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Math Help - Indefinite Integral Problem- Can anyone check my work

  1. #1
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    Indefinite Integral Problem- Can anyone check my work

    \int (\frac{2}{3x^4})dx
    \int (2\times{3x^{-4}})dx
    \int (6x^{-4})dx
    6\int (x^{-4})dx
    6 (\frac{x^{-3}}{-3})+c

    -2x^{-3}+c

    \frac{-2}{x^3}+c

    Thanks!
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Jim Marnell View Post
    \int (\frac{2}{3x^4})dx

    \int{ (2\times {\color{red}3} x^{-4}})dx


    The three in first step was in denominator
    the second step should be


    \frac{1}{3}\int (2\times{x^{-4}})dx


    Thanks!
    Red
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  3. #3
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    \int (\frac{2}{3x^4})dx

    \frac{1}{3}\int (2\times{x^{-4}})dx

    \frac{1}{3}\int (2x^{-4})dx

    \frac{1}{3}\times{2}\int (x^{-4})dx

    \frac{2}{3}\times{\frac{x^{-3}}{-3}}+c

    \frac{-2}{9}x^{-3}+c

    \frac{\frac{2}{9}}{x^3}+c

    I'm not sure if my final step is right. Thanks for any help!
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Jim Marnell View Post
    \int (\frac{2}{3x^4})dx

    \frac{1}{3}\int (2\times{x^{-4}})dx

    \frac{1}{3}\int (2x^{-4})dx

    \frac{1}{3}\times{2}\int (x^{-4})dx

    \frac{2}{3}\times{\frac{x^{-3}}{-3}}+c

    \frac{-2}{9}x^{-3}+c

    \frac{\frac{{\color{red}-}2}{9}}{x^3}+c

    You forgot "-" sign , his can further be written as

    \frac{-2}{9x^3}+c

    I'm not sure if my final step is right. Thanks for any help!
    Red

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