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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Find the Antiderivative sin(x)^2

integral

sin^{2} (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

\frac{d}{d x} y = lo g_{2} (x)

\frac{d}{d x} (ln (\frac{1}{x}))

\int (\frac{( x ^{3} )}{( x ^{4} - 5 )}) d x, u = x^{4} - 5

x \to 1 - lim (\frac{( x - 1 )}{( x ^{2} - 4 )})

(- 3, 3), (5, 9)

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