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

\frac{d}{d x} (6 cos (π x))

x \to + 0 lim (\frac{sin ( 4 x )}{tan ( 2 x )})

f (x) = a x + b

\frac{d}{d x} ((4 x^{2} + 3)^{2})

y = x (x^{4} + 1)

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