The math help thread

Wow, break up lines and use more parentheses. So you used integration by parts and it looks like you let

u = sec(x)
dv = sin(x)
du = sec(x)tan(x)dx
v = -cos(x)

∫udv = vu - ∫vdu

Keep track of your du, dx and what you're substituting.

From here (the bolded part):
-cos(x) sec(x) - ∫-cos(x)du

= -cos(x)sec(x) + [cos(x)] ∫du
= -cos(x)sec(x) + [cos(x)] ∫sec(x)tan(x)dx
= -cos(x)sec(x) + [cos(x)] (sec(x) + c)

You cannot pull cos(x) out of the integration sign (Note that cos(x) is actually equal to 1/u).

Nothing's wrong with his integration/differentiation steps, just missing integration constant. Also, you can solve this problem by using substitution (I know it's not the question asked, but just wanna make it clear)