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Math Help - Need help with an integral

  1. #1
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    Need help with an integral

    1 / sqrt(2x)

    I tried splitting things up but I'm just running myself in circles at this point. Two methods I tried are:

    pulling 1/sqrt(2) out so I get

    1/sqrt(2) * 1/sqrt(x) <---But I can't integrate that

    I also tried to rationalize by multiplying top and bottom by sqrt(2x) but I just end up with something I still can't integrate.

    A really convoluted thing I did was change the sqrt(2x) to 2x^1/2

    Separate 1/2 out of that so I get 1/2 * x^-1/2 and integrate from there. No luck, as I just end up with 2sqrt(x) / 2, which is not the right answer. Can anyone shed some light on this?

    p.s. - sorry, I'm not quite sure how to use pretty print, u-sub is in the next section so i'm trying to do it the hard way first.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Smile

    Hello,
    Here's a clue
    put \sqrt{x} = t
    and go on

    feel free to ask if there's is still trouble

    Adarsh
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  3. #3
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    Thanks

    Adarsh,

    Thank you for your reply, but I'm not quite sure I'm catching on.

    I thought 1 / sqrt(2) * 1 / sqrt(x) was the the way to go, but no so sure.
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    ..

    put \sqrt{x} = t
    differntiate both sides
    \frac{dx}{2\sqrt{x}}=dt
    dx=2\sqrt{x}dt
    put this in
    \int{\frac{dx}{\sqrt{2x}}}
    you get
    \int{\sqrt{2}dt}
    so answer is
    =\sqrt{2}t + c
    =2\sqrt{x}+c

    Adarsh
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