Question

How do you do this question?

Answer 1

Explanation:

∫ dt / (cos²(t) ⁹√(1 + tan(t)))

If u = 1 + tan(t), then du = sec²(t) dt.

∫ du / ⁹√u

∫ u^(-1/9) du

9/8 u^(8/9) + C

9/8 (1 + tan(t))^(8/9) + C