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Math Help - Is Wolfram Alpha or my Textbook correct?

  1. #1
    s3a
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    Is Wolfram Alpha or my Textbook correct?

    My answer agrees with the before-last step of Wolfram Alpha (which is to say that my answer is equal to that of Wolfram Alpha's) however my textbook has a similar but different answer. (not in the related identity kind of way as far as I can tell)...so am I just missing something?

    (My work is attached and #45 is the problem I am referring to)

    Any input would be greatly appreciated!
    Thanks in advance!

    P.S.
    Wolfram Alpha's work: http://www.wolframalpha.com/input/?i=integral+1%2Fsqrt(x^2+%2B+16)

    P.P.S.
    My textbook's answer: ln(sqrt(x^2 + 16) + x) + C ----> which basically is missing the 1/4 multiplication, isn't it?
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  2. #2
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    Quote Originally Posted by s3a View Post
    My answer agrees with the before-last step of Wolfram Alpha (which is to say that my answer is equal to that of Wolfram Alpha's) however my textbook has a similar but different answer. (not in the related identity kind of way as far as I can tell)...so am I just missing something?

    (My work is attached and #45 is the problem I am referring to)

    Any input would be greatly appreciated!
    Thanks in advance!

    P.S.
    Wolfram Alpha's work: http://www.wolframalpha.com/input/?i=integral+1%2Fsqrt(x^2+%2B+16)

    P.P.S.
    My textbook's answer: ln(sqrt(x^2 + 16) + x) + C ----> which basically is missing the 1/4 multiplication, isn't it?
    \ln\left(\frac{u}{4}\right) + C = \ln{u} - \ln{4} + C = \ln{u} + C
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  3. #3
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    Quote Originally Posted by s3a View Post
    My answer agrees with the before-last step of Wolfram Alpha (which is to say that my answer is equal to that of Wolfram Alpha's) however my textbook has a similar but different answer. (not in the related identity kind of way as far as I can tell)...so am I just missing something?

    (My work is attached and #45 is the problem I am referring to)

    Any input would be greatly appreciated!
    Thanks in advance!

    P.S.
    Wolfram Alpha's work: http://www.wolframalpha.com/input/?i=integral+1%2Fsqrt(x^2+%2B+16)

    P.P.S.
    My textbook's answer: ln(sqrt(x^2 + 16) + x) + C ----> which basically is missing the 1/4 multiplication, isn't it?
    ln({sqrt(x^2 + 16}/4) + x) + C
    = ln(sqrt(x^2 + 16) + x) -ln(4)+ C
    = ln(sqrt(x^2 + 16) + x) + D where D=C-ln(4)
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