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Math Help - Integration By Parts

  1. #1
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    Exclamation Integration By Parts

    Question:
    \int x.3^x dx



    Attempt:

    u=x , dv= 3^x
    du =dx , v= \frac{3^x}{ln3}

    = x.\frac{3^x}{ln3}-\int \frac{3^x}{ln3} dx

    How to integrate the last part ??

    Please answer in steps , Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Question:
    \int x.3^x dx



    Attempt:

    u=x , dv= 3^x
    du =dx , v= \frac{3^x}{ln3}

    = x.\frac{3^x}{ln3}-\int \frac{3^x}{ln3} dx

    How to integrate the last part ??

    Please answer in steps , Thank you
    Just like you did when you said
    " dv= e^x, v= \frac{3^x}{ln 3}"!

    \int \frac{3^x}{ln 3}= \frac{1}{ln 3}\int 3^x dx
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