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Math Help - integral??

  1. #1
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    integral??

    hey uhh.. my teacher never taught me how to differentiate log/ln functions or integrate them.. so i am asking, what is the integral of ln(t^2 - 3t + 3)
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  2. #2
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    \int ln(t^{2}-3t+3)dt

    This is a rather tough one if you've never been shown anything as you claim.

    Try using parts.

    Let u=ln(t^{2}-3t+3), \;\ dv=dt, \;\ v=t, \;\ du=\frac{2t-3}{t^{2}-3t+3}dt
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  3. #3
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    Quote Originally Posted by elpermic View Post
    hey uhh.. my teacher never taught me how to differentiate log/ln functions or integrate them.. so i am asking, what is the integral of ln(t^2 - 3t + 3)
    I'd suggest to start by using integration by parts:

    \int u \, dv = uv - \int v \, du.

    Let u = \ln (t^2 - 3t + 3) \Rightarrow du = \frac{2t - 3}{t^2 - 3t + 3} \, dt and dv = dt \Rightarrow v = t.

    Now you have some spade work to do.
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  4. #4
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    basically all you have to do is use the chain rule if you know that.

    ln(t^2 + 3t + 3) is 1/(t^2 + 3t + 3) x d/dt(t^2 + 3t + 3)

    hope that helps
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  5. #5
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    Quote Originally Posted by doneng View Post
    basically all you have to do is use the chain rule if you know that.

    ln(t^2 + 3t + 3) is 1/(t^2 + 3t + 3) x d/dt(t^2 + 3t + 3)

    hope that helps
    What you mean is

    Quote Originally Posted by doneng View Post
    To get the derivative basically all you have to do is use the chain rule if you know that.

    ln(t^2 + 3t + 3) is 1/(t^2 + 3t + 3) x d/dt(t^2 + 3t + 3)

    hope that helps
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