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

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

Popular >

integral of 4sin(2x)

\int 4 sin (2 x) d x

- 2 cos (2 x) + C

Solution steps

\int 4 sin (2 x) d x

Take the constant out:

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

= 4 \cdot \int sin (2 x) d x

Apply u-substitution

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

= 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

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

Use the common integral:

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

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

Substitute back

u = 2 x

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

Simplify

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

= - 2 cos (2 x)

Add a constant to the solution

= - 2 cos (2 x) + C

\frac{d}{d x} ((x + π)^{2})

\frac{d}{d x} (x^{3} ln (1 + x^{2}))

\int_{0}^{3} \frac{x - 2}{x ^{2} - 3 x - 4} d x

x y^{6} y^{^{'}} = x^{7} + y^{7}

\int_{1}^{4} \frac{5}{x ^{2} + 4 x + 4} d x