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Problem with INTEGRALS

  1. Mar 1, 2008 #1
    I cant' solve this two integrals :

    [tex]\int[/tex] (ln x)[tex]^{2}[/tex]

    [tex]\int[/tex] cos[tex]^{4}[/tex](x)
  2. jcsd
  3. Mar 1, 2008 #2
    You do both of them by parts.

    You can rewrite this as:

    [tex]\int (lnx)(lnx) dx[/tex]


    u = lnx
    dv = lnx dx

    To integrate lnx dx, you have to do it by parts again. After that, it is very simple.

    Again, you can rewrite this integral as something you could do by parts.

    [tex]\int cos^{3}xcosx dx[/tex]

    u = cos^{3}x
    dv = cosx dx

    Last edited: Mar 1, 2008
  4. Mar 1, 2008 #3
    The answer of the first question is x*((ln x)^2) - 2x*(ln x) + 2x , you can check your answer.

    As for the second one, my approach would be to write the integrand as
    ((cos x)^2)*(1 - ((sin x)^2)) , and then finish this off by using the trigonometric identities for (cos x)^2 and sin 2x .

    Lastly, try to use as many problems as you can in your spare time and take notes for choosing the most suitable method in a problem you encounter.
  5. Mar 2, 2008 #4
    Hi , thank you very much for the answers !!

    By the way , I just can't solve another one :

    [tex]\int[/tex]( x[tex]^{2}[/tex]-2x+3)lnx dx
  6. Mar 2, 2008 #5


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    Staff Emeritus
    Science Advisor

    Again, straight forward by parts: let u= ln(x), dv= (x2- 2x+ 3)dx.
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