What is the integral of sin(2x+4) ?

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

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integral of sin(2x+4)

\int sin (2 x + 4) d x

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

Solution steps

\int sin (2 x + 4) d x

Apply u-substitution

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

= \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}{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 + 4

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

Simplify

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

Add a constant to the solution

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

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

\frac{d y}{d x}, y = 7 x^{2} + 6 y x

\int e^{- θ} cos (8 θ) d θ

\frac{\partial}{\partial x} (\frac{1}{x y ^{2} - x ^{2} y})

x \to 0 lim ((e^{x} + x)^{\frac{1}{x}})

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