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Math Help - partial fraction - integration

  1. #1
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    partial fraction - integration

    can someone explain the underlined steps?

    -how does the top line reduce to u-1 in the numerator. isnt (u+1) - 1 = u

    -bottom line - is it just a "u" substitution?

    thanks
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  2. #2
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    here the problem..sorry!
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  3. #3
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    Quote Originally Posted by calculus0 View Post
    can someone explain the underlined steps?

    -how does the top line reduce to u-1 in the numerator. isnt (u+1) - 1 = u

    -bottom line - is it just a "u" substitution?

    thanks
    Hi calculus0,

    what you have in the numerator is

    \frac{1}{2}(u+1)-1=\frac{1}{2}(u+1)-\frac{1}{2}(2)=\frac{1}{2}(u+1-2)
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  4. #4
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    Quote Originally Posted by Archie Meade View Post
    Hi calculus0,

    what you have in the numerator is

    \frac{1}{2}(u+1)-1=\frac{1}{2}(u+1)-\frac{1}{2}(2)=\frac{1}{2}(u+1-2)

    where did the 2 come from? where it is -1/2(2)

    thank you
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  5. #5
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    Quote Originally Posted by calculus0 View Post
    where did the 2 come from? where it is -1/2(2)

    thank you
    the -1 is brought inside the brackets using -1=-\frac{2}{2}

    then we have 0.5 multiplied by 2 seperate terms
    so they can be brought inside with 0.5 as common factor

    \frac{1}{2}(u+1)-1=\frac{1}{2}(u+1)-\frac{2}{2}=\frac{1}{2}(u+1)+\frac{1}{2}(-2)

    and now \frac{1}{2} is a common factor

    so the -2 can be brought inside the brackets.
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  6. #6
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    Thanks!!
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