This page on "Integrals that Can and Cannot Be Done" suggests that, almost surprisingly, Mathematica can express the following integral in terms of elementary functions:
However, that code currently returns the following:
2/3 Hypergeometric2F1[3/4, 1, 7/4, -Tan[x]^2] Tan[x]^(3/2)
which is totally different from what the tutorial says (both answers are correct, but the actual output is obviously not elementary).
Why does this happen? How can I get the form in terms of elementary functions?