What is the integral of cos^2(u) ?

The integral of cos^2(u) is 1/2 (u+1/2 sin(2u))+C

integral of cos^2(u)

\int cos^{2} (u) d u

\frac{1}{2} (u + \frac{1}{2} sin (2 u)) + C

Solution steps

\int cos^{2} (u) d u

Rewrite using trig identities

= \int \frac{1 + cos ( 2 u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 + cos (2 u) d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d u + \int cos (2 u) d u)

\int 1 d u = u

\int cos (2 u) d u = \frac{1}{2} sin (2 u)

= \frac{1}{2} (u + \frac{1}{2} sin (2 u))

Add a constant to the solution

= \frac{1}{2} (u + \frac{1}{2} sin (2 u)) + C

\int_{0}^{25} x d x

x y^{^{'}} = x^{3} + 17 x^{3} y

\int 4 e^{9 x} d x

t an g e n t f (x) = x^{4} - 25 x^{2} + 144, at x = 1

\int \frac{d}{1} (y) d x

What is the integral of cos^2(u) ?
The integral of cos^2(u) is 1/2 (u+1/2 sin(2u))+C