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

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

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integral of sin(-2x)

\int sin (- 2 x) d x

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

Solution steps

\int sin (- 2 x) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - 2 x

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

Simplify

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

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

Add a constant to the solution

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

x \to 6 lim (6)

x \to - 1 lim (\frac{3 + x}{x ^{2} - 1})

\int e^{- 3 x} cos (4 x) d x

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\frac{d ^{2}}{d x ^{2}} (x ln (x))