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Math Help - Help on another Definite Integral problem

  1. #1
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    Help on another Definite Integral problem

    I'm lost on this one, just need a starting point.

    \int_{x=1}^{x=2} (6e^{3x}-\frac{1}{x})dx

    Thanks for any help!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Jim Marnell View Post
    I'm lost on this one, just need a starting point.

    \int_{x=1}^{x=2} (6e^{3x}-\frac{1}{x})dx

    Thanks for any help!
    for 6e^{3x} use the sub u=3x

    The 2nd one needs to be memorized. Here is the hint

    \frac{d}{dx}\ln(x)=\frac{1}{x} so

    \int \frac{1}{x}dx=...
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by Jim Marnell View Post
    I'm lost on this one, just need a starting point.

    \int_{x=1}^{x=2} (6e^{3x}-\frac{1}{x})dx

    Thanks for any help!
    Just integrate term by term and factor out your constants. I'll get you started:

    6 \int^{2}_{1} e^{3x} dx - \int^{2}_{1} \frac{1}{x} dx

    * For the first one, do a u-substitution with u = 3x

    Does that help you get started?
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  4. #4
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    yep, thanks for getting me started!
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  5. #5
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    for the 1st term, would it equal, u=3x,,,, du=3,,, then,,, 6e^u(3)?
    I think thats the term thats confusing me the most
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jim Marnell View Post
    for the 1st term, would it equal, u=3x,,,, du=3,,, then,,, 6e^u(3)?
    I think thats the term thats confusing me the most
    Consider \int 6e^{3x}~dx

    Let u = 3x

    \Rightarrow du = 3~dx

    \Rightarrow \frac 13 ~du = dx

    \int 6e^{{\color{red}3x}}~{\color{blue}dx} = \int 6e^{\color{red}u} \cdot {\color{blue}\frac 13~du}

    = 2 \int e^u~du
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