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Math Help - A tricky trig sub integral.

  1. #1
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    A tricky trig sub integral.

    Tricky for me at least:

    integrate: 10x^2/sqrt(4x-x^2)

    I worked it out to this:

    30arcsin((x-2)/2)-5sin(2arcsin((x-2)/2))-20sqrt(4-(x-2)^2)+C

    I got pretty close to the answer I know because when I asked Wolfram to differentiate this it gave me

    5x^2/sqrt(4x-x^2)

    Maybe I made a mistake reverting to x from theta? I was a bit confused about how to handle sin(2theta) even though I drew a diagram of the right triangle. That's why I wrote sin(arcsin...) which I'm not sure is correct? Any clarification is appreciated
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  2. #2
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    While you were at the Wolfram site, you should've asked for a solution to your integral and at least look to see if your substitution is correct!
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  3. #3
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    The problem is the Wolfram site's answer is so convoluted and used techniques we haven't covered. I'm doing the problem again and I think I'm coming to the right answer though! We shall see.
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  4. #4
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    Yes I made a mistake somewhere along the way. The answer is

    60arcsin((x-2)/2)-10sin(2arcsin((x-2)/2))-40sqrt(4-(x-2)^2)+C

    Thanks for the suggestion!
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