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

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

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integral of sin(1/2)x

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Simplify

sin (\frac{1}{2}) \frac{x ^{2}}{2} : \frac{1}{2} sin (\frac{1}{2}) x^{2}

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

Add a constant to the solution

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

e^{6}, e^{x}, x = 0

x \to + 2 - lim (\frac{∣ x - x ∣}{x - 2})

\frac{d y}{d x} = \frac{3 x}{3 + x ^{2}}

y^{^{'}} + x \cdot e^{- x^{\frac{2}{2}}} = 0

\int (x - 1) cos (\frac{x}{3}) d x

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