Formulas to be used: (in order of appearance in the Solution part below)
Trigonometric double-angle identity:
Difference rule of integration:
Constant multiple rule of integration:
Constant multiple rule of differentiation:
Trigonometric rule of integration:
Solution:
The given function has no direct integral, but can be solved by thinking of a trigonometric relationship that can be easily manipulated and integrated. In this case, the double-angle identity for cosine is used.
Using the double-angle identitiy for cosine
Isolating the term on the left side
Making the coefficient of term to be 1
The working equation for can now be integrated using -substitution, as will be shown.
Integrating both sides of the equation
Taking the integral using the difference rule and
constant multiple rule
and Using -substitution and differentiating it using the constant multiple rule
, which is 
