What is the integral of (-1)/4 sin(2x) ?

The integral of (-1)/4 sin(2x) is 1/8 cos(2x)+C

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integral of (-1)/4 sin(2x)

\int \frac{- 1}{4} sin (2 x) d x

\frac{1}{8} cos (2 x) + C

Solution steps

\int \frac{- 1}{4} sin (2 x) d x

Take the constant out:

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

= \frac{- 1}{4} \cdot \int sin (2 x) d x

Simplify

= (- \frac{1}{4}) \cdot \int sin (2 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= (- \frac{1}{4}) \cdot \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= (- \frac{1}{4}) \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= (- \frac{1}{4}) \frac{1}{2} (- cos (u))

Substitute back

u = 2 x

= (- \frac{1}{4}) \frac{1}{2} (- cos (2 x))

Simplify

(- \frac{1}{4}) \frac{1}{2} (- cos (2 x)) : \frac{1}{8} cos (2 x)

= \frac{1}{8} cos (2 x)

Add a constant to the solution

= \frac{1}{8} cos (2 x) + C

x \to 0 lim (ln (x) + 1)

\frac{d}{d x} ((lo g_{e} (x))^{2})

\int 70 sin^{4} (x) cos^{3} (x) d x

\int_{1}^{2} 4 x^{2} d x

x \to 5 - lim (f (x))

What is the integral of (-1)/4 sin(2x) ?
The integral of (-1)/4 sin(2x) is 1/8 cos(2x)+C