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

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

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integral of sin^2(u)

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

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

Solution steps

\int sin^{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

\frac{\partial}{\partial z} (x \cdot y^{2} \cdot e^{z})

\frac{d}{d x} (3 x^{2} + 6 x + cos (x))

f (x) = \frac{7}{x}

x \to \infty lim (- 1 + \frac{1}{x})

y^{^{'}} = tan (x) (sec (x))^{4}

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