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Math Help - Integration by substitution - where am I going wrong?

  1. #1
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    Integration by substitution - where am I going wrong?

    The integral is:



    The substitution is: u = sqrt[x]


    I don't know where I am going wrong, I am wondering if hte text book i'm using could have a typo or something (these books do occasionally get stuff wrong).


    So what I did:

    u=sqrt[x] => x=u^2

    du/dx = (x^-1/2)/2 => dx = 2udu

    subtituting into the original integral and multiplying out we now have:



    And now i have no idea what to do :/




    According to the text book, the final answer is:

    1/2*ln(9/5)




    Where am I going wrong?
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  2. #2
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    In the integral \int_1^2\frac{2u}{4u^3-u}\,du, divide top and bottom of the fraction by u, then use partial fractions.
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  3. #3
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    Quote Originally Posted by GRM92 View Post
    The integral is:



    The substitution is: u = sqrt[x]


    I don't know where I am going wrong, I am wondering if hte text book i'm using could have a typo or something (these books do occasionally get stuff wrong).


    So what I did:

    u=sqrt[x] => x=u^2

    du/dx = (x^-1/2)/2 => dx = 2udu

    subtituting into the original integral and multiplying out we now have:



    And now i have no idea what to do :/ Mr F says: Now use a partial fraction decomposition.




    According to the text book, the final answer is:

    1/2*ln(9/5)




    Where am I going wrong?
    ..
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