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Math Help - Integral

  1. #1
    VkL
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    Integral

    Indefinite integral of ( lnx / x + 4x(lnx) dx


    Can someone help me with this?? IDK where to start even. I was thinking about letting u = ln(x), du = 1/x then I ended up with.............(1/4) integral (u/u)du
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  2. #2
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    Quote Originally Posted by VkL View Post
    Indefinite integral of ( lnx / x + 4x(lnx) dx


    Can someone help me with this?? IDK where to start even. I was thinking abou tlettign u = ln(x) but i dont see what i can do with its diffrential 1/x. Or maybe I am wrong?
    With your suggested sub:

    \int \frac{\ln{x}}{x+4x(\ln{x})^2}~dx = \int \frac{\ln{x}}{x(1+4(\ln{x})^2)}~dx = \int \frac{u}{1+4u^2}~du

    Can you do it now?
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  3. #3
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    \int \frac{\ln{x}}{x + 4x(\ln{x})^2} \, dx

    \int \frac{\ln{x}}{1 + 4(\ln{x})^2} \cdot \frac{1}{x} \, dx

    u = \ln{x} ... du = \frac{1}{x} \, dx

    \int \frac{u}{1 + 4u^2} \, du

    can you finish?
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  4. #4
    VkL
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    Oh I see my mistake. I added the 4 and the 1 ... and took (1/5) out of the intagral.I understand how you got to that now (both of you) Now I do integration by parts? It would be nice if 1 of you can actually do it out step by step, because I often mess up on this.

    Or...I just saw an easier way, The integral can become [ (u/1) + (u/4u) ] du and then this is very simple to integrate...is this correct?
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  5. #5
    VkL
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    ^^Nvm I don't think u can do that. haha oooops.
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