Answer:
[tex]\frac{1}{4}[/tex]sin2x + [tex]\frac{1}{2}[/tex] x + c
Step-by-step explanation:
using the trigonometric identity
• cos² x = [tex]\frac{1}{2}[/tex](cos2x + 1) and
∫cos ax = [tex]\frac{1}{a}[/tex]sin ax
hence
∫(1 - [tex]\frac{1}{2}[/tex](cos2x + 1)dx
= ∫(1 - [tex]\frac{1}{2}[/tex]cos2x - [tex]\frac{1}{2}[/tex])dx
= ∫([tex]\frac{1}{2}[/tex] - [tex]\frac{1}{2}[/tex]cos2x)dx
= [tex]\frac{1}{2}[/tex]x - [tex]\frac{1}{4}[/tex]sin2x + c
where c is the constant of integration
