5. For sec / tan and csc / cot tricky trig integrals, Todd or Steven isn't super helpful when the powers are smol. Here's a guide to computing I := sec^3 x dx.

(a) Use integration by parts to expand this integral. Hint: only one choice for u makes dv easy to integrate.

(b) The integral you get of the form v du is still complicated. Again Todd or Steven is not helpful here. Use a trig identity to convert all the trig functions in this integral to only have sec x's.

(c) Use the fact that sec x dx = ln |sec x + tan x| + C to proceed computing I = sec^3 x dx.