Integral of $\cos^2 x$

Find the integral $$\int \cos^2 x \; dx$$ Use the trigonometric identity $\; \cos^2 x = \dfrac{1}{2} (1 + \cos (2x))$ to write
$$\int \cos^2 x \; dx = \dfrac{1}{2} \int (1 + \cos (2x)) \; dx$$
Use the sum rule of integrals $\quad \displaystyle \int (f(x) + g(x) ) dx = \int f(x) dx + \int g(x) dx$ to rewrite the integral as $$\int \cos^2 x \; dx = \dfrac{1}{2} \int dx + \int \cos (2x)) \; dx$$ Use the common integrals $\displaystyle \int \; dx = x$ and $\displaystyle \int \cos (2x) dx = \dfrac{1}{2} \sin (2x)$ to write the final result as $$\boxed { \int \cos^2 x \; dx = \dfrac{1}{2} x + \dfrac{1}{4} \sin (2x) + c}$$

More References and Links

1. University Calculus - Early Transcendental - Joel Hass, Maurice D. Weir, George B. Thomas, Jr., Christopher Heil - ISBN-13 : 978-0134995540
   
2. Calculus - Gilbert Strang - MIT - ISBN-13 : 978-0961408824
   
3. Calculus - Early Transcendental - James Stewart - ISBN-13: 978-0-495-01166-8