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Evaluate Integral

  1. Jan 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Evaluate [tex]\int[/tex][tex]\frac{5x+5}{x^2+1}[/tex]


    2. Relevant equations



    3. The attempt at a solution
    5*[tex]\int[/tex][tex]\frac{x+1}{x^2+1}[/tex]

    5*[tex]\int[/tex][tex]\frac{x}{x^2+1}[/tex]+[tex]\int[/tex][tex]\frac{1}{x^2+1}[/tex]

    The first term's value is (1/2)ln(x2+1) but what is the second term?
     
  2. jcsd
  3. Jan 14, 2010 #2
    for the second term, consult a table of integrals
     
  4. Jan 14, 2010 #3

    Mark44

    Staff: Mentor

    arctan(x)
    Don't forget that both antiderivatives are multiplied by 5, and don't forget your constant of integration.
     
  5. Jan 14, 2010 #4
    We were never instructed to refer to any tables, and I don't suspect that we should have to. And we haven't done anything as complex as arctan(x) yet.

    The method to evaluate the integral should be fairly simple. It's the beginning of a calculus 2 class.
     
  6. Jan 14, 2010 #5
    Yes well that doesn't really change the fact that the antiderivative of 1/(1+x^2) is arctan(x) does it? And arctan(x) is not that complex, it's actually quite simple.
     
  7. Jan 14, 2010 #6
    I'm not doubting that the antiderivative of 1/(x^2+1) is arctan(x). That's just not the method my teacher wants me to use because haven't learned inverse trig functions yet. Maybe I went about the problem the wrong way from the beginning?
     
  8. Jan 14, 2010 #7

    Dick

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    You did it exactly right. If you don't know the antiderivative is arctan(x) then you have to derive it using a trig substitution. Put x=tan(u).
     
    Last edited: Jan 14, 2010
  9. Jan 15, 2010 #8

    vela

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    Staff Emeritus
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    You probably did learn how to differentiate arctan(x) last semester. If you recognized the integrand was the derivative, you could just write the answer down for the second integral.

    Have you learned using trig substitutions to do integrals yet?
     
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