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Math Help - Restricted values of x for an indefinite integral?

  1. #1
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    Restricted values of x for an indefinite integral?

    Hi all,

    I did this problem for my assignment:

    integrate: -4cos^2(x)tan^3(x)

    I answered:

    4ln(abs(cos(x))) - 2cos^2(x) + C

    Would this answer be considered correct? Wolfram alpha has one extra step after this answer, something about restricting the x values? Thanks for any clarification.
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  2. #2
    CSM
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    Tan is just sin/cos so your expression becomes (-4sin^3(x)/cos(x))
    which integrates to 4 ln(cos(x))-cos(2x)+c
    that's all. No restrictions to x. Maybe wolfram gives a plot or something, and of course you cannot plot a graph for x being infinite
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  3. #3
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    Oh I think I understand. The thing is, Wolfram's second last step WAS the answer I posted, and they got from that answer to the one you gave. I was confused about how to go from mine to yours, but I think it's from using the (1/2)(1+cos(2x)) = cos^2(x) identity? Because the 1 ends up being absorbed into the C constant. Is that the step?

    This is what wolfram says:

    "Which is equivalent for restricted x values to:
    = 4 log(cos(x))-cos(2 x)+constant"

    where log is the natural log
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  4. #4
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    The restriction relates to the fact that x cannot be any odd multiple of \frac{\pi}{2}

    since the function has cosx in the denominator.

    Your answer is equivalent to Wolfram's as only an identity was used.
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  5. #5
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    Quote Originally Posted by CSM View Post
    Tan is just sin/cos so your expression becomes (-4sin^3(x)/cos(x))
    which integrates to 4 ln(cos(x))-cos(2x)+c
    that's all. No restrictions to x. Maybe wolfram gives a plot or something, and of course you cannot plot a graph for x being infinite
    log(cos(x)) does not exist for all x....

    -Dan
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