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Math Help - anti-derivatives

  1. #1
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    anti-derivatives

    sorry for multiple posts today, i'm studying for my calc final and just wanna make sure i know the correct order of solving these.

    "solve the anti-derivative"
    <br />
f(x) = \frac{1}{x}(lnx + 3)

    do i solve them separately? or distribute the \frac{1}{x}?
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by JGaraffa View Post
    sorry for multiple posts today, i'm studying for my calc final and just wanna make sure i know the correct order of solving these.

    "solve the anti-derivative"
    <br />
f(x) = \frac{1}{x}(lnx + 3)

    do i solve them separately? or distribute the \frac{1}{x}?
    Well, again, use substitution z := \ln x+3, which gives you that dz = \tfrac{1}{x}\,dx and hence

    \int \tfrac{1}{x}(\ln x+3)\, dx=\int z\, dz=\ldots
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  3. #3
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    got it, thanks man.

    i just posted a reply in the other thread "definite integral" which you responded to, i'm still a little confused if i'm solving it right (the numbers came out really high) if you could just check it out that would be great.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by JGaraffa View Post
    sorry for multiple posts today, i'm studying for my calc final and just wanna make sure i know the correct order of solving these.

    "solve the anti-derivative"
    <br />
f(x) = \frac{1}{x}(lnx + 3)

    do i solve them separately? or distribute the \frac{1}{x}?
    Again observe that 1/x is the derivative of \ln(x)+3 so what is the derivative of:

    (\ln(x)+3)^2 ?

    CB
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