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Math Help - Indefinite integrals

  1. #1
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    Indefinite integrals

    I'm very confused about this section. Apparently I need to use the substitution rule but I always seem to mess up, especially with fractions. Can anyone help?

    Here's an example:

    Integral of: x/sqrt x+1


    From what I understand you set x+1 = u
    you then take the derivative of u which is 1 and set that equal to u'
    From here I tend to mess up...
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  2. #2
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    Quote Originally Posted by Yami Sorceress View Post
    I'm very confused about this section. Apparently I need to use the substitution rule but I always seem to mess up, especially with fractions. Can anyone help?

    Here's an example:

    Integral of: x/sqrt x+1


    From what I understand you set x+1 = u
    you then take the derivative of u which is 1 and set that equal to u'
    From here I tend to mess up...
    u = x + 1 \Rightarrow \frac{du}{dx} = 1 \Rightarrow dx = du.

    So the integral becomes \int \frac{u - 1}{\sqrt{u}} \, du = \int \sqrt{u} - \frac{1}{\sqrt{u}} \, du and you should be able to integrate each term. Then substitute back u = x + 1.
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