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Math Help - Integration by Substitution

  1. #1
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    Integration by Substitution

    How do I find the indefinite integral:

    <br /> <br />
\int\frac{5}{{(3x-1)}^3} dx<br />
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  2. #2
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    Quote Originally Posted by millerst View Post
    How do I find the indefinite integral:

    <br /> <br />
\int\frac{5}{(3x-1)^3} dx<br />
    I've aded the brackets that should have been included. Substitute u = 3x - 1.
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    make u = 3x-1 \Rightarrow \frac{du}{dx} = 3

    therefore

     \frac{5}{3}\int \frac{du}{dx}\frac{1}{u^3}~dx

    Can you take it from here?
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  4. #4
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    <br /> <br />
\int\frac{5}{(3x-1)^3} dx<br />

    So the answer works out to?

    <br /> <br />
\frac{-5}{6(3x-1)^2} + C<br />
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  5. #5
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