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

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

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integral of (2sin(x))

\int (2 sin (x)) d x

- 2 cos (x) + C

Solution steps

\int 2 sin (x) d x

Take the constant out:

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

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

Use the common integral:

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

= 2 (- cos (x))

Simplify

= - 2 cos (x)

Add a constant to the solution

= - 2 cos (x) + C

\frac{d}{d x} (\frac{3 x ^{3}}{2})

(y e^{x y} cos (2 x) - 2 e^{x y} sin (2 x) + 2 x) + (x e^{x y} cos (2 x) - 3) y^{^{'}} = 0

x \to 0 lim ((1 - 6 x)^{\frac{5}{x}})

\frac{d y}{d x} - sin (x) y = 2 sin (x)

d er i v a t i v e g (t) = 5 (cos (π t))^{2}