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Math Help - integration by substitution help

  1. #1
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    integration by substitution help

    Ok, so i have a problem from my book that I can't figure out how to start,

    so the integral is from 0 to 4 (not important) and it is (x/(1+2x)^1/2 ) dx

    thats x over radical 1+2x

    i can't see any value in the equation for "u" that will remove x from the equation. Could someone please explain what you would select for "u" and why? Do you have to modify the integrand before proceeding?
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  2. #2
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    That root is annoying so let's get rid of it by putting u=\sqrt{1+2x} (get the new bounds for u according this substitution!), which can be rewritten backwards as u^2=1+2x. Now differentiate and make the substitutions.
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  3. #3
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    i dont understand, if i differentiate 1 + 2x then i no longer have an x term and I cant remove the x in the numerator...

    i must be missing something...
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  4. #4
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    Quote Originally Posted by mothra View Post
    i dont understand, if i differentiate 1 + 2x then i no longer have an x term and I cant remove the x in the numerator...

    i must be missing something...
    You've been given the substitution to use. Have you been taught how to integrate by making a substitution? If so, please post all your working and say where you get stuck.
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  5. #5
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    yes, ive been taught to integrate by substitution, but can you not see how this problem is atypical and confusing? I have not been taught to substitute anything other than "u" and i dont see how subing u^2 as 1+2x will help me, other than by removing the root, can someone maybe go through the problem step by step with explanations, sorry im just lost
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  6. #6
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    As per Krizalid's suggestion, the substitution u^{2}=1+2x

    means that x=\frac{u^{2}-1}{2}, \;\ dx=udu

    See?. Can you make the subs now?. Don't forget to change the limits of integration. That is a common oversight.
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  7. #7
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    Quote Originally Posted by galactus View Post
    As per Krizalid's suggestion, the substitution u^{2}=1+2x

    means that x=\frac{u^{2}-1}{2}, \;\ dx=udu

    See?. Can you make the subs now?. Don't forget to change the limits of integration. That is a common oversight.
    Thank you, I guess I have never made multiple substitutions in the same equation so I wasn't thinking in those terms. I verified my answer by using integration by parts on the same problem and it checked out. I was just required to solve the problem using substitution for some reason (because james stewart is an ass)
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