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Math Help - antiderivative with natural logs

  1. #1
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    antiderivative with natural logs

    my prof posted the answers and his is different than mine, any step by step help to show what i'm doing wrong?

    his answer = \frac{(-ln x -2)}{x^2}

    "find the antiderivative":
    <br />
f(x) = \frac{1}{x} (lnx + 3)


    i tried using substitution
    <br />
u = lnx + 3
    h(u) = \frac{1}{x} u
    <br />
= \frac{1}{x} (lnx + 3)

    .....stuck.
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  2. #2
    Senior Member Pinkk's Avatar
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    The professor made a mistake; that's the derivative, not the antiderivative.
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  3. #3
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    can you explain to me the process of finding that antiderivative?

    a little confused on how to go about it.
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  4. #4
    Senior Member Pinkk's Avatar
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    To find the antiderivative we have to perform an indefinite integral for \frac{1}{x}(\ln x +3). For this particular function, it's best to use u-substitution. Let u = \ln x + 3. Then du = \frac{dx}{x}, so \int \frac{1}{x}(\ln x + 3)\,dx = \int u\, du = \frac{u^{2}}{2} + C. Now substituting our expression for u, we see that the antiderivative is \frac{1}{2}(\ln x + 3)^{2} + C.
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  5. #5
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    perfect, thanks!
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