What is the integral of sin^{(2)}(x) ?

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

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integral of sin^{(2)}(x)

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

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

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

Add a constant to the solution

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

x \to 16 lim (x + x^{2})

4 + t^{6}

x \to - 2 lim (- x^{2} + 9 x - 4)

n = 1 \sum \infty \frac{2}{( n + 1 ) !}

x \to 0 lim (ln ((1 + \frac{1}{x})^{x}))

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