i)∫tan(x)dx =∫sinx/cosx dx
let u=cosx
du/dx=-sinx
---> -∫du/u =-ln(u) =-ln(cosx) +C
ii)a(t)=t3+sec2t
v(t)=t^4/4 + tan(t) +C
whent=0, v=4, C=4
v(t)=(t^4)/4 + tan(t) +4
x(t)=(t^5)/20 -ln(cos(t)) +4t +C
when x=6, t=0, C=6
hence x=(t^5)/20 -ln(cos(t)) +4t +6