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Math Help - Help me ! integral

  1. #1
    Newbie
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    Oct 2008
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    Red face Help me ! integral


    1. \int ln(2x+1)dx
    2. \int e^{2x}sin3xdx
    3 \int \frac{r^{3}}{\sqrt{4+r^{2}}}dr

    I'm from Vietnam,I can't do it, help me !
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  2. #2
    MHF Contributor
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    Quote Originally Posted by butbi9x View Post

    1. \int ln(2x+1)dx
    2. \int e^{2x}sin3xdx
    3 \int \frac{r^{3}}{\sqrt{4+r^{2}}}dr

    I'm from Vietnam,I can't do it, help me !
    Hi

    1. You can integrate by parts

    \int ln(2x+1)dx = x ln(2x+1) - \int \frac{2x}{2x+1}dx

    \int ln(2x+1)dx = x ln(2x+1) - x + \frac{1}{2} ln(2x+1)

    2. Twice by parts

    3. By parts with u'(r) = \frac{r}{\sqrt{4+r^{2}}} and v(r)=rē
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  3. #3
    Super Member
    Joined
    Jun 2008
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    One way to do the third one is to sub u^2 = 4+r^2

    And just to add on running-gag's advice for number 2, you can treat the integral as the unknown and solve for it.
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