What is the integral of sin^2(1/2 x) ?

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

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integral of sin^2(1/2 x)

\int sin^{2} (\frac{1}{2} x) d x

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

Solution steps

\int sin^{2} (\frac{1}{2} x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 - cos (x)) d x

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 (x) d x

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 x - \int cos (x) d x)

\int 1 d x = x

\int cos (x) d x = sin (x)

= \frac{1}{2} (x - sin (x))

Add a constant to the solution

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

\frac{d}{d x} (9 x^{4})

\int \frac{x}{2 - 3 x} d x

\frac{d}{d x} (\frac{1}{( 3 x + 8 ) ^{2}})

\frac{\partial}{\partial x} (\frac{3 x}{y})

x \to - 1 - lim (x + 2)

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