Thread: 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?

Originally Posted by s3a

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?

Originally Posted by s3a

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)