Question

Two students are asked to compute the indefinite integral \int 2 \sec ^{2}(x) \tan (x) d x Student 1 finds \int 2 \sec ^{2}(x) \tan (x) d x=\sec ^{2}(x) while

student 2 finds that \int 2 \sec ^{2}(x) \tan (x) d x=\tan ^{2}(x) The two students ended up with different answers. Who is right, who is wrong, and how (it ispossible that both are correct/incorrect)? Hint: it will be helpful to recall some trig identities.

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