- #1

- 6

- 3

$$\int{\frac{1}{\sqrt{x^2+4}}}dx$$

I answered $$\ln({\frac{\sqrt{x^2+4}}{2}+\frac{x}{2}})+C$$

The answer sheet gave:

$$\ln({\sqrt{x^2+4}+x})+C$$

I couldn't see where I had gone wrong, so I tried differentiating my answer in Wolfram Alpha and the answer sheet one as well and both gave

$$\frac{1}{\sqrt{x^2+4}}$$

I'm confused as this suggests that both are correct answers to the question. Can somebody please tell me what is going on as I thought every function had a unique integral? Are both or only one of the answers correct?

PS There should be absolute value brackets around my integral answers but I'm not sure how to do them in LaTeX.