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Math Help - Just another integration problem

  1. #1
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    Just another integration problem

    integral (x^6)ln(x)dx

    The thing is... I have the exam in 2 days and this is the main thing I am havin problems with!

    I tried makin u=x^6
    and then integratin by parts which didnt seem to work!

    I ended up gettin (x^6)(lnx)-(6x^5)(lnx^2)
    Is this completely wrong... do I continue to integrate... Is there another way to do this?
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  2. #2
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    So another Idea I had was to make u=x^7
    and then basically just sub it in! And then using log laws I get that the answer is this

    1/49 int lnu du and I can go from there... but is that right and how do I know which to use... is it just trial and error?
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  3. #3
    Super Member malaygoel's Avatar
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    Quote Originally Posted by taryn View Post
    integral (x^6)ln(x)dx

    The thing is... I have the exam in 2 days and this is the main thing I am havin problems with!

    I tried makin u=x^6
    and then integratin by parts which didnt seem to work!

    I ended up gettin (x^6)(lnx)-(6x^5)(lnx^2)
    Is this completely wrong... do I continue to integrate... Is there another way to do this?
    substitute lnx = t

    Keep Smiling
    Malay
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  4. #4
    Eater of Worlds
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    Quote Originally Posted by taryn View Post
    integral (x^6)ln(x)dx

    The thing is... I have the exam in 2 days and this is the main thing I am havin problems with!

    I tried makin u=x^6
    and then integratin by parts which didnt seem to work!

    I ended up gettin (x^6)(lnx)-(6x^5)(lnx^2)
    Is this completely wrong... do I continue to integrate... Is there another way to do this?
    Use integration by parts:

    u=lnx; du=\frac{1}{x}dx; dv=x^{6}dx; v=\frac{x^{7}}{7}

    \frac{1}{7}x^{7}lnx-\int\frac{1}{7}x^{7}\frac{1}{x}dx

    \frac{x^{7}lnx}{7}-\frac{x^{7}}{49}+C
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  5. #5
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    ahh cool! I got the same answer doin it the other way as well but this way seems just a little bit easier! Thanks for all your help! I really appreciate it!
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