What is the integral of f(x)=sin(2x) ?

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

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Find the Antiderivative f(x)=sin(2x)

integral

f (x) = sin (2 x)

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

Solution steps

\int sin (2 x) 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

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

Simplify

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

Add a constant to the solution

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

f (x) = \frac{1}{( x ^{3} )}

\frac{d}{d x} (e^{\frac{1}{x}})

\frac{d}{d x} (a^{x})

1 x

\frac{1}{( tan ( x ) )}

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