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Math Help - Integrations!

  1. #1
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    Integrations!

    1.  \int xdx / \sqrt{4+5x} .
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  2. #2
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    Well there're lots of ways of doing this.

    I keep the following: put t=\sqrt{4+5x}.
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  3. #3
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    I tried plugin u=4+5 and dv=x but I got a mess. Can someone show me?
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  4. #4
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    But you're integrating by parts, that's not necessary in this case.

    We can write my substitution as x=\frac{t^2-4}5, now dx=\frac{2t}5\,dt. Substitute those in the integral now, what do you get?
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  5. #5
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    \int \frac{x}{\sqrt{4+5x}}~dx

    t=\sqrt{4+5x} \implies x = \frac{t^2-4}{5}

    Now

    \int \frac{\frac{t^2-4}{5}}{t}~dx=\int \frac{t^2-4}{5t}\frac{2t}{5}~dt
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