration with arctan
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 18th 2009, 08:26 PM
  4. Tricky integration (arctan x^2)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 4th 2008, 02:53 AM
  5. arctan integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 13th 2008, 07:13 PM

Search Tags


/mathhelpforum @mathhelpforum