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Thread: Integration By Parts

  1. #1
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    Exclamation Integration By Parts

    Question:
    $\displaystyle \int x.3^x dx$



    Attempt:

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

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

    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:
    $\displaystyle \int x.3^x dx$



    Attempt:

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

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

    How to integrate the last part ??

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

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