The discussion revolves around the integration of a function involving trigonometric identities, specifically the integral of tan(x)sec²(x). Participants are evaluating their respective solutions and questioning the correctness of each other's approaches.
The discussion includes varying opinions on the correctness of the solutions provided. Some participants assert that one solution is correct while another is almost correct, indicating a nuanced understanding of the differences between the two answers. There is no explicit consensus on a single correct answer, but guidance has been offered regarding the nature of the solutions.
Participants are working under the constraints of homework rules, which may limit the depth of their explanations or the completeness of their solutions. There is a focus on identifying mistakes rather than providing final answers.
Your solution is correct, and your friend's solution is almost correct. Your friend wrote ##\frac{\tan x^2} 2 + C##, but possibly meant to write ##\frac{\tan^2(x)} 2 + C##. Although this is different from what you found, the corrected answer from your friend differs only by a constant from your answer. Note that ##\sec^2(x) = \tan^2(x) + 1##, so ##\frac{\sec^2(x)}{2} = \frac{\tan^2(x)}{2} + \frac 1 2##Sarah00 said: