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

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

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integral of 2sin(x)+sin(2x)

\int 2 sin (x) + sin (2 x) d x

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

Solution steps

\int 2 sin (x) + sin (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 2 sin (x) d x = - 2 cos (x)

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

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

Add a constant to the solution

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

\frac{d}{d x} (1 - \frac{1}{x ^{2}})

\frac{d y}{d x} = \frac{x ^{2} + y ^{2} + x y}{x ^{2}}

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

\frac{\partial}{\partial x} (x y + 3 y)

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

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