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Please Help Integration!

  1. Feb 6, 2008 #1
    Please Help!! Integration!

    can anyone help me solve the following integration? thanks a lot.

    [tex]\int[/tex] [tex]x^5[/tex]cos[tex](x^3)[/tex] dx
     
  2. jcsd
  3. Feb 6, 2008 #2

    mjsd

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    you really should show some more effort. ie. show us what you have tried, what you know and tell us what you have problems with.


    hint: try look for a substitution to make the integrand look nicer, then you can try by parts.
     
  4. Feb 6, 2008 #3
    I have tried to do it by part.

    If I make [tex] u=cos(x^3), dv=x^5 dx [/tex], the grade of x, which is in the [tex] cos(x^3) [/tex], won't be reduce.

    If I make [tex] u=x^5, dv=cos(x^3) dx [/tex], I can't solve the [tex] \int cos(x^3) dx[/tex].

    I have thought if there is some way to make it look nicer (like [tex]u=x^3[/tex] ),but I still can't work out a better substitution.

    Could you give me some more advice?
     
  5. Feb 6, 2008 #4
    try
    [tex]u=x^3,dv=x^2\cos(x^3)dx[/tex]

    have you learned partial substitution ?
     
  6. Feb 6, 2008 #5

    mjsd

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    here I suggested a two-step process,
    substitiion: u = x^3 seems ok
    then by parts in new variable

    then put answer back in x.
     
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