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

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

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integral of 1/2 sin(x)

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

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

Solution steps

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

Use the common integral:

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

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

Simplify

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

Add a constant to the solution

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

x \to 8 + lim (lo g_{5} (x - 8))

\int_{0}^{2} \frac{x}{x + 1} d x

\frac{d}{d x} (lo g_{5} (\frac{6 x ^{3} + 4}{2 x ^{3} - 3}))

(4, - 3), (12, 0)

\int_{2}^{3} \frac{25}{3 - x} d x

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