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Math Help - Integration involving ln

  1. #1
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    Integration involving ln

    \int 7x ln (2x) dx

    Could any please tell me what to set as my dv, u, v and du?
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  2. #2
    Member Miss's Avatar
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    Quote Originally Posted by Archduke01 View Post
    \int 7x ln (2x) dx

    Could any please tell me what to set as my dv, u, v and du?
    What do you think?
    Actually If we assume dv=ln(2x)dx, What will happen?
    How will find v in that case ?
    And suggest to take v=?
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  3. #3
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    Quote Originally Posted by Miss View Post
    What do you think?
    Actually If we assume dv=ln(2x)dx, What will happen?
    How will find v in that case ?
    And suggest to take v=?
    Well clearly we would need to get the integral of dv. I know the integral of ln x is x ln x - x + C, but what would it be considering that it's 2x in our problem?
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  4. #4
    Member Miss's Avatar
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    Quote Originally Posted by Archduke01 View Post
    Well clearly we would need to get the integral of dv. I know the integral of ln x is x ln x - x + C, but what would it be considering that it's 2x in our problem?
    And this becomes by using integration by parts !
    You will make integration by parts to find your v.
    then you will do integration by parts for the main integral!

    This suggest to take dv=7xdx and u=ln(2x)

    For your question about \int ln(2x) \, dx \,\ :
    Spoiler:

    ln(2x)=ln(2)+ln(x) .

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  5. #5
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    Quote Originally Posted by Miss View Post
    And this becomes by using integration by parts !
    You will make integration by parts to find your v.
    then you will do integration by parts for the main integral!

    This suggest to take dv=7xdx and u=ln(2x)

    For your question about \int ln(2x) \, dx \,\ :
    Spoiler:

    ln(2x)=ln(2)+ln(x) .

    Thank you for the detailed response, daddy-o. And you're right, it's actually easier if you set dv as 7x.
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