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Math Help - Integrationw ith substitution

  1. #1
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    Integrationw ith substitution

    Hi

    I'm so sorry for more questions, I really cant get the answer and have no idea where I went wrong, please please help me out! It's 2 questions and I have attached my attempts at them, labeled accordingly.

    Thank you so so much!
    Attached Thumbnails Attached Thumbnails Integrationw ith substitution-integration-questions-.jpg   Integrationw ith substitution-attempt-question-1.jpg   Integrationw ith substitution-attempt-question-2.jpg  
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Integrationw ith substitution

    For the second one use the hint:
    \int \left ( \frac{x}{2 - x} \right ) ^2 dx

    Let y = 2 - x, so x = 2 - y and dx = -dy.
    \int \left ( \frac{x}{2 - x} \right ) ^2 dx = \int \left ( \frac{2 - y}{y} \right ) ^2  (-dy) = - \int \frac{(2 - y)^2}{y^2} dy

    Now multiply things out.

    -Dan
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  3. #3
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    Re: Integrationw ith substitution

    Your error was trying to use "partial fractions" when the numerator has the same degree as the denominator. "Partial fractions" can only be used on "common fractions" where the numerator has degree lower than the denominator. Instead start by doing the indicated division: \frac{x^2}{(2- x)^2}= \frac{x^2}{x^2- 4x+ 4}= -1+ \frac{4(x- 1)}{(x- 2)^2}. Now you can use "partial fractions" on the fraction. It will, of course, give the same result as topsquark's suggestion.
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  4. #4
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    Re: Integrationw ith substitution

    Hi thank you both very much!

    I have a problem with the partial fractions still, cant get the answer..can you help me detect my mistakes?

    Thank you so much!
    Attached Thumbnails Attached Thumbnails Integrationw ith substitution-dsc_2754.jpg  
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